an introduction to ocean remote sensing (2nd ed.) [s. martin, 2014]

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-FM CUUK2533/Martin ISBN: 978 1 107 01938 6 November 26, 2013 12:15

AN INTRODUCTION TO OCEAN REMOTE SENSING

Second edition

Fully updated, with significant new coverage of advances in satellite oceanography andresults from new satellite missions, the second edition of this popular textbook intro-duces students to how remote sensing works, how to understand observations from Earth-observing systems, and the observations’ importance to physical and biological oceanog-raphy. It provides full explanations of radiative transfer, ocean surface properties, satelliteorbits, instruments and methods, visible remote sensing of biogeochemical properties,infrared and microwave retrieval of sea surface temperature, sea surface salinity retrieval,passive microwave measurements, scatterometer wind retrieval, altimetry and SAR. Thisnew edition also includes descriptions of the online archives where data can be obtained,and where readers can obtain online tools for working with the data – enabling hands-onengagement with real-world observations.

This is an ideal textbook for graduate and advanced undergraduate students takingcourses in oceanography, remote sensing and environmental science, and provides a prac-tical resource for researchers and Earth science professionals working with oceanographicsatellite data.

seelye martin is an Emeritus Professor in the School of Oceanography at the Universityof Washington. He has been involved with passive microwave, visible/infrared and radarice research since 1979, and has made many trips to the Arctic for research on sea iceproperties and oceanography. Professor Martin has served on a number of NASA andNOAA committees and panels involving remote sensing and high latitude processes. From2006–2008, he worked at NASA Headquarters as Program Manager for the Cryosphere,where he also served as program scientist for the ICESat-1 and ICESat-2 missions. From2009–2012, he worked in a variety of roles for the NASA high-latitude IceBridge remotesensing aircraft program. For this work, in 2012 he was awarded the NASA ExceptionalPublic Service Medal.


AN INTRODUCTION TO OCEANREMOTE SENSING

second edition

SEELYE MARTINSchool of Oceanography, University of Washington


University Printing House, Cambridge CB2 8BS, United Kingdom

Published in the United States of America by Cambridge University Press, New York

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It furthers the University’s mission by disseminating knowledge in the pursuit ofeducation, learning and research at the highest international levels of excellence.

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Second edition published 2014

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To the memory of my motherLucy Gray Martin

April 19, 1915–June 13, 2002


Contents

Preface page xiList of chemical symbols xivList of mathematical symbols xvList of abbreviations and acronyms xxi

1 Background 11.1 Introduction 11.2 Definition of remote sensing 31.3 Satellite orbits 41.4 Geosynchronous satellites 121.5 Sun-synchronous satellites 131.6 Imaging techniques 151.7 Processing levels, archives, data records and processing 221.8 Past, present and pending satellite missions 26

2 Ocean surface phenomena 352.1 Introduction 352.2 Ocean surface winds and waves 352.3 Ocean currents, geostrophy and sea surface height 462.4 Sea ice 50

3 Electromagnetic radiation 533.1 Introduction 533.2 Descriptions of electromagnetic radiation 533.3 Ways to describe EMR 613.4 Radiation from a perfect emitter 663.5 The ideal instrument 71

4 Atmospheric properties and radiative transfer 794.1 Introduction 794.2 Description of the atmosphere 794.3 Molecular absorption and emission 864.4 Scattering 90

vii


viii Contents

4.5 Atmospheric attenuation 964.6 Application to the ideal instrument 994.7 The radiative transfer equation 1014.8 Specific solutions of the radiative transfer equation 1054.9 Diffuse transmittance and skylight 110

5 Reflection, transmission and absorption at the atmosphere/ocean interface 1135.1 Introduction 1135.2 The interface 1155.3 Transmission across an interface 1225.4 Absorption and scattering properties of seawater 1265.5 Reflection from foam 135

6 Ocean color 1366.1 Introduction 1366.2 Absorption and scattering by phytoplankton, particulates and

dissolved material 1396.3 Ocean color satellite instruments 1476.4 SeaWiFS, MODIS, VIIRS and their calibrations 1526.5 Atmospheric correction and retrieval of the water-leaving radiance 1596.6 Surface validation data sets and the vicarious calibration 1696.7 Chlorophyll reflectance and fluorescence 1716.8 The empirical, semi-analytic and biogeochemical algorithms 1746.9 The Pre-Aerosol, Clouds and ocean Ecosystem (PACE) mission 192

7 Infrared observations of sea surface temperature (SST) 1947.1 Introduction 1947.2 What is SST? 1977.3 Properties of AVHRR, MODIS and VIIRS bands used in the SST

retrieval 2007.4 Atmosphere and ocean properties in the infrared 2037.5 SST algorithms 2087.6 Cloud-detection and masking algorithms 2217.7 Error and bias of the data sets 2277.8 Other GHRSST data sets and merged products 2297.9 Illustrations and examples 231

8 Introduction to microwave imagers 2368.1 Introduction 2368.2 General antenna properties 2378.3 Measurement of a surface radiance with an antenna 2428.4 Conical scanners and microwave surface emissivity 2448.5 Antenna pattern correction (APC) 2458.6 Passive microwave imagers 248


Contents ix

9 Passive microwave observations of the atmosphere and ocean surface 2609.1 Introduction 2609.2 Atmospheric absorption and transmissivity in the microwave 2609.3 Radiative transfer in the microwave 2669.4 Dependence of the emissivity on surface waves and foam 2739.5 Temperature and salinity 2859.6 Open ocean algorithms 2889.7 WindSat retrieval of wind speed and direction 2959.8 Sea ice algorithms 300

10 Introduction to radars 30810.1 Introduction 30810.2 Radar equation 30910.3 Determination of σ within an FOV 31310.4 Range binning 31510.5 Doppler binning 31910.6 Oceanic backscatter 324

11 Scatterometers 33111.1 Introduction 33111.2 Background 33311.3 How scatterometers derive the wind velocity 33611.4 NSCAT scatterometer 34211.5 AMI and ASCAT scatterometer 34311.6 The rotating beam scatterometers 34611.7 Advantages and disadvantages of the different scatterometers 35411.8 The ISS-RapidScat 35511.9 Cross-calibrated multi-platform winds (CCMP) 356

11.10 Applications and examples 356

12 The altimeter 36212.1 Introduction 36212.2 Shape of the Earth 36312.3 Past, present and future altimetric satellites 36812.4 TOPEX/POSEIDON 36812.5 JASON-1/JASON-2 37812.6 Altimeter interaction with a specular sea surface 38012.7 Effect of surface waves on the altimeter return 38512.8 Errors and biases in retrieval of sea surface height 38912.9 Applications and examples 393

13 Imaging radars 40113.1 Introduction 40113.2 Background 402


x Contents

13.3 Resolution of side-looking radars (SLRs) 40913.4 How the SAR achieves its resolution 40913.5 RADARSAT-2 SAR 41513.6 Other operational SARs 42213.7 Applications and examples 423

14 Other instruments: the gravity missions, ICESat-1 and -2, CryoSat-2, SMOSand Aquarius/SAC-D 436

14.1 Introduction 43614.2 Gravity missions 43614.3 The ICESat-1, ICESat-2 and CryoSat-2 missions 44114.4 SMOS and Aquarius/SAC-D 449

Appendix 455References 458Index 489

The color plates will be found between pages 000 and 000


Preface

Since the publication of the first edition a decade ago, the variety and use of ocean observingsatellites has continued to grow. Combined with a similar expansion in computer resourcesand in surface receiving and distribution networks, this growth has greatly increased ourknowledge of the properties of the upper ocean and the overlying atmosphere.

Ten years ago, many satellites were large, managed by single countries and carriedmultiple sensors. Now, by international agreement, different countries collaborate on con-stellations of smaller satellites that fly in complementary orbits and focus on a singleoceanic or atmospheric feature such as biology, winds or sea surface temperature (SST).Many of these data sets such as SST from the constellations are available in a commonformat from public archives that also provide software tools for working with the data.These constellations and their archives greatly improve research opportunities for studentsand professionals.

For remote sensing, the use of the electromagnetic spectrum combined with our under-standing of the oceanic surface and atmospheric properties has stimulated innovationsin instrumentation. Satellite remote sensing also uses gravity measurements that haveimproved our knowledge of the Earth’s geoid, measured the ice loss from the major icecaps, and monitored changes in the ocean circulation. Many of the experimental sensorsof the 1980s are now the operational tools of oceanography. These include narrow-bandoptical sensors to estimate biological productivity, infrared sensors to measure sea sur-face temperature that approach an accuracy necessary to observe climate change, passivemicrowave sensors that provide global cloud-independent observations of winds and seasurface temperature and salinity, and altimeters capable of measuring sea surface height towithin 2 cm.

Because remote sensing involves many disciplines, the book provides under one coverthe necessary background in electromagnetic theory, atmospheric and seawater properties,physical and biological oceanography, physical properties of the sea surface and the prop-erties of satellite orbits. The contents range from the reflective and emissive properties ofclouds and foam to the radar-scattering properties of ocean waves, to the optical propertiesof plankton-associated pigments. It also includes many examples. The book describesthe development of satellite oceanography from 1975 to 2013, and outlines pending

xi


xii Preface

missions. The book requires only an introductory knowledge of electromagnetic theoryand differential equations.

The text divides into five parts. Chapters 1–3 introduce satellite systems, ocean surfaceproperties and electromagnetic theory. Chapters 4–7 discuss remote sensing in the visibleand infrared spectrum, including atmospheric properties, the ocean/atmosphere interface,the visible retrieval of ocean color and the infrared retrieval of sea surface temperature.Chapters 8 and 9 discuss the passive microwave, including antennas, instruments, atmo-spheric properties and the retrieval of ocean surface and atmospheric variables. Chapters10–13 discuss the active microwave, including a variety of radars to retrieve wind speed anddirection, sea surface height and images of the ocean surface. Finally, Chapter 14 describesa variety of gravity and sea surface salinity missions, and sea ice and ice sheet laser andradar altimeter satellites.

I began this book during 1993–94, when I was a visiting scientist at the NationalInstitute of Polar Research in Tokyo. I wrote the second draft following my retirementfrom the University of Washington in 2011. The book benefited from my work with theNational Aeronautics and Space Administration (NASA); from my service on committeesin 1980s and 1990s, from 2006–2008 when I worked at NASA Headquarters as programmanager for the cryosphere, and from 2009–2012, when I performed a variety of servicesfor the Airborne Operation IceBridge (OIB) program. I am grateful to NASA for theseopportunities. I particularly thank Dixon Butler, who was head of the Earth ObservingSystem (EOS) program, and Waleed Abdalati and Jack Kaye for their support during mytime at headquarters.

At the University of Washington, I taught remote sensing both singly and jointly withMiles Logsdon. I thank Miles and all of our students, who always managed to focus onthose points that I did not understand. In my teaching and writing, I benefited from the classnotes of Dudley Chelton, James Mueller and Carlyle Wash, and the textbooks of CharlesElachi, George Maul, Ian Robinson and Robert Stewart.

At NASA Goddard Space Flight Center (GSFC), I thank Ziauddin Ahmad, Gene Eplee,Don Cavalieri, Josephino Comiso, Charles McClain, Claire Parkinson, Jeremy Werdelland Meng-Hua Wang; at the Jet Propulsion Laboratory (JPL), Ron Kwok, Lee-Lueng Fu,Ben Holt and Simon Yueh. At MacDonald, Dettwiler and Associates (MDA), I thankJeff Hurley and Wendy Keyser. At the National Oceanic and Atmospheric Administration(NOAA), I thank Alexander Ignatov, Boris Petrenko and Mayra Pazo; at Oregon StateUniversity, Dudley Chelton; at Earth and Space Research, Gary Lagerloef and Hsun-YingKao; at Remote Sensing Systems, Chelle Gentemann, Tom Meissner and Frank Wentz; atNASA Headquarters, Paula Bontempi. I also thank Peter Wadhams from the University ofCambridge and Peter Minnett from the University of Miami for their encouragement andsupport. At Cambridge University Press, I thank Kirsten Bot, Laura Clark, Susan Francisand David Mackenzie for their help and support. For his careful line-by-line reading of themanuscript, I thank my freelance editor, Steven Holt.

At the University of Washington, I thank Jamie Morison, Cecilia Peralta-Ferriz as wellas the staff of the UW Libraries for their support and for their extensive online collection


Preface xiii

of journals. For their critical readings of draft chapters I thank Peter Cornillon for Chapter1 and Boris Petrenko for Chapter 7. I also thank Alexander Ignatov for his help withunderstanding the NOAA SST processing. Any errors are my own.

I thank my son and daughter, Carl William Coryell-Martin and Maria Elizabeth Coryell-Martin, for putting up with all this even after they have left home and my wife, Julie EstherCoryell, for her optimism that I might finish the book, for reading all of the chapters indraft and for her support. Finally, I ask the reader to remember that each of the satellites,instruments and algorithms described in this book began as an idea generated by a singleindividual or a small committee.


Chemical symbols

Ar ArgonCH4 MethaneCO Carbon monoxideCO2 Carbon dioxideFe IronH2O WaterN2 NitrogenN2O Nitrous oxideO2 OxygenO3 OzoneHα, Hβ, Hγ Hydrogen lines in the Fraunhofer spectrumMg–I Magnesium–iodine lineO2-A Oxygen-A line

xiv


Mathematical symbols

Symbol Unit DefinitionA m2 Area, or instrument aperture areaAe m2 Effective antenna aperture areaAFOV area Antenna half-power field-of-viewAi(400) m−1 Reference absorption at 400 nm; i refers to particulates or

CDOMa(λ) m−1 Volume absorption coefficienta(λ; θ , φ) – Ratio of gray-body to blackbody absorption; in VIR, the

absorptance, in microwave, the absorptivityaCDOM m−1 CDOM absorption coefficientaw m Amplitude of ocean surface wavesaw(λ), ap, aφ , aT m−1 Absorption coefficients for seawater, particulate,

phytoplankton and total absorptionB W m−2 sr−1 Brightness, used for radiance in the passive microwaveB tesla m−1 Magnetic field vectorBf J m−2 sr−1 Frequency form of spectral brightnessb(λ) m−1 Volume scattering coefficient of seawaterbb(λ), bbw(λ) m−1 Backscatter coefficient of pure seawaterbbT(λ) m−1 Total backscatter coefficient of seawater°C Degrees CelsiusCa mg Chl-a m−3 Chlorophyll concentrationCw, C1 – Concentrations of open water and sea icec m s−1 Speed of light in vacuumc(λ) m−1 Volume attenuation coefficient of seawaterD cm, m Aperture diameter of a lens or length of an antennad (λ) – Normalized absorption depthda(λ) m Absorption depth of radiation in seawaterE W m−2 Irradiance, the incident flux density per unit areaE V m−1 Electric field vectorE J Energy of a photonE0 V m−1 Reference amplitude of an electric field vectorEd(λ, 0+) W m−2 Downwelled solar irradiance measured just above the ocean

surface

xv


xvi Mathematical symbols

ER(χ , ψ) km Height of reference ellipsoid above Earth’s center of massEu(0−) W m−2 Upwelled solar irradiance just below the water surfaceEV, EH V m−1 Vertically and horizontally polarized components of the

electric field vectore(λ; θ , φ) – Emissivity, which is the ratio of gray-body to blackbody

radiancee0 – Temperature- and salinity-dependent emissivity of a specular

ocean surfaceF(λ, z) W m−2 nm−1 Solar irradiance at a height z in the atmosphereFn – Normalized power or radiation patternFS(λ) W m−2 nm−1 solar irradiance at the top of the atmosphereF ′

S(λ) W m−2 nm−1 FS(λ) attenuated by two passes through the ozone layerf s−1 Coriolis parameterf Hz Frequencyf(x) V m−1 Antenna illumination patternf L m Focal lengthf N s−1 Nyquist sampling frequencyfp(T, λ) W m−3 sr−1 Planck blackbody radianceG – Antenna gainG0 – Maximum antenna gainGR – Gradient ratio used in the derivation of sea ice concentrationg m s−2 Acceleration of gravityH km Radial distance of a satellite from Earth’s center of massH1/3 m Significant wave heightHz s−1 Cycles per secondh length Height of satellite above ocean surfacehS length Height of sea surface above Earth’s center of masshs length Temporal mean of sea surface heighth J s Planck constant, 6.626 × 10−34 J sI deg Inclination, the angle between the Earth’s rotation axis and

the normal to the orbit planeI(r, θ , φ) W sr−1 Radiant intensityI0 W sr−1 Maximum radiant intensityi Imaginary part of complex numberJ JoulesK Degrees Kelvink, kim m−1 Real and imaginary part of the wavenumberk m−1 Vector wavenumberkB J K−1 Boltzmann constant, 1.38 × 10−23 J K−1

kw m−1 Wave number of ocean wavesL mm Columnar equivalent of non-raining cloud liquid waterL(λ) µW cm−2 nm−1 sr−1 Radiance

W m−3 sr−1 (Alternative units of L)LA(λ) µW cm−2 nm−1 sr−1 Path radiance generated by aerosol atmospheric scatteringLE km Equatorial separation between successive orbits


Mathematical symbols xvii

Lf (λ) J m−2 sr−1 Frequency form of spectral radianceLR (λ) µW cm−2 nm−1 sr−1 Path radiance generated by Rayleigh scatteringLs(λ) µW cm−2 nm−1 sr−1 Solar radiance at the top of the atmosphereLT(λ) µW cm−2 nm−1 sr−1 Total radiance received at the satelliteLw(λ) µW cm−2 nm−1 sr−1 Water-leaving radiance[Lw(λ)]N µW cm−2 nm−1 sr−1 Normalized water-leaving radianceLλ(λ) µW cm−2 nm−1 sr−1 Wavelength form of spectral radiancel m Length of an imaging radarM W m−2 Exitance, or emitted flux or power densityN(χ , ψ) m Geoid undulation, or height of geoid relative to the

reference ellipsoid ERNp, nepers – Units of atmospheric absorption used in microwaveNET K Noise-equivalent delta-temperatureNEL µW cm−2 nm−1 sr−1 Noise-equivalent delta-radianceNEσ 0 – Noise-equivalent delta-sigma-zeron – Real part of the index of refractionP – For radiometers, subscript indicates V or H polarization.

For radars, subscript indicates VV or HH polarizationP(θ ) sr−1 Atmospheric scattering phase functionPR – Polarization ratio used in the derivation of sea ice

concentrationPR(θ ) sr−1 Rayleigh atmospheric scattering phase functionp kg m−1 s−2 Atmospheric pressureQ – Coefficient used in description of the water-leaving

radianceR(λ) – Plane irradiance reflectanceR(λ, 0−) – Irradiance reflectance evaluated just below the surfaceR0 km Distance from radar to targetRc mm, µm Radius of curvature of the sea surfaceRF(λ) – Irradiance reflectance of foamRR mm h−1 Rain rateRrs(λ) – Remote sensing reflectancer length Radiusr length Vector radius (r, θ , φ)r(θ ) – Unpolarized radiance reflectanceS psu SalinitySN – Signal-to-noise ratioSS psu Surface salinityT °C, K TemperatureT °C, K Mean temperature of the lower troposphereT(θ ) – Interface transmittanceT3, T4, T5 K AVHRR brightness temperatures for bands 3, 4, 5T22, T23, T31, T32 K MODIS brightness temperatures for bands 22, 23, 31,

32TA K Antenna temperature


xviii Mathematical symbols

Ta K Air temperatureTb K Brightness temperatureTb °C Buoy or bulk temperatureTBV, TBH K Vertically and horizontally polarized components of

brightness temperaturesText K Extraterrestrial brightness temperature exclusive of the

SunTgal K Brightness temperature of the Milky Way galaxyTS °C, K Ocean surface skin temperatureTsfc °C, K Externally supplied surface temperature to algorithmsTsol K Solar contribution to the antenna brightness temperatureTsun K Solar brightness temperatureTuniv K The 2.7-K Universe background temperatureTw s Period of ocean surface wavest Timet – In the visible/infrared, the atmospheric transmittance; in

the microwave, the atmospheric transmissivitytD(λ) – Diffuse transmittanceU m s−1 The scalar wind speed at a 10-m heightU0 m s−1 Spacecraft velocityULOS m s−1 Line-of-sight wind speed, the wind speed in the

azimuthal look direction of a passive microwaveradiometer

u, v m s−1 x- and y-components of an ocean currentV mm Equivalent height in liquid water of the columnar water

vaporv m s−1 Local phase speed of lightw m Width of an imaging radarx length Vector position (x, y, z)X, Y – Coefficients used in discussion of particulate scattering

propertiesXS length Imaging radar cross-track swath widthYS length Imaging radar along-track swath widthZH km Reference height for the top of the atmosphereα deg Scattering angle relative to the forward directionα – Angstrom exponent used to describe aerosolsαS sr Solid angle resolution of an ideal optical instrumentβ(α, λ) km−1 sr−1, m−1 sr−1 Atmospheric and oceanic volume scattering functionβ(α, λ) sr−1 Oceanic scattering phase functionβ0 km−1 sr−1, m−1 sr−1 Isotropic scattering phase functionβT, βw, βp, βφ m−1 sr−1 Total, pure seawater, particulate and phytoplankton

volume scattering functionE J Energy difference associated with a change in the

internal state of a molecule or atomf Hz, MHz Instrument bandwidth, also used to describe Doppler

shift


Mathematical symbols xix

hion m Range delay caused by atmospheric free electronsT45 K Temperature difference between AVHRR channels 4 and 5,

T45 = T4 – T5

T53 K Temperature difference between AVHRR channels 5 and 3,T53 = T5 – T3

x, y m Radar resolution in the cross-track and along-track directionθ1/2 deg Half-power beamwidth; for imaging radars, the half-power

beamwidth in the cross-track directionø1/2 deg Half-power beamwidth in the along-track directionε farad m−1 Electrical permittivityε(λ, λ0) – Single-scattering color ratio for aerosolsε0 farad m−1 Permittivity in vacuumεr – Complex dielectric constant, εr = ε′+ iε′′

ζ m Sea surface height relative to the geoidζ D m Dynamic height, or the oceanographic height calculated from

the vertical density structureη – Complex index of refraction, η = n + iχη m Vertical displacement of ocean surface wavesηM – Main beam efficiency of a microwave antennaθ deg Incidence, look or zenith angleθ S deg Solar zenith angleθv deg View or scanκA, κE, κS km−1 Atmospheric absorption, extinction and scattering coefficientsκR km−1 Rayleigh scattering attenuation coefficientκoxy km−1 Oxygen absorption coefficientκvap km−1 Water vapor absorption coefficientλ nm, µm Radiation wavelengthλw mm, m Wavelength of ocean surface wavesµ henry m−1 Magnetic permeabilityµ0 henry m−1 Vacuum permeability W m−4 sr−1 The atmospheric radiative source termρ kg m−3 Density of seawaterρa kg m−3 Density of airρH, ρV – Horizontal, vertical reflection coefficientsρ ion TECU Free-electron columnar densityρw(λ) – Extraterrestrial reflectance generated by the water-leaving

radiance[ρw(λ)]N – Normalized extraterrestrial reflectanceσ siemens m−1 Electrical conductivityσ m2 Radar scattering cross sectionσ 2 – Mean-square sea surface slopeσ 0 – Normalized radar scattering cross section (pronounced

sigma-zero)σ N – Standard deviation of noise


xx Mathematical symbols

σ VV, σ HH, σ HV, σ VH – Normalized radar scattering cross section for VV, HH, HVand VH transmitting and receiving

ση m Root-mean-square sea surface heightτ s Pulse duration or lengthτ (λ) – Optical depthτA – Optical depth associated with aerosol scatteringτOZ – Optical thickness of the ozone layerτR(λ) km Rayleigh optical thickness W Radiant flux or powerN W Noise generated internally to an instrumentT W Total radiant flux or power transmitted by an antenna(V, H) W V-pol or H-pol radiant flux received by an antennaλ W µm−1 Spectral form of the radiant fluxσ W Received power corrected for atmospheric attenuationø deg Azimuth angleøR deg Azimuthal angle relative to the wind directionøW deg Azimuthal wind directionχ – Imaginary part of the index of refractionχ , ψ deg Latitude, longitude sr Solid angleE s−1 Angular rotation of the EarthM sr Main beam solid angle of a microwave antennaP sr Pattern solid angle of a microwave antennaω s−1 Radian frequency of an electromagnetic waveω 0 (λ) – Single-scattering atmospheric albedoωA(λ) – Aerosol single-scattering albedoωR(λ) – Rayleigh single-scattering albedo


Abbreviations and acronyms

A-Train The A- or afternoon train is a constellation of satellites in thesame orbit with a 1:30 pm equator crossing time.

AATSR Advanced ATSR (ESA)ABI Advanced Baseline Imager (instrument on GOES-R)ACSPO Advanced Clear-Sky Processor for Ocean (NOAA)ADEOS-1, -2 Advanced Earth Observing Satellite (Japan)AGC Automatic Gain Control (altimeter function)AHRPT Advanced High Resolution Picture Transmission (METOP)ALOS Advanced Land Observing Satellite (Japan)ALT Altimeter on TOPEX/POSEIDONAMSR Advanced Microwave Scanning Radiometer (Japan) on

ADEOS-2AMSR-E AMSR-EOS (Japan) on AQUAAOML Atlantic Oceanographic and Meteorological Laboratory (NOAA)AOP Apparent Optical PropertiesAPC Antenna Pattern CorrectionAPT Automatic Picture Transmission (data transfer mode for AVHRR)AQUA Second major EOS satellite (not an abbreviation)ASAR Advanced SAR (ENVISAT)ASCAT Advanced Scatterometer (METOP)ATSR Along-Track Scanning Radiometer (ESA)AVHRR Advanced Very High Resolution Radiometer (United States)AVISO Archiving, Validation and Interpretation of Satellite

Oceanographic data (France)CalTech California Institute of TechnologyC-band Frequencies of about 5 GHzCCMP Cross-Calibrated Multi-Platform (mind dataset)CDOM Colored Dissolved Organic MaterialCHAMP CHAllenging Minisatellite Payload (German gravity mission)Chl-a Chlorophyll-a

xxi


xxii Abbreviations and acronyms

CDR Climate Data RecordCEOS Committee on Earth Observation SatellitesCONAE Comision Nacional de Actividades Espaciales (Argentinian

Space Agency)CNES Centre National d’Etudes Spatiales (National Center for Space

Studies, France)CryoSat-2 ESA radar satellite for Sea ice and ice sheet studiesCRTM Community Radiative Transfer ModelCSA Canadian Space AgencyCZCS Coastal Zone Color ScannerdB DecibelsDMSP Defense Meteorological Satellite Program (United States), also

name of a satelliteDOD Department of Defense (United States)DORIS Doppler Orbitography and Radiopositioning Integrated by

Satellite (France)ECMWF European Centre for Medium-range Weather ForecastsEDR Environmental Data RecordEFOV Effective Field-Of-View; shape of the FOV after time-averagingEM ElectroMagneticEMR ElectroMagnetic RadiationENVISAT Environmental Satellite (ESA)EOS Earth Observing System (United States, with international

components)ERS-1, -2 European Remote-sensing SatelliteESA European Space AgencyESMR Electrically Scanned Microwave Radiometer (United States)EUMETSAT European Organization for the Exploitation of Meteorological

SatellitesFLH Fluorescence Line HeightFM Frequency ModulationFOV Field-Of-View, see also EFOV, IFOVFRAC Full Resolution Area Coverage (AVHRR, MODIS, VIIRS)FY Feng Yun (Wind and Cloud) as in FY-1C and FY-1D; name of

satellite (China)FY First Year, as in first-year sea iceGAC Global Area Coverage (AVHRR data mode)Gbit Gigabit or 109 bitsGCOM Global Change Observation Missions (Japan)GDAS Global Data Assimilation System (NCEP)GEO Group on Earth Observations


Abbreviations and acronyms xxiii

GES DISC Goddard Earth Sciences, Data and Information Services Center(NASA)

GEOSS Global Earth Observation System of SystemsGLAS Geoscience Laser Altimeter System (United States)GLI Global Imager, ocean color instrument on ADEOS-2 (Japan)GMES Global Monitoring for Environment and Security (European

satellite program)GOCE Gravity Field and Steady-State Ocean Circulation Explorer (ESA)GODAE Global Ocean Data Assimilation ExperimentGOES Geostationary Operational Environmental Satellite (United

States)GHz GigahertzGHRSST GODAE High Resolution STTGIOVANNI Geospatial Interactive Online Visualization ANd aNalysis

Infrastructure; often written as GiovanniGMPE GHRSST Multi-product Ensemble (UK Met Office)GRACE Gravity Recovery and Climate ExperimentGSM Garver–Siegel–Maritorena algorithm (ocean biology)HH Antenna that transmits and receives with an H-polarizationH-pol Horizontally polarizedHRD Hurricane Research Division (NOAA)HRPT High Resolution Picture Transmission (AVHRR data transfer

mode)HV Antenna that transmits with an H-polarization and receives with a

V-polarizationHY Haiyang (Ocean) satellite as in HY-1 (China)IAPSO International Association for Physical Sciences of the OceanICESat Ice, Cloud and land Elevation Satellite (United States)IEEE Institute of Electrical and Electronics EngineersIFOV Instantaneous Field-Of-View, or Instrument Field-Of-ViewIJPS Initial Joint Polar-orbiting operational satellite System (United

States, EUMETSAT)IOP Inherent Optical PropertiesIPO Integrated Project Office (NPOESS)IR InfraredITCZ Inter-Tropical Convergence ZoneJASON-1, -2, -3 United States/Frame altimeter satellites (Not an abbreviation)JAXA Japan Aerospace Exploration Agency (replaced NASDA)JERS-1 Japanese Earth Resources SatelliteJMA Japan Meteorological AgencyJMR Jason Microwave RadiometerJPL Jet Propulsion Laboratory (NASA), operated by CalTech


xxiv Abbreviations and acronyms

JPSS Joint Polar Satellite SystemK-band Frequencies between 11 and 36 GHzKu-band Frequencies of about 14 GHzKOSMOS USSR satellite seriesLAC Local Area Coverage (data mode for AVHRR)L-band Frequencies of about 1 GHzLRA Laser Retroreflector ArrayM-AERI Marine-Atmosphere Emitted Radiance Interferometer (United

States)Mbps Megabits-per-secondMCSST Multi-Channel Sea Surface Temperature (algorithm)MEDS Maritime Environmental Data Service (Canada)MERIS Medium Resolution Imaging Spectrometer (ENVISAT)METEOSAT Geosynchronous Meteorology Satellite (EUMETSAT)METOP-A, -B, -C METeorologie OPerationnelle (Operational Meteorology)

(EUMETSAT satellite)MHz MegahertzMOBY Marine Optical BuoY (ocean color calibration buoy near Hawaii)MODI Moderate Resolution Visible/Infrared Imager (China)MODIS Moderate Resolution Imaging Spectroradiometer on TERRA,

AQUAMODTRAN Program for calculation of atmospheric transmissivityMOS Modular Optical Scanner (Germany)MSL Mean Sea LevelMVIRSR Multispectral Visible–Infrared Scanning Radiometer (China)MY Multiyear, as in multiyear sea iceNASA National Aeronautics and Space Administration (United States)NASDA National Space Development Agency (Japan), see JAXANCEP National Centers for Environmental Prediction (NOAA)NDBC National Data Buoy Center (United States)NDT Nitrate-Depletion TemperatureNESDIS National Environmental Satellite Data and Information Service

(United States)NIR Near-infraredNLSST NonLinear SST (algorithm)NOAA National Oceanic and Atmospheric Administration (United

States)NOAA-18, -19, . . . Names of NOAA operational polar orbiting satellitesNOMAD NASA bio-Optical Marine Algorithm DatasetNPOESS National Polar-orbiting Operational Environmental Satellite

System (United States)NPP NPOESS Preparatory Project (United States)


Abbreviations and acronyms xxv

NRCS Normalized Radar Cross SectionNSCAT NASA Scatterometer (ADEOS-1)NWP Numerical Weather PredictionOC3M Ocean Chlorophyll Version 3 MODIS bio-optical algorithmOC4 Ocean Chlorophyll Version 4 SeaWiFS bio-optical algorithmOBPG Ocean Biology Processing Group (NASA)OCTS Ocean Color and Temperature Sensor (Japan)OISST Optimally Interpolated SSTOKEAN Series of satellites (Russia/Ukraine)OLS Optical Line Scanner (visible/infrared instrument on DMSP)OVWM Ocean Vector Wind MissionOW Open Water (sea ice algorithms)PALSAR Phased Array L-Band SAR (Japan)Pixel Abbreviation for picture elementPMEL Pacific Marine Environmental Laboratory (NOAA)POD Precision Orbit DeterminationPO.DAAC Physical Oceanography Distributed Active Archive (NASA JPL)POES Polar Operational Environmental Satellite (United States)POLDER Polarization and Directionality of the Earth’s Reflectances

(France), ocean color instrument on ENVISATPOSEIDON Premier Observatoire Spatial Etude Intensive Dynamique Ocean

et Nivosphere, French contribution, TOPEX/POSEIDONsatellite.

PRF Pulse repetition frequencypsu Precision salinity units (units of oceanic salinity)RA-2 Radar Altimeter-2 (ENVISAT altimeter)RADARSAT-1, -2 SAR satellites (Canada)RGB Red–Green-Blue color mixingRGPS RADARSAT Geophysical Processing System (United States)rms Root-mean-squarerss Root-sum-of-the-squaresRTE Radiative Transfer EquationSAC-D Satelite de Aplicaciones Cientıficas-DSAR Synthetic Aperture RadarSASS SEASAT-A Satellite Scatterometer (United States)ScanSAR Wide-swath SAR imaging mode (partial abbreviation)SDR Sensor Data RecordSeaBAM SeaWiFS Bio-optical Algorithm Mini-WorkshopSEASAT First ocean observing satellite (1979, United States)SeaWiFS Sea-viewing Wide Field-of-view Sensor (United States)SeaWinds Radar vector wind instrument (not an abbreviation)SEVIRI Spinning Enhanced Visible and Infrared Imager (EUMETSAT)


xxvi Abbreviations and acronyms

SGLI Second-generation GLobal Imager (Japan)SIRAL SAR Interferometric Radar Altimeter (ESA)SLAR Side-Looking Airborne RadarSLR Side-Looking RadarSLR Satellite Laser RangingSMMR Scanning Multichannel Microwave Radiometer (United States)SMOS Soil Moisture and Ocean Salinity instrument (ESA)SSALT Solid State Altimeter on TOPEX (France)SSH Sea Surface HeightSSM/I Special Sensor Microwave/Imager (United States)SSMI/S Special Sensor Microwave Imager/Sounder (SSM/I upgrade)SSS Sea Surface SalinitySST Sea Surface TemperatureSWH Significant Wave Height (H1/3)TECU Total Electron Content Unit (1 TECU = 1016 electrons m−2),

columnar concentration of free electronsTERRA First major EOS satellite (not an abbreviation)TIR Thermal-InfraredTIROS-N Television Infrared Observation Satellite-N (early version of

POES satellite)TIW Tropical Instability WavesTMI TRMM Microwave Imager (Japan)TMR TOPEX Microwave RadiometerTOA Top Of the AtmosphereTOGA-TAO Tropical Ocean Global Atmosphere–Tropical Atmosphere OceanTOMS Total Ozone Mapping SpectrometerTOPEX TOPography EXperiment (United States/France)TRMM Tropical Rainfall Measuring Mission (United States/Japan)TRSR Turbo Rogue Space Receiver BlackJack GPS receivers (Satellite

GPS receivers used on JASON-1)UK Met Office United Kingdom Meteorological OfficeUTC Universal Time CoordinatedUV UltravioletVAM Variational Analysis MethodVH Antenna that transmits with a V-polarization and receives with an

H-polarizationVIRR Visible and Infrared Radiometer (China)VIIRS Visible/Infrared Imager/Radiometer Suite (NPP instrument)VIR Visible/InfraredVNIR Visible/Near-InfraredV-pol Vertically polarizedVV Antenna that transmits and receives with a V-polarization


Abbreviations and acronyms xxvii

WindSat Polarimetric radiometer for vector wind measurements (not anabbreviation)

WVSST Water Vapor Sea Surface Temperature (algorithm)X-band Frequencies of about 10 GHz

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-01 CUUK2533/Martin ISBN: 978 1 107 01938 6 November 25, 2013 13:47

1

Background

1.1 Introduction

During the past forty years, rapid technological growth has advanced the ability of satellitesto observe and monitor the global ocean and its overlying atmosphere. Because of similaradvances in computer hardware and software, it is now possible to acquire and analyze, atshort time delays, large satellite data sets such as the global distribution of ocean waves, thevariations in sea surface height associated with large-scale current systems and planetarywaves, surface vector winds and regional and global variations in ocean biology. Theimmediate availability of these data allows their assimilation into numerical models, wherethey contribute to the prediction of future oceanic weather and climate.

The ocean covers approximately 70% of the Earth’s surface, is dynamic on a varietyof scales, and contains most of the Earth’s water as well as important marine ecosystems.The ocean also contains about 25% of the total planetary vegetation, with much of thisrestricted to a few coastal regions (Jeffrey and Mantoura, 1997). Regions of high biologicalproductivity include the Grand Banks off Newfoundland, the Bering Sea and Gulf ofAlaska, the North Sea and the Peruvian coast. Between 80% and 90% of the world’s fishcatch occurs in these and similar regions. For its role in climate, determination of thechanges in ocean heat storage and measurement of the vertical fluxes of heat, moisture andCO2 between the atmosphere and ocean are critical to understanding global warming andclimate change.

Large-scale ocean currents carry about half of the heat transported between the equatorand the poles; the atmosphere transports the remainder. Away from the polar regions,the combination of these transports with the large oceanic heat capacity relative to theatmosphere means that the ocean moderates the global climate and improves the habitabilityof the continents (Stewart, 1981; Chelton, 2001). For the polar regions, the recent increasein the melting of the Greenland and Antarctic icecaps and the dramatic decrease in thearctic summer sea ice cover (Comiso, 2010) show that the ability to monitor the extent andthickness of the Arctic and Antarctic ice covers is important both for short-term navigationneeds and for long-term climate studies. All these examples illustrate the need to monitorand observe the ocean on a range of local to global scales.

1


2 Background

The growth in satellite systems has been driven in part by technology and in part bysocietal concerns. Societal concerns include the importance of the ocean to national securityand naval operations, global commerce, the prediction of severe storms and hurricanes,fisheries management, the extraction of offshore gas, oil and minerals, and public healthand recreation. Regarding commerce, in 2012, there were about 100 000 ships engagedin commerce, oil, gas and mineral exploration, fisheries and recreation (Allianz, 2012).Increasingly, these concerns also include global sea level rise and the change in the arealextent of the Arctic and Antarctic sea ice. In addition, about half of the global populationlives within 200 km of the coast, where fourteen of the seventeen largest cities are coastal. Ofthese, eleven are Asian, including Bangkok, Jakarta, Shanghai, Tokyo, Ho-Chi-Minh City,Calcutta and Manila (Creel, 2003). These populations are vulnerable to natural hazardssuch as the storm surge and flooding associated with the combination of sea level riseand hurricanes or typhoons. There are also public heath considerations associated withthe oceanic disposal of urban runoff, sewage and garbage, and with the monitoring andprediction of the growth of pathogenic organisms such as red tides. Satellite observingsystems and the interpretation of the resultant data play a central role in addressing theseconcerns.

In the 1970s, the United States launched the first ocean remote sensing satellites. Sincethat time, many countries have launched satellites that carry oceanographic instrumenta-tion, and, as Section 1.8 describes, beginning in about 2002 there has been an internationaleffort to organize satellites from different countries into what are called observing “con-stellations”. These constellations are made up of satellites that carry similar instruments,observe the same oceanic variables and fly in complementary orbits, so that the coverageby a single satellite is enhanced by observations from the other constellation members. Thedata from the constellation are then placed in a common format and distributed among theparticipants and other interested parties.

With these observations, there is an emphasis on the rapid dissemination of the data tothe various government and private-sector users, and the use of this near-real-time data innumerical models and in other areas such as search-and-rescue, oceanographic researchcruise support and the routing of cargo ships to avoid storms. Examples of the oceanicvariables observed by these satellites include sea surface temperature (SST), the height anddirectional distribution of ocean swell, wind speed and direction, atmospheric water contentand rain rate, the changes in sea surface height associated with ocean tides, currents andplanetary waves, concentrations of phytoplankton, sediments and suspended and dissolvedmaterial, and the areal extent and types of polar sea ice.

Prior to the 1980s, such properties were determined from dedicated and expensive shipexpeditions, or in the polar regions from surveys made from aircraft, drifting ships andice islands. This meant that the ocean could be surveyed only slowly and incrementally.At present, satellite imagers can make simultaneous observations of the desired variableswith scales of 1–1,000 km that are difficult to observe even from multiple ships. Forvariables such as the near surface air temperature that are not retrievable by remote sensing,some satellites are designed to relay data from moored and drifting buoys that make direct


1.2 Definition of remote sensing 3

measurements of such quantities to national data centers. Even for those ocean depths thatare inaccessible to satellite observations, instruments called Argos floats are deployed inlarge numbers that profile the ocean interior and periodically come to the surface, wherethey report their observations by satellite.

Because satellites survey a variety of oceanic properties with near global coverageand at intervals of 1–10 days, then rapidly transmit these observations to national andinternational forecast centers, these data are of great operational importance. In addition,the observations contribute to long-term studies and numerical modeling of global climatechange, sea level rise, and the decadal-scale atmospheric and oceanographic oscillations,including the Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), ElNino/Southern Ocean Oscillation (ENSO), and Arctic Oscillation (AO).

In the following, Section 1.2 defines remote sensing and describes its oceanographicapplications. Section 1.3 describes the satellite orbits used in remote sensing and summa-rizes the hazards faced by satellites. Sections 1.4 and 1.5 describe the geosynchronous andSun-synchronous satellites. Section 1.6 discusses the imaging techniques used by satellitesin Sun-synchronous and other low Earth orbits. Section 1.7 describes the different process-ing levels of satellite image data and the NASA data archives. Section 1.8 gives a briefhistory of the changes in satellite remote sensing over the past forty years, describes theinternational context of these observations, and presents a table of past, present and pendingsatellite missions through 2015.

1.2 Definition of remote sensing

Earth remote sensing is primarily defined as the use of electromagnetic radiation to acquireinformation about the ocean, land and atmosphere without being in physical contact withthe object, surface or phenomenon under investigation. Remote sensing is not uniqueto electromagnetic radiation, as this book shows, there are also techniques for studyingchanges in ocean circulation and ice sheet properties through observations of gravityanomalies. Unlike shipboard measurements of quantities such as SST or wind speed, whichare direct measurements made at a point by a thermometer or anemometer, remote sensingmeasurements of such quantities cover broad areas and are indirect, in that the geophysicalquantity of interest is inferred from the properties of the reflected or emitted radiation.The sensors can range from a radiometer mounted on a ship, oil platform or aircraft to amultispectral satellite imager. The following briefly describes the concepts behind remotesensing and the various observing bands.

Because the satellite instrument is not in physical contact with the phenomena underinvestigation, its properties must be inferred from the intensity and frequency distribution ofthe received radiation. This distribution depends on how the received radiation is generatedand altered by its propagation through the atmosphere. This radiation has three principalsources: blackbody radiation emitted from the surface, reflected solar radiation, and, forthe directed energy pulses transmitted by satellite radars, the backscattered energy received


4 Background

at the sensor. The properties of the received radiation also depend on the sensor, whichmust be designed so that its observing wavelengths are appropriate for the phenomenon inquestion. Finally, the received data must be organized into images or data sets so that thespatial distributions of the quantity under investigation can be viewed. This is the generallyaccepted definition of remote sensing; in the past decade, it has been expanded to includethe use of satellite measurements of gravity to infer changes in land, ice sheet and oceanproperties.

Because of the atmospheric contributions to the reflected and received radiationdescribed in Chapters 4 and 9, there are three electromagnetic wavelength bands or win-dows, called the visible, infrared and microwave, through which the ocean is viewed. In thevisible and extending into the near infrared, the observations depend on reflected sunlightand are restricted to daytime cloud-free periods. Because the visible spectrum contains theonly wavelengths at which light penetrates to oceanic depths of order 10–100 m, visibleobservations yield the only information on the depth-averaged color changes associatedwith phytoplankton and sediment concentrations. In the infrared, the observations measurethe blackbody radiation emitted from the top few micrometers of the sea surface. Althoughthese observations are independent of daylight, infrared satellite observations are restrictedto cloud-free conditions.

In the microwave and especially at the longer microwave wavelengths, the surfacecan be viewed through clouds and is obscured only by heavy rain. Microwave observationsdivide into passive and active. Passive microwave instruments observe the naturally emittedblackbody radiation, which can be used to retrieve such atmosphere and ocean surfaceproperties as the areal extent of ice cover, the atmospheric water vapor and liquid watercontent, sea surface temperature (SST), salinity, and, through the directional dependenceof the sea surface roughness, the vector wind speed.

In contrast, different kinds of radars make active measurements; these instrumentstransmit pulses of energy toward the ocean, then receive the backscatter, so that theyprovide their own illumination. The active microwave instruments include imaging radars(the Synthetic Aperture Radar or SAR), directed, pulsed vertical beams (altimeter), severalpulsed fan beams at oblique angles to the satellite orbit (scatterometer), and an obliquerotating pulsed beam (also scatterometer). The scatterometers are highly directional radarsthat receive the backscatter from relatively small surface areas. Together, these instrumentsprovide information on the roughness and topography of the sea surface, wind speed anddirection, wave heights, directional spectra of ocean surface waves and the distribution andtypes of sea ice.

1.3 Satellite orbits

The orbit of an Earth-observing satellite divides into two parts, the satellite motion inits orbit plane relative to the Earth’s center of mass, and the satellite position relative tothe rotating Earth. The time-dependent position of the satellite in its orbit is called the


1.3 Satellite orbits 5

satellite ephemeris. For the rotating Earth, the orbit is frequently described in terms of itsground track, which is the time-dependent location of the surface intersection of the linebetween the satellite and the Earth’s center of mass. The point directly beneath the satelliteis called the satellite nadir. The first of the following sections considers the theoretical caseof satellite motion in its orbit plane, and describes how the addition of the Earth’s rotationdetermines the satellite ground track; the second considers the actual space environmentof these satellites, and the constraints imposed on the satellites and their instruments byspace debris and uncontrolled satellites, gravity-induced orbit perturbations, solar stormsand radiation, and radio-frequency interference (RFI).

1.3.1 Satellite orbits and their applications

Rees (2001, Chapter 10), Elachi (1987, Appendix B) and Duck and King (1983) surveythe commonly used, near circular orbits used in remote sensing. These orbits are describedin a rectangular coordinate system with its origin at the Earth’s center of mass. The z-axisis in the northerly direction and co-located with the Earth’s rotation axis, the x-axis isin the equatorial plane and points in the direction γ of a star in the constellation Aries, andthe y-axis is in the direction appropriate for a right-handed coordinate system. Relative tothese axes, the six Keplerian orbital elements describe the satellite location. Because twoof these are specific to elliptical orbits, for circular orbits, the six elements are reduced tofour.

As Figure 1.1 shows, these four elements are as follows. First, the right ascension ofthe ascending node, or simply the ascending node , is the angle between the x-axis andthe point at which the orbit crosses the equator. Second, the radial distance H is the heightof the satellite above the Earth’s center of mass. Third, the orbit true anomaly θ is theangular position of the satellite in its orbit relative to . Fourth, the inclination I is theangle between the Earth’s axis and the normal to the orbit plane with the convention thatI is always positive. Of these variables, I and specify the orientation and position ofthe orbit plane relative to the fixed stars; H and θ specify the satellite position within theorbit plane. The advantage of this description is that I, and H are either fixed or slowlyvarying, so that, over short periods, θ describes the instantaneous satellite position. Basedon the magnitude of I, there are three kinds of orbits. If I = 90°, the orbit is polar; if I <

90°, the orbit is prograde and precesses in the same direction as the Earth’s rotation as inFigure 1.2; if I > 90°, the orbit is retrograde and precesses in the opposite direction.

In remote sensing, interest is generally not in the satellite position in its orbit, but ratherin its location on its surface ground track. For a non-rotating spherical Earth, the orbittrack is a great circle, or, on the Mercator map shown in Figure 1.2(a), a simple sine wave(Elachi, 1987, Section B-1–4). Because of the Earth’s rotation, the orbit track is steadilydisplaced to the west, yielding the succession of tracks shown in Figure 1.2(b). On thetracks, the numbers i, ii, iii mark the beginning and end of each orbit, where, for example,the points marked ii are at the same time and geographic location. Another orbit property


6 Background

N

IEarth’s rotation

Progradeorbit

ΩΩ

z

x

yEquator

Normalto orbit plane

Equatorplane

H

x

Ascending node

θ

γ

γ

y

View from North Pole

N

Fig. 1.1. For a circular orbit, the Keplerian parameters used to describe the orientation of the orbitplane and the satellite position along the orbit.

Equator

N

Equator

N

EastWest

EastWest

Earth’s rotation

LE

iii

0o

360o

360o

iii iiiiii

Orbitdisplacement

(a)

(b)

Fig. 1.2. Mercator map of the satellite ground track for the orbit shown in Figure 1.1 and for(a) non-rotating Earth and (b) rotating Earth. See the text for further description. (Adapted fromElachi (1987, Figure B-6).



N

S

Geosynchronous orbit

Sun-synchronous orbit

Low-inclination orbit

Eq

Fig. 1.3. Examples of the Sun-synchronous, geosynchronous and low-inclination orbits, where “Eq”is the equator. (Adapted from Asrar and Dozier (1994), Figure 3).

concerns the equatorial separation LE between successive orbits. If division of a multipleof the equatorial circumference by LE is an integer, the orbit is an exact repeat orbit, sothat, after a given period of time, the satellite repeats the same track lines. This propertyis particularly valuable for instruments such as the altimeter, since it allows successivemeasurements of sea surface height along the same ground track.

The three common Earth observation orbits are called geosynchronous, Sun-synchronous, and near equatorial low inclination (Figure 1.3). There is also a fourthaltimeter orbit used for observations of sea surface topography that is at a slightly higheraltitude than the Sun-synchronous orbits, and there are also various low-altitude non-Sun-synchronous orbits used for observations of phenomena such as winds and rainfall. Thefollowing summary shows that each particular orbit has advantages and disadvantages.Because no single orbit allows coverage of all space and time scales, there is no suchthing as a “perfect” satellite orbit or system. Instead, the choice of orbit depends on thephenomenon under investigation.

The geosynchronous orbits are located at an altitude of 35 800 km above the equator.The geostationary orbit is a special case; it lies in the Earth’s equatorial plane (I = 0°). Inthis orbit, although the satellite is orbiting the Earth such that it moves in and out of theEarth’s shadow, its position remains over a fixed equatorial location so that it continuouslyobserves the same surface area. The plane of the more general geosynchronous orbit istilted relative to the equator (I = 0°), so that, although the mean surface position of thissatellite is stationary, its ground path is described by a figure eight centered on the equator(Elachi, 1987). The period of a geosynchronous satellite is 23.93 hours, which is the timein which the Earth rotates around its axis relative to the fixed stars. In contrast, the 24-hourday is the time between successive noons, defined as when the sun is directly overhead, sothat the length of day is determined from a combination of the Earth’s rotation about itsaxis and the Earth’s rotation in its orbit.


8 Background

Satellite orbit plane

Earth

90 dayslater

Orb

it pl

ane

Fig. 1.4. Rotation of the plane of a Sun-synchronous orbit in the Earth–Sun orbit plane.

Operators and managers of geosynchronous satellites work in terms of a “geosyn-chronous belt”, defined as the region extending 200 km above and below the geosyn-chronous altitude and ±15° in latitude (IADC, 2007; Weeden, 2010). Within this belt, thesatellites occupy slots that measure about 2° in longitude, where their operators try to main-tain the satellite within a 0.1° box (Weeden, 2010). In Earth observations, geosynchronoussatellites provide observations of weather, SST and ocean color, and provide data relayservices.

The Sun-synchronous orbit is retrograde with I > 90°, and has an altitude of about 800km, or a much lower altitude than the geosynchronous orbits. The Sun-synchronous periodis about 90 minutes, corresponding to about sixteen orbits per day. The reason why thisorbit is called Sun-synchronous is that throughout the year each orbit crosses the equatorat the same local time of day. Consequently, is not constant, but changes slowly withtime. The drift occurs because of the Earth’s equatorial bulge, which causes the plane ofa near polar orbit to rotate slowly around the pole (Rees, 2001). For a retrograde orbit,the inclination and orbit height can be set so that the orbit rotates about 1° per day in theecliptic or Earth–Sun plane, and in an equal but opposite direction to the orbital motionof the Earth around the Sun. Relative to the fixed stars, the Sun-synchronous orbit planerotates once per year, so that its orbit plane remains at a constant angle to the line betweenthe Sun and Earth. Figure 1.4 shows the change in the angular position of the orbit in theEarth–Sun plane as the Earth moves an angular distance of 90° in its orbit, during a periodof approximately 90 days.

Sun-synchronous satellites are the most common of the ocean-observing satellites andare often referred to as polar orbiters. Their orbits are described in terms of their daytimeequatorial crossing times, as in a 0730 descending or a 1330 ascending orbit, wheredescending refers to a southward satellite velocity, ascending refers to a northward velocity,and the crossing time is local. The orbits are also described in terms of their crossing times,



as “early morning”, “mid-morning” and “early afternoon”. Because the Sun-synchronousequator crossings always occur at the same local time of day, satellites in this orbit canmake daily observations of SST or ocean chlorophyll at the same time in their diurnal cycle.Since cloudiness over the ocean generally increases throughout the day, the crossing timecan be chosen to minimize cloudiness under the satellite.

One difficulty with this orbit is that, because of the tilted orbit plane, the satellite does notpass directly over the poles. This means that the regions around the poles may be excludedfrom instrument coverage; this lack of coverage is called the “hole at the pole”. Figures4.2 and 9.18 give examples of the swath coverage for this orbit, and show that, dependingon the instrument, a single Sun-synchronous satellite can provide near global coverage at1–2-day intervals.

The near-equatorial low-inclination orbit used for missions such as the Tropical RainfallMeasuring Mission (TRMM) is circular with an altitude of 350 km and an inclination angleof 35°. This orbit covers approximately half the globe, and, in a one-month period, observesany specific area at every hour of the day with a sampling rate that is roughly twice thatof a polar orbiter. The advantage of this orbit is that it allows TRMM to determine thevariability of tropical rainfall throughout its diurnal cycle. The successor to this missionis the joint US/Japanese Global Precipitation Measurement (GPM) Core mission, with agreater inclination angle of 65° that is scheduled for launch in 2014. Another member of theGPM constellation in a similar orbit is the Indian/French Megha-Tropiques rainfall missionwith an inclination angle of 22° that was launched in 2010.

Finally, the altimeter occupies an orbit designed to measure sea surface height. Becausethe tidal bulge associated with the 12- and 24-hour tides always lies directly beneath asatellite in a Sun-synchronous orbit, some altimeters operate at a higher non-synchronousaltitude of 1200–1400 km. Consequently, the orbit is not in phase with the tides and thesatellite experiences a smaller atmospheric drag. Altimeter satellites in this orbit includethe US/French TOPEX/POSEIDON JASON-1, JASON-2 and the forthcoming JASON-3mission discussed in Chapter 12.

1.3.2 The satellite environment: Solar storms, radiation pressure, theSouth Atlantic Anomaly, gravitational perturbations, space debris, graveyard

orbits and radio frequency interference (RFI)

In space, various factors perturb the satellites, their orbits and their instruments. First, thelunar and solar gravity fields and radiation pressure from the solar wind exert forces onthe satellites and perturb their orbits. Second, there are two bulges in the Earth’s gravityfield called libration points, one over India (105° W) and the other at the longitude of theUS Rocky Mountains (75° W), that also affect the orbits (Weeden, 2010). For this reason,all satellites have engines and carry fuel so that they can maintain their desired orbits.Third, the satellite can be damaged or destroyed by collisions with space debris or other,sometimes decommissioned, satellites.


10 Background

The NASA Orbital Debris Program Office (NASA, 2012a) monitors space debris; ESA(2012a) describes the ESA monitoring of debris. As of 2009, ESA (2012a) states that therewere 14 000 catalogued pieces of space debris, and approximately 600 000 uncataloguedpieces of debris with dimensions greater than 1 cm. Depending on their relative velocity,even a small object can damage or destroy a satellite. In the low Earth orbits (LEO), themaximum amount of debris occurs at two altitudes: the polar orbit altitudes at 800–1000km and the altimeter satellite altitude of 1400 km. For the geosynchronous belt, the amountof debris is about two orders of magnitude less than in LEO.

ESA (2012a) describes the growth in the amount of debris and its sources. For example,in January 2007, the Chinese use of an anti-satellite missile to destroy the Sun-synchronousFeng-Yun 1C satellite led to a 25% increase in catalogued debris. In February 2009, thefirst accidental collision of two satellites occurred in LEO when the American commercialsatellite, Iridium-33, collided with a Russian military satellite, Kosmos-2251, destroyingboth satellites and generating a large amount of debris. For the rest of 2009, five satellites,namely the remote sensing satellites AQUA and Landsat-7 at altitudes of about 700 km,the Space Station and Space Shuttle at an altitude of 400 km, and a NASA Tracking andData Relay Satellite (TDRS-3) in geosynchronous orbit, maneuvered to avoid collisionswith debris (David, 2010). Based on the current growth in satellite debris, Donald Kesslerhas forecast the occurrence of what is called a “Kessler” syndrome or cascade, where thefrequency of collisions will increase at such a rate and generate so much debris that all ofthe satellites in LEO would be destroyed (Kessler interview in David, 2010).

For geosynchronous satellites, Weeden (2010) states that, in 2010, there were 1238catalogued objects in the geosynchronous belt, of which 391 were under control, 594 weredrifting, 169 had been captured by the libration points, and the remainder were lost orundocumented. He also describes the fate of the Intelsat Galaxy-15 satellite that, during asolar storm in April 2010 when the satellite was positioned at 130° W, lost contact withits ground controllers. Because of this, it drifted east toward the North American librationpoint, and received the nickname “Zombiesat”. As it drifted east, its transponders continuedto receive and transmit data broadcast from the ground, causing both radio interference andhazards to other satellites. This situation continued until January 2011, by which time thesatellite had passed through the orbital slots of about fifteen communication satellites, whenIntelsat restored communications with Galaxy-15, and returned it to a safe position (SpaceNews, 2011).

Given these problems with space debris, 11 nations with space programs and ESA formedthe 12-member Inter-Agency Space Debris Coordination Committee (IADC, 2012). TheIADC recommends that, to avoid further generation of debris, two protected regions beestablished. The first contains the LEO, which IADC defines as the global region extendingin altitude from the surface to 2000 km, and covering the Sun-synchronous and altimeterorbits; the second contains the geosynchronous orbits (GEO). For LEO, IADC (2007)recommends that, when the satellite approaches the end of its lifetime, it be deorbited intothe atmosphere. For GEO, IADC recommends that a satellite approaching its end of serviceshould be placed into a graveyard orbit located at an altitude of about 100–200 km above



1.000

0.500

0.200

0.100

0.050

0.020

0.010

0.005

0.002

–135 –90 –90 0 45 90 135 180

60

45

30

15

0

–60

–45

–30

–15

Fig. 1.5. Graphic of the South Atlantic Anomaly (SAA) showing the contours of the relative prob-ability for space systems to suffer single anomalous events caused by high-energy protons at analtitude of 1000 km. See the text for further description. (Reprinted from Brautigam (2002, Figure8), copyright 2002, with permission from Elsevier.)

the geosynchronous belt. For both sets of orbits, to minimize the generation of debris bybreak-up of the satellites, all fuel tanks should be depressurized and any energy containedin momentum wheels should be depleted.

Another satellite hazard is that solar storms and flares generate highly charged particlesthat can cause temporary or permanent damage to satellite electronics. Such storms aremonitored by the NOAA Space Weather Prediction Center (SWPC), which issues warningsto satellite operators (SWPC, 2012). These particles are primarily a problem at GEOaltitudes, but for LEO, and as Brautigam (2002) describes, they occur in a location overSouth America called the South Atlantic Anomaly (SAA). The SAA is a permanent anomalyin the Earth’s magnetic field, generated by the misalignment between the axis of the Earth’srotation and the axis of the magnetic field. This misalignment means that the chargedparticles in the Van Allen belt dip down toward the Earth’s surface in an area over Braziland the South Atlantic Ocean (Figure 1.5). Within this region, high-energy protons cancause temporary or permanent damage to the spacecraft electronics. Dodd et al. (2010)describe the effect of the SAA on the Moderate Resolution Imaging Spectroradiometer(MODIS) instrument on the AQUA and TERRA spacecraft. For these satellites, the high-energy particles can reduce the efficiency of instrument detectors and can cause bits to flipspontaneously in computer circuitry, which led to a decision that, when the spacecraft is inthe SAA, no critical commands are to be sent to it.

Finally, as Chapter 9 discusses in more detail, in the microwave, the limited spectrumavailable for remote sensing observations and the presence of many other broadcast sources


12 Background

strongly affect the satellite observations by causing radio-frequency interference (RFI). AsChapter 9 discusses, the growth in the number of direct broadcast satellites, includingsatellite radio, television and telephone, the existence of powerful space observation radarsand the pressures to open up new radio spectra for these purposes and for cellular commu-nications at the surface have increased the presence of RFI, led to a reduction in the widthof bands used for Earth observations, and, in some cases, reduced the global coverage ofthe remote sensing observations.

1.4 Geosynchronous satellites

The geosynchronous satellites important to oceanography include observation, weatherand data relay satellites. The website GOES (2012) summarizes the different kinds ofgeosynchronous satellites, which are classified according to their scanning methods, calledspin-scan and fixed orientation. The spin-scan satellites consist of a cylindrically symmetricspinning part, mounted on a non-spinning section that contains the antennas for broadcastingthe data to ground stations. The spinning section is oriented such that its long axis is parallelto the Earth’s rotation axis, where its rotation rate is about 100 revolutions per minute. Oneach spin, a visible/infrared sensor sweeps across the Earth’s disk where the resultant dataare stored or broadcast. On the next revolution, the north–south sensor view angle changesslightly, and the scan is repeated. From such multiple scans, it takes about 20 minutesto create an image of the Earth’s disk. The spinning helps keep the satellite in thermalequilibrium and stabilizes the satellite in its orbit.

Satellites that use this technique are the European Meteosat series and the out-of-serviceJapanese Geostationary Meteorological Satellite (GMS) series (GOES, 2012).

Newer satellites such as the US Geostationary Operational Environmental Satellites(GOES) series have a fixed orientation and use a different scanning technique. For thiscase, the images are acquired by a scanner that employs two mirrors, one sweeping acrossthe Earth’s disk, the other stepping north-to-south. The future EUMETSAT and Japanesesatellites will employ similar systems.

The two European agencies involved with ocean remote sensing are the European SpaceAgency (ESA), founded in 1973, and the European Organization for the Exploitationof Meteorological Satellites (EUMETSAT), founded within ESA in 1986. ESA has theoverall responsibility for space programs; EUMETSAT manages the geosynchronous andSun-synchronous weather satellites (EUMETSAT, 2012). In 2012, the ESA governingcouncil included members from nineteen countries: Austria, Belgium, the Czech Republic,Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands,Norway, Portugal, Romania, Spain, Sweden, Switzerland and the United Kingdom. Undera special agreement, Canada is also a member of the council (ESA, 2012b).

A network of geosynchronous weather satellites provides global coverage between±60° latitude. As of February 2012, NOAA maintains two GOES satellites. These satel-lites, called GOES East and GOES West are located over the equator at approximately


1.5 Sun-synchronous satellites 13

60

0

30

–60

–30

0 30–30 60–60 90–90 120–120 150–150 180–180

GOES-East 75 W

GOES-West 135 W

MTSAT 145 E

Meteosat 0 E

Meteosat 57 E

Fig. 1.6. Field-of-view of the five geosynchronous meteorological satellites that provide near-globalcoverage. The boxes give the names of the satellites and their center longitudes; the ovals show theirrespective coverage. See the text for further description. (Reprinted from Vignola et al. (2012, Figure6), copyright 2012, with permission from Elsevier.)

75° W and 135° W, or at the longitudes of the east and west coasts of the United States.EUMETSAT maintains two spin-scan geosynchronous weather satellites called Meteosat,one over the Atlantic at approximately 0° and the other over the Indian Ocean at about60° E. Russia and India also maintain satellites at 75° E, although India generally reservesits data for domestic use. Japan maintains its geosynchronous weather satellite, called theMulti-functional Transport SATellite-2 (MTSAT-2) at 145° E. Consequently, the globe iscovered by five overlapping fields-of-view (Figure 1.6), placed at approximately equalintervals around the globe, with a sixth from China at 105° E.

These five satellites produce publically available imagery at about 3-hour intervals. Eventhough these imagers cannot view the polar regions, they provide sequential visible andinfrared imagery of clouds and SST patterns at 20–30-minute intervals for the equatorialand temperate latitudes. The second class of geosynchronous satellites is constituted by thedata relay satellites, which transfer data from the polar orbiters to the ground. The UnitedStates maintains the Tracking and Data Relay Satellite System (TDRSS) that consists ofabout four active satellites and three on standby. TDRSS is the primary communicationlink between the TERRA and AQUA spacecraft and the surface. ESA, China and Japanalso maintain data relay satellites.

1.5 Sun-synchronous satellites

Several countries maintain operational Sun-synchronous satellites with oceanographicinstrumentation, where the term operational means that the data from these satellites are


14 Background

regularly used in oceanographic or atmospheric forecasting. In the United States, threegovernment agencies operate satellites with ocean applications. The National Aeronauticsand Space Administration (NASA) maintains a series of research satellites, the NationalOceanic and Atmospheric Administration (NOAA) maintains the operational meteorologi-cal and oceanographic satellites, and the Department of Defense (DOD) maintains the twoDefense Meteorological Satellite Program (DMSP) meteorological satellites with oceano-graphic applications that are administered by NOAA. Other operational Sun-synchronoussatellite programs include the Russian Meteor series and the Chinese Feng Yun (Wind andCloud) FY-1C and FY-1D series.

In the United States, the NOAA satellites are launched by NASA, administered byNOAA, and carry instruments from France and the United Kingdom. Previous to 1994, theDOD and NOAA maintained parallel sets of operational satellites. For NOAA, the PolarOperational Environmental Satellite (POES) program administered these satellites, whichwere called POES or NOAA satellites. The DMSP satellites carry the visible–infraredOptical Line Scanner (OLS) and the passive microwave Special Sensor Microwave/Imager(SSM/I). As Chapters 9 and 10 discuss, the SSM/I and the post-2003 Special SensorMicrowave Imager/Sounder (SSMI/S) modification of the SSM/I provide time series of seaice extent.

The POES satellites were built by NASA and operated by NOAA. During constructionand before launch, these satellites are described by letters, as in NOAA-K; after launchthey are described by numbers, so that, for example, NOAA-K became NOAA-15. Inaddition to a variety of instruments used to gather atmospheric data as input to numericalweather forecasts, the principal oceanographic instrument on the NOAA satellites is the vis-ible/infrared Advanced Very High Resolution Radiometer (AVHRR) used for SST retrieval.AVHRR observations began in 1978 with the launch of the Television Infrared ObservationSatellite-N (TIROS-N); the first AVHRR specifically designed for SST retrieval was theAVHRR/2 launched in 1981 on NOAA-7. The AVHRR data are continuously broadcast inan open format, so that with the use of a relatively simple ground station these data can bedownloaded over most of the globe. As Chapter 7 discusses, AVHRR observations providea three-decade time series of global SST.

Like their current replacements, the NOAA satellites operated at altitudes between 830km and 870 km, where the orbit of the morning satellite was such that the satellite descendedor moved south across the equator with local crossing time of 0730, while the orbit of theafternoon satellite had an ascending equator-crossing time of 1330. For POES, becausethe crossing times of the two satellites are approximately 6 hours apart, with nighttimeequator crossings of approximately 1930 ascending and 0130 descending, the satellitesacquired imagery from almost every point on the Earth’s surface at 6-hour intervals. Forcomparison, the DMSP satellites operate at a nominal altitude of 830 km with dawn–duskcrossing times.

In 1994, a presidential decision transferred the management of all these satellites to thenew National Polar-orbiting Operational Environmental Satellite System (NPOESS). Thepurpose of NPOESS was to reduce the number of operational satellites from four to three,of which the United States would provide two satellites; the Europeans, one. NPOESS


1.6 Imaging techniques 15

also transferred operation of the DMSP satellites to NOAA. As part of this transition,the European METeorologie OPerationnelle-A (Operational Meteorology or METOP-A)satellite launched in October 2006 joined the observing constellation.

NPOESS also carried out the planning and construction of the NPOESS PreparatoryProject (NPP) satellite, designed to be the transition between POES and NPOESS. AlthoughNPP was completed and launched in October 2011, then renamed the Suomi-NPP after theinventor of the spin-scan satellite, the construction costs of the other NPOESS satellites sogreatly exceeded their budget that in February 2010 the NPOESS program was terminated.Its replacement is the Joint Polar Satellite System (JPSS), which is a collaboration betweenNOAA and NASA, where NOAA operates the satellites and NASA acquires them (JPSS,2013a). In 2013, the JPSS space segment consists of the Suomi-NPP in an early afternoonorbit, a DMSP satellite in a dawn–dusk orbit and METOP-B in a mid-morning orbit. Inabout 2017, the satellite JPSS-1 will replace Suomi-NPP, where JPSS-1 has a 7-year lifetimeand will carry the same instruments as Suomi-NPP (JPSS, 2013b).

The coverage of these satellites is as follows. The DMSP satellite is in early morningorbit with a descending equator-crossing time of 0530 local. The next in the series is themid-morning METOP-B satellite with a descending crossing time of 0930 local, whereMETOP-B also carries an AVHRR. Finally, Suomi-NPP has an early afternoon ascendingcrossing time of 1330 (CGMS, 2012). These three satellites provide coverage of mostof the Earth’s surface at 4-hour intervals. Suomi-NPP carries the replacement for theAVHRR, called the Visible/Infrared Imager/Radiometer Suite (VIIRS). Chapter 7 describesthe AVHRR; the following and Chapters 6 and 7 describe VIIRS.

1.6 Imaging techniques

Satellites use several scanning methods to generate images. As Section 1.4 describes,the geosynchronous satellites use spin-scan or fixed-orientation step-scanners to acquireimages. For the Sun-synchronous and other low Earth orbits, in the visible/infrared satellitesuse different but related scanning techniques to generate images. As Chapters 8, 10 and 14show, different scanning methods are used by passive and active microwave instruments.Section 1.6.1 describes the geometry used for a sensor viewing the Earth’s surface, thenshow for a simple telescope how the surface field-of-view changes with view angle. Sections1.6.2–1.6.4 discuss three scanning techniques used with low Earth orbits called cross-trackor whiskbroom, along-track or pushbroom, and what this book calls hybrid whiskbroom,where each of these depends on the satellite motion along its trajectory. Section 1.6.5concludes with a discussion of resolution.

1.6.1 Viewing the Earth’s surface

Figure 1.7 shows the terminology and geometry for a satellite sensor viewing the Earth’ssurface. On this figure, the point on the surface beneath the satellite is its nadir point; thepoint observed by the instrument is its scan point. Zenith means directly overhead. The


16 Background

θ

θ V

Sensor

S

Satellitenadir point

Satellitescan point

Sun

θ

Fig. 1.7. The angles used to describe the sensor view direction and the solar angle relative to aspherical Earth. θV is the view or scan angle that is associated with the satellite sensor and definedrelative to satellite nadir. θ is the viewing zenith angle and θS is the solar zenith angle, both definedrelative to the local vertical at the satellite scan point.

angle between the nadir line and the instrument look direction is the scan angle θV and, atthe scan point, the angle between the view direction and the local vertical is the viewingzenith or look angle θ . At off-nadir view angles, θ and θV differ because of the Earth’scurvature. The figure shows that the solar zenith angle θS is also measured relative to thelocal vertical. Given that oceanic surface properties are functions of the viewing zenithangle θ , the following chapters primarily use θ to describe the operation of the satelliteinstruments (View angles, 2013).

Many optical instruments employ telescopes with circular lenses and apertures to viewthe Earth at a variety of view angles (Figure 1.8). For this case, the instrument solid angle = A/r2 is a constant, where A is the surface area observed by the telescope atnadir and r is the distance from the instrument to the surface. The surface area is alsocalled the instrument field-of-view or equivalently the instantaneous field-of-view (IFOV),or often simply the field-of-view (FOV). For a nadir view, the FOV is a circle; because ofthe Earth’s curvature at off-nadir view angles, the FOV is an ellipse.

1.6.2 Cross-track or whiskbroom scanners

The next sub-sections describe three scanning techniques that are primarily used in the vis-ible/infrared and in low Earth orbits, while Chapter 8 describes the analogous microwavescanners. First, whiskbroom scanners construct images from the combination of the satel-lite motion along its trajectory and the rotation of a telescope–mirror combination relativeto the spacecraft. For these instruments, three directions describe the scan: along-track isin the direction of the satellite trajectory, cross-track is at right angles to the trajectory



r

ΔA

ΔΩ

ΔΩ

Sensor

Earth’s surface

θ V

Ω

Fig.. 1.8. The surface area observed by an optical instrument with a constant-solid-angle field-of-view, for nadir and off-nadir view angles.

Rotating mirror

Calibrator

λ

Satellite nadir track

Scandirection

Field-of-view

Swath width

Cross-track

Along-track

λ λ λ λ λ

(a) (b)

Along-scan

Detector

1

1 2 3 4 5

Fig. 1.9. Schematic drawing of a cross-track or whiskbroom scanner. The circles show the fields-of-view. The gray ellipse shows the instrument FOV. The radiation from the FOV is focused on thedetector, also shown in gray. (a) Single-Wavelength scanner. (b) Multi-wavelength scanner. The λ1

are the center wavelengths of the detectors.

and along-scan is in the scan direction of the sensor on the surface. Examples of whiskb-room instruments include the AVHRR and the Sea-viewing Wide Field-of-View Sensor(SeaWiFS).

For this scanner, Figure 1.9 shows a schematic drawing of the surface scanning patternand operation of idealized single and multichannel instruments. The single-channel scannerin Figure 1.9(a) collects radiation from the FOV at a single wavelength band; the multichan-nel scanner in Figure 1.9(b) collects radiation from the same FOV at several wavelength


18 Background

bands. The instrument operates as follows. For each wavelength band, the detectors arefocused on a mirror mounted at a 45° angle to its axis of rotation that rotates uniformlyaround 360°. At the same time as the rotating mirror sweeps the FOV across the surface, thesatellite motion moves it along the satellite trajectory, so that an image is constructed fromthe successive parallel scans. Because the mirror rotates as the satellite advances, the scanlines lie at an oblique angle to the satellite trajectory. The figure also shows a calibrationsource that is held at a constant radiance. The source is located such that, after completionof a surface scan, each channel views and stores a calibration value. A great advantage ofthe cross-track scanners is that the sensors are calibrated once per rotation.

A property of the whiskbroom scanners is that, as the off-nadir angle increases, the FOVincreases and its shape changes from a circle to an ellipse. The growth in FOV can be large.For a Sun-synchronous satellite at an altitude of 800 km, the FOV area at θV = 45° exceedsits nadir value by a factor of 1.5 in the along-track direction and by a factor of 3.5 in thealong-scan direction; at 55°, the area exceeds its nadir value by factors of respectively 2and 6. For these scanners, the mirror rotation rate is set so that on successive scans thenadir FOVs are adjacent to one another. Consequently, as the off-nadir FOVs increase inarea they overlap. Because of this growth in the FOV with angle, the overall shape of ascan resembles a bowtie, so that this growth in FOV with increasing off-nadir scan angle iscalled the bowtie effect.

The received data are also averaged over short periods of time into a series of successivetime blocks. This further increases the FOV, where the time-averaged FOV is called theeffective field-of-view (EFOV). As Section 1.7 describes in more detail, on the groundthe data are resampled to a uniform grid, where each cell in the grid has the area of thenadir FOV. Given the increase in both atmospheric interference and EFOV with increasingzenith angle, data taken at θV greater than 45–55° are noisier than data taken near nadir.Finally, some sensors such as the Optical Line Scanner (OLS) on the DMSP satellite andthe Day–Night Band (DNB) on VIIRS use a variety of techniques such as a variable-focustelescope to adjust the instrument solid angle so that the FOV area is independent of lookangle.

1.6.3 Along-track or pushbroom scanners

In contrast to the whiskbroom scanner, the pushbroom scanner uses long linear arraysof sensors to observe the surface in the cross-track direction, where each sensor, or, formultiple bands, each set of sensors, is focused on a specific track line beneath the satellite(Figure 1.10). For this instrument, the nadir FOV is a circle; the off-nadir FOVs are ellipses.The advantage of this technique is that the dwell time, or time interval for which the sensoris focused on a specific surface area, is greater than for the whiskbroom. Because it allowsone to obtain a greater signal-to-noise ratio and a higher spatial resolution than is possiblefor whiskbroom sensors, this increased dwell time is one of the most useful propertiesof the pushbroom instruments. Examples include the 30-m resolution Enhanced Thematic



Detectors

IFOVs

λλ λ

λ(b)(a)

λ

Lens system

Lens system

1λ1 2

3 4

5

Fig. 1.10. A schematic representation of the along-track or pushbroom scanner. (a) Single-wavelengthscanner. (b) Multi-wavelength scanner. The ellipses show the FOVs; the gray ellipses are simultane-ously viewed by the strip of detectors. Part (b) shows how the dark gray ellipse is viewed at multiplebands by the strip of dark gray detectors. See the text for further description.

Mapper Plus (ETM+) on the LANDSAT-7 satellite, the German Modular Optical Scan-ner (MOS) on the Indian IRS-P3 and the ESA Medium Resolution Imaging Spectrometer(MERIS) on ENVISAT with its 1200-km swath width. The advantages of the pushbroomscanner are longer dwell time and better spatial resolution; the disadvantages are that theindividual sensors can lose their calibrations relative to one another, making the instru-ment less accurate. Also, given that the pushbroom scanner requires one sensor for eachsurface pixel, the pushbroom instruments generally have a narrower swath width than thewhiskbrooms, because otherwise the large number of required sensors would generate anunwieldy instrument.

1.6.4 Hybrid cross-track scanner

Third, the need for wide-swath, high-spatial-resolution scanners led to the developmentof hybrid cross-track scanners that combine the properties of the whisk and pushbroomscanners. The hybrid scanner uses linear arrays of sensors with their long axis oriented inthe along-track direction. These arrays receive radiation from within a large-aspect-ratioelliptical FOV with its along-track length much longer than its cross-scan length. Theadvantage of this scanner is that it provides a way to increase dwell time and obtain highresolution from a wide-swath instrument while still permitting calibration of the sensors ateach rotation.


20 Background

Examples include MODIS on TERRA and AQUA with its 2300-km swath width, andVIIRS on Suomi-NPP with its 3000-km swath width. At nadir, the overall MODIS FOVdimensions are 10 km in the along-track direction and 1 km in the cross-scan direction(Barnes et al., 1998; Wolfe et al., 2002). In the along-track direction, and depending onthe observational wavelength, the number of detectors is 10, 20 or 40, corresponding to thenadir resolution of 1.0, 0.5 and 0.25 km. As listed in Table A.2 in the Appendix, MODIS has36 spectral bands, where, at nadir, 29 of the bands have a 1-km resolution, five have a 0.5-kmresolution, and two have a 0.25-km resolution. The advantage of this scanning techniqueis that, if this multiple-detector system were replaced by a single-sensor whiskbroom, themirror would have to spin ten times as fast to obtain the same spatial resolution, reducingthe dwell time and increasing the noise, both by a factor of ten. A problem that occurs withthe MODIS sensor is the bowtie effect, where, at the swath edge, the 1-km nadir resolutionincreases to 2 km in the along-track direction and 5.6 km in the cross-track direction (Wolfeet al., 2002).

VIIRS on Suomi-NPP is the replacement for AVHRR and MODIS, and has a similarset of along-track sensors to MODIS. As Table A.3 in the Appendix shows, althoughVIIRS has a better spatial resolution than MODIS, it has only 22 bands compared with the36 MODIS bands (Welsch et al., 2001). Of these bands, one is the Day–Night Band (DNB)discussed in Section 1.6.2; the others are discussed below. Compared with MODIS, thesmaller number of VIIRS bands reduces the VIIRS complexity, cost and weight relative toMODIS (VIIRS, 2012a). VIIRS gathers data using a rotating telescope and linear arraysof along-track sensors. VIIRS has a cross-track view angle of ±56° and a 3000-km swathwidth, which is 30% greater than the MODIS swath width.

At nadir and similar to MODIS, the VIIRS FOV extends about 12 km in the along-trackdirection and 750 m in the along-scan direction. Within the instrument, the FOV radiancesare focused onto two linear detector arrays, one for the sixteen 750-m resolution bands,called “Moderate” or “M” bands, and one for the five 375-m resolution bands, called“Imaging” or “I” bands, where these resolutions are at nadir. The Moderate bands havesixteen detectors in the along-track direction; the Imaging bands have 32 (VIIRS, 2012b).A unique feature of VIIRS is that, in the along-scan direction, each detector is made up ofthree sub-detectors. VIIRS uses these sub-detectors to partially correct for the bowtie effectby constraining the increase in the field-of-view with scan angle. As the following shows,VIIRS compensates for this increase by having the number of along-scan sensors decreaseas the view angle increases.

Figure 1.11 shows the configuration of the VIIRS along-scan sensors, and, for specificvalues of the scan or view angle θV, the approximate IFOV dimensions for the M-bands.For 0° < θV < 32°, three sensors determine the IFOV, where, as Figure 1.11(a) shows forthe nadir case, the FOV generated by the sensors is nearly square and measures 0.75 km ×0.75 km. For 32°< θV < 45°, the number of sensors that determine the IFOV decreases fromthree to two, yielding at 32° an IFOV of 1.1 km × 1.3 km, so that it remains approximatelysquare. For angles greater than 45°, the number of sensors decreases from two to one,yielding at 45° an IFOV measuring 1.6 km × 1.6 km.



762

m

786 m262 m

Along-scan direction

1100

m

1260 m630 m

1600

m

1600 m

Alo

ng-t

rack

dire

ctio

n

32o < < 45o < 32oθ V θ V θ V45o < < 56o

Fig. 1.11. The along-scan configuration of the number of detectors used to determine the FOV as afunction of view angle for the VIIRS Moderate resolution bands. The gray rectangles represent thesensors used in the retrieval of the surface radiance, while the ranges of angles above the rectanglesshow the range of applicability of the sensor configuration in terms of the view angle; the adjacentdimensions give the size of the surface FOV for (a) nadir view, (b) θV = 32 and (c) θV = 45. Seethe text for further description. (Adapted from Guenther et al. (2011)).

For comparison of the MODIS and VIIRS IFOVs, Figure 1.12 shows the dependence oftheir along-scan dimension on scan angle, and, for VIIRS, shows how the reduction in thenumber of sensors reduces the along-scan IFOV dimension. Because of the reduction inthe number of sensors with view angle, the along-scan dimensions of the IFOV increase bya factor of two, instead of by the factor of six that occurs for MODIS. Finally, for differentlocations on the swath, Figure 1.13 compares the IFOV of the AVHRR, MODIS and VIIRSbands.

1.6.5 Resolution

As the next section describes in detail, the data from these instruments are resampled into auniform grid, where the grid spacing approximately corresponds to the nadir FOV diameter.Each element in the grid is called a pixel, which is the abbreviation for picture element.Typically, for AVHRR and SeaWiFS, the pixel measures 1 km by 1 km, referred to as a1-km pixel, where the pixel area equals that of the nadir FOV. For this case, the instrument isalso described as having a 1-km resolution, meaning that objects smaller than 1 km cannotbe distinguished by the imager. In the visible, infrared and passive microwave, resolution isdefined as equal to the nadir FOV. For radars and as Section 13.2.2 describes, the definitionof resolution is different, in that the smallest pixel size equals half the resolution.


22 Background

MODIS 1 km

VIIRS 375 m

MODIS 500 m

MODIS 250 m

VIIRS 750 m

Scan angle (deg)

0 10 20 30 40 50 600

1

2

3

4

5

6

7

Alo

ng-s

can

surf

ace

leng

th o

f the

IFO

V (

km)

Fig. 1.12. The length of the along-scan scale of the IFOV for the different MODIS and VIIRS imagemodes. See the text for further description. (From Guenther et al. (2011), used with permission.)

Nadir ~750 km ~1500 km, swath edge

AV

HR

R

V

IIRS

Mod

erat

eR

esol

utio

n

2.3 km

1.6

km

6.7 km

2.5

km

0.75 km 1.2 km

0.75

km

1.1

km

1.6

km

1.6 km

1.14 km

1.14

km

MO

DIS

1.0 km

1.0

km

2.0

km

6.0 km

Fig. 1.13. Comparison of the sizes of the IFOVs of the AVHRR, the MODIS 1-km bands and theVIIRS Moderate resolution bands at nadir, mid-swath, excepting MODIS, and swath edge. See thetext for further description. (Adapted from Zhou (2011, slide 4), for AVHRR and VIIRS, and fromWolfe et al. (2002), for MODIS.)

1.7 Processing levels, archives, data records and processing

In the following, Section 1.7.1 discusses the different processing levels for satellite dataand Section 1.7.2 gives a short description of the US data archives. Section 1.7.3 describesthe forms of satellite data records called sensor data records (SDRs), environmental datarecords (EDRs) and climate data records (CDRs), and the restrictions imposed on their


1.7 Processing levels, archives, data records and processing 23

processing. Finally, for different geophysical variables, Section 1.7.4 describes the variouscenters that produce CDRs.

1.7.1 Processing levels for satellite image data

Processing of the swath data from these scanners is usually described as a series of stepsor processing levels, which consist of the following (Parkinson et al., 2006, p. 31).

Level 0. This is the downloaded unprocessed engineering outputs from the sensor at fullresolution. All communication artifacts such as headers, duplicate data and telemetryerrors are removed. The Level-0 data are provided to the data archives.

Level 1A. At the archives, the Level-0 data are processed into full-resolution files withunits of digital counts that are annotated with related ancillary data such as timereferences, calibration coefficients and geolocation information.

Level 1B. The Level-1A data are converted to sensor units such as radiances or bright-ness temperatures written in digital counts and presented in an along-track swathformat corresponding to the instrument scan lines. In the scan line presentation, thegeographic distance between data points corresponds to the cross-track dimensionof the nadir FOV. Appended files contain geolocation data and information on dataquality. The Level-1B files are in a computer-friendly format and can be downloadedfrom the data centers for further analysis. Not all instrument data have a Level-1Bequivalent.

Level 2. The Level-1 data are processed into geophysical data products such as SSTor sea ice cover in a swath format with the same resolution as Level 1. Using SSTas an example, Chapter 7 shows that its calculation involves the use of data frommultiple channels, application of a cloud mask, correction for atmospheric emissionand attenuation caused by water vapor and interpretation of the received radiances interms of the physical properties of the ocean surface and atmosphere.

Level 3. The geophysical data product is mapped to a uniform grid with gaps for regionswith no data. An example would be a global daily grid of SST. On this grid, the datagaps associated with the swaths as well as the cloud-induced gaps in the Level-2product remain at Level 3.

Level 4. The geophysical information at Level 3 is combined with data from multiplesatellite and in situ measurements to produce a gap-free product on an uniform grid.For SST, this product is calculated by an optimal interpolation scheme that combinesdata from a variety of satellite and in situ observations such as the temperaturesreported by buoys.

1.7.2 The data archives

For NASA, the data processing from earth sciences missions takes place at twelve archivesand data processing centers. The ocean-related centers include the Alaska Satellite FacilitySAR Data Center (ASF, 2013b), the National Snow and Ice Data Center Distributed Active


24 Background

Archive Center (NSIDC, 2013c), the NASA Ocean Biology Processing Group (NASA,2013b), and the Physical Oceanography DAAC (PO.DAAC) at the Jet Propulsion Labo-ratory (PO.DAAC, 2013). Under US law, NASA cannot charge for data. Each of thesewebsites can be accessed through the Goddard Earth Sciences, Data and Information Ser-vices Center (GES DISC), which provides a gateway to earth science data (NASA, 2013a).The centers provide an archive for data, as well as processing tools, and, for the GES DISC,a web-based application called Geospatial Interactive Online Visualization ANd aNalysisInfrastructure (GIOVANNI, or more commonly Giovanni), which is a way to access, ana-lyze and visualize remote sensing data without having to download the data (Giovanni,2013). These archives provide user support and insure that data is accessible.

1.7.3 Kinds of data records

Following the classification by the National Research Council (2004), there are at leastthree kinds of data records used in satellite oceanography. The first is the sensor data record(SDR); these are antenna radiances that are time-tagged, geolocated and calibrated, but notnecessarily suitable for long-term reliability. The second is the environmental data record(EDR) that is a geophysical product such as the SST that is derived from the SDR. TheEDR is processed once, is designed for operational use and is not suitable for long-termclimate research. The third is the climate data record (CDR) that is a geophysical productexpressed in a time series of sufficient length, consistency and continuity that it can beused to determine variability and changes in climate. As described below, the CDRs aremulti-satellite, long-time-period time series that, for use in climate research, have beencalibrated, validated and frequently reprocessed. Examples of CDRs include SST, oceancolor, sea ice concentration and extent, and surface winds. A CDR is sometimes calledan earth science data record (ESDR), a thematic CDR (TCDR) or a fundamental CDR(FCDR).

The generation of the CDRs must follow these guidelines (National Research Council,2004, Box ES-1).

Instrument calibration. Before launch, the instrument must be calibrated against knownstandards such as those maintained by the National Institute of Standards and Tech-nology (NIST). Then, any changes in calibration during the ascent-to-orbit must bedetermined and the on-orbit calibration must provide for continuous monitoring ofthe sensor performance. The calibration scheme must allow determination of therelation of the on-orbit calibration to the surface reference calibration (Turpie et al.,2012). Examples of on-orbit calibrations include, for thermal infrared instruments, aview of a 300-K blackbody and of cold space during each whiskbroom revolution.For measurements of ocean color, because the Moon has about the same radianceas the ocean, the ideal on-orbit calibration includes monthly lunar views (McClain,2009). These calibrations must be part of the operational data stream. To permitcross-calibration between pairs of satellites that make similar measurements, there


1.7 Processing levels, archives, data records and processing 25

should be overlap periods of at least two years for the pair. In summary, during theinstrument lifetime, there must be a documented trail of the sensor properties fromthe initial surface calibration to the final on-orbit calibration.

Vicarious calibration. An ongoing program of surface measurements provides an addi-tional source of calibration, where, using ocean color as an example, the surface mea-surements consist of radiance and chlorophyll measurements made at fixed buoys andby ships. This comparison with in situ data is called a “vicarious” calibration, where,for ocean color, the radiances received at the satellite instrument are compared withthose measured at a surface buoy, then any offsets are removed from the radiances.Because determination of these offsets requires 30–50 measurements, the vicariouscalibration can take as long as two or three years. The combination of the on-orbitand vicarious calibration must provide well-defined levels of uncertainties.

Algorithm testing and reprocessing. Funds and computational resources must be avail-able for algorithm testing, and, as improvements to the algorithms or calibrationsbecome available, for reprocessing of the entire CDR data set. Also, the operationalprocessing must produce Level-3 data sets that can be easily examined to understandany geographic and temporal trends in the data (Turpie et al., 2012). The critical issueis that the calibration and radiance data among the different satellites that contributeto the long-period time series must be in a common format that can be processedretrospectively. An important example of reprocessing discussed below in Chapters 9and 11 occurs with the vector wind retrievals from the passive microwave SeaWindsinstrument launched in 2003. Initially, the algorithm for this data set was valid onlyfor wind speeds of less than 20 m s−1 and rain-free conditions; Meissner and Wentz(2009) extended the algorithm to include winds speeds as large as 30 m s−1, whichgreatly improved its value.

1.7.4 Processing and archive centers

The production of EDRs and CDRs takes place at a small number of specific centers. Thefollowing is a list by geophysical data product of some of the groups that produce andarchive these products.

Ocean biology. With the help of numerous national and international investigators,the Ocean Biology Processing Group (OBPG) at the Goddard Space Flight Centerprocesses the ocean biology products. As Chapter 6 describes, Giovanni is the archivefor many of these CDRs.

Infrared sea surface temperature. As Chapter 7 describes, the NOAA Center for SatelliteApplications and Research (STAR) provides a cloud-filtered infrared SST daily EDRproduct for a variety of forecast applications. The NOAA National OceanographicData Center (NODC) reprocesses the EDRs into what are called the Pathfinder SSTCDRs. PO.DAAC also archives SST products; PO.DAAC has its own Facebook page.


26 Background

Passive microwave products. The private company Remote Sensing Systems (RSS)does the initial processing on much of the US microwave data, and provides a varietyof vector and scalar wind products, microwave SSTs and a variety of atmosphericproducts. All these data sets are reprocessed into CDRs.

Altimetry. The French Centre National d’Etudes Spatiales (CNES) and the JPLPO.DAAC maintain the altimeter records from the TOPEX and JASON satellites;since it tracks sea level rise, this is a critically important CDR.

Active microwave winds. JPL is also responsible for the US active microwave windmissions and, as Chapter 11 describes, produces a number of wind CDRs that arearchived at PO.DAAC.

Sea ice. The passive microwave sea ice time series of area and extent is monitoredand produced using algorithms from the Goddard Space Flight Center, and isarchived at the NASA National Snow and Ice Data Center (NSIDC). The syn-thetic aperture radar (SAR) imagery of sea ice is archived at the Alaska SatelliteFacility (ASF).

Salinity. The JPL PO.DAAC archives the Aquarius salinity data.

1.8 Past, present and pending satellite missions

Ocean remote sensing began in the United States in the 1970s. By the 1980s and early1990s, the success of the early US satellites had led ESA and Japan to launch their ownmissions. As of 2013, there are at least eleven countries or groups of countries with ocean-observing instruments or satellites: Brazil, Canada, ESA, India, Japan, People’s Republicof China (mainland China), Republic of China (Taiwan), Republic of Korea (South Korea),Russia, Ukraine and the United States. Of these countries, Canada has the RADARSATSynthetic Aperture Radar (SAR) satellites, the Japanese Aerospace Exploration Agency(JAXA) has the Global Climate Observation Missions (GCOM), the Indian Space ResearchOrganization (ISRO) has the OCEANSAT satellites, the China National Space Adminis-tration (CNSA) has the Feng Yun (Wind and Cloud) series and ESA has the METOP andthe new Sentinel series. Within the European Union, France, Germany and Italy have theirown space programs. In the following, Section 1.8.1 gives a brief history of the US oceano-graphic satellite research programs, Section 1.8.2 describes the growth of the internationalGlobal Earth Observation System of Systems (GEOSS) that was conceived in 2003, andSection 1.8.3 reviews oceanographic satellite missions through 2015.

1.8.1 Growth of US oceanographic satellite missions

Wilson (2001) and Wilson, Apel & Lindstrom (2001) describe the three generations ofNASA oceanographic satellites between 1970 and 2000. The first generation consists of the1960–1965 NASA Television Infrared Observation Satellite Program (TIROS) satelliteswith their emphasis on infrared observations, the scatterometer experiments on the 1973


1.8 Past, present and pending satellite missions 27

Skylab, the launch and operation of the US Navy 1975 GEOS altimeter satellite, and theoperation between 1973 and 1976 of the single-channel Electrically Scanned MicrowaveRadiometer (ESMR) on the NIMBUS-5 satellite. These missions demonstrated the potentialfor scatterometer wind retrieval, satellite altimetry and the passive microwave retrieval ofsea ice properties.

Based on these and a variety of aircraft experiments, the second generation consists ofthe 1978 launch of the TIROS-N, SEASAT and NIMBUS-7 satellites. TIROS-N carried theforerunner of the AVHRR that began the SST time series (TIROS, 2013), which was the firstof the NOAA satellite series. SEASAT carried four pioneering instruments; a multichannelpassive microwave radiometer called the Scanning Multichannel Microwave Radiometer(SMMR), a wind scatterometer, a SAR and a radar altimeter. Although SEASAT failed after99 days of operation, it was immediately followed by the launch of NIMBUS-7. AlthoughNIMBUS-7 lacked the altimeter, SAR and scatterometer, it carried the Coastal Zone ColorScanner (CZCS) and a microwave imager similar to that on SEASAT. CZCS operated until1986, SMMR and NIMBUS-7 operated until 1988.

The first- and second-generation satellite observations provided successful demonstra-tions of the retrieval of SST, ocean surface height, ocean color, surface winds and seaice properties. Beginning in about 1985, for the third-generation missions, Wilson (2001)shows that NASA took a different approach. Briefly, NASA set two requirements: that theoceanographic community contribute to the mission justification, planning and support,and that each future mission have a non-NASA partner, where the second requirement wasin part prompted by cost overruns on the Space Shuttle. The first requirement led to a seriesof joint studies with the oceanographic community, the results of which led NASA to focuson four areas: sea surface height or altimetry; biological ocean color or productivity; seaice properties; and the land, ice and open ocean applications of SAR.

These studies and the partnership requirement led to the following missions: (1) the1987 continuation of the NIMBUS-7 passive microwave observations by the US Depart-ment of Defense on the DMSP satellites; (2) completion of the NASA Alaska SARFacility (ASF, later renamed the Alaska Satellite Facility), which became operational inSeptember 1991 and the concomitant NASA agreements with Canada, ESA and Japanfor ASF reception of their satellite SAR data; (3) the 1991 French launch of the UnitedStates/France TOPEX/POSEIDON altimeter mission; (4) the 1995 US launch of the Cana-dian RADARSAT SAR satellite; (5) the 1995 launch of the NASA wind scatterometer(NSCAT) on the Japanese Advanced Earth Observing Satellite (ADEOS); and (6) thecontract with Orbital Science Corporation for the purchase of ocean color data from theSeaWiFS instrument launched in 1997.

The NASA demand for scientific justification and partners in future missions is onereason for the long delay between the launch of NIMBUS-7 in 1978 and the TOPEXaltimeter in 1991. Another reason is that it took years to analyze the ocean color, SARand scatterometer data collected by the second-generation missions, so that, parallel to thethird-generation planning and instrument development, there was an additional effort toprepare computationally for the new missions.


28 Background

Beginning in the mid-1980s, there were increasing concerns about the effects of climatechange on global food supplies, and the increased vulnerability of coastal populations toviolent weather and enhanced coastal erosion, storm surge and flooding. These createda demand for (1) better forecast capability for storms such as typhoons and hurricanes,(2) satellite support for modeling efforts in physical and biological oceanography, and (3)long-term time series of oceanic and sea ice variables. These served as the basis for theplanning and launch of large multinational projects such as the NASA Earth ObservingSystem (EOS), which took place with the launch of two large multi-instrumented satellites:TERRA in 1999 and AQUA in 2002. Two additional large satellites were launched in 2002:the ESA ENVISAT (Environmental Satellite) and the Japanese ADEOS-2 (Advanced EarthObserving System), but ADEOS-2 failed within a year. EOS was originally conceived asa 15-year program, where 15 years was assumed sufficient to observe the onset of globalchange, with the lifetime of each satellite and its replacements being approximately fiveyears.

As Assar (2011) describes, there were two criticisms of these large multi-instrumentedsatellites and in particular of the EOS program. First, the placement of many instrumentson a single platform meant that, as occurred with ADEOS-2, a failure in the common powersupply could destroy the entire mission. Second, and for EOS in particular, the reuse ofthe same instrument design over the proposed 15-year observational period meant that theinstruments would be frozen into the designs of the 1980s.

The critics therefore suggested that the large platforms be replaced by constellationsof smaller satellites that would replicate the EOS observations, provide a way to updateinstrument technology, replace failed instruments with less cost and facilitate internationalparticipation. Because of these criticisms as well as cost considerations, the EOS missionsrepresented by AQUA and TERRA were shortened to a five-year program, where someof their observations were incorporated into JPSS, some were taken over by dedicatedsatellites and some were incorporated into non-US satellites.

1.8.2 The growth of international programs and observing constellations

The fourth generation consists of the transition of the various national programs to interna-tional observing constellations. In 2002, as Lautenbacher (2006), Christian (2005) and GEO(2012) describe, ministers from about 60 countries and the European Commission estab-lished the Group on Earth Observations (GEO) with the goal of implementing a GEOSSprogram within the ten-year period 2005–2015. The purpose of GEOSS is to gather allcivilian satellite programs into a voluntary coordinated program.

As GEO (2012) describes, another purpose of GEOSS is to link existing national andinternational planned and existing satellite systems into a single system and promote com-mon formats for data storage and access. Its specific goals are to reduce national costs andimprove efforts in areas such as climate change, reduction of the loss of human life andproperty due to disasters, and understanding of the water cycle and weather forecasting


1.8 Past, present and pending satellite missions 29

(GEO, 2012; Lautenbacher, 2006). Where gaps exist in the data coverage, GEO supportsthe development of new satellite systems, encourages individual national space programs toincrease the value of their satellite observations through participation in international con-stellations, and encourages the assimilation of satellite and in situ data into-near-real-timenumerical forecast models.

The GEOSS satellite programs are coordinated by the Committee on Earth Observa-tion Satellites (CEOS), founded in 1984, which has the responsibility for organizing theobserving constellations (CEOS, 2012). The four major CEOS ocean-related constellationsinclude sea surface topography, ocean color, ocean vector winds and SST as well as theocean-related precipitation missions. When, for example, Japan launches its ocean colorsatellite GCOM-C1, its orbit and equator-crossing time will be coordinated with similarmeasurements by other countries. The JPSS described in Section 1.5 is an example of anobserving constellation.

Another example is the international Afternoon Constellation or A-Train (NASA,2012b), which consists of seven satellites flying in the same 1330 local northward equator-crossing Sun-synchronous orbit. Within the A-Train, all of the satellites overfly a givenlocation within seconds to minutes of each other. Although the A-train focus is on clouds,water vapor and hurricane research, the AQUA satellite, which occupies the second posi-tion in the A-Train, carries the Japanese Advanced Microwave Scanning Radiometer-EOS(AMSR-E) instrument used for observations of sea ice and SST. A recent event illustratesthe strength of the constellation concept. In October 2011, the AMSR-E on AQUA failed. InMay 2012, it was replaced with the AMSR2 instrument launched on the Japanese CGOM-W1 satellite that carried only the AMSR2 and that was positioned to fly in the A-Train justahead of AQUA, thus maintaining the continuity of the observations.

For the period 2010–2020, the ESA contribution to GEOSS consists of the five Sentinelsatellites within the ESA Global Monitoring for Environment and Security (GMES) pro-gram (ESA, 2012c). Two of these satellites, Sentinel-1 and Sentinel-3, are ocean-related.Sentinel-1 consists of a pair of dedicated synthetic aperture radar (SAR) satellites that willfly in the same Sun-synchronous orbit at different equator-crossing times that will providedaily coverage of ocean features such as oil spills, sea state, sea ice and the directional prop-erties of ocean waves. Sentinel-3 is a pair of Sun-synchronous satellites that will observesea surface temperature, ocean surface topography and ocean color.

Similarly, the Japanese contribution to GEOSS is the Global Climate Observation Mis-sions (GCOM) (JAXA, 2012). There are two GCOM satellites, both of which carry onemajor instrument. The first is the GCOM-Weather mission (GCOM-W1) that carries theAMSR2, as described above. The second is the GCOM-Climate satellite (GCOM-C1),scheduled for launch in 2014, which will observe ocean color using the Second-generationGLobal Imager (SGLI). Each GCOM satellite is designed to have a five-year lifetime,and there are three satellites planned for each series with a one-year overlap, so that, forexample, the series GCOM-C1, -C2, -C3 will extend over a thirteen-year period (Shimoda,2010). Finally, JAXA and NASA are jointly building the Global Precipitation Mission(GPM) Core Observatory Scheduled for launch in 2014, which will serve as the successor

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Table 1.1. Past, present and near-future ocean satellite missions through 2015.

Launch year andlifetime Country or agency Mission name and instruments Oceanographic observations

1978 (3 months) SEASAT Sea surface height, SAR, vectorwinds, passive microwaveAltimeter

SAR, Synthetic Aperture RadarSASS, SEASAT-A Satellite ScatterometerSMMR, Scanning Multichannel Microwave Radiometer

1978–1987 United States NIMBUS-7 Passive microwave, ocean colorCZCS, Coastal Zone Color ScannerSMMR

1985–1990 US Navy GEOSAT Sea surface heightAltimeter

1991–2001 ESA ERS-1, -2, Earth Resources Satellite Winds, SAR, SSTAMI, Advanced Microwave Instrument (combination

of SAR and wind scatterometer)ATSR, Along-Track Scanning Radiometer

1992–1998 Japan JERS-1, Japanese Earth Resources SatelliteSAR

SAR for land, ocean observation

1992–2006 United States/France TOPEX/POSEIDON Sea surface heightNASA altimeterPoseidon altimeter (France)

1995– Canada RADARSAT-1 SAR1996–2006 India IRS-P3, Indian Resource Satellite Ocean color

MOS, Modular Optical Scanner (Germany)WiFS, Wide Field-of-view Sensor

1996–1997 Japan ADEOS-1, Advanced Earth Observing Satellite Ocean color, windsNSCAT, NASA Scatterometer (United States)OCTS, Ocean Color and Temperature Sensor

1997– United States/Japan TRMM, Tropical Rainfall Measuring Mission Rainfall, SSTTMI, TRMM microwave imager

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1997–2010 United States/OrbitalScience Corp.

SeaStar satellite Ocean colorSeaWiFS, Sea-viewing Wide Field-of-view Sensor

1999–2010 India IRS-P4 (OCEANSAT-1) Ocean colorOCM, Ocean Color Monitor (Germany)

1999–2001 China FY-1C, Feng Yun-1C (Wind and Clouds-1C) SSTMVIRSR, Multispectral Visible/IR Scanning Radiometer

1999–2009 United States QuikSCAT Vector windsSeaWinds

1999–2008 Republic of China ROCSAT, Republic of China Satellite Ocean colorOCI, Ocean Color Instrument

1999– United States TERRA Ocean color, SSTASTER, Advanced Spaceborne Thermal Emission and

Reflection Radiometer (Japan)MISR, Multi-angle Imaging SpectroradiometerMODIS, Moderate Resolution Imaging Spectroradiometer

1999–2008 South Korea KOMPSAT, Republic of Korea Satellite Ocean colorOSMI, Ocean Scanning Multispectral Imager

2001– United States/France JASON-1 Sea surface topographyPoseidon altimeter

2002–2012 ESA ENVISAT, Environmental Satellite SST, SAR, ocean colorAATSR, Advanced Along-Track Scanner RadiometerASAR, Advanced SARMERIS, Medium Resolution Imaging SpectrometerRA-2, Radar Altimeter-2

2002– United States AQUA Ocean color, passive microwaveMODIS, Moderate Resolution Imaging SpectroradiometerAMSR-E, Advanced Microwave Scanning Radiometer-EOS

(Japan)2002– United States/Germany GRACE, Gravity Recovery and Climate Experiment Gravity mission2002–2012 China FY-1D SST, ocean color

MVIRSR, Multispectral Visible/IR Scanning Radiometer(cont.)

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Table 1.1. (cont.)

Launch year andlifetime Country or agency Mission name and instruments Oceanographic observations

2002–2004 China HY-1A, Haiyang-1 (Ocean-1) Ocean color2002–2003 Japan ADEOS-2 Passive microwave, vector

winds, ocean colorAMSR, Advanced Microwave Scanning RadiometerGLI, Global ImagerSeaWinds (NASA)

2003– US Navy/NPOESS Coriolis/WindSat Passive microwave vector winds2003–2009 United States ICESat

GLAS, Geoscience LaserAltimeter System

Sea ice, ice sheet, topography

2006–2011 Japan ALOS, Advanced Land Observing SatellitePALSAR, PhasedArray L-band SAR

SAR

2006– China FY-3AVIRR, Visible/Infrared RadiometerMODI, Moderate Resolution Visible/Infrared Imager

Ocean color, SST

2006– ESA METOP-AASCAT, Advanced ScatterometerAVHRR-3, AdvancedVery High Resolution Radiometer

Ocean winds, SST

2006– Canada RADARSAT-2 SAR2007– ESA SMOS, Soil Moisture and Ocean Salinity Sea surface salinity2007–2011 China HY-1B, Haiyang-1B Ocean color2008– United States/France/

EUMETSATJASON-2 altimeter Sea surface topography

2009– India OCEANSAT-2 (IRS-P7)OSCAT, OCEANSAT Scatterometer

Ocean winds, ocean color

2010– ESA CryoSat-2SIRAL, Synthetic Aperture Interferometric Radar Altimeter

Sea ice, ice sheet topography

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2011– United States/Brazil AQUARIUS Sea surface salinity2011– United State NPOESS Preparatory Project (Suomi-NPP)

VIIRS, Visible/Infrared Imaging/Radiometer SuiteSST, possibly ocean color

2011– France/India Megha-TropiquesMADRAS, Microwave Analysis and Detection of Rain and

Atmospheric Structures

Precipitation

2012– Japan GCOM-W1AMSR-2, Advanced Microwave Scanning Radiometer

Sea ice, SST

2012– ESA METOP-BASCAT, Advanced ScatterometerAVHRR-3, Advanced Very High Resolution Radiometer

Ocean winds, SST

2013 India/France SARAL (Satellite with Argos and ALtika)AltiKa (Ka-band altimeter), Argos (data relay)

Follow-on altimeter to EnvisatAlt

2013 Japan ALOS, Advanced Land Observing SatellitePALSAR, Phased ArrayL-band SAR

SAR

2014 NASA/CNES/NOAA JASON-3POSEIDON-3B altimeter

Sea surface topography

2014 Japan GCOM-W1SGLI, Second GenerationGlobal Imager

Ocean color

2014 ESA Sentinel-3 SST, possibly ocean color2014 NASA/JAXA Global Precipitation Mission Core

GPM Microwave Imager Dual-Frequency PrecipitationRadar (DPR)

Precipitation

2015 United States ICESat-2Laser altimeter

Ice sheet, sea ice topography

2015 United State/Germany GRACE-2 Gravity mission

Derived from CEOS (2013), and from various NASA sources.


34 Background

to TRMM and as the basis for the GPM satellite constellation, with contributions fromFrance, India, EUMETSAT and NOAA (GPM, 2012).

A related effort to GEOSS is the Global Ocean Data Assimilation Experiment (GODAE)now called GODAE OceanView (GODAE, 2012a, 2012b). In 1999, GODAE was initiatedto work on the problem of global operational oceanography, meaning the development forthe ocean of near-real-time modeling, forecasts and dissemination of results. In contrast toGEO, GODAE is a working-level group, and is focused on the incorporation of satelliteand in situ data into global and regional oceanic models. Clark et al. (2009) describe thein situ and satellite aspects of GODAE. As an example, they describe the use of data fromtide gauges, satellites, observations of glacier and ice cap melting and ocean warming toprovide operational estimates of sea level rise. As Chapter 7 discusses, another example arethe values of SST that are produced by different national and international groups under thename GODAE High Resolution Sea Surface Temperature (GHRSST) (GHRSST, 2012a).The GHRSST data sets are produced in a common format by a number of different countriesfrom a variety of satellite and in situ estimates, where in 2013 there are about sixty differentGHRSST data sets as described by GHRSST (2013c).

1.8.3 Satellite missions through 2015

Table 1.1 lists the major past, present and pending ocean satellite missions through 2015,giving the launch date and, if known, the lifetime, the country providing the satellite, themission name, its oceanographic instruments and its purpose. Under the satellite name, thetable lists the ocean-related instruments and, if another country provides the instrument,adds that country’s name in parentheses. For satellites that have been approved (funded)but not launched, there is no dash (–) after their launch year. To shorten the table, mostoperational systems such as POES, JPSS and DMSP are excluded, and several of the radarmissions are omitted and described in Chapter 13.

The table shows the growth in the number and diversity of satellite missions since 1995.During 2000–2010, the table shows the trend away from the large multi-instrumentedmissions such as TERRA, AQUA and ENVISAT to constellation members that carry oneor two instruments. For the constellations, the loss of a single satellite and instrument isless expensive and easier to replace, as well as enhancing the possibility of internationalparticipation.


2

Ocean surface phenomena

2.1 Introduction

This chapter summarizes those open ocean and floating ice properties that modify thesurface and affect the emitted and reflected radiation at all frequencies. For the openocean, these properties include wind-generated capillary and gravity waves, breaking waves,the generation and decay of foam, and the modulation of short waves by long wavesand currents. Natural and human-generated slicks also suppress short waves. At longertime periods and over larger spatial scales, ocean currents, eddies and Rossby and Kelvinplanetary waves generate large-scale changes in ocean surface elevation. Polar ice propertiesthat affect the radiation include the areal extent and type of pack ice, and the presence andsize of icebergs.

In the following, Section 2.2 discusses the oceanic winds and the ocean surface waveproperties important to remote sensing: in particular the difference between the short-period capillary waves and the longer-period gravity waves, the changes that occur in thegravity-wave profile with increasing wave amplitude, the growth of capillary waves on thesurface of the longer-period waves, the effect of wave breaking and the generation of foam.Because foam consists of air bubbles and is highly reflective, it changes the reflectivity andemissivity of the ocean surface, which makes it important at all remote sensing frequencies.The section also discusses the distribution of wave surface slopes as a function of azimuthangle relative to the wind direction. Although this topic seems obscure, it is essential fordetermination of sun glint, which can overwhelm satellite observations at all frequencies,and for the measurement of vector wind speeds at microwave frequencies. The sectionconcludes with a discussion of surface slicks. Section 2.3 discusses the changes in seasurface height induced by ocean currents and long-period planetary waves, and Section 2.4discusses sea ice.

2.2 Ocean surface winds and waves

Surface winds play a dominant role in the modification of the temperate ocean surface. Themost common process is the wind generation of ocean waves. Another is that the surfacewind stress and the atmospheric heat exchange drive the ocean circulation. Figure 2.1 shows

35


36 Ocean surface phenomena

Windspeed (m s–1)0 12 18 24

0

5

10

15

Num

ber

of o

ccur

renc

es (

%)

6

Fig. 2.1. Comparative histograms of the 10-m wind speed obtained from SSM/I data (shaded area)and from co-located NCEP pressure data (line). Both data sets consist of 6.8 × 1010 measure-ments taken between January 1992 and December 1997. The bin sizes for the winds are 1.2 m s−1.(Courtesy of Remote Sensing Systems, Santa Rosa, CA, used with permission.)

the distribution of the global wind speeds over ice-free waters derived by two methods: first,from satellite passive microwave Special Sensor Microwave/Imager (SSM/I) observationsof wind magnitudes using the techniques described in Chapter 9; second, from winds co-located with satellite observations and derived from National Centers for EnvironmentalPrediction (NCEP) gridded surface pressures. For this figure and throughout the book,the surface wind velocity corresponds to the wind measured at a 10-m height, called the10-m wind speed U. Figure 2.1 shows that, for both distributions, the peak in the windspeed distribution lies between 5 and 8 m s−1, where about 40% of the wind speeds lie inthis range with a mean wind speed of about 7 m s−1. Although wind speeds greater than12 m s−1 strongly contribute to the generation of waves and foam and to the transfer ofmomentum to currents, they occupy only 10% of the histogram.

As Phillips (1977) describes, the wind-driven wave amplitudes and range of excitedwavelengths depend on the turbulent energy flux from the atmosphere to the sea surface.This flux in turn strongly depends on the temperature stratification above the sea surface.If the atmosphere is warmer than the surface, then the atmosphere is stably stratified sothat, for the same wind speed, the turbulent flux is less than for an unstable stratification.Consequently, for the same wind speed, a stronger flux yields more waves and roughness,while a weaker flux yields less. Slicks also affect the surface response. In summary, thefrequency and amplitude distribution of the wind-induced surface waves depends not onlyon U, but also on the ocean–atmosphere temperature difference and on the presence orabsence of slicks.


2.2 Ocean surface winds and waves 37

5

10

15

20

25

30

35

40

45

50

Wavelength (cm)0 2 4 6 8 10 12

Wav

e ph

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spee

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m s

–1)

Gravity waves

Capillary-gravity waves

Phase speed minima (1.8 cm)

Fig. 2.2. Comparison of the phase speed for capillary-gravity waves (dashed line) and for pure gravitywaves (solid line) plotted versus wavelength for seawater. The vertical line marks the phase speedminimum for capillary waves. See text for additional information.

The wind-generated wavelengths range from less than a centimeter to hundreds ofmeters, where, depending on the observational window of the satellite instrument, all ofthese wavelengths are important to remote sensing. Long ocean waves are dominatedby gravity, but, for centimeter-scale waves, the effects of surface tension or capillaritybecome important. For a surface tension appropriate to seawater, Figure 2.2 compares thephase speed of pure gravity waves with that of capillary-gravity waves (Phillips, 1977).The figure shows that the gravity-wave phase speed increases with wavelength, while thecapillary-gravity-wave phase speed has a minimum at a wavelength of 1.8 cm. Figure 2.2also shows that, for the same wavelengths, capillary-gravity waves propagate faster thangravity waves and that surface tension is important up to wavelengths of about 7 cm.Although these capillary-gravity waves are short relative to long gravity waves, their pres-ence and distribution relative to the wind direction strongly contribute to microwave remotesensing.

As observation of any pond or puddle shows and as Kawai (1979) demonstrates in hislaboratory experiments, capillary-gravity waves with wavelengths close to the phase speedminimum immediately form and grow following the onset of a gust. These waves achievean equilibrium distribution around the minimum wavelength within a few seconds of thewind onset, are independent of position, and rapidly decay when the wind ceases. If thewind continues blowing, the frequency of the largest amplitude or dominant wave shifts tolower frequencies and longer wavelengths. This is also the case for capillary-wave growthon an existing swell field (Donelan and Pierson, 1987, p. 4975).



The generation of ocean swell differs from capillary waves, in that ocean swell can begenerated at great distances from the observation site where the swell properties are modi-fied only slowly by changes in the wind speed. The evolution of long-period wind-generatedwaves can be described as a function of either time or fetch, where fetch is defined as thedownwind distance from a coast. The time description applies to the onset at a specifictime of a uniform wind over an initially calm water surface far from any coast. Capillarywaves appear first, followed by the formation of high-frequency gravity waves. As timeproceeds, waves form at lower frequencies with longer wavelengths and greater amplitudes,so that the width and size of the distribution of wave amplitudes versus frequency increasewith time. The wave growth continues until the energy input from the wind equals theenergy dissipation by breaking and viscosity. At this time, an equilibrium is reached wherethe wave spectrum is independent of position. In contrast, the fetch description applies toa steady wind blowing off a coast, where the wave spectra are independent of time anddepend primarily on wind speed and fetch (Huang et al., 1990, especially their Figure 1).Consequently, the waves increase in amplitude and length with increasing fetch. At dis-tances far from the coast, the wave spectrum again reaches a wind-speed-dependentequilibrium.

Seasonally, the strongest winds and largest waves in the Northern Hemisphere occur inthe winter North Atlantic and North Pacific. In the Southern Hemisphere, the strongest windsand largest waves occur during the austral winter in the Southern Ocean, a circumpolar seaunobstructed by landmasses. Kinsman (1984) states that a fetch of 1500 km is sufficient forthe development of the largest observed storm waves. Of these, the largest peak-to-troughwave amplitude observed to date was about 34 m, as recorded by the USS Ramapo in 1934 inthe central North Pacific (Kinsman, 1984, p. 10). Characteristic wavelengths within stormsrange from 150 m in the North Atlantic to 240 m in the Southern Ocean. Long-period swellhas been observed with lengths as long as 600 m (Kinsman, 1984).

2.2.1 Change in the wave profile with increasing amplitude

Ocean surface waves are described in terms of their amplitude aw, which is defined ashalf the peak-to-trough wave height, their wavenumber, kw = 2π/λw, and their radianfrequency, ωw = 2π/Tw, where Tw is the wave period, λw is the wavelength, and thesubscript w distinguishes these terms from those used to describe electromagnetic waves.If η is the wave height measured from the mean free surface and x is parallel to the wavepropagation direction, the small-amplitude waves are described as follows:

η = aw sin(kwx − ωwt) (2.1)

The non-dimensional form of the wave amplitude is the wave slope awkw. At smallamplitudes or for awkw 1, gravity waves are pure sinusoids; as awkw increases, thewave shape is described by the addition of higher-order harmonics. For three differentawkw, Figure 2.3 shows the change in the shape of wave profile from Equation (2.1), where



0.4

0.2

0.1Air

Water

Mean free surface

η

Fig. 2.3. Comparison of the profiles of a single-frequency gravity wave for the different values of thewave slope awkw given above each wave. The vertical axis is exaggerated by 60% to emphasize thechange in wave shape with amplitude.

the profiles are derived from a third-order expansion of the classic Stokes wave solution(Lamb, 1945, Section 250, Equation 3). The top curve in Figure 2.3 corresponds to λw =100 m and aw = 1.6 m, and is a nearly perfect sinusoid. For the middle curve and the samewavelength, aw increases to 3.2 m, and for the bottom curve, to 6.4 m. Comparison of thesecurves shows that the addition of the nonlinear terms forms a wave with a broad troughand a narrow sharp crest, so that the wave tends toward a trochoidal shape (Kinsman, 1984,p. 255). This change in shape with increasing amplitude from a pure sinusoid to a trochoidalshape has important implications for passive microwave and altimeter observations of thesurface and, as the following shows, for wave damping and breaking.

From Lighthill (1980, pp. 453–454), the largest possible amplitude amax that a gravitywave can attain is given by

amaxkw = 0.444 or amax = 0.0706λw (2.2)

so that a 100-m-long wave has a maximum amplitude of 7 m. As the waves approachthis maximum height, theoretical investigations show that the crest remains symmetric andtends toward a 120° interior angle. Measured over a quarter wavelength, the maximumwave slope is about 15°.

For large-amplitude gravity and capillary-gravity waves, one effect of this curvatureincrease at the crest is that, as Kinsman (1984, p. 538) describes, energy transfer fromthe long waves leads to the formation of capillary waves on the downwind side ofthe wave crest (Figure 2.4). Because capillary waves are rapidly damped by viscosity,the energy transfer from the long waves is dissipated, yielding a decrease in the long-waveamplitude. For this reason, these waves are called parasitic capillaries. Because these cap-illaries form downwind of the wave crest, instruments sensitive to wave roughness havea greater response looking upwind than looking downwind, which, as Chapters 9 and 11show, contributes to how active and passive microwave instruments determine the windspeed and direction.



Wind and wave propagation direction

Fig. 2.4. The growth of the parasitic capillary waves just beyond the crest and on the forward face ofan ocean wave. The vertical scale is exaggerated.

Parasitic capillaries

High-vorticity regionthat becomes turbulent

Propagation direction

~10 cm

Bore-like crest

Wind

Fig. 2.5. An interpretative drawing and a video frame of a small wind-generated gravity wave losingenergy through parasitic capillaries. (Figure 1 from Jessup and Zappa (1997), C© 1997 AmericanGeophysical Union, reproduced/modified by permission of AGU, courtesy of Andrew Jessup.)

2.2.2 Wave breaking, energy absorption, and the properties of foam

If the wind continues to add energy to a long wave and as its amplitude increases toward itsmaximum, the wave breaks. In contrast, instead of breaking, capillary-gravity waves loseenergy to shorter parasitic capillaries and to non-breaking turbulence. For example, Figure2.5 is a photograph and drawing of a large-amplitude, 10-cm-long wave in a wavetank,and shows a turbulent but non-breaking region at the crest and parasitic capillaries on thedownwind face.

Long-wave, deep-water breaking occurs as follows. If the winds are strong enough, asthe crest approaches a 120° wedge shape, the crest spills forward down the front face of the



wave and breaks (Donelan and Pierson, 1987). This is called whitecapping, which begins tooccur for wind speeds greater than about 3 m s−1 (Melville, 1996; Anguelova and Webster,2006). Wave breaking restores equilibrium to the surface by reducing the wave amplitude,expels small seawater droplets into the air, and entrains air bubbles into the water column,generating a transient layer of foam. At wind speeds between 9 and 11 m s−1, spumeproduction begins to occur, where spume consists of droplets blown from the wave crests.

Figure 2.6 shows three photographs of the wave breaking and foam generation associatedwith a North Atlantic storm. The winds are gusting to 25–30 m s−1; the reported waveheights are 12–15 m. The photographs illustrate the surface roughness, foam and spumethat accompany these strong winds. In another example, Figure 2.7, an oblique low-altitudeaircraft photograph of the Japan Sea, shows that, for a wind speed of 17 m s−1, foamcovers an appreciable fraction of the surface. Each of these photographs shows that highwind speeds, wave breaking and foam occupy an appreciable fraction of the ocean surface.Perkowitz (2000) states that, at any time, 2%–3% of the ocean surface is covered by foam,an area equivalent to that of the United States. As Chapter 9 shows, parasitic capillaries,breaking waves and foam must be considered in remote sensing of the sea surface.

The effects of droplet expulsion by the wave breaking are also important for visibleremote sensing. Perkowitz (2000) shows that droplet expulsion transfers sea salt intothe atmospheric marine boundary layer at a global rate of 109 metric tons per year. Becausethe aerosol generated by this expelled sea salt reduces the transmittance of the marineboundary layer, its properties must be modeled for ocean color retrieval. Foam also changesthe reflective and emissive properties of the sea surface. In the visible spectrum, becausefoam is much more reflective than seawater, it can falsify the retrieval of ocean color. In themicrowave, because foam has different emissive properties than seawater, and increases inareal extent with wind speed, it contributes to the retrieval of the scalar and vector windspeed.

Frouin et al. (1996) and Moore et al. (2000) summarize the physical properties ofwhitecap foam. It consists of two parts, surface foam that is made up of small volumesof air surrounded by thin layers of seawater, and subsurface bubbles that result fromthe injection of air into the water column by breaking waves. From field observations atwind speeds of 8 m s−1, Lamarre and Melville (1996) show that the bubbles in the watercolumn occur to depths of at least 3 m, where the void fraction immediately below thesurface is about 20%, and where the air bubble concentrations fall off exponentially with ane-folding depth of 0.18 m (for examples, see Melville, 1996, Figure 3; and Baldy, 1993).This combination of bubbles on the surface and bubbles rising slowly at depth means thatthe bubble presence is sustained for about half a wave period or for as long as 10–20 s(Lamarre and Melville, 1996; Koepke, 1984).

Although the area and duration of the foam patches depend on fetch, wind speed and airand water temperature, Callaghan et al. (2008) show from field work that the areal extentof foam coverage approximately depends on U 3, where this power-law fit breaks into twoparts. First, for a wind speed range of 3.7–11.25 m s−1, the foam coverage increases withconsiderable scatter from 0 to 1%, where the upper end of this range marks the onset of


Fig. 2.6. Examples of the ocean waves and wave breaking associated with a storm in the NorthAtlantic during December 1991. The winds are gusting at 25–30 m s−1, the reported wave heightsare 12–15 m. Large breaking waves (top); shorter waves breaking while riding on longer waves(middle); and short, strongly wind-forced breaking waves (bottom). (Photographs by E. Terrill andW. K. Melville; Figure 1 from Melville (1996), with permission, from the Annual Review of FluidMechanics, Volume 28, C© 1996 by Annual Reviews, courtesy of W. K. Melville.)



Fig. 2.7. Oblique photograph of wave breaking and foam generation on the Japan/East Sea takenthrough the front window of a Twin Otter meteorological flight on February 28, 2000. The ambientair temperature was about −8 °C, the aircraft altitude was about 38 m, the flight direction was 330°and the wind speed was 17 m s−1 from 340°, so that the camera is looking into the wind and towardRussia. (Meteorological and flight data courtesy of Djamal Khelif; photograph courtesy of Jon Stairs,used with permission.) See color plate section.

droplet spume production. Second, for speeds in the range of 9–23 m s−1, the foam coveragecontinues to increase as U 3, but at a slower rate. This yields a coverage of at least 4% forwinds greater than 14 m s−1 and 8% for speeds greater than 20 m s−1. Goddijn-Murphyet al. (2011) and Anguelova and Webster (2006) provide excellent reviews of foam studiesand the dependence of foam coverage on wind speed.

2.2.3 Root-mean-square amplitude and significant wave height

In many instances, the wave field can be described as the sum of a collection of waveswith random amplitudes, wavelengths and propagation directions. Just like the single-frequency wave, the resultant wave amplitude is described in terms of the wave heightη (x, y, t), where x and y lie in the plane of the mean free surface, and where for use in thenext section the x-axis points downwind, the y-axis crosswind. For these definitions, η ≡ 0,

where the overbar indicates an average over a long period of time, and the root-mean-square(rms) displacement ση is defined as

σ 2η = η2 (2.3)

This parameter is frequently used to describe the amplitude of a field of random waves. Forthe simple sine wave in (2.1), σ 2

η = a2w/2.



MSL

H1/3ση

Fig. 2.8. A field of random waves with a nearly Gaussian amplitude distribution, and greatly exag-gerated amplitudes. The figure shows the mean sea level (MSL) and the rms and significant waveheights.

The wave amplitude can also be described in terms of the significant wave height (SWH)or H1/3. Significant wave height has an unusual definition; it is defined as the averagecrest-to-trough height of the one-third largest waves. For remote sensing, H1/3 is used todescribe the ocean swell properties observed by the satellite altimeter. The definition ofH1/3 is apparently based on how a mariner might estimate the wave height from a ship; itwas used in the early wave forecast models (Kinsman, 1984). Wunsch and Stammer (1998,p. 233) describe H1/3 as “an archaic, but historically important” term for wave height.Paraphrasing Kinsman (1984, p. 302), there is nothing particularly significant about H1/3,it is just another average. Chelton et al. (2001b) review H1/3 and state that it can be writtenin terms of ση, where

H1/3 = 4ση (2.4)

Figure 2.8 illustrates ση and H1/3 for a numerically generated wave field. For a narrow-wavelength bandwidth, Equation (2.4) is exact. For broader bandwidths, the coefficientin Equation (2.4) decreases from 4 to 3. Because Chelton et al. (2001b) show that thischange has a negligible effect on the altimeter retrieval, Equation (2.4) is a reasonableapproximation.

2.2.4 Azimuthal distribution of sea surface slopes

The azimuthal distribution of wave slopes relative to the wind direction affects remotesensing in three ways. First, at all frequencies, the sea surface and the facets generated bythe wave slopes can reflect sunlight directly into the instrument and overwhelm the desiredobservations. Viewing a water surface from a hillside or building shows that, in the visible,the solar reflection from the wind-roughened surface forms a bright diffuse spot composedof many transient reflecting facets. This phenomenon is called sun glint or sun glitter.Second, the wave slopes diffuse the sunlight transmitted across the ocean interface intothe interior and affect the water-leaving radiances contributing to the ocean color retrieval.



Third, because the wave slopes have an azimuthal distribution relative to the wind direction,active and passive microwave observations can retrieve both wind speed and direction.

In the discussion of this azimuthal dependence, the total mean-square slope σ 2 and thealongwind and crosswind rms components of the wave slopes, σL, σC, are defined as

σ 2L = η2

x, σ 2C = η2

y, σ 2 = σ 2L + σ 2

C (2.5)

For the sine wave in (2.1), the mean-square slope is σ 2L = a2

wk2w/2. In what may be the most

cited paper in the remote sensing literature, Cox and Munk (1954) use aerial photographsof sun glint taken under different wind conditions near Hawaii to describe the angulardistribution of the reflecting slopes as a function of wind speed. Their results show thatthe largest slopes occur in the upwind and downwind directions, with the smallest in thecrosswind direction, and that the magnitude of the slopes varies smoothly with azimuthangle. They also find that large slopes are more likely to occur in the upwind than in thedownwind direction.

Cox and Munk (1954, p. 206) suggest that the source of this asymmetry is due to parasiticcapillary formation on the forward wave faces. Consequently, the reflection of the sun onthe sea surface forms an ellipse, with its long axis parallel to the wind and its short axisat right angles, where the ellipse is slightly broader in the upwind direction. For 1 < U <

12 m s−1, Cox and Munk (1954) and Wu (1990), who reanalyzes their data with the additionof many modern studies, show that the ratio of the crosswind to alongwind mean-squareslopes σ 2

C/σ 2L varies from 0.6 to 1.0 with a mean of 0.8.

In terms of notation used by Mobley (1994, Section 4.3), Cox and Munk (1954) find alinear dependence of the mean slopes on wind speed,

σ 2L = AU, A = 3.5 × 10−3s m−1

σ 2C = BU, B = 2.8 × 10−3s m−1 (2.6)

In his reanalysis, Wu (1990) finds that the slopes vary with the logarithm of U; for U <

7 m s−1, the various components of σ 2 increase slowly, whereas for U > 7 m s−1, theyincrease more rapidly.

2.2.5 Surface slicks

From field experiments, Cox and Munk (1954) also show that the addition of an oil slickwith thickness of order 1 µm causes a reduction of the surface slopes from their clean-water values by a factor of two or three, and the disappearance of waves with lengthsless than about 0.3 m. As Chapter 13 shows, this damping makes it possible for radars toobserve oil slicks. The oceanic sources of these slicks divide into natural and man-made,and into biogenic and petroleum slicks (Clemente-Colon and Yan, 2000). Man-made oilslicks result from accidental spills, the illegal discharge of petroleum products from shipsand from harbor runoff. There are also natural petroleum seeps in the Gulf of Mexico andin the Santa Barbara Channel off southern California. Plankton and fish produce biogenic



z y

x

Free surface Lines of constant density

Sea surface height

ζGeoid

v

u

Cold, dense inshore waters Warm, less dense offshore waters

vG

Fig. 2.9. Geostrophic flow in the Northern Hemisphere along a line of constant latitude where thefigure is based on the Gulf Stream. The figure shows the free surface (solid line), the geoid orequipotential surface (dotted line), the lines of constant density (dashed lines) and the velocitiesresulting from the geostrophic balance. The variable ζ is the sea surface height as defined for thealtimeter. (Adapted from Stommel (1966, Figure 1).)

slicks, which also result from waste discharged from factory fishing vessels. Because theseslicks greatly reduce the short-wave amplitudes, they are visible in radar imagery.

2.3 Ocean currents, geostrophy and sea surface height

The upper layers of the ocean are dominated by wind-driven features such as the GulfStream, Kuroshio, Antarctic Circumpolar Current and coastal upwelling. Combined withevaporation in the tropics, cooling in the north and south, and seasonal heating and cooling,the wind stress determines the vertical mass fluxes in the upper ocean and maintains itsdensity structure (Wunsch, 2002).

For the rotating Earth, the geostrophic flow approximation describes the relation amonggeostrophic currents, density structure and sea surface height. In the vertical, the approxi-mation assumes that the ocean is in near hydrostatic balance, so that

dp

dz= −gρ(p, S, T ) (2.7)

In Equation (2.7), p is pressure, g is the acceleration of gravity, ρ is density, S is salinityand T is temperature. The variables p, S and T are measured by oceanographic instrumentsand are often given in terms of the time t and rectangular coordinates x, y and z thatrotate with the Earth (Figure 2.9). From Cushman-Roisin (1994), these coordinates followthe convention that z is parallel to gravity and increases upward, while x and y lie in thehorizontal plane with x parallel to longitude and y parallel to latitude.


2.3 Ocean currents, geostrophy and sea surface height 47

In the horizontal, the approximation neglects the time-dependent and nonlinear termsin the equations of motion (Cushman-Roisin, 1994). Geostrophic flow is then derivedfrom a balance between the horizontal pressure gradients and the Coriolis force. In thefollowing, f = 2E sin χ is the Coriolis parameter, where E = 7.727 × 10−5 s−1 is theEarth’s angular rotation and χ is latitude. For the x and y components of the geostrophicvelocity, uG and vG, the approximation yields

ρfvG = dp

dx, ρfuG = −dp

dy(2.8)

Combination of Equations (2.7) and (2.8) gives for vG at a height z, relative to a referencelevel z0,

vG(x, y, z) = g

f

∫ z

z0

dρ

dxdz + v0(x, y, z0) (2.9)

with a similar equation for uG. In Equation (2.9), v0 is an unknown reference velocitydepending on z0. Measurement of v0 at any depth, including the free surface, combinedwith knowledge of the interior density distributions, permits calculation of the absolutevelocity profile.

For these flows, Figure 2.9 shows a schematic drawing of the distribution of densityand sea surface height on a constant-latitude line across a flow similar to the Gulf Stream.The arrows show the v-components of geostrophic velocity, the dashed lines are constantdensity surfaces, the solid line is the sea surface height and the dotted line is the geoid.As Chapter 12 describes, the geoid is the equipotential surface along which there are noparallel components of acceleration, which corresponds to mean sea level in the absenceof external forcing.

In the ocean, the uneven density distributions lead to the displacement of the sea surfaceheight above and below the geoid. For example, from the schematic diagram in Figure 2.9,the onshore waters are cold and dense while the offshore waters are warm and less dense.Within these water masses, if two columns of seawater are defined such that they extendbetween the sea surface and the same deep surface of constant pressure, the columns havethe same mass. But, because the onshore column is denser than the offshore, its height isless than that of the offshore column. This height difference ranges from 1 m across theGulf Stream to 10 cm or less across ocean eddies.

There is an important difference between the relative measurement of sea surfaceheight in the classical oceanographic analysis and the altimeter measurement. In the clas-sic oceanographic analysis, sea surface height is a relative measurement called dynamicheight, ζD (x, y). Dynamic height is calculated relative to a reference depth or pressurefrom integration of the vertical density anomalies derived from individual oceanographicstations and sections (Pond and Pickard, 1986, Chapter 8). The stations consist of deepCTD (conductivity–temperature–depth) casts, from which the density anomalies are deter-mined. The reference depth is called the level of no motion; if there is motion at this depth,the surface displacement and the geostrophic velocities are measured relative to arbitrary



constants. At the sea surface, the geostrophic velocities can be written in terms of the slopeof the dynamic height (Knauss, 1997):

vG(x, y, 0) − v0(x, y, z0) = g

f

dζD

dx, uG(x, y, 0) − u0(x, y, z0) = − g

f

dζD

dy(2.10)

On the left-hand side of Equation (2.10), the height at which the surface velocities areevaluated is approximated as z = 0, and v0 and u0 are the arbitrary constant velocities.Because of the uncertainty concerning the depth or even in some cases the existence ofthe level of no motion, it is very difficult to determine absolute geostrophic velocities fromoceanographic observations.

In contrast and as Chapter 12 shows, the altimeter measures the height of the sea surfacerelative to the Earth’s center of mass. The sea surface height (SSH) is then defined as thedifference ζ (x, y, t) between the sea surface and the geoid. Because this is an absolutemeasurement, changes in the height measured by the altimeter are generated not onlyby geostrophic flows, but also by other processes including tides, seasonal heating andcooling, and changes in atmospheric pressure. To calculate the ζ -contribution due only togeostrophy, these other sources must be removed. Following their removal and substitutingfor the Coriolis parameter, Equation (2.10) becomes

vG(x, y, 0) = g(2E sin χ )−1 dζ

dx, uG(x, y, 0) = −g(2E sin χ )−1 dζ

dy(2.11)

Because Equation (2.11) is written in terms of the absolute surface displacement ζ , theunknown u0 and v0 in Equation (2.10) no longer appear. This means that the direct mea-surement of sea surface slope yields the surface geostrophic velocity. Given this result andprovided that coincident surveys of the ocean interior are available, then from (2.9) theinterior geostrophic velocity profile can be calculated.

There are at least three qualifications concerning the geostrophic balance. First, inthe vicinity of the equator where χ goes to zero, the denominators of Equation (2.11) alsoapproach zero and the geostrophic approximation breaks down. Consequently, the dynamicsof equatorial flows differ from those at higher latitudes. Second, real oceanographic flowsare not steady, but vary with time. For this case, the geostrophic balance is supplementedby a small acceleration term. Because this imbalance in the geostrophic equations is verysmall and generally unobservable by direct oceanographic measurements, the geostrophicvelocities are still derived from Equations (2.9) and (2.10). Third, even given an altimetermeasurement of ζ in Equation (2.11), the derived geostrophic surface velocities are notnecessarily the true surface velocities. The reason for this is that, in the surface boundarylayer, the velocity tends not to be in geostrophic balance; rather the flow responds tothe turbulent stresses generated by the wind and waves. Even though these wind effectsdominate the upper 100 m of the ocean, because geostrophic velocities are dominant belowthis depth, their associated pressure gradients determine the sea surface slope so that therelation between the interior flows and the surface slopes still holds (Wunsch and Stammer,1998).


2.3 Ocean currents, geostrophy and sea surface height 49

Table 2.1. Space and time scales of oceanic phenomena.

Phenomenon Surface length scales Period Comments

Western boundarycurrents (GulfStream, Kuroshio)

130 cm/100 km Days to years Position is variable, with a25% variability intransport

Basin-scale gyres(North Atlantic,North Pacific)

50 cm/(3–10) × 103 km One to manyyears

25% variability

Mesoscale eddies 10–25 cm/100 km 100 days 100% variabilitySmall eddies 10 cm/10–100 km 1–2 days 100% variabilityEastern boundary

currents30 cm/100 km Days to years 100% variability, with

possible reversals indirection

Equatorial currents 30 cm/5000 km Months to years 100% variabilityTides 1 m/1–100 km 1 day 100% variabilityCoastal upwelling 10 cm/10–100 km 1 day to 1 week 100% variabilityRossby and Kelvin

waves10 cm/1000 km Months 100% variability

Adapted from Stewart (1981, Table 1) and Chelton (2001, Figure 3).

Table 2.1 gives typical length and time scales for a variety of oceanographic flows. In thesurface-length-scales column, the first number is a characteristic height while the second isthe horizontal scale of the motion. The shortest spatial scales over which these flows occurcorrespond to the Rossby radius of deformation, which ranges from about 10 km in theArctic, via 60 km at mid-latitudes, to 200 km in the tropics; the shortest time scale is 1–2days (Cushman-Roisin, 1994). The largest spatial scales are basin-wide, which in the Pacificcorrespond to 10 000 km. The different scales are related, for example western boundarycurrents such as the Gulf Stream and Kuroshio consist of a vigorous northern flow, with across-stream length scale of about 100 km, and a diffuse return flow that occupies the restof the basin with scales of order 104 km. Superimposed on the time-averaged flows is alarge variety of time-dependent flows that occur at different time and space scales, are oftenreferred to as mesoscale eddies, and can have energy levels that are one or more orders ofmagnitude greater than those of the mean flows (Wunsch and Stammer, 1998).

Finally, the alternation between La Nina and El Nino is an important example of planetaryflow phenomena. The transition between them is the source of dramatic changes in thetropical atmosphere, generates equatorial Kelvin and Rossby waves, alters the physicaland biological properties of the equatorial Atlantic and Pacific, and affects global climate.During the past century, La Nina conditions have been interrupted at three-to-seven-yearintervals by an occurrence of El Nino, of which that in 1997–98 was one of the strongeston record (McPhaden, 1999, McPhaden et al., 2011).



2.4 Sea ice

The sea ice covers of the Arctic and Antarctic Oceans experience strong seasonal cyclesand play a major role in the modification of the heat and salt flux to the underlying ocean.Wadhams (2000) provides an excellent introduction to sea ice with many photographs. Intheir Arctic and Antarctic atlases, Zwally et al. (1983), Parkinson et al. (1987) and Gloersenet al. (1992) describe the ice properties and provide many photographs. Comiso (2010)also provides a valuable reference on the current state of the Arctic and Antarctic sea ice,and on the remote sensing tools used to study it.

As Chapter 9 discusses, the Arctic and Antarctica sea ice cover exhibit a cyclicalbehavior, with a maximum sea ice extent during the respective winter, and a minimumduring summer. In the Arctic, the most prominent feature of the summer areal extent isthat, during the four-decade period of satellite observations, the extent has been decliningat a rate of 9%–10% per decade, with, in 2007, a minimum extent that was about 50% ofits initial value (Comiso et al., 2008). At the same time, the Antarctic extent has remainedroughly constant, with no observable trends (Comiso, 2010, Chapter 6).

Because the Arctic Ocean is a nearly enclosed basin surrounded by land, while theAntarctic Ocean surrounds the Antarctic continent and is itself surrounded by open ocean,the kinds of sea ice that form in each region differ from one another. In the north, the ArcticOcean has a small oceanic vertical heat flux and an annual snowfall of about 200 mm(Wadhams, 2000). Its major ice types include young ice, first-year ice, which is less thanone year old, has not survived a summer, and has thicknesses of 1–2 m, and multiyear ice,which is older than first-year ice with thicknesses of 2–4 m. As Cavalieri (1994) describes,the newly formed young ice has a high-salinity surface layer that gives it a distinctivemicrowave signature.

First-year ice has a less saline surface layer, with salt and air inclusions in its near-surfacelayers, whereas multiyear ice has a hard upper surface consisting of nearly fresh water. Inthe summer, all categories of Arctic sea ice approach the freezing point, so that, as the icedesalinates, the upper surface melts and fresh water melt ponds form on the surface. Theice that survives the summer refreezes, forming multiyear ice. These changes in surfaceproperties permit the retrieval of ice extent by passive microwave instruments. Ice thicknesscan also be retrieved as follows. Because ice is less dense than seawater, it floats with itssurface elevated a vertical distance above the waterline, where this height is called thefreeboard. As Chapter 14 discusses, measurements of the freeboard using laser and radaraltimeters permit the retrieval of the sea ice thickness.

In contrast, for the seas around the Antarctic continent and at the ice margins in theNorth Atlantic and Pacific where large ocean waves are generated in the adjacent openocean, sea ice forms differently. In the presence of waves, the combination of the surfaceheat loss with the wave-induced mixing cools the upper ocean to the freezing point andsometimes even induces a slight supercooling. This means that, once freezing begins, iceformation occurs throughout the upper layer as small millimeter-scale crystals, called frazilcrystals, float to the surface. As these crystals collect on the surface, the resultant slurry,


2.4 Sea ice 51

a

b

Fig. 2.10. Shipboard photographs of sea ice in the Greenland Sea. (a) A slurry of frazil ice crys-tals called grease ice. (b) Pancake ice. (Courtesy of Richard Hall and Peter Wadhams, used withpermission.)

called grease ice, damps out the short-period waves in a manner similar to an oil slick, andgives the surface a smooth appearance (Figure 2.10(a)).

When this ice reaches a thickness of about 100 mm, its surface begins to freeze, which,combined with the long-period ocean swell propagating through the ice, breaks the surface



into floes with diameters of 0.3–0.5 m, called pancake ice (Figure 2.10(b)). Because ofwave-induced collisions, the pancakes grow raised rims. The presence of these rims causesan increase both in their atmospheric drag coefficients and in their radar reflectivity. AroundAntarctica, this is the dominant mechanism for ice formation, where as time goes on thesepans aggregate into collections of large floes. In the North Atlantic, this mode of iceformation also occurs in an ice edge feature called the Odden (Wadhams, 2000). Thisformation of frazil and pancake ice also occurs in the wind-generated regions of open watercalled polynyas. As Chapter 13 shows, both ice types are visible in SAR imagery.

Because the Antarctic oceanic vertical heat flux is about five times that in the Arctic,the first-year sea ice thicknesses are only about 0.7 m (Wadhams, 2000, Section 2.3.2).Also, the snow blowing off the continent as well as that generated by moisture flux fromthe adjacent open ocean means that snow accumulation depths on Antarctic ice are muchgreater than on Arctic ice, with characteristic thicknesses of 0.5–0.7 m. The combinationof thinner ice and much greater snow accumulation means that, for much of this ice,its interface is depressed below sea level. Consequently, seawater intrudes into the snowabove the ice surface and freezes to the upper ice interface. As Chapter 9 discusses, thisfreezing process may explain why Antarctic sea ice has different microwave signatures thanArctic ice. Finally, because most of this ice melts in summer, there is much less Antarcticmultiyear ice.


3

Electromagnetic radiation

3.1 Introduction

This chapter describes those properties of electromagnetic radiation (EMR) relevant toremote sensing. Specifically, Section 3.2 gives a brief description of the nature of elec-tromagnetic radiation, its propagation in different media and its polarization. Section 3.3describes several different ways of describing radiation fluxes. Section 3.4 discusses black-body radiation, Planck’s equation and the concepts of emission and absorption. Section 3.5discusses the basic optics applicable to an instrument operating in the visible and infrared,then describes the operation and spatial resolution of an ideal instrument. The sectionconcludes with a discussion of terms such as bandwidth and signal-to-noise ratio that areapplicable to real instruments.

3.2 Descriptions of electromagnetic radiation

As many textbooks describe, EMR has a dual nature, in that it behaves both as discretequanta of radiation and as electromagnetic waves (Jackson, 1975; Born and Wolf, 1999).In the quantum description, radiation propagates as photons, which are massless, discretebundles of energy released by atomic or molecular changes of state.

The energy E carried by each packet is

E = hf (3.1)

where f is the frequency, in cycles per second or Hz, and h = 6.626 × 10−34 J s is the Planckconstant. When the radiation is generated by only a small number of molecular sources, thequanta are discrete; when the number of sources is increased, the classical wave solutiondescribes the radiation.

In the wave description, Maxwell’s equations govern the radiation, where the param-eters that describe the medium through which the radiation propagates are the magneticpermeability μ, the electrical permittivity ε and the electrical conductivity σ . The threedifferent media of oceanographic concern are vacuum, atmosphere and ocean. These areeach assumed to be homogeneous isotropic media that are non-magnetic and contain nofree charges. For each of these, μ = μ0, where μ0 is the vacuum permeability and ε

53


54 Electromagnetic radiation

λ

z

x

y

E

B

Fig 3.1. The electric and magnetic field components of an electromagnetic wave for a plane-polarizedwave.

and σ are constant. In the atmosphere and vacuum, σ = 0, while in the ocean, σ isnon-zero.

The plane-wave solution to Maxwell’s equations is given in terms of an electric fieldvector E and a magnetic field vector B, where the bold type indicates a vector and B andE are perpendicular to each other and to the propagation direction (Figure 3.1). With thisnotation, the electric field component of the plane-wave solution has the form

E = E0 exp[i(kz − ωt)] (3.2)

with an analogous form for B. In (3.2), E0 is the complex wave amplitude, k = k + ikim

is the complex wavenumber with real and imaginary parts k and kim, and ω is the wavefrequency in radians per second. The real part k of the complex wavenumber k is related tothe wavelength λ by k = 2π/λ ; ω is related to the wave period T by ω = 2π/T and to thewave frequency by ω = 2πf .

The wavelength λ has units of length, which, depending on the observing window, isexpressed in m, µm (micrometers or 10−6 m) or nm (nanometers or 10−9 m); the wavefrequency f is in units of Hz, MHz (megahertz or 106 Hz) or GHz (gigahertz or 109 Hz).Because the early optics experimenters worked with light at different wavelengths, wavepropagation in the visible/infrared is generally described in terms of wavelength; becausethe early microwave experimenters worked with frequency, propagation in the microwaveis described in terms of frequency. Also, given the secrecy surrounding the development ofradar during World War II, specific microwave frequencies are often described by letters,the most commonly used in this book being C-band (4–8 GHz), X-band (8–12 GHz)and Ku-band (12–18 GHz). Table A.1 in the Appendix gives this terminology in moredetail.


3.2 Descriptions of electromagnetic radiation 55

AM

FM, TV,Cell phones

Passive microwaveremote sensing

Thermal infrared

300 m

30 cm

300 μm

Satelliteradar

Fre

quen

cy106

109

1012

1015

(1 GHz)

(1 kHz)

(1 THz)

300 nm

Radio, TV

Microwave

Infrared

Visible

Ultraviolet

X-ray

30 μm

3 μm

3 cm

3 mm

30 m

3 m

30 nm

3 nm

3 km

Ground-to-spacecommunicationsand radar

Wav

elen

gth

Near infrared

Fig 3.2. The electromagnetic spectrum and its uses as a function of frequency and wavelength. Thegray bars show the bands used in satellite remote sensing.

3.2.1 Uses of the electromagnetic spectrum

Satellite remote sensing takes place in a crowded electromagnetic spectrum that, espe-cially in the microwave, restricts the location and width of the observational frequencies.Figure 3.2 shows some of the allocations of the US electromagnetic spectrum as a functionof frequency and wavelength. At 105 Hz, the amplitude-modulated (AM) radio band ischaracterized by km-long wavelengths that are not used in satellite remote sensing. Thehigher frequencies of 107–108 Hz contain the frequency-modulated (FM), TV and cellularphone bands. The frequencies between 109 and 1011 Hz (1–100 GHz) contain passive andactive microwave remote sensing plus a large variety of commercial and military com-munications and ground radar operations. The infrared bands occur at 1013–1014 GHz;the narrow visible band occurs at 1015 GHz; the ultraviolet (UV) region is at higherfrequencies.

Although the frequency allocation presented in Figure 3.2 appears relatively uncrowded,this is because of the small scale of the figure. For the United States and the frequency



Table 3.1. Subregions of the spectrum for theultraviolet through infrared wavelengths.

Name Abbreviation Wavelength band

Ultraviolet UV 10–400 nmUltraviolet-B UV-B 280–320 nmVisible V 400–700 nmNear infrared NIR 0.7–3.5 µmVisible/near infrared VNIR 0.4–3.5 µmThermal infrared TIR 3.5–20 µmVisible/infrared VIR 0.4–20 µm

Adapted from Kramer (1994) and Thomas and Stamnes(1999).

range 9 khz to 1000 GHz, the National Telecommunications and Information Administrationprovides the detailed frequency allocation both as a downloadable chart and as a document(NTIA, 2012). This chart shows the large variety of users and the resultant pressures on theremote sensing bands, especially in the frequency range 1–20 GHz. As Chapter 9 shows, atthese frequencies, radiation propagates through the atmosphere and clouds with little or noattenuation. Hence there are many users in this range, including military and civilian radars,aircraft navigation, satellite direct broadcast and communications, and cellular telephonesystems. These users place enormous pressures on the frequency bands used by remotesensing; indeed, they have forced changes in the assigned frequencies and have restrictedtheir bandwidths.

As Section 9.3.3 describes in greater detail, for the microwave frequencies, radiationfrom these users can interfere with Earth observations, causing radio-frequency interfer-ence (RFI), either from broadcast transmissions received directly at the satellite or fromcommunication satellite transmissions that are reflected from the ocean surface back tothe instrument. RFI can have direct effects on satellite observations, both for the passivemicrowave and for the radars.

The visible and infrared (VIR) wavelengths occur between approximately 0.4 and 20µm. These wavelengths are heavily used in remote sensing, but, except for occasionallaser usage and some light pollution at night, they are unaffected by other users. They are,however, affected by cloud cover, aerosols and fog. Table 3.1 shows the terminology andabbreviations used to describe the wavelength bands within and adjacent to the VIR. Thevisible spectrum lies between 0.4 and 0.7 µm, and approximately divides into the followingcolors: 400–440 nm, violet; 440–500 nm, blue; 500–550 nm, green; 550–590 nm, yellow;590–630 nm, orange; and 630–700 nm, red.

The UV band occurs at shorter wavelengths than the visible; for completeness, the tablelists the wavelength range of the biologically important UV-B radiation, which destroysDNA and causes skin cancer. The near-infrared (NIR) band occurs at longer wavelengths



than the visible, and like the visible, is dominated by reflected solar radiation. The thermal-infrared (TIR) band includes those wavelengths dominated by thermal emission fromthe Earth’s surface, which, as Chapter 7 shows, are used in the retrieval of sea surfacetemperature.

3.2.2 Dispersion relation and index of refraction

The dispersion relation governs the propagation of EMR in different media and its atten-uation in the ocean. From Jackson (1975, Chapter 10), the general form of the dispersionrelation is

k2 = ω2με − iωμσ (3.3)

In vacuum, the conductivity σ = 0, so (3.3) becomes

k2 = ω2μ0ε0 (3.4)

where the subscript 0 indicates vacuum quantities. The propagation velocity or phase speedv of the radiation is

v = ω/k = λf (3.5)

so that, in vacuum, the speed of light c can be written as

c = 1√

μ0ε0 = 3 × 108 ms−1 (3.6)

In other materials, v is the local speed of light that can differ from c; for example, in waterthe speed of light is about 0.75c. Unlike ocean waves in deep water, where the phase speedincreases with wavelength, for a homogeneous medium, v is constant.

Radiation in the atmosphere propagates at approximately the same speed as in vacuum,and in all three media, μ = μ0. Because σ > 0 for seawater, EMR propagation becomesmore complicated, and the dispersion relation becomes (Born and Wolf, 1999)

k2 = ω2μ0ε0[(ε/ε0) + iσ/(ωε0)

](3.7)

To rewrite Equation (3.7) into a more useful form, the complex dielectric constant εr isdefined as

εr = ε′ + iε′′ (3.8)

where ε′′ = ε/ε0, with 0 ε′ 1, and ε′′ = σ/(ε0ω). Substitution of c from (3.6) and εr

from (3.8) into (3.7) gives

k = (ω/c)√

εr (3.9)



To simplify this expression further, the index of refraction η is defined as η = √εr and

written as η = n + iχ , where n is the real part and χ is the imaginary part. From thisdefinition,

k = (ω/c)(n + iχ ) (3.10)

From Born and Wolf (1999), substitution of Equation (3.10) into the plane-wave propagationequation gives

E = E0 exp[i(kz − ωt)] exp(−ωχz/c)

(a) (b) (3.11)

In Equation (3.11), (a) is an oscillatory wave solution where k = ωn/c so that the wavepropagates with a phase speed c/n; (b) is a damped exponential.

Because the wave energy is proportional to E2 and from term (b) above, as the radi-ation propagates through water, the energy decays as exp(−2ωχz/c), or equivalently asexp(−4πχz/λ). The absorption coefficient a (λ) is therefore defined as

a(λ) = 4πχ/λ (3.12)

For the energy decay, the absorption depth da is defined as the 1/e decay distance,

da = [a(λ)]−1 = λ/(4πχ ) (3.13)

For distilled water, which has similar properties to seawater, and for λ ranging from theultraviolet to the microwave, Figure 3.3 shows the real and imaginary parts of η. The moststriking feature of the figure occurs forχ in the vicinity of the visible wavelengths, whereit experiences a change in magnitude by a factor of 1010. This narrow region, for whichJackson (1975) and Mobley (1994) discuss the physics, is the only part of the spectrumwithin which light propagates to appreciable oceanic depths. Specifically, for blue light ofλ = 440 nm propagating in water, χ = 9 × 10−10, yielding a da of about 40 m, whereas forλ = 10 µm in the infrared, χ= 0.05, so that da = 16 µm, which is much smaller than in thevisible. Chapter 5 uses η to describe the reflection and refraction of radiation incident onthe interface, and, for the visible, uses direct measurements of the absorption coefficient todiscuss the dependence of da on λ.

3.2.3 Polarization and the Stokes parameters

For remote sensing, the intensity and frequency distribution of the radiation that is emittedor reflected from a surface permits inference of the surface properties. As next discussed,the polarization of the radiation is equally important. Following Jackson (1975, Chapter 7),the most general electromagnetic plane wave can be represented as the vector sum of twowaves with frequency f propagating in the z-direction, the first with an electric field vectorof magnitude Ex parallel to the x-direction, the second of magnitude Ey parallel to the



Wavelength (m)

visi

ble

10010–110–210–310–410–510–610–710–8

10 –8

10 –10

10 –2

10 –6

10 –4

10

10 1

0

100.2

10–0.2

100.8

100.4

100.6

101

101.2

100

Imag

inar

y pa

rt (

)

Rea

l par

t (n)

χ

Fig 3.3. Plots of the real and imaginary parts of the index of refraction η over the wavelength domainof interest. The two figures have different vertical scales; the pair of vertical lines marks the visiblespectrum. (Adapted from Mobley (1995); data from Segelstein (1981).)

y-direction. For the resultant wave, description of the time-dependence of the vector fieldE is an important part of remote sensing.

First, for the special case when the resultant E points in a single direction, the waveis linearly polarized. Second, if the two components have equal magnitudes but differentphases, then E rotates around the z-axis at the frequency f and the wave is circularlypolarized. Looking into the wave, if the rotation is counter-clockwise, the wave is left-circular polarized, with the reverse definition for a right-circular polarized wave. Third, ifthe two components have unequal magnitudes, the wave is elliptically polarized. Fourth,radiation from sources such as the Sun can be randomly polarized, meaning that E takesdifferent directions at random.



z

y

x

(Sideview)

z

xSurface

V-pol

(3D view)

Surface

z

y

x

(Sideview)

z

x

H-pol

(3D view)

θ

Surface

Surface

Fig 3.4. The difference between the plane of the electric field vector for vertically polarized (V-pol)and horizontally polarized (H-pol) radiation, determined relative to the Earth’s surface.

As Jackson (1975) shows, the four Stokes parameters completely describe the propertiesof a plane electromagnetic wave that is arbitrarily polarized. The first two Stokes parametersare the vertically (V-pol) and horizontally (H-pol) polarized components of the radiation.For Earth remote sensing, and as Figure 3.4 shows in a three-dimensional perspective viewand in sideview, V-pol and H-pol are defined relative to the Earth’s surface. The H-polcomponent of E lies in the plane that is parallel to the surface; the V-pol component isat right angles to the H-pol and lies in the vertical plane. Given these definitions, theenergy in the electric field E2 is proportional to E2

V + E2H, where the subscripts indicate

polarization. This division into V- and H-pol is possible only for 0 < θ < π /2; at θ = 0 orvertical incidence, E lies completely in the horizontal plane.

For the other two Stokes parameters, as Jackson (1975) and Yueh (1997) describe, thethird Stokes parameter is proportional to the real part of the correlation between the V-and H-pol components of E; the fourth Stokes parameter is proportional to the imaginarypart of this correlation. An alternative way to describe these components is that the thirdparameter is the difference between the electromagnetic components offset by ±45° fromthe V- and H-pol components in the x–y plane; the fourth parameter is proportional to thedifference in relative intensity between the left-circular and right-circular components ofthe electromagnetic wave.

As Chapters 9–13 describe, because the polarization of the emitted or reflected radiationdepends on the state of the ocean surface, instruments sensitive to V- and H-pol are often usedin microwave remote sensing. For example, measurement of the frequency, polarization and


3.3 Ways to describe EMR 61

y

z

x

r

dA = r2 sin θ dθ dφ

r sin θ

θ

φ

Fig 3.5. The spherical coordinate system.

intensity of the radiation emitted or reflected from the ocean surface allows determinationof the surface temperature and salinity, the wind speed and direction, and whether thesurface is ice-covered or ice-free. Although the third and fourth Stokes components are lesscommonly used than V- and H-pol, as Chapter 9 shows, the WindSat passive microwaveradiometer measures vector wind speed by the simultaneous retrieval of the four Stokesparameters.

3.2.4 Review of solid geometry

Much of this book uses different forms of the spherical coordinate system shown inFigure 3.5, where r is the radial distance, θ is the zenith angle and φ is the azimuthangle. The figure also shows the differential area dA generated by small changes in θ andφ. The definition of the differential solid angle d is

d = dA/r2 = sin θ dθ df (3.14)

The solid angle has units of steradians (sr), where there are 4π sr in a sphere. NASA oftenuses orthogonal radians to describe the solid angle measured by an optical instrument sothat the AVHRR, for example, has a solid angle resolution of 1.3 mr × 1.3 mr, wherethe milliradian, mr, equals 10−3 radians. For comparison, Section 3.5.1 shows that theresolution of the human eye is about 0.25 mr, or five times smaller than the AVHRRresolution.

3.3 Ways to describe EMR

There are several ways to describe the propagation and intensity of EMR. These descriptionsare specifically concerned with the flux of energy, or power, in units of joules per second or



E

Fig 3.6. The irradiance incident on the half plane.

watts, and the radiation incident on or emitted from a surface. The discussion begins withthe radiant flux .

1. The radiant flux is the rate at which energy is transported toward or away from asurface, with units of watts (W). For example, the total radiant flux or power emitted bythe Sun is S = 3.9 × 1026 W.

2. The radiant intensity I = d/d is the radiant flux per unit solid angle, with units ofW sr−1, and is used in the description of radiation propagating from a point source.From the definition of , and because there are 4π steradians in a sphere, the Sun has aradiant intensity of I = 3.1 × 1025 W sr−1.

3. The flux density d/dA has units of W m−2, and is the radiant flux per unit area thatis either incident on or emitted from a unit surface area. The incident flux density iscalled the irradiance E; the emitted or outgoing flux density is the exitance M. The bookfollows the oceanographic convention and uses the irradiance E for both incident andoutgoing radiation. As an example, consider a 1-m2 square panel at right angles to theSun at the Earth’s orbit. For a mean Earth–Sun distance of 1.5 × 108 km, the solid anglesubtended by this panel is 4.4 × 10−23 sr, so that the incident irradiance on the panel isE = 1400 W m−2.

The use of the symbol E for irradiance is unfortunate, since it can be confused with theelectric field vector E, even though E is proportional to E2. There are three forms ofirradiance, scalar irradiance, vector irradiance, and plane irradiance (Mobley, 1994). Thescalar irradiance is the irradiance incident on a spherical sensor from all directions; thevector irradiance is irradiance divided into its orthogonal spatial components; the planeirradiance, which is primarily used in this book, consists of the fluxes that are incident oremitted in all directions above or below the half plane, weighted by the cosine of their angleto the vertical. The plane irradiance then, is the radiation collected by a flat-plate sensor.

Imagine a 1-meter-square plate placed on the ocean surface that collects all of theradiation incident on it. An example is the flat-plate collector shown in Figure 3.6; thismeasures the plane irradiance and is often referred to as a cosine collector. The reason for



ΔA

(a)

Φ

θ(b)

ΔA

Fig 3.7. A beam of plane-parallel radiation incident on (a) a plane at right angles to the propagationdirection and (b) a plane tilted at an angle θ . The tilt reduces the magnitude of the irradiance incidenton A.

the cosine weighting is as follows. If a beam of plane-parallel radiation is normally incidenton a plane, then an element of area A receives an irradiance /A. But if the plane istilted at an angle θ relative to the normal, then the component of A normal to the beamis reduced by an amount cos θ , so that the irradiance incident on A is also reduced bycos θ (Figure 3.7). For this reason, although a flat-plate detector collects radiation from allangles in the upper half plane, the off-normal radiation is weighted by cos θ . Finally, in thetreatment of visible radiation in and above the ocean, the plane irradiance is divided intoits upward Eu and downward Ed components.

4. The radiance L has units of W m−2 sr−1 and is defined as the radiant flux propagatingtoward or away from a surface in a specified direction within a solid angle d. Radiance isa difficult but important concept. Its value is that it describes the radiative flux collectedby a tube pointed at a surface at an arbitrary angle, which is one way to describe asatellite sensor that observes the Earth’s surface. The flux is emitted from or incident ona differential unit area dA inclined at an angle θ to the direction of energy propagation,and is written

L ≡ d2

d dA cos θ(3.15)

Figure 3.8 shows a schematic diagram of a tube-like radiance meter pointed at a surface. Theinstrument captures the radiance that propagates within the solid angle and is emittedor reflected from the area A, which is inclined at an angle θ relative to the incidentradiation, and where A cos θ is the component of the surface in the look direction. FromEquation (3.15), this means that the radiance incident on the detector is

L = 2

A cos θ(3.16)



Detector

Lightbaffles

Tube ΔΩ

Δ A

θ

Surface

Projected area

Fig 3.8. A schematic diagram of a radiance meter viewing the surface. (Radiance meter adapted fromKirk (1996, Figure 5.6).)

Because several surfaces of oceanographic interest have radiances that are independent oflook angle, there are great advantages to this terminology, so the concept of radiance willbe used frequently in the following chapters.

Traditionally, emitted radiances are called radiance with the symbol L; incident radiancesare called brightness with the symbol B. These terms are often used independently ofdirection, with the brightness B used in passive microwave radiometry for both incomingand outgoing radiation, and the radiance L similarly used in ocean color observations. AsFigure 3.8 shows, radiance is the appropriate description of radiation to use with telescope-like instruments that observe the ocean surface at oblique angles and gather light or radiationwithin a specified solid angle. For propagation in free space, or when radiance is used withθ = 0, it is called a field radiance.

The concept of radiance can be difficult to understand. To provide a better understanding,the following sections first discuss some useful approximations, definitions and properties ofradiating surfaces, use the radiance to describe the operation of an ideal optical instrument,and conclude with examples. As the following sections show, radiance can be understoodin terms of the radiant flux collected by a tube pointed at an extended flat surface. Radianceis the natural unit to use with this concept and corresponds to the radiant flux collected bya satellite sensor.



3.3.1 Lambert surfaces

Lambert surfaces have the useful property that their emitted radiance is independent ofdirection; as this and subsequent chapters show, these surfaces are of particular importancefor ocean remote sensing in the visible/infrared. The term can also be used with reflectors,so that foam and clouds, for example, can be considered as Lambert or Lambertian reflectorsof sunlight, such that, for a large range of look angles in the VIR, the reflected radiance isindependent of direction. For a plane Lambert surface, a simple relation exists between theirradiance E and the radiance L. Calculation of E by integration of L over the upper halfplane yields

E = d

dA= L

∫ 2π

0dθ

∫ π/2

0cos θ sin θ d θ = πL (3.17)

Chapter 5 uses this relation in discussion of the radiances backscattered from the oceaninterior.

3.3.2 Spectral properties

Because satellite instruments observe the ocean at specific frequencies or wavelengthsand within specific bandwidths of f or λ, the behavior of the electromagnetic radiationwithin these narrow windows must be determined. To deal with these windows, the spectralforms of the radiant flux and the radiance are next defined, where the adjective spectralmeans “per unit wavelength” or “per unit frequency” (Mobley, 1994, Chapter 1). Thespectral form of the radiant flux with regard to wavelength is

d

dλ

∣∣∣∣λ

= λ (3.18)

which has units of W m−1, so that, for a narrow-wavelength band with center wavelengthλc, the energy received in a spectral window is approximately λ(λc) λ. The equivalentform in frequency is

d

df

∣∣∣∣f

= f (3.19)

with units of W s−1. The spectral radiance is written in terms of wavelength and frequencyas

dL

dλ

∣∣∣∣λ

= Lλ anddL

df

∣∣∣∣f

= Lf (3.20)

where Lλ has units of W m−3 sr−1 and Lf has units of J m−2 sr−1. Similar forms existfor the spectral irradiance and intensity. In the literature, the adjective “spectral” and thesubscripts λ and f are frequently omitted for brevity, even though their absence impliesthat the non-spectral quantities are integrated over a range of wavelengths or frequencies



(Mobley, 1994, Chapter 1). The following initially uses the spectral notation, while thesubsequent chapters do not.

3.4 Radiation from a perfect emitter

In 1900, Max Planck showed that, for a perfect emitter or radiator held at a constant uniformtemperature, the spectral radiance is a function only of temperature and wavelength, orequivalently of temperature and frequency. Such a radiator is called a blackbody radiator,or blackbody. In its ideal form, this black surface would be rough and non-reflective.This concept can be applied to opaque surfaces such as the ocean in the thermal infraredand microwave, and to small uniform regions of volume emitters such as gases. Planck’sequation gives the spectral radiance emitted by a blackbody,

Lλ (λ, T ) = 2hc2

λ5 exp[(hc/λkBT ) − 1](3.21)

Equation (3.21) has units of W m−3 sr−1, where these units can be interpreted as watts perunit area per unit solid angle per unit wavelength. In (3.21), h is the previously definedPlanck constant, c is the speed of light and kB = 1.38 × 10−23 J K−1 is the Boltz-mann constant. For later use, the right-hand side of Equation (3.21) will be defined as thePlanck function fP(λ, T ). One important fact about blackbodies is that they are Lambertsurfaces.

Figure 3.9 compares the spectral irradiance derived from Planck’s equation for anidealized Sun with a blackbody temperature of 5900 K, the measured solar irradiance atthe top of the atmosphere (TOA) and the solar irradiance measured at the surface for asolar zenith angle θS = 60°. The 5900-K solar irradiance is calculated as follows. The solarradius is 7.0 × 105 km, and the Earth–Sun separation is 1.5 × 108 km, so, at the TOAthe solar disk subtends a solid angle of 6.8 × 10−5 sr. If the solar disk is assumed to be ablackbody Lambert radiator, the irradiance follows from the definition of E and Equation(3.16).

The TOA solar irradiance data are from the best current estimate of the irradiancespectrum, based on computations by Robert Kurucz of the Harvard–Smithsonian Observa-tory, courtesy of Robert Cahalan. At the TOA, the fine structure in the solar irradiance iscaused by Fraunhofer absorption lines associated with the solar photosphere. As Figure 3.9shows, the 5900-K curve nearly matches the TOA irradiance, and the solar irradiance peaklies within the visible spectrum. The bottom solid curve shows the solar irradiance at theEarth’s surface, where, to separate the curves, θS is set equal to 60° so that solar irradianceis reduced by a factor of two. As Chapter 4 discusses further, the source of the additionalgaps and fine structure in the surface irradiance is attenuation by atmospheric gases. Finally,each of the curves shows the asymmetry in Planck’s equation relative to its maximum; atthe shorter UV wavelengths, the radiance decreases very rapidly with decreasing λ; at thelonger thermal wavelengths it falls off more slowly as λ increases.


3.4 Radiation from a perfect emitter 67

0.4 0.7 1.0 1.5 2.0 2.5

2.0

1.5

1.0

0.5

0

Wavelength (μm)

Visible

Spe

ctra

l irr

adia

nce

(GW

m–3

)

Fig 3.9. Comparison of the solar irradiance at the top of the atmosphere (upper solid curve) withPlanck’s equation at T = 5900 K (dashed line), and with the solar irradiance at the surface for a 60°solar zenith angle (lower solid curve). The visible spectrum lies within the pair of vertical lines; seethe text for further description and for data sources.

log(λ)

lo

g [s

pect

ral r

adia

nce

(W s

r–1

m–3

)] 14

12

10

8

6

4

2

6000K

3000K

1500K

300K

150K

75K

750K

1 μm 10 μm100 nm 100 μm

Fig 3.10. Comparison of the spectral blackbody radiances at the specified temperatures.

3.4.1 Properties of Planck’s equation

For several different blackbody temperatures, Figure 3.10 shows the dependence of Planck’sequation on wavelength and displays several interesting properties.

1. The Wien displacement law gives the dependence on temperature of the wavelength ofmaximum radiance in Planck’s equation. This wavelength is proportional to 1/T, so thatwarm bodies emit their maximum radiation at shorter wavelengths than do cold bodies.



2. The Stefan–Boltzmann law describes the temperature dependence of the total radianceor energy under the curve for Planck’s equation, and shows that the total increasesas T 4.

3. At any wavelength, there is always some emitted radiation, so that, if a specific radianceis observed at a particular wavelength, there is only one possible associated brightnesstemperature. This means that, ignoring the atmosphere and if the ocean radiance ismeasured at any wavelength with a sufficient degree of accuracy, the surface brightnesstemperature is uniquely determined.

If there were no atmosphere, then, from Planck’s equation, the sea surface temperaturecould be inferred from a single measurement of the surface radiance at almost any wave-length. In the real world, because the atmosphere absorbs, radiates and scatters radiation,in most cases the radiances received at the satellite differ from those emitted at the surface,which greatly complicates the retrieval.

3.4.2 Frequency form of Planck’s equation

Substitution of the invariant λf = c, and its differential dλ = −(c/f 2)df into Equation(3.21) yields the frequency form of Planck’s equation:

Lf (f ) = 2hf 3

c2 exp[hf/(kBT ) − 1](3.22)

with units of J m−2 sr−1. Also, quantities such as the solar irradiance and the atmosphericattenuation are often given as functions of inverse wavelength in units of cm−1; whenwritten in terms of inverse wavelength, the resultant form of Planck’s equation is similar toEquation (3.22).

3.4.3 Limiting forms of Planck’s equation

There are two limiting forms of Planck’s equation, the long-wavelength or Rayleigh–Jeansapproximation that is applicable to the microwave and the short-wavelength approximation.Because of its application to the microwave, the Rayleigh–Jeans approximation is the mostimportant; it is valid at low frequencies or long wavelengths, where λ or f must satisfy thefollowing inequality:

hf /(kBT ) = hc/(λkBT ) 1 (3.23)

Substitution of (3.23) into (3.22) yields

Lf = 2kBTf 2/c2 = 2kBT /λ2 (3.24)

At long wavelengths, Equation (3.24) shows that the spectral radiance Lf is a linearfunction of temperature. In the microwave, because of this linear dependence, the brightnesstemperature and radiance are often used interchangeably.


3.4 Radiation from a perfect emitter 69

For high frequencies or short wavelengths, hf /kBT 1. Substitution of this limit intoPlanck’s equation gives

Lf ∼ f 3 exp[−hf /(kBT )] (3.25)

Equation (3.25) shows that the radiance decreases exponentially as frequency increases. Insummary, at high frequencies or short wavelengths, the radiance falls off exponentially withincreasing frequency or decreasing temperature; at low frequencies or long wavelengths,it decreases as f −2 and, at a fixed frequency, increases linearly with temperature. Thisdifference in behavior at the short and long wavelengths is consistent with the asymmetryshown in Figures 3.9 and 3.10, and makes remote sensing possible at the long microwavewavelengths.

3.4.4 Thermal emission

As Thomas and Stamnes (1999, Chapter 5) show, a surface has four possible ways tointeract with radiation. It can emit radiation into the surrounding environment, and canabsorb, reflect or transmit the radiation incident upon it. Regarding emission, most objectsradiate less efficiently than a blackbody and have a directional dependence to their radiation.Since the blackbody is by definition the most efficient possible radiator, other objects mustradiate either less or equally efficiently. Because of this difference, non-blackbody radiatorsare called gray bodies, where their radiation properties are defined in terms of a spectralemissivity e(λ; θ, φ). The emissivity is defined as the ratio of the gray-body radiance to theblackbody, and is written

e(λ; θ, φ) = Lλ(λ, T ; θ, φ)/fP(λ, T ) (3.26)

By definition, a blackbody radiator has no directional dependence, so that blackbodiesare Lambert emitters and absorbers. Since the blackbody is the most efficient emitter,0 ≤ e ≤ 1.

The emissivity has several important properties. First, it generally depends on λ, so thatthe magnitude of the emissivity and its directional properties are functions of wavelength.For example, in the infrared and for θ less than about 45°, the emissivity of open water andthat of sea ice are both approximately given by e = 0.98. In contrast, in the microwave andat the commonly used 50° look angle, the ocean emissivity is 0.4, and the sea ice emissivityis approximately 0.8. Thus, at microwave frequencies, sea ice can have a greater brightnesstemperature than seawater. Second, the emissivity can be regarded as a physical surfaceproperty that is nearly independent of temperature and depends on the nature of the surfaceor substance. Even if two surfaces have the same physical temperature and are observedat the same λ, as long as they have different emissivities, they can be distinguished by thedifferences in their emitted radiances.

For a blackbody emitter, Figures 3.11(a) and (b) compare the angular dependences ofthe intensity and radiance. The intensity has a spherical envelope and the radiance has ahemispherical envelope so that its distribution is Lambertian. The difference between the



(a) (b) (c)I(θ) L(θ)

TS TS TS

Fig 3.11. Comparison of (a) the angular dependence and magnitude of the intensity and (b) theradiance emitted from a blackbody with (c) the radiance emitted from an arbitrary gray body, allat the same surface temperature TS. For the gray body, the semicircular line shows the blackbodyradiance at the same temperature.

two cases occurs because of the cos θ term in Equation (3.15). Figure 3.11(c) also showsthe radiance distribution for an arbitrary gray-body at the same temperature. Gray bodyradiances can depend on θ and are always less than or equal to the blackbody radiances atthe same temperature.

For radiation incident on a gray body where e < 1, the incident radiation can be absorbed,reflected, or transmitted. The spectral absorptance a(λ; θ, ϕ) is defined as the ratio of thespectral radiance absorbed by the gray body to the incident radiance. In the microwave, theabsorptance is called the absorptivity. For a blackbody, all the energy incident on its surfaceis absorbed, whereas for a gray body only part is absorbed, with the remaining energyreflected or transmitted. Examples of non-emitting bodies include a perfect reflector, suchas an ideal mirror, and a perfect transmitter, such as an ideal sheet of glass through whichradiation can pass without losses.

3.4.5 Kirchhoff’s law

For the special case of a surface within an isothermal enclosed system that is in thermalequilibrium with its surroundings, Kirchhoff’s law states that the surface must absorb andemit energy at the same rate, so that

a(λ; θ, ϕ) = e(λ; θ, φ) (3.27)

Why is this so? Consider Figure 3.12, which shows a hypothetical gray body located insidea black box, where both the gray body and the surrounding blackbody are at temperatureT. Suppose that the gray body has an emissivity e = 0.5, but an absorptance a = 1.Consequently, the temperature of the black box would decrease with time, while that of thegray body would increase. For a closed system with no work done on it, this temperaturebehavior violates the second law of thermodynamics. To avoid this violation, the emissivitymust equal the absorptance so that matter must absorb and emit radiation in the sameway. Therefore, for a specific substance, measurement of its absorption properties alsodetermines its emission properties.


3.5 The ideal instrument 71

T

T

Fig 3.12. A hypothetical gray body inside a black box.

For the situation shown in Figure 3.12 and for radiances incident on the body, a fractiona will be absorbed, and a fraction (1 – a) will be reflected. Simultaneously, the bodyemits radiances with an emissivity e = a, so that the system remains in thermal balance. AsThomas and Stamnes (1999, p. 133) state, the restrictive form of Kirchhoff’s law in Equation(3.27) “has much broader applicability and for practical purposes may be considered anexact relationship for planetary surfaces.” Chapter 4 applies this concept to gases, whichpermits derivation of an important source term in the radiative transfer equation.

Similarly to the definition of a(λ), t(λ) is defined as the ratio of transmitted to incidentenergy, and r(λ) is the ratio of reflected to incident energy. For the general case of radiationincident on a surface of a medium that transmits, reflects and absorbs, from conservation ofenergy and in the absence of nonlinear effects, so that radiation incident at λ is not reflectedat 2λ,

a(λ) + t(λ) + r(λ) = 1 (3.28)

In Equation (3.28), the reason why the variables have no angular dependence is that,as Chapter 5 shows, the angular dependence of the reflected incident energy dependsstrongly on the nature of the surface and can range from Lambertian to specular. For anon-transmitting interface,

a(λ) + r(λ) = 1 (3.29)

Chapter 5 uses this equation in the discussion of reflection and absorption at the sea surface.

3.5 The ideal instrument

The previous material is valid for all remote sensing wavelengths. In contrast, this sectionexamines the properties of a simple telescope that operates in the VIR, where Chapter 9 pro-vides a related discussion of microwave antennas. In the following, Section 3.5.1 describesthe Rayleigh criterion and its role in determination of the instrument resolution. Section



D

Δθ

Imag

e pl

ane

Fig 3.13. The diffraction of two line sources of light by a slit.

3.5.2 calculates the resolution of an ideal, vertically oriented instrument and the energyflux it receives from the surface. Section 3.5.3 repeats the calculation for an instrument atan arbitrary orientation and shows that for radiation from a Lambert surface the receivedenergy flux is independent of look angle. Finally, Section 3.5.4 discusses bandwidth andthe treatment of noise.

3.5.1 The Rayleigh criterion

This book makes use of two different Rayleigh criteria, both called the Rayleigh criterion.The first concerns the resolving power of lenses and apertures; the second concerns thescattering of radiation from surfaces. This section discusses the first case; Section 5.2 dis-cusses the second. For the first, all optical instruments have apertures, where the apertureis the area of the light-gathering lens or opening that separates the sensor from the environ-ment. As the following discusses, the diffraction of light at the aperture edge determinesthe minimum angular resolution of the instrument. The assumption that the aperture isa two-dimensional slit simplifies the discussion; except for a multiplicative constant, theanalysis is also correct for a circular opening.

Figure 3.13 shows the relevant two-dimensional geometry. Consider two line sourcesof light with an angular separation θ , where the sources are separated from an imageplane by an aperture of width D. Because of the wave nature of light, each line sourcegenerates a diffraction pattern on the image plane, where the vertical extent of this patternvaries inversely with D. For a very small θ , the patterns overlap, making it impossible todiscriminate between the images of the two light sources. Light diffraction at the apertureedge thus sets an inescapable lower limit to the angular resolution of the instrument.Quantitatively, the Rayleigh criterion states that the two sources can be distinguished onlyif the following relation holds:

θ ≥ λ/D (3.30)



For two point sources and a circular aperture, Charman (1995) shows that Equation(3.30) becomes

θ ≥ 1.22λ/D (3.31)

These relations give the limiting minimum angular resolution of an optical instrument. Forexample, Charman states that the Rayleigh criterion approximately gives the resolution of ahealthy human eye. For a pupil diameter of D = 3 mm, and for blue light of λ = 0.45 µm,Equation (3.29) gives θ = 0.2 mr, which for a 1-m separation between the eye and objectcorresponds to a surface resolution of about 0.2 mm.

3.5.2 The simple telescope

This and the next section derive the radiant flux received by an idealized nadir-lookingand slant-looking instrument viewing a Lambert surface, and show that the received fluxis independent of look angle. Figure 3.14 shows the idealized optical instrument. In Figure3.14(a), the angles and instrument size are greatly exaggerated for clarity; for the humaneye or the AVHRR, Figure 3.14(b) shows the instrument solid angles and fields-of-viewdrawn approximately to scale.

Figure 3.14(a) shows that the instrument consists of a lens with a focal length fL, anaperture area A and a sensor or detector area AS. For photographic film, the detector areais determined by the diameter of the individual grains of silver nitrate on the film; for aneye, by the size of the nerve endings in the retina; for a satellite sensor, by the area of acharge-coupled device on the focal plane. The instrument is at a height h above the surface,the FOV from which the sensor collects radiation is AFOV and the differential element of theFOV is AF. From geometric considerations, the solid-angle resolution of the instrumentis

α = AS/f2L = AFOV/h2 (3.32)

Equation (3.32) applies only if the Rayleigh criterion in (3.31) is satisfied. Given the desirein some cases to make the FOV as small as possible, Equation (3.32) shows that this canbe done by reducing the size of the sensor element and by increasing the focal length.However, if the Rayleigh criterion is not satisfied, then, no matter how long the focal lengthor how small the sensor, the resolution cannot be improved.

If the Rayleigh criterion is satisfied, then the radiance that is emitted or reflected fromeach element of surface area AF and focused on the detector propagates within the solidangle = A/h2, as outlined by the dashed lines on Figure 3.14(a). The instrument isthen defined by two solid angles, the instrument resolution α and . The solid angleα determines the FOV; determines the magnitude of the energy flux incident on thedetector. Given the nadir-looking instrument in Figure 3.14, the incident radiant flux IN

is calculated on the assumption of there being no atmospheric interference, a narrow-beaminstrument with α 1, and a Lambert reflecting or emitting surface. For these assumptions,



aperture

fL

h

AFOV

α

ΔΩ

AS

Aarea

(b)(a)

ΔAF

Fig 3.14. A schematic drawing of an ideal telescope. (a) The instrument drawn to an exaggeratedscale; (b) the instrument resolution and solid angles drawn approximately to scale for the AVHRR orhuman eye.

IN follows from the definition of L in Equation (3.15) with cos θ 1 for the narrow-beaminstrument, so that, in differential form,

d2IN = LddAF (3.33)

From (3.33), calculation of IN involves integrating the radiation from each element ofsurface area over the entire FOV, and over the solid angle subtended by the aperture. Onthe further assumption that the aspect ratio of the beam is so small that each differentialsurface area subtends the same , then ФIN can be written

IN = L

∫AFOV

dAF

∫

d = LAFOV (A/h2) = LAα (3.34)

For the nadir-viewing instrument, Equation (3.34) shows that the energy flux received atthe detector is a product of the surface radiance, the aperture area and the instrument solidangle, where the last two parameters are determined by the instrument design. Note that,



fL

AFOV

α

ΔΩ

AS

Ah1

θ

(b)(a)

h

ΔAF

Fig 3.15. A schematic drawing of the slant-looking instrument. (a) Exaggerated scale; (b) approxi-mately to scale.

if the distance from the surface is doubled, the radiant flux remains the same. As the nextsection shows, this is also true for an instrument that views the surface at an off-nadir angle.

3.5.3 Slant-looking instrument

Figure 3.15 shows the same instrument pointed at the surface at an off-nadir angle θ , againin an exaggerated view and with the resolution approximately to scale. The distance fromthe telescope to the surface is h1 = h/cos θ , where, at h1, the field-of-view at right anglesto the look direction is A1 = αh2

1 and the projection of this area onto the surface plane is

AFOV = αh21/cos θ (3.35)

As with the nadir-looking instrument, the radiation from each differential surface areaAF received by the instrument lies within the solid angle = A/h2

1. For this case,because the aperture A is now further from the surface, is smaller than its nadir-lookingvalue. From the definition of radiance,

d2IN ≡ L d dAF cos θ (3.36)



Integration of (3.36) over the surface field-of-view and the solid angle defined by theaperture gives

IN ≡ L(A/h21) αh2

1 = αAL (3.37)

Equation (3.37) shows that the slant case gives the identical result to the vertical case.For off-nadir view angles, an increase in FOV compensates for the reduction in ,so that the radiant flux received at the sensor is identical to the nadir-viewing result inEquation (3.34). Consequently, for a Lambert surface, a narrow-beam instrument and atransparent atmosphere, the radiance received by the instrument is independent of θ .

Equation (3.37) shows the advantages of working in terms of radiance, especially forLambert surfaces. Here are two additional examples. First, consider a sheet of bond paperthat is illuminated by fluorescent lights. Because of its microscale-roughened surface,when the paper is viewed at a variety of distances and look angles, the distribution of lightscattered from the paper is approximately Lambertian. From Equation (3.37) and for aneye with a constant pupil dilation, as long as the solid angle defined by each nerve endingwithin the eye is smaller than the solid angle defined by the paper, then, consistently withdaily experience, the radiant flux received from the paper is approximately independent oflook angle and distance.

Second, consider the light from the Sun and stars. Because the solar disk subtends anangle from Earth of about 0.5° or 10 mr, which is much greater than the 0.2 mr resolutionof the human eye, it is very dangerous to look directly at the Sun. This occurs because, inEquation (3.35), the eye resolution α is less than the angle subtended by the Sun, so that theentire solar radiance is focused on a single nerve ending, yielding the potential for severeeye damage. In contrast, a star several light-years away with the same size and radiance asthe Sun subtends a solid angle much less than 0.2 mr subtended by the eye. The result ofthis is that, even though the Sun and distant star have the same radiance, the radiant fluxreceived from the star within the eye is much less than that received from the Sun, so oneye damage occurs.

3.5.4 Finite-bandwidth instrument and treatment of noise

For a real instrument, the center wavelengths and bandwidths are tailored to the phenomenaunder investigation and to the atmospheric windows. If the detector is characterized by acenter wavelength λc and a bandwidth λ, where λ is sufficiently small that the surfaceradiance is approximately constant at L(λc)λ, then the radiant flux IN incident on thedetector becomes

IN = AαL(λc)λ (3.38)

The detector and its accompanying circuitry convert IN into the electrical energy OUT.Within the instrument and as Figure 3.16 shows, a noise power N is defined so that at any



Instrument detector and circuitry

ΦIN

ΦIN

ΦOUT

Φ IN

ΦOUT

Time

Pow

er

ΦN = ΦOUT −

Fig 3.16. The generation of noise within the detector and its accompanying circuitry.

instant,

N = OUT – IN (3.39)

Because the standard deviation or rms uncertainty of the noise σN is calculated from thetime series of N, Equation (3.39) can be written as

IN = OUT ± σN (3.40)

Given σN and following Stewart (1985, Section 8.1), the signal-to-noise ratio SN of theinstrument is defined as

SN = IN

σN= L (λc) λAα

σN(3.41)

To make OUT as noise-free as possible, SN must be large. Examination of Equation (3.41)suggests several ways to do this.

The first is to make the aperture A large, which is easy in principle, but difficult in reality.For example, the lens diameter of the Hubble Space Telescope was limited by the size of thecargo bay on the Space Shuttle. Any increase in the lens area A means that the instrumentbecomes bigger and heavier, all of which increases the difficulty and expense of placingthe instrument in orbit.

The second is to make the solid angle α as large as possible. In most cases, however, thegoal is to make α small, so that the surface FOV is small.

The third is to choose λc and λ in such a way as to maximize the received power.Because λ and λc are generally chosen to provide specific environmental information,this might not be possible. As the next chapter shows, the location of λc is also in partdetermined by the location of the atmospheric windows and their properties, and, as the



earlier part of this chapter shows, by the presence of RFI in adjacent bands. Similarly, λ

is set either by the phenomenon under investigation, as occurs in biological studies in thevisible, or by the width of the atmospheric windows, as occurs in the thermal infrared.Given these restrictions, the easiest way to reduce SN is to reduce σN. This is done in twoways: first, by insuring that the instrument has a low thermal noise, which involves coolingthe instrument and shielding it from the Sun; and second, by averaging measurements of thesame area over a short enough time that the radiance L does not change. As the followingchapters show, both techniques are used to reduce noise.

Finally, because σN is an instrument-specific, nonlinear function of IN, σN is gen-erally defined relative to the magnitude of the input radiant flux, radiance or blackbodytemperature. This means that in the physical interpretation of the uncertainty, when OUT

is converted to a radiance or temperature, σN is converted to an uncertainty in the sameunits. For these conditions, σN is written as a noise-equivalent-delta-radiance (NEL), or,equivalently, a noise-equivalent-delta-temperature (NET), such that for the retrieved radi-ance or temperture the noise is expressed as an rms uncertainty. For example, an AVHRRobservation of an ocean surface temperature of 300 K might have an NET of 0.5 K. Forthis case, the instrument is described as having an NET of 0.5 K at 300 K.


4

Atmospheric properties and radiative transfer

4.1 Introduction

The atmosphere lies between the ocean surface and the satellite sensor, and greatly affectsthe transmission of radiation. The presence of fixed concentrations of atmospheric gasessuch as oxygen, carbon dioxide, ozone and nitrogen dioxide, plus the variable concentrationsof water vapor, means that only a few windows exist in the visible, infrared and microwavefor Earth observations. Even within these windows, the atmospheric absorption varies withthe concentration of water vapor and with the liquid water droplets and ice particles thatmake up clouds. The absorption is also affected by atmospheric aerosols, which includethe water droplets and salt nuclei in the marine boundary layer, and the particulate mattergenerated over land by urban pollution, biomass burning and volcanic eruptions that isadvected over the oceans.

In the following, Section 4.2 describes the vertical structure of the atmosphere and themolecular and aerosol constituents that affect the transmission of radiation. Sections 4.3and 4.4 describe the propagation, absorption and scattering of a narrow beam of radi-ation. For the different atmospheric constituents, Section 4.5 discusses the dependenceof transmissivity on wavelength and the role of these constituents in defining the atmo-spheric windows. To prevent the chapter from becoming overly long, this discussion isrestricted to the visible/infrared; Chapter 9 extends it to the microwave. Section 4.6 appliesthese results to the ideal instrument. Section 4.7 discusses the radiative transfer equation(RTE) and the atmospheric emission and scattering source terms. Section 4.8 derives twolimiting solutions of the RTE, one for the infrared and microwave windows where absorp-tion and emission dominate; the other for the visible wavelengths where absorption andscattering dominate. Section 4.9 concludes with a discussion of diffuse attenuation andskylight.

4.2 Description of the atmosphere

Figure 4.1 shows a characteristic vertical temperature profile of the atmosphere. The left-hand scale gives pressure in millibars; the right-hand scale gives the height above mean

79


80 Atmospheric properties and radiative transfer

0.0001

0.001

0.01

0.1

1

10

100

1000

100

90

80

70

60

50

40

30

20

10

180 190 200 210 220 230 240 250 260 270 280 290 300

Temperature (K)

Mesopause

Stratopause

Ozoneregion

Stratosphere

Thermosphere

Mesosphere

Troposphere

Temperature

Cumulonimbus Cirrus

Mt. Everest 8.9 km

Ionosphere

Pre

ssur

e (m

b)

Alti

tude

(km

)

Tropopause

Fig. 4.1. The one-dimensional structure of the atmosphere. (Adapted from Eos Science, SteeringCommittee (1989), not subject to US copyright.)


4.2 Description of the atmosphere 81

sea level; the horizontal scale is the temperature. Proceeding upward from the surface,the atmosphere divides into the troposphere, stratosphere, mesosphere and thermosphere,which are respectively separated from one another by the tropopause, stratopause andmesopause. The exosphere, which is not shown, lies above the thermosphere. Figure 4.1also shows the approximate height of the cloud formation region in the troposphere andlower stratosphere, the stratospheric region of ozone formation, and the ionosphere, whichconsists of the mesosphere, thermosphere and exosphere, and contains the ions and electronsgenerated by solar dissociation of atoms and molecules. For remote sensing purposes, thereare four important variable atmospheric constituents. These are water in the form of vapor,liquid and ice, aerosols, ozone and ionospheric free electrons. Each of these affects theatmospheric transmission and scattering properties at different wavelengths and on timescales ranging from hours to years.

Examination of the atmospheric temperature profile shows that the air temperatureoscillates vertically with height between 180 and 300 K, and illustrates the atmosphericstability. Proceeding upward from the surface, the troposphere is marginally stable and ischaracterized by strong vertical mixing up to the tropopause. Because of the mixing, thetropospheric variable components, which are primarily the different forms of water and avariety of aerosols, have time constants of order one day to one week. The stratospherelies above the tropopause and, within it, the temperature increases with height up to thestratopause. The principal variable constituent of the stratosphere is ozone. The stabletemperature profile means that the stratosphere is a region of weak vertical mixing, sothat the time constant of the ozone concentration variability is of order months. Abovethe stratopause, the temperature continues to vary with height, but remains in the range200–300 K.

The pressure scale on the left-hand side of Figure 4.1 shows that approximately 90% ofthe atmospheric gases are in the troposphere, with an additional 9.9% in the stratosphere.In the troposphere, Ulaby et al. (1981) show that the density of dry air ρa has the followingdependence on height:

ρa = ρ0 exp (−z/Ha) (4.1)

In Equation (4.1), ρ0 = 1.225 kg m−3 and the scale height Ha is about 9.5 km. Thisexpression is accurate for z 10 km; because of stratospheric ozone, at larger heights theobserved densities deviate from Equation (4.1). Because the troposphere contains most ofthe atmospheric gases and almost all of the water vapor, it is where most of the scatteringand absorption occurs.

Table 4.1 lists the constituents of the atmosphere and their relative weights and percent-ages. These divide into the well-mixed, constant constituents and the variable constituents.The constant constituents include oxygen, nitrogen and a variety of trace gases; because thetroposphere is well-mixed, their relative concentrations are constant regardless of location.The variable constituents are next discussed in the order of water, aerosols, stratosphericozone and free electrons.



Table 4.1. Major components of the atmosphere, theirmolecular weight (more formally, relative molecular mass)

and content by volume.

Constituent Molecular weight Volume fraction

Nitrogen (N2) 28.016 0.78Oxygen (O2) 32.00 0.21Argon (Ar) 39.94 9.3 × 10−3

Carbon dioxide (CO2) 44.01 3.5 × 10−4

Water vapor (H2O) 18.02 VariableOzone (O3) 47.99 VariableNitrous oxide (N2O) 44.01 0.5 × 10−6

Methane (CH4) 16.04 2 × 10−6

Carbon monoxide (CO) 28.01 Trace, variable

Adapted from Weast (1976) and Ulaby et al. (1981).

4.2.1 Atmospheric water

Atmospheric water occurs as water vapor, liquid water and ice crystals in clouds, rain andsnow. Beginning with water vapor, from Ulaby et al. (1981) and Chahine et al. (1983), thevertical profile of atmospheric water vapor ρv is described by

ρv = ρv0 exp (−z/Hv) (4.2)

where ρv0 is the surface density of water vapor and Hv 2.5 km is the water vaporscale height. Because Hv Ha, the water vapor is concentrated in the lower part of thetroposphere. From Equation (4.2), the total water vapor concentration is described eitherby ρv0, with units of g m−3, or by the columnar water vapor V, which is the total integratedamount of water vapor contained in a vertical column extending through the atmosphere.This book primarily uses V for water vapor; it is measured in units of g cm−2 or in terms ofthe height in mm of the columnar liquid water equivalent. Ulaby et al. (1981) and Chahineet al. (1983) show that ρv0 varies from 10−2 g m−3 in the winter polar regions to values aslarge as 30 g m−3 in the tropics, with an average surface value of 10 g m−3.

From Equation (4.2) and for the same cases, V ranges from 0.03 to 75 mm of columnarwater equivalent, with a global average of 25 mm. Since the total columnar mass of theatmosphere is equivalent to 10 m of liquid water, vapor accounts for only about 0.3% of theatmospheric mass. In spite of its small contribution to atmospheric mass, Section 4.5 showsthat water vapor is a major contributor to the atmospheric absorption. Chapter 9 describesthe retrieval of V from passive microwave data, and Figures 9.18 and 9.20 give examplesof its distribution, showing that most of the water vapor occurs in the tropics.

Liquid water and ice crystals occur in clouds and in the cloud-related phenomena ofrain, hail and snow. Liquid water occurs in two forms: as non-raining cloud liquid watermeasured as the columnar liquid water L in mm, and as the rain rate RR measured in



mm h−1. As Chapter 9 discusses in more detail, both L and RR are retrievable from passivemicrowave observations. L ranges from 0 to 0.25 mm, so that non-raining clouds containmuch less columnar water than the vapor, while RR has a characteristic value of 2 mm h−1

and a maximum of about 20 mm h−1 (Wentz and Spencer, 1998).

4.2.2 Clouds

Clouds are transient atmospheric features that consist of small ice and liquid water particles.The droplets that make up liquid water clouds have characteristic radii of 10 µm andconcentrations of 102–103 cm3. Droplets with radii of 100 µm fall out as rain (Petty,2006, Section 7.4.4; Baker, 1997). The ice crystal particles and liquid water dropletsparticipate in the vertical convection that mixes the troposphere, where this convection isin part driven by the evaporation, freezing and condensation of cloud water droplets andice crystals. This change of phase within clouds and especially at their edges contributes tocloud variability. Cloud properties vary with height; the lower troposphere contains marinestratus and cumulus consisting of water droplets, while the upper troposphere contains thehigh thin cirrus consisting of ice particles.

Under certain conditions, convective cloud anvils extend into the lower stratosphere. Inthe VIR, the liquid water droplets and ice crystals in clouds scatter and absorb radiation, sothat thick clouds make it impossible to view the surface. Compared with the ocean surface,thick clouds are reflective and generally colder. Because clouds occur in major weathersystems, such as typhoons, cyclones, and atmospheric fronts, and because they stand outin both temperature and reflectivity against the ocean and land background, they are usedby weather satellites to track storms.

At any time, clouds cover almost two-thirds of the globe. For example, Figure 4.2 showsa true-color composite image of the Earth taken on 20 March 2012 or at the spring equinox,by the Moderate Resolution Imaging Spectroradiometer (MODIS) on the AQUA spacecraft.Prominent land features include the North African desert and green vegetation in North andSouth America, southern Africa, India and southeast Asia. The plate shows cyclonic swirlsof cloud around Antarctica, a storm in the North Atlantic between Greenland and Europe,and another storm approaching the west coast of North America.

4.2.3 Atmospheric aerosols

Atmospheric aerosols consist of small liquid or solid particles from the Earth’s surfaceand are another important source of atmospheric variability. Aerosols divide into threecategories, namely marine- and land-generated aerosols in the troposphere and volcanicaerosols in the stratosphere. Marine aerosols occur in the marine boundary layer and aregenerated locally at the sea surface. They consist of a mixture of water droplets with radiiof 10 µm, with the addition of sea salt nuclei from breaking waves (Stewart, 1985). Landaerosols are generated over land, then advected over the ocean. Examples include desert



Fig. 4.2. True-color composite image of the Earth taken by the Moderate-Resolution Imaging Spec-troradiometer (MODIS) on 20 March 2012. The image consists of one day of Sun-synchronous orbitalpasses from the sunlit side of Earth. For several swaths, the arrows mark the direct reflection of thesun from sun glint; the letters a, b and c mark storms that are shown on the cloud liquid water figurein Figure 9.18. See the text for additional description. (Image courtesy of NASA, not subject to UScopyright.) See color plate section.

dust, industrial and urban pollutants, and smoke and soot from biomass burning. Typicaldesert sources include dust from the North African Sahara Desert that is advected over theAtlantic Ocean to distances as far away as Florida, dust from the southwest African desertsadvected over the South Atlantic, and dust from the East Asian Gobi Desert advectedover the Pacific. Industrial and urban pollutants are generated in Europe, Russia, NorthAmerica, and southern Asia, where this material is advected over the North Atlantic, theArctic Ocean, and the North Pacific and Indian Oceans.

Soot and particulate matter are seasonally generated by biomass burning in parts ofMexico, Central and South America, Africa and Asia, where these particulates are advectedover their respective adjacent seas (Wang et al., 2000). Typically, the scale height of theaerosol layer for land- and marine-based aerosols is about 1 km, so that 90% of the aerosolsare confined to within 2 km of the sea surface (Gordon and Castano, 1987). Volcanoes areanother important source of aerosols; volcanic emissions carry micrometer-scale dropletsof sulfuric acid and other suspended particulates into the troposphere and stratosphere. AsChapter 7 shows, this material can cause changes in atmospheric absorption for periods of1–3 years after the initial eruptions.

4.2.4 Ozone

Ozone is the principal component of the stratosphere and forms via the dissociation ofoxygen molecules by solar radiation. It is a stable chemical species with a residence time oforder months and a seasonal variability. Figure 4.3 gives the typical distribution of ozonewith height for mid-latitude summer and winter, and shows that its concentration is less in



0 0.1 0.2 0.3 0.4 0.5 0.6

70

60

50

40

30

20

10

0

Density (mg m–3)

Hei

ght (

km)

Summer

Winter

Fig. 4.3. Comparison of ozone profiles derived from the standard MODTRAN cases of mid-latitudesummer and mid-latitude winter, where Section 4.5 describes the MODTRAN program and cases.

summer than in winter. Stratospheric ozone is of great importance because it absorbs UV-B,which occurs in the range 280–320 nm and causes skin cancer (Thomas and Stamnes,1999). For ocean remote sensing, the importance of ozone is that it attenuates visibleradiation with a seasonal and latitudinal dependence, so that, as Chapter 6 shows, it mustbe considered in the retrieval of ocean color. The ozone layer is also important because ofthe austral summer ozone hole in the Southern Hemisphere and a less intense but similar holein the Northern Hemisphere. Other tropospheric gases that exhibit long-term variability aregreenhouse gases such as methane and carbon dioxide. Although their long-term changesare important to atmosphere properties, they affect satellite-observed radiances only overdecadal periods.

4.2.5 Ionospheric free electrons

Free electrons are generated in the ionosphere by solar-driven molecular dissociation (Chel-ton et al., 2001b; Bird, 1998). These electrons occur at heights of 100–1000 km and, becausethey form reflective layers at certain frequencies, have a great effect on terrestrial radiocommunications. Because molecular dissociation occurs in sunlight with the moleculesbeing restored at night, the densities have a strong diurnal cycle. Figure 4.4 compares theday and night profiles of electron density and shows the nighttime decrease in density.The columnar concentration of the free electrons is given in units of TECU, the TotalElectron Content Unit, where 1 TECU = 1016 electrons m−2 (Chelton et al., 2001b). The



102 103 104 105 106

300

200

100

80

60

40

20

0

Alti

tude

(km

)

DayNight

Ionosphere

Electron density (cm–3)

Fig. 4.4. The day/night difference in electron density versus altitude (altitude scale as on original.(Redrawn from Bird (1998), not subject to US copyright.)

columnar concentration varies diurnally between 10 and 120 TECU and interannually withthe 11-year solar cycle, which had minima in 1997 and 2008 and maxima in 2001 and 2013.The importance of these diurnal and interannual changes is that the electron density affectsthe electromagnetic phase speed, which as Chapter 12 shows must be accounted for in thealtimeter retrieval.

4.3 Molecular absorption and emission

As Chapter 3 describes, atoms and molecules absorb and emit radiation in discrete quanta.An isolated molecule emits radiation by making a transition from a higher to a lowerquantized energy state, which occurs when an electron moves to a lower orbit, or fromchanges in its rotational or vibrational molecular state. If E is the change in the internalmolecular energy and h is the Planck constant, this energy change is governed by thefollowing relation:

hf = E (4.3)

The reverse occurs during a transition from a lower to a higher energy state, when themolecule absorbs energy. Equation (4.3) shows that the frequency at which radiation is


4.3 Molecular absorption and emission 87

f

Rad

ianc

eR

adia

nce

f

Fig. 4.5. Comparison of a line spectrum and its broadened form. (Modeled after the water absorptionline at 22 GHz, Equation (5.19) from Ulaby et al. (1981).)

emitted or absorbed is determined by the magnitude of E. Because these molecular statechanges occur in discrete steps, each molecular species generates different line absorptionand emission spectra.

In the atmosphere, emission and absorption do not occur in discrete lines, but, because ofprocesses called line broadening, they occur in spectral bands. Two of these processes arecalled Lorentz and Doppler broadening. Lorentz broadening occurs because, for moleculargas layers at a characteristic pressure and temperature, molecular collisions perturb theenergy level spacing of the individual molecules and broaden the spectral lines. As the gaspressure, density or temperature increases, Lorentz broadening increases. Doppler broad-ening occurs because the gas molecules are in motion. Each gas molecule with a velocitycomponent toward or away from the viewer generates a Doppler shift in the line absorptionor emission spectra, where the sum of these shifts generates line broadening. Because thepeak and spread of this velocity distribution increase with increasing temperature, Dopplerbroadening also increases with temperature. The Lorentz and Doppler broadening are theprincipal broadening mechanisms; together they generate what is called the Voigt lineshape, shown approximately in the lower frame of Figure 4.5 (Ulaby et al., 1981, Section5.3; Liou, 1980).

4.3.1 Molecular extinction

The terminology used to describe the transmission of radiation in the atmosphere depends onthe choice of wavelength window. In the visible/infrared, it is called the transmittance; in themicrowave, the transmissity (Ulaby et al., 1981, page 187, Table 4.1). In the visible/infrared,and depending on the source, the atmospheric attenuation of radiation divides into two parts:the attenuation of a narrow beam of radiation generated by a discrete source such as a laser



Gas layer

T, p

Δz

L(z) L(z + Δz) = L(z) – κA(λ)L(z)Δz

Fig. 4.6. Attenuation of an irradiance by a gas layer, where the λ-dependence of E is omitted. Seethe text for further description.

or spotlight, and the attenuation of radiation generated by an extended source, such as thatcreated by solar reflection from the ocean surface, or from any surface large compared withthe instrument FOV. The narrow-beam case yields what is called the beam transmittanceor simply the transmittance. The extended source yields the diffuse transmittance, which,because it depends on scattering, is important only in the visible. The symbol t with a varietyof subscripts will be used for both terms. The discussion of the diffuse transmittance isdelayed until Section 4.9.1 after the Rayleigh scattering discussion; the following discussesbeam attenuation.

Consider a parallel beam with irradiance L propagating in the direction z and incident ona layer of gas with differential thickness z, where the gas consists of a single molecularspecies at a constant temperature T and pressure p (Figure 4.6). Within the gas layer,there are two kinds of attenuation: molecular absorption and scattering of radiation outof the beam. If the sources of radiation due to scattering and blackbody emission areneglected, Beer’s law states that the change in the irradiance as it passes through the layeris proportional to the incident irradiance (Kidder and Vonder Haar, 1995), so that

L(λ) = − [κA(λ) + κS(λ)] L(λ, z)z (4.4)

In Equation (4.4), L(λ, z) is the incident radiance, L(λ) is the change in radiance acrossthe gas layer, κA(λ) is the volume absorption coefficient and κS(λ) is the volume scatteringcoefficient. In the atmosphere these coefficients have units of m−1 or km−1. If the extinctioncoefficient is defined as κE(λ) = κA(λ) + κS(λ), then (4.4) becomes

L/L(z) = −κE(λ)z (4.5)

where κE is sometimes called the attenuation coefficient. Because Equation (4.5) is validfor narrow collimated beams, it also applies to the intensity and the irradiance. Rewriting(4.5) in a differential form gives

dL

dz= −κEL or

dL

L= −κE dz (4.6)


4.3 Molecular absorption and emission 89

so that, for κE constant, the decay is exponential. The magnitude of κE depends on T, pand the gas constituent. For identical processes in the ocean, and as Chapter 5 shows, thevolume absorption coefficient is written as a(λ), the volume scattering coefficient as b(λ)and the attenuation coefficient as c(λ), where a, b and c have units of m−1 (Mobley, 1994).

For the atmosphere, κE is sometimes given in units of decibels per km, or dB km−1,where dB is a measure of the relative power or energy, defined as follows. If L0 is a referenceirradiance and L is the measured value, then

dB = 10 log10(L/L0) (4.7)

Equation (4.7) shows that a decrease of a factor of 10 in the transmitted irradiance corre-sponds to −10 dB; a 50% reduction, to −3 dB.

4.3.2 Optical depth and transmittance

In the application of the extinction model to the atmosphere, for each molecular constituent,Equation (4.6) is integrated across the atmosphere. The surface boundary conditions arethat, at z = 0, L = L0. Integration of Equation (4.6) from the surface to an arbitrary heightz gives

L(z) = L0 exp

[−

∫ z

0κE(z)dz

](4.8)

Equation (4.8) leads to the definition of two important terms, the optical depth or thicknessτ (λ) and the transmittance t(λ). For brevity in the following, the λ-dependence is omitted.The optical thickness τ can be defined relative to any reference height or path orientation.For a vertical path originating at the surface, the optical thickness τ (λ) is written as

τ (z) =∫ z

0κE(z)dz (4.9)

If the top of the atmosphere (TOA) occurs at the height z = zH, then for the entire depth ofthe atmosphere, its optical thickness τ is

τ =∫ zH

0κE(z)dz (4.10)

Given τ , the atmospheric beam transmittance or transmissivity t is defined from Equation(4.10) by t = exp(−τ ), so that L(zH) = L0 exp(−τ ) = L0t . From these definitions, a trans-parent atmosphere has τ = 0 and t = 1; an opaque atmosphere has τ = and t = 0. Theadvantage of t and τ is that, unlike κ , they are dimensionless.

4.3.3 Emission

For gases, the form of Kirchhoff’s law described in Section 3.4.5 applies in a slightlydifferent form that allows derivation of the relation between absorption and emission



(Thomas and Stamnes, 1999, Section 5.3.1). Given a black box containing a small volumeof gas, where the gas and its surrounding walls are in thermal equilibrium, Kirchhoff’s lawalso states that emission equals absorption on a per-unit-volume basis. For a gas volumeof width z, where the z-direction is arbitrary, the radiance absorbed in the gas from thewalls is

Labsorbed = −κA(T , p, λ)fP(λ, T )z (4.11)

Therefore, the thermal emission from the gas in the direction z must be

Lemitted = κA(T , p, λ)fP(λ, T )z (4.12)

so that the absorptance a = −κA z and the emissivity e = κA z. Since the direction z isarbitrary, Equation (4.12) shows that the emitted radiance is the product of the absorptioncoefficient and the Planck function and is isotropic.

Although restrictive conditions govern this relation, Thomas and Stamnes (1999) statethat it applies to the real atmosphere. For the case of a strongly directional solar radiationincident on an atmospheric layer, the absorption has a directional dependence, while theatmosphere radiates isotropically, so that, even though the absorption and emission constantsare equal and opposite, the incident and emitted radiances are not equal. Under theseconditions, the atmosphere heats up during the day and cools at night. As the followingshows, the radiative source term in (4.12) is particularly important at the infrared andmicrowave wavelengths.

4.4 Scattering

Scattering has at least two effects on a narrow beam of radiation that is observed at anarbitrary point. The first is the previously discussed case of energy loss from scattering outof the beam; the second occurs for a sensor viewing the atmosphere or ocean in a specificdirection, where an energy gain can occur from scattering of solar or other external energysources into the observation direction. The first is a loss from the beam; the second, anunwanted gain. Scattering divides into single and multiple scattering.

In single scattering, a photon experiences at most one collision along its path. An exampleof single scattering is a searchlight beam viewed at a distance. On clear nights, becauseof the photons that are single-scattered from the beam, the beam retains its pencil-likeshape to a distant observer. In contrast, for an evening with rain or fog, multiple scatteringoccurs, so that the beam might be visible only as a diffuse glow around the beam source.In many cases, single scattering can be modeled analytically, while multiple scattering ismore complex and is generally modeled numerically.

The previous section shows that absorption and emission are scalar processes. Becauseof its strong directional dependence, scattering is a more complicated vector process.Figure 4.7 defines the variables and coordinates used in the scattering discussion. FollowingKirk (1996) and Thomas and Stamnes (1999), the scattering properties are derived fromconsideration of a plane wave of irradiance E propagating along the z-axis and incidenton a small gas volume dV = dAdz, where dA = dx dy is perpendicular to the incident


4.4 Scattering 91

α

dΩ

E(z)

dI(α)

dy

dx

z

E(z + dz)dz

Fig. 4.7. The geometry used in the definition of the volume scattering function.

irradiance. Within this volume, because a fraction of the incident flux is scattered intoangles other than the propagation direction, the magnitude of E decreases with distancealong the path.

The following assumptions are assumed to govern the scattered energy. First, the volumedA dz is sufficiently small that within it only single scattering takes place. Second, thescattered power has an axisymmetric distribution about the propagation direction so thatit is only a function of the scattering angle α, and is described in terms of the angulardistribution of the intensity dI (α)within a solid angle d. Third, there is no fluorescenceor energy emitted at secondary wavelengths, so that the scattered radiation has the samewavelength as the incident.

The power incident on the volume is = E dA; from the definition of I in Section 3.3,the power scattered into any direction is d2 = dI d. The volume scattering functionβ(α, λ) is defined as the ratio of the power scattered per unit length and per unit solid angleinto a particular direction to the total power incident on the volume:

β(α, λ) = dI (α)

E dA dz= d2

dz d(4.13)

From (4.13), β(α, λ) has dimensions of m−1 sr−1. This equation can be rewritten as

d2(α) = β(α) d, dz (4.14)

where the λ-dependence of β is omitted.To calculate the power loss per unit length, Equation (4.14) is integrated over all angles

except for the forward direction, which is excluded because radiation propagating in thisdirection is not lost from the beam. The integration is from 0 to 2π in φ, and from 0+ to π

in α, where the “+” subscript on 0 means that the forward direction is excluded. The resultof this integration is

d

0 dz= 2π

∫ π

0+β(α) sin α dα (4.15)



Equation (4.15) can be described as the ratio of the flux scattered per unit length to theincident flux. It is independent of α and depends only on wavelength. Division of thenumerator and denominator of the left-hand side of (4.15) by dA and noting that the powerlost from the beam is a negative number transforms Equation (4.15) into a form similar to(4.5). Consequently, κS(λ) can be written as

κS(λ) = 2π

∫ π

0+β(α) sin α dα (4.16)

Equation (4.16) relates the volume scattering coefficient to the integral of the volumescattering function. Using (4.16), the following section discusses the limiting case ofisotropic scattering and defines the scattering phase function P(α).

4.4.1 Isotropic scatter and the scattering phase function

For the isotropic case, the scattered radiation is the same in all directions, so that

β(α) = constant = β0 (4.17)

Substitution of β0 into (4.16) gives

κS(λ) = 4πβ0 (4.18)

By analogy with (4.18) and for all forms of β, the scattering phase function P (α) is definedas

P (α) = 4πβ(λ, α)/κS(λ) (4.19)

From (4.19), P (α) has units of sr−1 and, for isotropic scatter, P (α) 1. Also, β can writtenas

β(λ, α) = P (α)κS(λ)/4π (4.20)

so that P (α) contains its angular dependence and κS(λ) contains its λ-dependence. Giventhese definitions, the dependences of scattering on α, λ and the gas constituents are easilydescribed.

4.4.2 Rayleigh and aerosol scattering

The description of scattering from molecules and particles in the atmosphere and oceandivides into two parts: Rayleigh or molecular scattering, and Mie (pronounced “me”) oraerosol scattering. The type of scattering depends on the size of the molecular or aerosolscatterer relative to the incident wavelength, or on the magnitude of the parameter q, definedas

q = 2πa/λ (4.21)

In (4.21), a is the radius of the molecule or particle and λis the incident wavelength. Formolecular scattering, a 0.1 nm and for visible light with λ 500 nm, q 10−3. For this


4.4 Scattering 93

α

Isotropic

Rayleigh

Fig. 4.8. Comparison of the dependence of the scattering function on scattering angle α for theisotropic (dashed line) and Rayleigh scattering (solid line) cases.

case where q 1, there exists a simple closed-form solution called Rayleigh scattering. Asq approaches 1, diffraction of the incident radiation around the particle generates a strongforward scattering, which has a complicated mathematical form and is called Mie scattering.Examples in the atmosphere include scatter from water droplets and aerosols. In the visible,Rayleigh scattering dominates, with additional contributions from Mie scattering at smallaerosol concentrations. In the infrared, Rayleigh scattering is negligible, and Mie scatteringis also neglected because infrared remote sensing depends on the absence of all heavyclouds and aerosols. At the microwave wavelengths, Rayleigh and Mie scattering occurfrom cloud water droplets and from raindrops, with scattering increasing at the shortermicrowave wavelengths.

4.4.3 Molecular or Rayleigh scattering

From Thomas and Stamnes (1999), Rayleigh scattering can be written as follows:

PR(α) = 3/4(1 + cos2 α), κR(λ) ∼ λ−4 (4.22)

where the subscript R refers to Rayleigh scatter. Figure 4.8 compares the Rayleigh scatteringphase function with the isotropic case, and shows that PR(α) is symmetric about the foreand aft directions. Because κR(λ) varies as λ−4, scattering increases as λ decreases.

For example, as λ decreases from 700 to 400 nm, or by about a factor of 2, the magnitudeof the Rayleigh scattering increases by a factor of almost 16. As Section 4.9.2 discusses, theradiance generated by Rayleigh scatter is called “skylight”, which provides an additionalsource of radiance to direct sunlight and is one of the reasons why shadows are notblack.

For the entire depth of the atmosphere and at the standard surface atmospheric pressureof p0 = 1013.25 mb, the Rayleigh optical thickness at standard pressure τRO is

τRO(λ) = 0.0089λ−4(1 + 0.0113λ−2 + 0.00013λ−4) (4.23)



Table 4.2. The λ-dependence of theRayleigh optical thickness at standard

pressure from Equation (4.23).

λ (nm) τRO (λ)

400 0.390500 0.152600 0.072700 0.038

(Evans and Gordon, 1994, their Equation (10); Hansen and Travis, 1974). If τR(λ)is theRayleigh optical thickness at an arbitrary surface pressure, then

τR(λ) = τRO(λ)(p/p0) (4.24)

For selected λ, Table 4.2 lists the wavelength dependence of τRO(λ).At first glance, there appears to be a discrepancy between the blue color of the sky

perceived by the eye and the λ−4dependence of the Rayleigh scatter; Smith (2005) statesthat, to the human eye near zenith, the sky appears blue with a wavelength of about 475 nm.Given the fourth-power dependence of the Rayleigh scatter, the question arises as to whythe sky is blue instead of violet, which would correspond to a wavelength closer to 400 nm(Figure 4.9). There are two reasons for the blue color, the first relating to the interaction ofthe Rayleigh scatter with the solar spectrum, the second relating to how the eye perceivesthis spectrum. From Figure 3.9, the solar spectrum peaks at about 460 nm, and falls off atshorter wavelengths. Smith (2005, Figure 3) shows that the product of the solar spectrumand the Rayleigh scatter is a continuous spectrum with two peaks, one at about 410 nm, theother at about 470 nm.

The color perceived from this spectrum depends on the physiological response of the eye,in particular on the color sensitivity of the three types of cones that exist in the eye, wherethe peaks in their respective sensitivities occur in the blue, green and red. Even thoughthe skylight spectrum contains energy at all visible wavelengths, it can be modeled for theeye as a combination of white light and a line spectrum, which is centered at 475±5 nm.It is this combination of the skylight spectrum and the properties of the cones that meansthe eye perceives the sky as blue (for further discussion, see Bohren (undated)).

4.4.4 Aerosol or Mie scattering

When the scatterers become comparable or larger in size relative to the incident wavelength,the scattering becomes strongly biased in the forward direction. For aerosol scattering inthe marine boundary layer, Figure 4.10 compares the isotropic and Rayleigh phase functionwith an approximate solution called a Henyey–Greenstein function (Gordon and Castano,


Fig. 4.9. Why is the sky blue? (From xkcd (2013), figure courtesy of xkcd, used with permission.)

Angle (degrees)–180 –90 0 90 180

Log

P( )

2.0

1.5

1.0

0.5

0

–0.5

–1.0

RayleighIsotropic

Aerosol

θ

Fig. 4.10. Comparison of the scattering function for isotropic and Rayleigh scattering with a strongforward-scattering aerosol phase function that approximates a marine aerosol. See the text for addi-tional description.



1987). As the figure shows, Mie scattering is characterized by a large forward-scatteredcomponent; it is also characterized by either a weak λ−1 or non-existent (λ0) wavelengthdependence. In summary, molecular scatter has a strong wavelength dependence and ananalytic solution that increases with decreasing wavelength; aerosol scatter has a weakwavelength dependence that increases more slowly with decreasing wavelength and astrongly forward-scattered numerical solution.

4.5 Atmospheric attenuation

This section discusses the atmospheric transmittance in the VIR; Section 9.2 discusses themicrowave transmissivity. The total transmittance is given by the sum of the individualoptical thicknesses or equivalently by the product of the individual transmittances for thedifferent molecular species and processes. When only molecular absorption and scatteringare important, the total optical thickness τtotand transmittance ttot can be written

τtot = τR + τCO2 + τO3 + τH2O + · · ·ttot = tR · tCO2 · tO3 · tH2O · · · (4.25)

For a nadir-looking satellite, the radiance LH received from a surface radiance L0 is simply

LH = ttotLO (4.26)

From this point on, the subscript on ttotwill be dropped. Given these definitions, the nextthree figures examine the dependence of t on λ for several different molecular constituentsand for atmospheric conditions ranging from tropical to sub-polar.

For the different constituents and atmospheric conditions, the transmittances are derivedfrom the MODTRAN code (Anderson et al., 1995). MODTRAN is part of a series of widelyused computer codes (LOWTRAN, MODTRAN, HITRAN, FASCODE) that describe theradiative properties of the atmosphere at a variety of resolutions in wavelength. Cloughet al. (2005) review the publically available radiation codes and databases. Table 4.3 liststhe six default MODTRAN atmospheres with the values of their water vapor surface andcolumnar densities. In the table, “Tropical” refers to latitudes less than 30°; “Mid-latitude”to 30°–45°; “Sub-arctic” to 45°–60°. The table shows that, for these cases, V lies between5 and 50 mm.

For these atmospheres, three attenuation cases are considered: first, the contributionsto t of several atmospheric molecular constituents and values of V for the wavelengthband 0.2–15 µm; second, a detailed examination of the molecular and Rayleigh scatteringcontributions to t for the UV/VNIR wavelengths 0.2–1.0 µm; third, the variations in tassociated with the seasonal ozone variability for 0.25–0.80 µm (250–800 nm).

For the six MODTRAN cases, a vertical path across the atmosphere and a wavelengthrange of 0.2–15 µm, Figure 4.11 shows the contributions to t from five molecular con-stituents, oxygen (O2), nitrous oxide (N2O), ozone (O3), carbon dioxide (CO2) and watervapor (H2O), as well as the total transmittance. Examination of the contributions from each


4.5 Atmospheric attenuation 97

Table 4.3. The dependence of atmospheric water vaporin the MODTRAN standard cases.

Case NameSurface densityρv0 (g m−3)

Columnar liquidwater equivalentV (mm)

1 Tropical 17.3 482 Mid-latitude

summer13.0 35

3 Mid-latitudewinter

3.5 11

4 Sub-arcticsummer

8.7 25

5 Sub-arcticwinter

1.3 5

6 1976 Standardatmosphere

5.6 17

molecule shows that, although O2 has an important absorption region in the near infrared,O2 and N2O are minor contributors to t. Between 9 and 10 µm, O3 generates a majorabsorption region and, as the next figure shows in more detail, blocks the transmission ofultraviolet radiation at wavelengths shorter than about 0.35 µm.

For λ > 3 µm, the combination of CO2 and water vapor primarily determines thetransmittance. The CO2 provides a long-wavelength cutoff at about 14 µm and some majoropaque regions at shorter wavelengths. Between 1 and 14 µm, water vapor determinesmuch of the shape of the transmittance and is the dominant contributor to the variability.The total transmittance shows that, for λ > 3 µm, or in the region where thermal emissionis important, the three wavelength windows used in the SST retrieval are 3–4 µm, 8–9 µmand 10–12 µm. As Chapter 7 discusses in detail, the transmittance at 3–4 µm is leastdependent on water vapor while that at 10–12 µm is most dependent.

For a more detailed examination of the range of 0.20 < λ < 1 µm (200 < λ< 1000 nm),and for the two extreme tropical and sub-arctic winter MODTRAN cases, Figure 4.12 showsthe contributions of O2, O3, water vapor and Rayleigh scattering to the total transmittance.The major difference between Figures 4.11 and 4.12 is that, for λ< 1 µm, Rayleighscattering becomes important. Examination of the curves also shows that O3 provides asmall but important transmittance change around 600 nm and attenuates the ultraviolet.O2 generates two absorption regions in the near infrared, where the region at about 762 nmis called the oxygen-A band, and also completely attenuates the ultraviolet, although atshorter wavelengths than O3. The water vapor contributions affect only a few specificbands occurring at wavelengths greater than about 600 nm. Consequently, over much ofthe visible spectrum, water vapor absorption can be ignored. Finally, at the short visible



0 2 6 8 10 11 12 13 14 15Wavelength (μm)1.3750.936

H2O

Tota l

O2

N2O

O3

CO2

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

Tra

nsm

ittan

ce

93 4 5 71

Fig. 4.11. The wavelength dependence of the transmittance for the visible and infrared wavelengthsfor the five major molecular contributors to atmospheric absorption and for the values of the columnarwater vapor represented by the six MODTRAN atmospheres in Table 4.3. The H2O curves correspondin order of decreasing transmittance to sub-arctic winter, mid-latitude winter, 1976 standard, sub-arctic summer, mid-latitude summer and tropical. The arrows at 0.936 µm and 1.375 µm mark thewater-vapor absorption bands used in the discrimination of high cirrus clouds discussed in Chapter 7.See the text for further description.

wavelengths or for λ< 600 nm, the combination of O3 attenuation and Rayleigh scatteringdetermines most of the variability in the absorption.

Because the effect of variable O3 is difficult to see at the scale of Figure 4.12, Figure 4.13shows the difference between the summer and winter transmittances associated with themid-latitude summer and winter MODTRAN ozone distributions, as shown by the profilesin Figure 4.3. Figure 4.13 shows that the summer transmittance is greater in the ultravi-olet for 300–350 nm, and increases slightly in the visible for 450–700 nm. As Chapter 6discusses, the ocean color retrieval accounts for this ozone-induced change in the visibletransmittance. In summary, Figures 4.11 and 4.12 show that, in the visible/infrared, theatmosphere has a number of spectral windows or regions that permit surface observations.Most of the visible wavelengths are transparent, although strongly attenuated by Rayleighscattering at the shorter wavelengths. Additional windows occur in the NIR between0.8 and 0.9 µm, and in the TIR at 3–4 µm, 8–9 µm and 10–12 µm. Between these windows


4.6 Application to the ideal instrument 99

1.0

0.5

0200 300 400 500 600 700 800 900 1000

Wavelength (nm)

O2

O3

H2O

Rayleigh scattering

Total

O2-A Band

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

Tra

nsm

ittan

ce

Fig. 4.12. The wavelength dependence of the atmospheric transmittance for oxygen, ozone and watervapor, and Rayleigh scattering, for the two extreme MODTRAN cases of tropical and sub-arcticwinter. For water vapor, the lower curve corresponds to the winter case.

and as Section 4.8.1 describes, satellite instruments called sounders use the opaque regionsto determine the temperatures at different depths in the atmosphere.

4.6 Application to the ideal instrument

For the ideal nadir-viewing telescope described in Section 3.5.2 that views the ocean throughan attenuating atmosphere, Equation (3.37) can be written as

IN = tαAL (4.27)



4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

–0.5250 300 350 400 450 500 550 600 650 700 750 800

Wavelength (nm)

Cha

nge

in tr

ansm

ittan

ce (

10–2

)

Fig. 4.13. The difference between the MODTRAN mid-latitude summer and winter transmittanceassociated with the decrease in summer ozone.

Plane-parallel atmosphere

Sensor

T(z), p(z)

θ

Surface

z

r

x

Fig. 4.14. The coordinate system used in the discussion of a sensor viewing the surface through aplane-parallel atmosphere.

so that, for a fixed λ, varies linearly with t. Suppose that the satellite views the Earthat an off-nadir angle. If the curvature of the Earth can be neglected and the atmosphericvariables p, T and κE have a plane-parallel distribution so that they are functions of z alone,then the off-nadir case also has a simple solution.

For an off-nadir look angle, Figure 4.14 shows that the sensor views the surface atan incidence angle θ and along a radial r. Because T and p are functions of z alone,κE(T , p, λ) = κE(z, λ), and, with the explicit λ-dependence omitted, κE can be written as


4.7 The radiative transfer equation 101

κE(z) = κE(r cos θ ). For constant θ , if κE is integrated along a slant path between the surfaceand the satellite, then LH = L0 exp(−τ ′), where

τ ′ =∫ rH

0κE (r) cos θ dr (4.28)

where rH is the radial height of the TOA along θ . With the change of variable in Equation(4.28) from r to z, and noting that the secant is defined by sec θ = 1/cos θ so that r = z

sec θ , Equation (4.28) can be written

τ ′ =∫ zH

0κE(z) sec θ dz = −τ (zH) sec θ (4.29)

From Equation (4.29) and for the slant-looking case, the radiance received at the satelliteis

LH = L0e−τ sec θ = L0tsec θ (4.30)

From (4.30), the solutions for the off-nadir and nadir cases have the same form, except thatτ is replaced by τ sec θ , and t is replaced by tsec θ . Given the finite-bandwidth instrumentdescribed in Section 3.5.4, Equation (3.38) becomes

IN = L(λc)λ AαStsec θ (4.31)

For an instrument looking at the surface through a purely attenuating plane-parallel atmo-sphere, Equation (4.31) gives the general form of the received radiant flux. As Chapter 7shows, the sec θ dependence in (4.31) is important in the infrared retrieval of SST.

Equation (4.31) also shows that, in some cases, the θ -induced variability is not important.For example, suppose that the atmospheric transmittance is 0.8 and that θ varies from 0 to45°. Although the increase in path length is 41%, the attenuation varies only by 10%, from0.8 at nadir to 0.73 at 45°. This means that in some cases whiskbroom scanners can be usedwithout correction for variable θ .

4.7 The radiative transfer equation

This section discusses the radiative transfer equation (RTE) and its attenuation and sourceterms. Sections 4.7.1 and 4.7.2 discuss the emission and scattering source terms, and, forthe beam transmittance case, Section 4.7.3 derives the solution for a radiance propagatingacross the entire atmosphere. In the following, the transmittance is separated into twocases: beam and diffuse transmittance. Beam transmittance occurs in the thermal infraredand microwave bands where there is no scattering of external radiation into the transmissionpath and where the attenuated radiance is supplemented by atmospheric emission. Diffusetransmittance occurs in the visible, where the radiation along the path is not only attenuatedas it propagates, but also supplemented by Rayleigh scattering into the path.

Consider the general case of a radiance at a location x = x, y, z propagating along thepath defined by the angles θ , φ. Along this path, the radiance loses energy by absorption



and scattering out of the path, and gains energy from thermal emission and by scatteringfrom external sources into the path. Combination of all these terms leads to the followingform of the RTE (Kirk, 1996):

d

drL(λ, x, θ, φ) = −κE(λ, x)L(λ, x, θ, φ) + (λ, x, θ, φ) (4.32)

In Equation (4.32), r is in the direction specified by θ , φ, where, in this direction, the left-hand side of the equation gives the change in radiance per unit length. On the right-handside, the first term describes the attenuation of the radiance by scattering and absorption;the second is the source term , given by

(x, θ, φ) = emit(x, θ, φ) + scat(x, θ, φ) (4.33)

In Equation (4.33), and as the following sections discuss, at the point x, emit(x, θ, φ)is the emission source term and scat(x, θ, φ) is the scattering source term generated byscattering into θ , φ from all directions other than the direction of propagation. To simplifythese definitions, their λ-dependence is omitted.

4.7.1 Thermal emission source term

From Equation (4.12), the thermal emission source term is

emit = κA(T , p, λ)fP(λ, T ) (4.34)

Because both the atmosphere and ocean are at temperatures of about 300 K, their emissionsare negligible in the visible, but must be considered in the infrared and microwave. Withinthe water column, because radiation at the infrared and microwave wavelengths cannotpropagate more than a few millimeters, thermal emission is neglected in all observationalbands.

4.7.2 Scattering source term

The scattering source term scat(x, θ, φ) is more complicated than the emission term, andis derived from consideration of a volume element at the point x with a length dr in the viewdirection. At this point, evaluation of the source term consists of the sum of the radiancespropagating in the direction θ , φ that are generated by the scattering into that directionfrom all of the external radiances incident on the volume element, except those alreadypropagating in the direction θ , φ. Figure 4.15 shows the scattering geometry. In this figure,an external radiance Lex from a source such as the Sun is incident on the origin at an angleθ ′, φ′. At the origin, a fraction of this radiance is scattered into the direction θ, φ toward thesensor, where α is the angle between the incident and scattered radiances.

For this geometry, scat can be written in terms of the volume scattering function β.Equation (4.13) defines β(α, λ) in terms of the power scattered per unit length and unitsolid angle from an incident irradiance. Mobley (1994, Chapter 5.2) shows that β can be


4.7 The radiative transfer equation 103

x

y

z

θʹθ

α

φʹ φ

Source Sensor

LexL

Fig. 4.15. The coordinate system and geometry used in discussion of the scattering source term.

Sensor

Source

ΔΩα

dz

L(α)d

dy

dx

ΔΩ

Lex

dzα

dr

Fig. 4.16. The coordinate system used in discussion of scattering into the beam.

alternatively defined as the radiance that is scattered per unit path length at an arbitrary pointinto the view direction from an external irradiance that is incident on the point at a relativeangle α. Figure 4.16 shows an expanded view of this geometry, where the scattering occursat the origin. The incident irradiance is Eex = Lex′, where Lex is a source of externalradiation such as the Sun and ′ is the angle subtended by the source. For this case,



Mobley (1994) shows that the radiance per unit path length received at the sensor fromscattering at the origin is

scat ≡ dL

dr= β(α)Lex ′ (4.35)

For multiple sources of external radiation, integration of (4.35) over all solid angles gives

scat(θ, φ) =∫

4

β(θ, φ; θ ′, φ′)Lex(θ ′, φ′)d′ (4.36)

where Lex represents all sources of external radiance. As Section 4.8.2 shows, given β andthe distribution of Lex, the right-hand side of (4.36) can be integrated to yield the scatteringsource term.

4.7.3 General solution for a radiance propagating across the atmosphere

This section derives the radiance received at the satellite for the beam attenuation case, andproceeds from integration of Equation (4.32) across the atmosphere along a path inclinedat an incidence angle θ . (This derivation follows the undated and unpublished course notesof J. L. Mueller and C. H. Wash, approximately 1984.)

For a plane-parallel atmosphere where dr = dz sec θ , Equation (4.32) becomes

cos θd

dzL(z) + κE(z)L(z) = (z) (4.37)

In (4.37), when the right-hand source term is set equal to zero, the solution of the homoge-neous equation has the form exp[−τ (z) sec θ ]. Given this homogeneous solution, Equation(4.37) is solved as follows.

First, the optical thickness τ is redefined for a path within the atmosphere originating atzH at the TOA, so that τ (z) becomes

τ (z) =∫ zH

z

κE(z)dz (4.38)

From this equation, τ (zH) 0, and, as z approaches the surface, the optical thicknessincreases.

Second, multiplying both sides of (4.37) by the term sec θ [exp(−τ (z) sec θ ] and inte-grating from z to zH yields∫ zH

z

exp(−τ (z) sec θ

) [dL

dz+ κE(z)L(z) sec θ

]dz

= sec θ

∫ zH

z

(z) exp(−τ (z) sec θ

)dz (4.39)

With the introduction of the dummy variable u = L(z) exp (−τ (z) sec θ), where Equation(4.38) defines τ , the left-hand side of Equation (4.39) can be integrated to yield∫ zH

z

du = L(zH) − L(z) exp[−τ (z) sec θ] (4.40)


4.8 Specific solutions of the radiative transfer equation 105

Therefore, for beam transmittance, the solution to Equation (4.39) is

L(zH) = L(z) exp[−τ (z) sec θ] + sec θ

∫ zH

z

(z) exp[−τ (z) sec θ]dz (4.41)

Physically, Equation (4.41) shows that the radiance received at the satellite from a sourceat height z consists of the radiance at z attenuated by the exponent of the optical thicknessplus the integral of the source term along the path between z and the TOA. Because ofthe absence of scattering in the infrared and microwave, Equation (4.41) is valid for bothextended and discrete sources of radiance; in the visible, it is valid only for discrete sources.For extended sources in the visible, Section 4.9 discusses the diffuse transmittance casewhere, in the first term on the right, the surface radiance is attenuated by the diffusetransmittance.

A change in variables from z to τ, where dτ = −κE dz, allows the second term on theright in Equation (4.41) to be written as

sec θ

∫ τ (z)

0

[(z)exp(−τ (z)sec θ )/κE(z)

]dτ (4.42)

In Equation (4.42), (z)can be either the scattering or the emission source function. Thisterm is called the path radiance, which is the radiance generated along the path between theheight z and the satellite by either scattering into the beam or molecular emission withinthe beam. As the next section shows, evaluation of Equation (4.42) at z = 0 or equivalentlyat τ (0) ≡ τgives the path radiance generated across the entire atmosphere.

4.8 Specific solutions of the radiative transfer equation

This section discusses specific solutions of the RTE. Section 4.8.1 derives the case applica-ble to the infrared and microwave where scattering is negligible. For the visible case wheremolecular scattering predominates, Section 4.8.2 derives the single-scattering Rayleighpath radiance. Section 4.8.3 then briefly discusses the single-scattering aerosol pathradiance.

Because the relative magnitudes of the scattering and emission terms vary greatly amongthe visible, infrared and microwave windows, it is easier to find an approximate solution toEquation (4.41) that is applicable to a specific window than to find a general solution. Thereare two reasons why these approximate solutions are successful; first, the ocean surfaceand atmospheric temperatures are both of order 300 K, and second, molecular scatteringis important only in the visible. From Planck’s equation, the temperature condition meansthat the ocean surface and atmosphere have their maximum radiance at a wavelength ofabout 10 µm.

Thus, in the visible, atmospheric emission can be neglected and Rayleigh and aerosolscattering dominate the RTE, where the solution is called scattering-dominant. In theinfrared and microwave, because of their longer wavelengths, scattering can be neglectedfor cloud-free conditions in the infrared and for almost all conditions except heavy rain in



the microwave. At these wavelengths, the RTE is primarily a balance between atmosphericabsorption and emission, where the solution is called absorption–emission-dominant. Thefollowing sub-sections first derive the RTE for the absorption–emission case, then derivethe scattering-dominant case.

4.8.1 Absorption–emission-dominant case

As Section 4.4.3 shows, for wavelengths longer than the visible, molecular scattering canbe neglected, so that, if aerosol scattering can be similarly neglected, the RTE can beapproximated as a balance between absorption and emission. This solution is particularlyapplicable to the infrared and microwave and is called the Schwarzschild equation. In theinfrared, because viewing the ocean surface requires cloud-free conditions, only negligiblemolecular scattering occurs, so the approximation holds. In the microwave, where thesurface can be viewed through clouds, the approximation holds for long wavelengths, but,as Chapter 9 describes in detail, breaks down under conditions of heavy rain.

For an absorption–emission balance with zero scattering, κE = κA. Because thermalemission is the only source term, substitution of Equations (4.34) and (4.42) into (4.41)gives the following solution of the RTE at the TOA:

L(zH) = L0 exp[−τ (zH) sec θ ] + sec θ

∫ τ

0fP(λ, T ) exp[τ ′(z) sec θ]dτ ′ (4.43)

In (4.43), L0 is the surface radiance, L(zH) is the TOA radiance and fP(λ, T ) is the Planckfunction defined in Equation (3.21). The first term on the right is the attenuated surfaceradiance, the second is the atmospheric emission source term. This important solution tothe RTE is applicable to the thermal infrared and microwave bands (Kidder and VonderHaar, 1995).

If the atmosphere can be characterized by a mean temperature T and mean τ , Equation(4.43) can be written

L(zH) = L0 exp (−τ sec θ ) + fP(T , λ)[1 − exp (−τ sec θ )

](4.44)

From the definition of t following Equation (4.10), (4.44) can be rewritten as

L(zH) = L0 t sec θ + fP(T , λ)(1 − t sec θ ) (4.45)

For this approximations, Equations (4.44) and (4.45) show that the radiance received atthe TOA divides into two parts: the left-hand term is the surface radiance L0 attenuatedby atmospheric absorption and the right-hand term is the atmospheric emission term pro-portional to the Planck function. As Chapter 7 shows, the simplified equation in (4.45) isused in the SST retrieval algorithms. In the microwave, and for surface and atmospherictemperatures of order 300 K, Equation (4.45) is also valid, and, as Section 9.3 shows, canbe linearized using the long-wavelength approximation.

Depending on the magnitude of the wavelength-dependent transmissivity, the receivedradiance is dominated by one of the two terms of (4.45). If the window is highly



transmissive, the ocean surface radiance dominates the received radiance; if the windowis weakly transmissive, the path radiance generated by thermal emission dominates. Forthe second case and depending on wavelength, the retrieved radiance is proportional to thetemperature at different levels in the atmosphere. Atmospheric sounders use these windowsto retrieve the atmospheric temperature profile (Kidder and Vonder Haar, 1995, Chapters 3and 6).

4.8.2 Single-scattering approximation

This section discusses the single-scattering approximation, which is primarily valid in thevisible wavelengths and has an analytic solution. Because thermal emission can be neglectedin the visible, scattering dominates the RTE. The single-scattering approximation dividesinto two parts. The present section derives the path radiance generated by an external sourcesuch as the Sun; Section 4.9.1 discusses the path radiance generated by an extended sourceof surface radiance where the diffuse transmittance describes the attenuation.

This section specifically derives the Rayleigh path radiance for molecular single scatter-ing and Section 4.8.3 states the result for aerosol single scattering, where the ocean colorretrieval uses both solutions. The atmosphere is divided into two layers: the stratosphere,where it is assumed that only ozone attenuation occurs with no scattering, and the tropo-sphere, where this derivation assumes that there is no absorption of visible light so thatthe radiance is attenuated by Rayleigh and aerosol scattering. The marine troposphere issometimes further divided into an upper layer where Rayleigh scattering dominates and alower layer where aerosol scattering dominates.

Before derivation of the Rayleigh path radiance, and following Mobley (1994), thespectral single-scattering albedo ω0(λ) is defined as

ω0(λ) = κS(λ)

κE(λ)= κS(λ)

κA(λ) + κS(λ)(4.46)

The term ω0(λ)is the ratio of the scattering coefficient to the extinction coefficient, and canbe considered as the probability that, as a photon travels a given distance, it will be scat-tered rather than absorbed. For pure scattering, ω0 = 1; for pure absorption, ω0 = 0.For Rayleigh single scattering, ω0(λ) ≡ ωR(λ) 1, where the subscript R stands forRayleigh. For aerosol single scattering, ω0(λ) is replaced by the aerosol single-scatteringalbedo ωA(λ), where

ωA(λ) = κAS(λ)/κAE(λ) (4.47)

In (4.47), κAS is the aerosol scattering coefficient and κAE is the aerosol extinction coeffi-cient. In general, ωA(λ) < 1 (Gordon and Castano, 1987).

In the following, the Sun is assumed to be the only source of external radiation, wherethe solar irradiance is approximated as a point source, located in Earth coordinates at thesolar zenith and azimuth angles θS, φS. With this notation, the solar irradiance at the TOAis described byFS(λ) δ(θ − θS, φ − φS), where δ(θ − θS, φ − φS) is the delta function.



Sensor

θ

Surface

θS

Solarirradiance

TOA

Sun

α A

B

C

FOV

Fig. 4.17. The coordinates and definitions used in the single-scattering discussion. The gray ellipseshows the sensor FOV. See the text for further description.

From Chapter 3, FS(λ) = LS(λ), where is the solid angle subtended by the Sunat the TOA and LS(λ) is the solar radiance. This means that the single-scattering caseapproximates the Sun as a bright point source in a black sky and neglects the additionalskylight term associated with Rayleigh scattering of the incident solar radiation.

The task is to calculate the path radiance observed by a satellite sensor viewing thesurface; with small changes, the same calculation applies to a sensor looking up from thesurface in a direction away from the Sun. Figure 4.17 shows the geometry of the source andsensor. For simplicity, the observing path and the solar irradiance are assumed to lie onthe same azimuth, so that θ and θS lie in the same plane. In this calculation, the surfaceradiance is neglected. At each volume element along the observing path, the incident solarradiation is scattered toward the sensor. Because each photon is scattered once only, thereis no further attenuation of the scattered radiance along the path, so that the integral alongthe path of the contribution from each path element equals the Rayleigh path radiance.Determination of the path radiance thus divides into two parts: calculation of the scatteringsource term at an arbitrary height z within the observing path, and the integration of thisterm along the entire path.



Calculation of the scattering source term at a height z, shown on Figure 4.17 as point A,proceeds as follows. If the solar irradiance F (λ, z)is attenuated only by Rayleigh scattering,then, at point A, the irradiance becomes

F (λ, z) = FS(λ)δ(θ − θS, φ − φS) exp[−τR(z)/ cos θS] (4.48)

In (4.48), τR(z) is the Rayleigh optical thickness derived from Equation (4.38) and anunspecified distribution of κR(z); in the final result, τRappears only as the optical thicknessfor the atmospheric depth of interest.

Second, at the point B located at an arbitrary height z within the observing path, aportion of the radiance is scattered toward the sensor. Substitution of Equation (4.48) intothe scattering source term in (4.36) and integration over all solid angles shows that, at z,the scattering source function can be written as

scat(λ, z; θ, φ) =∫

4

β(θ, φ, θ ′, φ′)F (λ, z) d′

= FS(λ)PR(α)κR(λ, z) exp[−τR(z) sec θS]/(4) (4.49)

In (4.49), the second line is derived from substitution of β from (4.20) into the first line.Equation (4.49) gives the Rayleigh scattering at a height z and for α, which is the differencebetween the direction of the observing path and the solar irradiance.

Substitution of the scattering source function (4.49) into the source term in Equation(4.42) and integration across the atmosphere along the path defined by θ gives the followingfor the Rayleigh path radiance LR(θ ):

LR(θ ) = [FS(λ)PR(α) sec θ/(4)

] ∫ τR

0exp

[ − τR(z)(sec θS + sec θ )]

dτR (4.50)

On Figure 4.17, LR is the Rayleigh path radiance evaluated at the TOA or at point C.Since Rayleigh scattering is the only source of attenuation, the τ in Equation (4.42) arereplaced by τR in (4.50). The single-scattering approximation also means that there isno further attenuation by scattering of the radiance as it propagates toward the sensor.Therefore, within the integral in Equation (4.50), the sec θ term is set equal to zero, so thatthe equation can be integrated to yield

LR(θ ) = FS(λ)PR(α) cos θS(1 − exp

[−τR(λ) sec θS])

/(4 cos θ ) (4.51)

For the real atmosphere, FS and LR are further attenuated by stratospheric ozone. Todecouple ozone attenuation and tropospheric scattering, it is assumed that attenuation takesplace only in the stratosphere while scattering takes place only in the troposphere. For asatellite sensor, LR is then determined by the downward attenuation of the solar irradiancethrough the ozone layer, the tropospheric Rayleigh scattering of this light back up towardthe sensor, and the further attenuation of the scattered radiance as it passes upward throughthe ozone layer. Because both the Sun and the sensor lie above the atmosphere, this situationis modeled by replacement of FS(λ) in (4.51) with the solar irradiance F ′

S(λ) attenuated by



two passes through the ozone layer. Given an ozone optical thickness of τOZ, F ′S(λ) can be

written as

F ′S(λ) = FS(λ) exp

[−τOZ (sec θ + sec θS)]

(4.52)

If the solar incidence angle is restricted to θS 45°, Equation (4.52) can be furthersimplified. For this range of angles, sec θS ≤ 1.4, and for the visible wavelength values ofτR(λ) from Equation (4.24) and Table 4.2, τR(λ) sec θS < 1, so that exp[−τR(λ) sec θS] 1 − τR(λ) sec θS. Substitution of this approximation and Equation (4.52) into (4.51) yields

LR(θ ) = F ′S(λ)PR(α)τR(λ)/(4 cos θ ) (4.53)

Equation (4.53) gives the single-scattering Rayleigh path radiance generated across theentire atmosphere and received at the satellite (Gordon and Castano, 1987). In Equation(4.41) and for z = 0, Equation (4.53) is the solution for the second term on the right. For thefirst term on the right in (4.41), if the source area is small, beam attenuation is applicable andτ is replaced with the sum of the Rayleigh and ozone optical thicknesses. For the case of anextended surface source in the visible, as Section 4.9.1 discusses, the diffuse transmittanceattenuates the surface radiance.

4.8.3 Aerosol single scattering

Unlike in the Rayleigh scattering case where ωR = 1, a typical value for ωA(λ) is about0.8 (Gordon and Castano, 1987). Given ωA(λ), Gordon and Castano derive the aerosolsingle-scattering solution in a manner similar to the derivation of Equation (4.52). If PA(α)is the aerosol phase function and τR(λ) is the aerosol optical depth, they find that the aerosolpath radiance LA received at the sensor is

LA(θ ) = ωA(λ)F ′S(λ)PA(α)τA(λ)/(4 cos θ ) (4.54)

Both Equations (4.53) and (4.54) will be used in the retrieval of ocean color that Chapter 6describes.

4.9 Diffuse transmittance and skylight

In addition to generating the path radiances, scattering determines the magnitude of twoadditional quantities: the diffuse transmittance that Section 4.9.1 discusses below and theskylight term that Section 4.9.2 discusses. The diffuse transmittance is less than the beamtransmittance, is important only in the visible, and applies to the case of a radiance generatedby an extended surface. The skylight term is generated for clear skies from the blue skyRayleigh scattering of the incident solar irradiance, which creates a downwelling irradianceincident from all directions above the horizon.


4.9 Diffuse transmittance and skylight 111

Sensor

θ

Surface

TOA

Fig. 4.18. Illustration of diffuse transmittance. The inner dark gray ellipse is the instrument FOV; theouter light gray ellipse is the region from which single scattering of surface radiances into the beamcontributes to the received radiance. The black dots show several examples of scattering sites. Seethe text for additional description.

4.9.1 Diffuse transmittance

As Gordon et al. (1983) and Wang (1999) describe, for radiances emitted from an extendedocean surface into a scattering atmosphere, the received radiance depends not only onthe radiance emitted within the instrument FOV, but also on radiances scattered into theinstrument solid angle from the surrounding area (Figure 4.18). This effect is most importantat the shorter visible wavelengths. The contributions from outside the FOV have two effects:first, the source of the received radiance is larger than the FOV; second, the receivedradiance is greater than it would be for beam attenuation alone. This scattering createsproblems when an ocean FOV is close to land or adjacent to sea ice, to icebergs or toany surface where the emitted or reflected radiance differs from that of the open ocean.Because of the contributions from these adjacent areas, the received radiance no longerrepresents the open ocean and is described as contaminated, as in land-contaminated. Forthis reason, ocean color observations can be used only if they are several pixels away fromland.



With the additional scattering contribution, the received radiance from an extendedsurface depends on wavelength, the solar illumination angle, the optical properties of theatmosphere, the instrument look angle and the angular distribution of the reflected radiationat the ocean surface. In most cases, the received radiance and the corresponding diffusetransmittance tD(λ, θ ) must be calculated numerically. Gordon et al. (1983) show fromnumerical calculations that, for Lambertian reflection of an external source from a uniformextended surface and for Rayleigh and aerosol single scattering, tDcan be approximated bythe following analytic expression:

tD(λ, θ ) = exp([ − τR(λ)/2 + τOZ

]sec θ

)(4.55)

Equation (4.55) provides an approximate, but useful solution. Examination of this solutionand of Figure 4.18 shows that the presence of scattering reduces the attenuation by afactor of 2, where this decrease is accompanied by an increase in the apparent FOV of theinstrument.

Gordon et al. (1983) also show that, although aerosol scattering also contributes to tD,this contribution is neglected because, for thin aerosols, the strong forward scattering meansthat the radiance is not appreciably attenuated, while for thick aerosols, the analysis breaksdown. From comparison of Equation (4.55) with numerical solutions, Wang (1999) foundthat, for non-absorbing or weakly absorbing aerosols and for τA 0.4 and θ 40°, theanalytic model is accurate to within 2%–3%. For τA 0.6 and θ 60°, Wang’s modifiednumerical model of the diffuse transmittance is accurate to within about 1%. For singlescattering, tD is used in the first term of Equation (4.41) to describe the attenuation of thesurface radiance.

4.9.2 Skylight

Skylight refers to the Rayleigh-scattered solar radiances that are associated with the bluecolor of the cloud-free sky. Because of skylight, the solar irradiance incident on the oceansurface divides into two parts: a direct solar term and a diffuse Rayleigh single-scatteringterm. Gordon and Clark (1981) combine these terms into a model for the downward planeirradiance Ed(0+) evaluated at a height z = 0+ just above the sea surface. They assume thatthe ozone attenuation occurs independently of the tropospheric Rayleigh scattering, thenshow from numerical calculations that Ed(0+) is given by

Ed(0+) = FS(λ) cos θS exp([ − τR(λ)/2 + τOZ

]sec θS

)= FS(λ) cos θS[tD(λ, θS)] (4.56)

Equation (4.56), which is used in the ocean color discussion, shows that the surface solarirradiance is also a function of tD.


5

Reflection, transmission and absorption at theatmosphere/ocean interface

5.1 Introduction

This chapter and the next address the case of solar reflectivity from the ocean interior. Forclear water, the present chapter addresses reflection and transmission at the interface, thendefines the terminology used to describe the backscatter of the transmitted radiation fromthe ocean interior. It also describes the attenuation of an irradiance propagating downwardin the interior. Using this terminology, Chapter 6 addresses how the properties of thebackscatter change when the water contains biological and other organic and inorganicconstituents. Both in the present chapter and in chapter 6, the focus is on the water-leavingradiance, which is the radiance from the interior that crosses the ocean/air interface, wherethis radiance is related to that received at aircraft and satellite sensors.

At all wavelengths, the properties of the radiance received at a satellite depend on thesmall-scale interaction of the radiation with the air/water interface. In the infrared, however,the ocean is so highly absorbing that absorption and emission are confined to the top 1–100 µm of the ocean, and in the microwave, they are confined to the top few mm. For thesebands and neglecting the atmosphere, the properties of the received radiance depend onlyon scattering and reflection at the ocean surface. Because in water, radiances propagate todepths of order 100 m only in the visible and near-ultraviolet, for the visible, the receivedradiances also depend on the backscatter of solar radiation in the ocean interior.

Specifically in the visible, two kinds of reflection take place (Figure 5.1). The first is thedirect or surface reflection at the interface of the solar radiance and skylight. The secondis the diffuse reflection associated with the water-leaving radiance that is generated by thepropagation of the incident solar radiance across the interface into the water column, wherea portion of this radiance is backscattered to recross the interface into the atmosphere. AsChapter 6 shows, the water-leaving radiance or luminosity of a water surface generatedby the interior scattering is essential to remote sensing in the visible and makes possiblethe retrieval of water column properties such as chlorophyll concentration. For clear oceanwater, this chapter considers two kinds of reflection, that which occurs from the oceansurface that occurs and the backscatter for radiances propagating to depths of 1–100 m.

To expand on luminosity, for clear skies and sunlight, Raman (1922) discusses howthe sea surface color is determined not by surface reflection of skylight, but by scattering

113


114 Reflection, transmission and absorption

Ocean surface

Scatterers

Directreflection

Water-leavingradiance

SensorSun

Fig. 5.1. Comparison of the direct reflection of sunlight at the sea surface with the diffuse reflectionassociated with the water-leaving radiance generated by scattering in the water column.

within the water column. As Section 5.4.1 shows, this occurs because the volume scatteringcoefficient for water has a form similar to Rayleigh atmospheric scattering while being160 times greater. For the Sun at zenith and neglecting absorption, the magnitude of thescattering coefficient means that a 50-m-deep column of water scatters as much light asabout 8 km of atmosphere, so that the water surface should be nearly as bright as the sky.Even including absorption, Raman shows that, under direct sunlight, scattering in the wateris the primary cause of the blue ocean color. For a dense cloud cover, the water columnscattering is reduced and the direct surface reflection of the forward-scattered sunlightpassing through the clouds determines the ocean color, so that the surface appears gray.

For radiation propagating in the water column, and from Equation (3.13), the absorptiondepth da is

da = a(λ)−1 (5.1)

To show the dependence of the absorption depth on wavelength, a non-dimensional depthis defined as d = da/λ and is plotted versus in Figure 5.2. The figure shows that d reachesits maximum in the visible and that, for λ > 3 µm, d < 1. Because of the strong absorp-tion outside of the ultraviolet visible/near-infrared wavelengths, transmission in the watercolumn is important only within a narrow window approximately centered on the visible.

For a flat interface and for the more complicated case where the surface is covered bywaves, Section 5.2 discusses the Fresnel equations and Snell’s law, which describe theinteraction of an incident radiance with the surface. Reflection from these waves generatessun glint or glitter, which is the random reflection of sunlight into the sensor. Section5.3 discusses the transmission of radiation across the interface. Section 5.4 discusses theabsorption and scattering properties of clear seawater, the transmission of an incidentradiance across the interface and its backscatter within the underlying water column, two


5.2 The interface 115

100 nm 1 μm 1 mm 1 m10 μm 100 μm 10 mm 100 mmlog λ

–2

0

2

4

6

8

visi

ble

log

d

Fig. 5.2. Wavelength dependence of the normalized attenuation depth d for 200 nm < λ < 0.5 m.The horizontal line shows where the absorption depth equals one wavelength.

kinds of remote sensing reflectances and the diffuse attenuation depth. Finally, because theair bubbles associated with a foam-covered interface occur both at the surface and withinthe water column, Section 5.5 describes reflection from foam.

5.2 The interface

For electromagnetic radiation incident on the air/water interface, depending on the interfaceproperties, some energy is reflected or scattered, some is absorbed and some is transmittedthrough the interface. For a radiance incident at a particular θ on a flat surface, the reflectionis mirror-like or specular, meaning that the angle of incidence equals the angle of reflection.For a rough surface, the reflection process is more complicated. From Rees (2001), thereare at least two ways of describing rough surfaces. The first is a general criterion fordistinguishing between rough and smooth surfaces, called the Rayleigh criterion, whichdiffers from the Rayleigh criterion for the resolving power of lenses described in Section3.5.1. The second describes the reflection of a radiance from a surface covered with capillaryand gravity waves.

In the following, Section 5.2.1 defines roughness using the Rayleigh criterion, anddescribes reflection and scattering from smooth and rough surfaces. Then, for a specularor flat surface, Section 5.2.2 discusses Snell’s law, which describe the reflection and trans-mission angles of a radiance incident on the surface at a specific angle, and the Fresnelequations, which describe the angular dependence of the magnitudes of the reflected andtransmitted radiance. Section 5.2.3 describes reflection from an interface covered with cap-illary and short gravity waves. If this surface can be approximated as a mesh of small flat



θ

ση

Fig. 5.3. Geometry for discussion of the Rayleigh criterion for scattering and specular reflection froma surface. (Adapted from Figure 3.10, Rees (2001.)

facets inclined at different angles to the horizontal where each facet serves as a specularreflector, then numerical solutions exist for the scattered radiance.

5.2.1 General scattering considerations

For surface reflection and scattering, the Rayleigh roughness criterion determines whetherthe surface is rough or smooth. Following Rees (2001), Figure 5.3 shows a radiance incidenton a surface, where ση is the rms surface height. In general, for a radiance incident at anangle θ and wavelength λ, the scattering is specular if

(ση cos θ )/λ < 1/8 (5.2)

If (5.2) is satisfied, which means that the roughness scale in the incident direction is smallcompared with the wavelength, then the surface is smooth, otherwise it is rough. Equation(5.2) shows that the scattering depends on three variables, ση, θ and λ. For ση and θ

constant, as λ increases, surface roughness becomes less important. For ση and λ constant,the roughness depends on θ . A surface that is rough at near-vertical incidence angles canbe smooth at near-grazing angles. In the limiting case where Equation (5.2) is not satisfiedat any angle, the reflection is Lambertian.

For four surfaces with increasing roughness, Figure 5.4 shows the reflection of an incidentradiance. Figure 5.4(a) shows specular reflection from a perfectly flat surface, where thereflected energy propagates at an angle equal and opposite to the incidence angle. Thisis the case of pure coherent specular scattering or reflection, meaning that the reflectedbeam has a specific phase relation with the incident radiance (Rees, 2001). For the small-roughness case, Figure 5.4(b) shows that the reflection occurs partly by coherent scatter inthe specular direction and partly by incoherent or diffuse scatter in all directions, whereincoherent scatter has a random phase relation with the incident radiance. As the roughnessincreases, specular scatter decreases and incoherent scatter increases. For a rougher surface,Figure 5.4(c) shows that the scatter becomes quasi-Lambertian, meaning that most of thescatter is random, with only a small coherent component in the specular direction. Finally,



Specular reflector

Quasi-Lambert reflector

Quasi-specular reflector

Coherent scatter Incoherent scatter

(a) (b)

(c) (d)

Lambert reflector

Fig. 5.4. Limiting forms of reflection and scattering from a surface. (a) Specular reflection, (b) quasi-specular, (c) quasi-Lambertian and (d) Lambertian. The Lambertian examples are valid only for anextended surface.

Figure 5.4(d) shows the idealized case of reflection from a perfectly rough surface, wherethe reflection is completely Lambertian. In the visible/infrared, examples of surfaces thatcan be approximated as Lambertian include foam and clouds.

5.2.2 Specular reflection and transmission at a planar interface

The reflection and transmission of radiation at a flat interface is described by two differentequations: Snell’s law, which governs the angles at which an incident radiance is reflectedand refracted, and the Fresnel equations, which determine the magnitudes of the reflectedand refracted radiances as a function of incidence angle.

Beginning with Snell’s law, consider the ideal case of a flat planar interface as in Figure5.4(a), with air above and water below, where the properties in each medium vary only withdistance upward or downward from the interface. This idealized physical situation appliesto both a flat surface and a rough surface approximated as a large number of small facets.Following Mobley (1994), the air/water interface is assumed to be an infinitesimally thinslab, across which the real part of the index of refraction changes in a stepwise mannerfrom its atmospheric value to its water value.

Also from Mobley, the incident radiance is assumed to interact linearly with the interface,so that the magnitudes of the reflected and transmitted radiances increase linearly with thatof the incident radiance, and nonlinear effects such as frequency doubling do not occur.Because the discussion is restricted to the macroscopic, photon–atom interactions at thesurface are not considered. Finally, the ocean is assumed to be sufficiently thick thatall of the transmitted radiation is absorbed before reaching the ocean bottom. For these



Interface

Transmitted

ReflectedIncident

θ i θr

θ t

nanw

Air

Water

Fig. 5.5. Reflection and refraction at a specular interface for an air-incident radiance.

conditions, the properties of the reflected and transmitted radiation are derived from thereal and imaginary parts of the indices of refraction of air and water.

Figure 5.5 shows the familiar figure for the specular reflection and transmission of anarrow beam of radiation incident on a flat, planar interface, where the term “narrow beam”means that the incident radiance occupies a small solid angle. The upper half plane is air;the lower half is water. The task is to describe the reflection and refraction of this beamas it intersects the ocean surface. This description divides into two parts: the geometry ofthe interaction with the surface and the relative magnitudes of the reflected and refractedradiances given by the Fresnel relations.

On Figure 5.5, na and nw are the real part of the index of refraction for air and water;θi, θr and θt are respectively the angles of incidence, reflection and transmission. Snell’slaw describes the geometry of the reflection, where the incidence and reflection angles areequal and opposite, so that θi = −θr. The transmitted radiance is refracted to an angle θt,given by

nw/na ≡ n = sin θi/ sin θt (5.3)

To simplify the following discussion, in Equation (5.3), n is set equal to the ratio of therefraction indices. For the visible wavelengths where na = 1 and nw 1.34, the solutionfor θt is found by setting n = 1.34. This value of n means that the speed of light in water isabout 75% of the speed in vacuum/atmosphere. Because n > 1 for an air-incident radiance,θt < θi.

The Fresnel equations give the magnitudes of the reflected and transmitted radiances rel-ative to the magnitude and incidence angle of the incident radiance. In the visible/infrared,the coefficients given below are constant. However, as Chapter 9 discusses, for low fre-quencies in the microwave, these coefficients depend on salinity. The following discussionfirst considers an unpolarized radiance incident on a specular surface, then the case of V-pol



and H-pol incident radiances. For the unpolarized case, the radiance reflectance r(λ, θr) isdefined as the ratio of the reflected and incident radiances:

r(λ, θr) = Lr(λ, θr)/Li(λ, θi) (5.4)

From the Fresnel equations, r (θi) can be written as the following function of θi and θt (Bornand Wolf, 1999; Mobley, 1994):

r(θi) = (1/2)([sin(θi − θt)/ sin(θi + θt)]

2 + [tan(θi − θt)/ tan(θi + θt)]2)

(5.5)

In (5.5), θi = 0 and θi and θt are related by Snell’s law. When the incident radiance isnormally incident, the reflectance becomes

r(0) = (n − 1)2/(n + 1)2 (5.6)

For reflection of a polarized incident radiance, the Fresnel relations are given by theV-pol and H-pol reflection coefficients ρV (θi) and ρH (θi) defined in a similar manner toEquation (5.4). Omitting the subscript on θi for brevity, then, for θ > 0, these coefficientsare written as follows (Stewart, 1985; Born and Wolf, 1999):

ρH(θ ) = [(p − cos θ )2 + q2

]/[(p + cos θ )2 + q2

]ρV(θ ) = [

(ε′ cos θ − p)2 + (ε′′ cos θ + q)2]/[

(ε′ cos θ + p)2 + (ε′′ cos θ + q)2](5.7)

In (5.7), ε′ = n2 − χ2 and ε′′ = 2nχ are the real and imaginary parts of the complexdielectric constant defined in Equation (3.8). The terms p and q are given by

p = (1/√

2)[(ε′ − sin2 θ )2 + ε′′2]1/2 + [ε′ − sin2 θ ]1/2

q = (1/√

2)[(ε′ − sin2 θ )2 + ε′′2]1/2 − [ε′ − sin2 θ ]1/2 (5.8)

For normal incidence, θ = 0 and the concept of V and H polarization loses its meaning, sothat, from (5.6), ρH(0) = ρV(0) = r(0).

For n = 1.34 and for an air-incident radiance, Figure 5.6 shows the θ -dependence of r,ρV and ρH. The figure shows that the polarized reflectances lie above and below r, and that,at θ ∼= 60 °, called the Brewster angle, ρV = 0. A useful property of the reflectance is that,for θ 50°, r is nearly constant at r ∼= 0.02, so that, for these angles, about 98% of theincident radiance is transmitted. For θ 50°, r increases rapidly.

5.2.3 Reflection from capillary waves

The reflectance of solar radiation from a wind-roughened ocean surface generates sun glint,which refers to the scattering of the incident solar radiance from the surface into the sensordirection. Because at all observational wavelengths, sun glint can overwhelm the reflected



Incidence angle (deg)0 10 20 30 40 50 60 70 80 90

0

0.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

Ref

lect

ance

H-pol V-pol

Unpolarized

Fig. 5.6. Radiance reflectance from a specular air/water interface as a function of incidence angle forthe visible wavelengths, and for unpolarized, H-pol and V-pol incident radiance.

or emitted ocean surface radiance, it must be avoided or masked. Accounting for sun glintis done as follows.

For a wind-roughened ocean surface, the concept of a unique reflection angle loses itsmeaning. To address this problem, Mobley (1995, 1999) assumes that the ocean surface iscovered only by wind-driven capillary waves with their slopes described by a wind-speeddependence similar to that given in Equations (2.6). He further assumes that the wavesurfaces can be approximated as a collection of congruent isosceles triangles, called facets,each of which serves as a specular reflector. This approximation is valid if the length scale ofeach facet is much greater than λ and if the deviation of the approximating planar facet fromthe actual wave surface is much less than λ (Rees, 2001). Equivalently, the approximationholds if the radius of curvature Rc of that part of the surface approximated by the facetsatisfies

Rc λ (5.9)

When (5.9) is satisfied, the radiation fields at the surface can be approximated by the fieldsthat occur at a tangent plane (Valenzuela, 1978; Wu and Smith, 1997). Since the shortwater wavelengths λw and their curvatures are in the range 1–10 cm, while in the vis-ible/infrared the radiation wavelengths λ are less than 20 µm, this condition is easilysatisfied. In contrast and as Sections 9.4 and 10.6.2 discuss for the passive and activemicrowave, because of the longer microwave wavelengths, this condition is not neces-sarily satisfied. Instead, scattering takes place from the short surface wavelengths that do



Fig. 5.7. The angular distribution of the reflection of a radiance incident on a surface with its roughnessproportional to wind speed. The source radiance is located on the far side of the hemisphere at θ =40° . Each box on the hemisphere represents an area 10° in zenith angle and 15° in azimuth. (Figure 2from Mobley (1999), C© Optical Society of America, used with permission.)

not satisfy Equation (5.9), and reflection takes place from the larger elements of surfacearea.

For a narrow beam of radiance in the visible/infrared incident on the surface at an angleθ and with the assumption that Fresnel reflection occurs from each facet and where multiplereflections are allowed to occur among the facets, Mobley (1999) numerically solves forthe angular distribution of the reflected radiances. For a source radiance at θ = 40° inan area that Mobley calls a quad, measuring 10° in zenith by 15° in azimuth, and forwind speeds U = 0, 2, 5 and 10 m s−1, Figure 5.7 shows the resultant distributions of thereflected radiances. For U = 0 or specular reflection, the figure shows the distribution ona hemisphere of the reflected radiances for 100 ray paths drawn from the source quad andreflected at the origin, where each dot shows the angular location of a single reflection. Forthis case, all of the incident radiances are reflected into the conjugate quad located at theequal and opposite angle from the incident radiance.

When the Sun is the source radiance, the reflection of the Sun at the origin alongthe conjugate angle is sometimes called the sub-solar spot. For the other three cases,5000 ray paths are used to construct the figures. These show that as the wind speedand capillary roughness increase, the angular extent of the reflected radiances increases,while the distribution of the reflected radiances remains centered on the conjugate quad.



For U = 10 m s−1, the angular distribution of the reflected radiances extends almost 120°in azimuth angle and slightly more than 90° in zenith angle.

By the principle of reciprocity, the opposite is true, in that, depending on wind speed,a sensor located in the solid angle defined by the source quad will observe radiancesfrom all of the darkened solid angles. For an instrument operating at any of the observingwavelengths, then, depending on wind speed and the look and Sun angles, the surface candirectly reflect sunlight into the sensor. This means that in either the instrument design orits data processing, care must be taken to avoid both direct solar reflection and sun glint.

5.3 Transmission across an interface

Within the visible and the adjacent ultraviolet wavelengths and depending on the waterclarity, solar radiances crossing the ocean interface can propagate to depths of order 100 mwithin the water column. As Section 5.4 describes, some of this radiation is backscattered,which generates an upward-propagating irradiance incident on the interface from below.Because an understanding of these interfacial processes is critical to biological remotesensing, this section discusses the change in properties associated with a radiance incidenton an interface both from above, called an air-incident radiance, and from below, called awater-incident radiance (Mobley, 1995). In the following, Section 5.3.1 discusses the caseof a radiance on an air–water specular surface from below and above, and Section 5.3.2discusses refractive convergence and divergence. Then, with some approximations, Section5.4 extends these concepts to the real ocean.

5.3.1 Radiance incident from below and above the interface

For an upward radiance incident on a specular interface, the propagation direction inFigure 5.5 is reversed, and Snell’s law becomes

sin θi/ sin θt = 1/n = 0.75 (5.10)

For an unpolarized upward radiance and from Equation (5.10), Figure 5.8 shows thedependence of r on incidence angle. For θi 30°, the figure shows that r is nearly constantat about 0.02, then at θi = 49° rises abruptly to r = 1, so that, for θi 49°, total reflectionoccurs. Consequently, an upward radiance incident on the interface at θi = 49° is refractedto θi = 90° on the atmosphere side of the interface so that the radiance is parallel to theinterface. For θi 49°, the radiances are internally reflected and there is no transmission, sothat as Figure 5.9(a) shows for the upward-propagating case, only radiation propagatingwithin the cone that subtends a total angle of about 98° crosses the interface. Once above theinterface, it is refracted to propagate within the entire hemisphere. Beneath the surface, anyradiance propagating in directions outside of this cone, called the shadow zone, is internallyreflected and does not cross the interface. This angular broadening of the radiances crossingthe interface is called refractive divergence.


5.3 Transmission across an interface 123

Incidence angle (deg)0 10 20 30 40 50 60 70 80 90

0

0.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

Ref

lect

ance

Fig. 5.8. The reflectance as a function of angle for the visible wavelengths and for an unpolarizedradiance incident on the water/air interface from below.

shadow zone

surface

Snell’s window

Snell’s cone

water

air

shadow zone

surface

Snell’s window

Snell’s cone

water

air

(a) (b)

Fig. 5.9. Radiation incident on the air/ocean interface from below (a) and above (b). The figure showsthe shadow zones, Snell’s cone and Snell’s window. See the text for further description.

For the reverse case of a radiance incident on a specular interface from above,Figure 5.9(b) and Equation (5.3) show that, for radiances incident at θi on a specularsurface, the angle of the transmitted radiance varies from 0° for a normal incidence angle,to 49° for grazing incidence. This means that, beneath the water surface, all of the inci-dent radiances are mapped into a 98° cone, so that, at the surface, the entire above-waterhemisphere is mapped into a disk, called Snell’s window (Sabbah et al., 2006). This diskis visible when swimming underwater and is shown in the RaDyO (2009) video.



Interface

Ocean

Air

Shadow zone49oShadow zone

Fig. 5.10. Radiation incident from below on the ocean surface. Because of the change in n acrossthe interface, radiances at θ > 49° are internally reflected and do not propagate across the interface,giving rise to a shadow zone within which all incident radiances are reflected.

For another view of this phenomenon, Figure 5.10 shows the refraction of several raypaths incident at different angles on a flat ocean/atmosphere interface. The figure showsthat the total reflection that occurs for θi > 49° generates the shadow zone, which is thesolid angle region within which incident radiances are totally reflected. Because radiancesincident from below within the shadow zone do not propagate across the interface, ifthe irradiance incident from below has a Lambertian distribution, then almost half of theincident radiation does not cross the interface. Figures 5.9 and 5.10 also suggest that lightpropagating upward within a narrow solid angle toward the interface is defocused into a largesolid angle in the atmosphere and vice versa, described above as refractive convergence anddivergence. Because of the importance of this phenomenon to the water-leaving radiance,the next section discusses it in detail.

5.3.2 Refractive convergence and divergence

For a narrow beam of unpolarized radiance incident from below and above on a planarinterface separating two media with indices of refraction n1 and n2, this section derives therelation between the radiances on the two sides of the interface.

Assume that a radiance is incident at an angle θ1 on an area AS at the interface(Figure 5.11). A fraction of the incident radiant flux is transmitted at an angle θ2. IfT (θ1) = 1 − r(θ1) is the unpolarized interface transmittance, where r is shown in Figures5.6 and 5.8, then at the interface the relation between the radiant fluxes 1 and 2 is

2 = T (θ1)1 (5.11)

For incidence angles less than about 40° and for an upward or downward radiance respec-tively incident on either air or water, T 0.98. The corresponding radiances propagatewithin the associated solid angles i , where i = 1, 2 indicates different sides of the


5.3 Transmission across an interface 125

InterfaceOcean

Air

ΔΩ1

θ2

θ1

ΔAS n2

ΔΩ2

n1

Φ1 , L1

Φ2 , L2

Fig. 5.11. An upward propagating radiance focused on an element of surface area at the ocean/airinterface, and the transformation of this radiance through refractive divergence as it crosses theinterface.

interface. Using the form of the radiance from Equation (3.16) and referring to Figure 5.11,Equation (5.11) may be written as

L2 cos θ2 2 = T (θ1)L1 cos θ1 1 (5.12)

By definition,

i = sin θi θi φi (5.13)

For both sides of the interface, calculation of i and the radiances proceeds as follows.Because the azimuthal angles φi lie in the plane of the interface, they are independent ofSnell’s law so that φ1 = φ2. The relation between the θi is determined from Snell’s lawin Equation (5.3):

sin θ1 = (n2/n1) sin θ2 (5.14)

Squaring both sides of (5.14), differentiating, and substituting i from Equation (5.13)into the result yields

1 cos θ1 = (n2/n1)22 cos θ2 (5.15)



Equation (5.15) gives the relation between the solid angles, incidence angles and refractionindices on the two sides of the interface and is called Staubel’s invariant (Mobley, 1994,p. 160).

Substitution of Staubel’s invariant in (5.15) into (5.12) gives

L2 = (n2/n1)2TL1 (5.16)

For T = 1, Equation (5.16) is called the fundamental theorem of radiometry (Mobley, 1994,p. 161). For the visible wavelengths and the case shown in Figure 5.11, where L1 is theupward radiance just beneath the surface, L2 is the water-leaving radiance, n = n1/n2 =1.34, and for θ1 < 40° or T 0.98, Equation (5.16) becomes

L2 = T L1 /n2 ∼= 0.55L1 (5.17)

For the opposite case of an air-incident radiance at θ < 50°, Equation (5.16) can be rederivedto yield

L1 = n2T L2∼= 1.76L2 (5.18)

In Equation (5.18), L1 and L2 are again respectively the radiances in the water and air.Examination of (5.17) and (5.18) shows that, for air-incident radiance, the transmittedradiance is reduced almost by half, whereas for the water-incident radiance, it is nearlydoubled. This illustrates an important difference between the transmitted radiant flux andthe radiance, in that, for the water-incident case and from Equation (5.11), the transmittedflux is reduced only by T or by a factor of 0.98, but, because this energy propagates withina larger solid angle on the atmosphere side of the interface, L2 from Equation (5.17) isreduced by 0.55. For the opposite case of an air-incident radiance, the radiant flux is againreduced by 0.98, while, from Equation (5.18), the transmitted radiance is nearly doubled.This enhancement is the reason never to look at the Sun from underwater, since its radianceis nearly doubled.

5.4 Absorption and scattering properties of seawater

For a range of wavelengths roughly centered on the visible, this section describes theabsorption and scattering of light within the water column. Specifically, Section 5.4.1discusses the absorption and scattering properties of optically clear seawater, where opti-cally clear means devoid of particles and dissolved substances. Smith and Baker (1981)summarize research showing that, in the visible, clear fresh water and seawater have thesame absorption and scattering properties, with no differences between fresh and saltwa-ter occurring for λ > 375 nm, and inconclusive differences occurring at shorter wave-lengths.

Section 5.4.2 describes how the absorption and scattering interact with the downwellingsolar irradiance to generate an upwelling irradiance. Section 5.4.3 describes how the passagethrough the interface modifies this irradiance to produce a water-leaving radiance Lw (λ, θ )in the atmosphere. Section 5.4.4 describes two kinds of remote sensing reflectance used in


5.4 Absorption and scattering properties of seawater 127

satellite retrievals and Section 5.4.5 concludes the section with a discussion of Kd(λ), thediffuse attenuation coefficient that governs the downward propagation of an irradiance inthe water column.

The oceanic optical and remote sensing properties divide into inherent optical properties(IOP) and apparent optical properties (AOP) (Mobley, 1994, 1995). The inherent propertiesdepend only on the nature of the medium and include the absorption, scattering and atten-uation coefficients and the Fresnel reflectances. The apparent optical properties depend onthe medium and on the directional structure of the ambient light field. In contrast, if theproperty is invariant with respect to either the radiance or observational direction, it is anIOP. The radiative transfer equation relates the AOP to the IOP. As this chapter discusses,examples of AOP used in oceanography are the diffuse attenuation coefficient Kd(λ), theirradiance reflectance immediately below the surface R(λ, 0−) and the remote sensingreflectance Rrs(λ).

For the IOP, even though the oceanic terminology used to describe extinction, absorp-tion, and scattering differs from that used in the atmosphere, the mathematical formulationis the same. In the ocean, a(λ) is the volume absorption coefficient, b(λ) is the scatteringcoefficient and c(λ) is the attenuation coefficient, corresponding to the atmospheric extinc-tion coefficient. The coefficients a, b and c have units of m−1. For the volume scatteringfunction, the terminology recommended by the International Association for Physical Sci-ences of the Ocean (IAPSO) is β (α, λ), with units of m−1 sr−1, which is the same symbolas that used in the atmosphere (Mobley, 1995). Further, the atmospheric scattering phasefunction P (α) is written for the ocean as β(α), also with units of sr−1 (Mobley, 1994).In the next chapter, subscripts will be added to these variables to distinguish between thetwo cases of absorption and scattering from clear seawater and from seawater containingsuspended and dissolved material.

5.4.1 Properties of clear seawater

From measurements of clear water in Crater Lake and the Sargasso Sea (Smith and Baker,1981), Figure 5.12 shows the dependence on wavelength of the absorption and scatteringcoefficients for 200–800 nm, where the vertical lines show the boundaries of the visiblespectrum. Figure 5.12(a) shows that the absorption has a minimum between 300 and 600nm, and increases rapidly at shorter and longer wavelengths. Within the visible wavelengths,the absorption minimum is offset toward the UV, where absorption increases within the red(600–700 nm) and within the short UV wavelengths. For comparison, Figure 5.12(b) showsthe volume scattering coefficient, which rapidly decreases with increasing wavelength.

Mobley (1994, p. 103) gives the volume scattering function, the phase function and thescattering coefficient of seawater as

β (α, λ) = 4.72 × 10−4 (λ0/λ)4.32 (1 + 0.835 cos2 α) m−1sr−1 (5.19)

β(α) = 0.06225(1 + 0.835 cos2 α) sr−1 (5.20)



0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Visible

(b)

Sca

tterin

g co

effic

ient

(m

–1)

Wavelength (nm)200 300 400 500 600 700 800 200 300 400 500 600 700 800

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5(a)

Abs

orpt

ion

coef

ficie

nt (

m–1

)

Visible

Wavelength (nm)

Fig. 5.12. The wavelength dependence of (a) the absorption and (b) the scattering coefficient for pureseawater. The vertical lines mark the visible spectrum. (Data from Smith and Baker (1981), courtesyof Curt Mobley.)

and

b (λ) = 7.58 × 10−3 (λ0/λ)4.32 m−1 (5.21)

In the above, λ0 = 400 nm. Comparison of Equations (5.20) and (5.21) with the Rayleighscattering described in Equation (4.23) shows that for both the atmosphere and ocean,molecular scattering strongly increases with decreasing wavelength. Given these similar-ities, oceanic scattering is sometimes incorrectly described as Rayleigh scattering. But,because seawater is a thousand times denser than air, its scattering properties are derivedfrom the Einstein–Smoluchowski consideration of small-scale fluctuations in the liquid, sothat the derivation differs greatly from that of Rayleigh scattering (Mobley, 1994).

The preceding equations allow the verification of Raman’s (1922) luminosity argumentin Section 5.1. Equation (4.56) shows that the skylight due to Rayleigh scatter is proportionalto τr(λ), which, as Equation (4.10) shows, equals the integration of the volume scatteringcoefficient across the atmosphere. For the ocean, b(λ) from Equation (5.21) is now usedto define an optical thickness analogous to τR. For λ = 400 nm and assuming that b(400)is independent of depth, if b is integrated over the top 50 m of the water column, then,from Equation (4.10), τw (400) = 0.379. Comparison of this number with the Rayleighoptical depths in Table 4.2 shows that the τw derived from a water column that is 50 m deepapproximately equals the τR generated from the entire height of the atmosphere. Thus, fora cloud-free sky and relatively clean water, the water surface and sky should be equallybright.

Within the water column, the attenuation depth da has a strong λ -dependence. For300 nm λ 800 nm, Figure 5.13 shows from Equation (5.1) the dependence of da onλ for a(λ) derived from two data sets; one from the field, the other from the laboratory.The lower curve is the oceanic Smith and Baker (1981) data set described above; the uppercurve is the Pope and Fry (1997) laboratory measurements of the absorption of clean freshwater in the range 380–700 nm. Dickey et al. (2011) point out the difficulty of making



300 350 400 450 500 550 600 650 7000

25

50

75

100

125

150

175

200

225

250

Wavelength (nm)

Abs

orpt

ion

dept

h (m

)

Visible

Fig. 5.13. The absorption depth for seawater; the horizontal dashed line marks the 10-m depth. Theupper curve shows the data from the clear-water case of Pope and Fry (1997); the lower curve, theclean-seawater data from Smith and Baker (1981), courtesy of Curtis Mobley. See the text for furtherdescription.

these laboratory measurements, especially in the vicinity of the absorption minima at420 nm, where da = 225 m, and observe that the Pope and Fry (1997) measurementsare the most accurate for pure water to date. For λ > 520 nm, the two curves are nearlyidentical; for wavelengths shorter than 520 nm, the curves diverge.

The horizontal line near the bottom of Figure 5.13 shows the 10-m absorption depth,so that, for light to propagate to depths greater than 10 m, its wavelength must fall in therange 350 nm ≤ λ ≤ 550 nm. This means that, in the visible, light penetration is stronglybiased toward λ < 550 nm, so that, in the ocean, light penetration occurs. The absorptiondata sets also show that da = 3 m at 640 nm and da = 0.4 m at 750 nm, so da decreasesrapidly with increasing wavelength.

5.4.2 Irradiance reflectance

This and the following section first define the plane irradiance reflectance R(λ, z), thenuse this reflectance to relate the water-leaving radiance to the incident solar irradiance andthe seawater scattering and absorption properties. Although the concept of irradiance ismuch simpler than radiance, because R(λ, z) is an apparent optical property that dependson the directional dependence of the incident light field, it is more difficult to calculate.



Ocean

Hypothetical reflector

Ocean interface

Atmosphere

Ed( )

Eu( )

λ

λ

Fig. 5.14. The location of and terminology for a hypothetical irradiance reflector located just beneaththe interface. See the text for further description.

Following Zaneveld (1995, Equation 27), R(λ, z) is defined as the ratio of the upwellingplane irradiance Eu(λ, z) to the downwelling irradiance Ed(λ, z) :

R(λ, z) = Eu(λ, z)/Ed(λ, z) (5.22)

Just below the interface, the irradiance reflectance is given by R(λ, 0−), where z = 0 refersto the water side of the interface, and, in practical terms, to a sufficient distance below theinterface so that water waves do not cause the optical measuring device to emerge throughthe surface.

As Figure 5.14 shows, the reflectance R(λ, 0−) can be thought of as a hypotheticalreflector located just below the ocean surface that represents all of the scattering andabsorption processes occurring in the water column. Its location separates the reflector fromthe problem of transmission through the interface. This reflectance is measured directly withspectral radiometers and, as the next chapter shows, is a function of such water properties asthe concentrations of chlorophyll and suspended sediments. Of equal importance, R(λ, 0−)is directly related to the water-leaving radiance, which can be measured by aircraft orsatellite. To derive the properties of this reflector, the spectral backward scattering coefficientbb(λ) is next defined (Mobley, 1995).

Similarly to the definition of the atmospheric scattering coefficient in Equation (4.16),bb(λ) is the integral of β(α, λ) in (5.19) over the upper half plane, or over π/2 ≤ α ≤ π ,where π is the backscatter direction, so that

bb(λ) = 2π

∫ π

π/2β(α, λ) sin α dα (5.23)

The reason for introducing bb(λ) is that, in combination with a(λ), it leads to a conceptuallysimple model for R(λ, 0−). To first order in the water column, radiative processes are abalance between absorption and scattering. If a downwelling photon is absorbed, it cannotbe scattered, but, if a photon is backscattered by suspended material or water molecules, it



becomes an upwelled photon (Mobley, 1994). The simplest models of this process assumethat R(λ, 0−) can be written as

R(λ, 0−) ≡ R(λ) ∼ bb(λ)/a(λ) (5.24)

In Equation (5.24), R(λ, 0−) is directly proportional to bb(λ) and inversely proportionalto a(λ), since for a large backscatter and small absorption, a strong upwelling irradianceis more likely than for the opposite case (Zaneveld, 1995; Mobley, 1994, pp. 493–496;Roesler and Perry, 1995). In the following discussion, R(λ) replaces R(λ, 0−). Gordonet al. (1988) describe a series of calculations for different optical properties of the waterand find that for solar zenith angles θS ≥ 20,

R(λ)

Q=

2∑i=1

li

(bb

a + bb

)i

(5.25)

In (5.25), l1 = 0.0949 and l2 = 0.0794, where these constants are derived numericallyand are called geometrical factors (Maritorena and Siegel, 2006). The factor Q can beconsidered as the factor that converts an upward irradiance into a vertically propagatingradiance, and, for ideal Lambertian conditions, Q π . For a range of θS and sea states,Mobley (1994, p. 495) shows that Q ranges from 3 to 6.

From Equation (5.25) and given the clear water absorption a, R(λ ) is easily calculated.Setting Q π , Figure 5.15 shows the reflectance curve for the Smith and Baker (1981)Pope and Fry (1997) data sets. The figure shows that, for both data sets and for λ greaterthan about 550 nm, the reflectance is near zero; as λ decreases, R(λ ) rises to its peak near400 nm. Because the peak in the solar radiance occurs at about 490 nm, the upwellingradiance generated by the product of the solar irradiance with seawater R(λ ) lies between400 and 490 nm and has the color blue. In contrast, the Pope and Fry (1997) curve forclear fresh water has a strong peak at about 415 nm, suggesting that the associated color isshifted to a deep blue.

Morel et al. (2010) shows that the clearest natural ocean waters occur in the SouthPacific gyre near Easter Island. These waters have very low concentrations of chlorophylland other dissolved and suspended substances. Their field investigation shows that, becauseof the low values of the absorption coefficient around the spectral minimum described byPope and Fry (1997), these waters have a deep blue or almost purple color (Dickey et al.,2011). For the clear fresh water in the 600-m-deep Crater Lake in Oregon, Strayed (2012,p. 271) describes the color as having “the most unspeakably pure ultramarine blue I’d everseen”.

5.4.3 Water-leaving radiance

As defined in Equation (4.56), Ed(0+) is the solar irradiance just above the interface.Therefore, the solar irradiance just below the interface Ed(0−) is approximately given by

Ed(0−) = T Ed(0+) (5.26)



400 450 500 550 600 650 700

0.05

0.1

0.15

0.2

0.25

Wavelength (nm)

Ref

lect

ance

Fig. 5.15. The subsurface reflectance of clear seawater, calculated from Equation (5.24). Upper curve,the clear-water case of Pope and Fry (1997); lower curve, clear-seawater data from Smith and Baker(1981), courtesy of Curtis Mobley. See the text for further description.

For the solar zenith angle θS < 50° and U < 16 m s−1, Kirk (1996, Figure 2.10) shows thatT is nearly constant at about 0.98, so that Ed(0−) is a linear function of Ed(0+). For largervalues of θS, Kirk shows that T is a function of θS and U.

Given Ed(0+) and R (λ), Equations (5.22) and (5.26) can be solved for Ed(0−) andEu(0−). If the radiance distribution within Eu(0−) is assumed to be quasi-Lambertian,then from Equation (3.17) the upwelling radiance just beneath the surface is Lup(λ, 0−) =Eu(0−)/Q, where Q is from Equation (5.25), so that

Lup(λ) = R(λ)T Ed(λ, 0+)/Q (5.27)

Substitution of Equation (5.27) into (5.17) shows that, just above the surface, the water-leaving radiance Lw(λ) becomes

Lw(λ, 0+) = T 2R(λ)Ed(λ, 0+)/n2Q ∼= 0.54R(λ)Ed(λ, 0+)/Q (5.28)

In (5.28), the factor T2 occurs because the solar radiation crosses the interface in thedownward direction and the upwelled radiation crosses it in the upward direction. In theright-hand term, the quantity 0.54 is derived from the squared ratio of T = 0.98 and n =1.34, again for the visible wavelengths.

Equation (5.28) gives the water-leaving radiance in terms of the downwelling radianceand the reflectance. Lw(λ) is further refined by definition of the normalized water-leaving



radiance [Lw(λ) ]N, which is sometimes written as nLw. In the derivation of [Lw(λ)]N,Lw(λ) is rewritten from substitution of Ed (0+) from (4.56) into (5.28), yielding

Lw(λ) = [T 2R(λ)FS(λ)/n2Q

]exp

[(−τr(λ)/2 + τOZ) sec θS

]cos θS (5.29)

In Equation (5.29), the terms in the left-hand square brackets are nearly independent ofθS; the other terms are the product of cos θS and the exponential term, which is the single-scattering diffuse transmittance tD(λ, θS) defined in Equation (4.55). Following Gordon andClark (1981), [Lw(λ)]N is derived by division of Lw(λ) in (5.29) by tD(λ, θS)cos θS so that

[LW(λ)]N = LW(λ)/[

tD(λ, θS) cos θS]=T 2R(λ) FS(λ)/(n2Q) (5.30)

Comparison of Equations (5.29) and (5.30) shows that [LW(λ)]N is independent of θS andcan be thought of as the radiance that exits the ocean for the case of a non-attenuatingatmosphere and the Sun at zenith (Gordon and Voss, 1999). The importance of [LW(λ)]N

is that it removes the θS term from LW and permits comparison of water-leaving radiancemeasurements made at different Sun angles.

5.4.4 Two kinds of remote sensing reflectance

From the above, the following defines two kinds of remote sensing reflectance. The first isthe remote sensing reflectance Rrs(λ), which is the ratio of LW(λ) to the solar irradianceat the surface, is a linear function of R(λ) and is derived from Equations (5.25) through(5.30):

Rrs(λ) = LW(λ)

Ed(λ, 0+)= [LW(λ)]N

FS(λ)= T 2R (λ)

n2Q= T 2

n2

2∑i=1

li

(bb(λ)

a(λ) + bb(λ)

)i

(5.31)

Unlike R (λ), Rrs(λ) has dimensions of sr-1. In the derivation of Equation (5.31), Ed(λ, 0+) iseither directly measured or taken from Equation (4.56); R(λ) is from (5.25). The reflectanceRrs(λ) is calculated just above the surface and because of its application to the analysis ofshipboard observations is frequently used in the literature. This form of the reflectance Rrs(λ)provides a connection between the satellite-measured AOP and the in-water-measured IOP.

Second, from Gordon and Voss (1999), the extraterrestrial reflectance ρW(λ) is the ratioof LW(λ) to the solar irradiance at the TOA, as in

ρw(λ) = πLw(λ)/[FS(λ) cos θS] = πT 2R(λ) tD(λ, θS)/n2Q (5.32)

In (5.32) the factor of π converts the solar irradiance to units of radiance and the thirdterm is derived from substitution of LW(λ) from (5.30). The term ρW(λ) is the ratio ofthe water-leaving radiance to the extraterrestrial solar radiance; its advantage is that it isdimensionless.

The analogous normalized reflectance [ρW(λ)]N is defined as

[ρW(λ)]N = ρW(λ)/tD(λ, θS) = π [LW(λ)]N/FS(λ) = πT 2R(λ)/(n2Q) (5.33)



which is the reflectance for the sun at zenith. The right-hand side of the equation showsthat [ρW(λ)]N is a function solely of the surface parameters and the irradiance reflectance.Finally, from Equations (5.31) and (5.33) and to a good approximation, the relation betweenthe remote sensing and normalized reflectances is [ρW(λ)]N = πRrs(λ) (Gordon and Voss,1999). Both ρw and Rrs are used in ocean color retrieval, and, with a variety of subscripts,ρ is used as the ratio of any surface or atmospheric radiance to the solar irradiance.

5.4.5 The diffuse attenuation coefficient

Another important AOP that can be retrieved by satellite is the diffuse attenuation coefficientfor the downwelling irradiance Kd(λ). As summarized in Lee et al. (2005), Equation (4.6)is assumed to govern the attenuation of the downward irradiance Ed(λ, z). For this case,Kd(λ, z) is a damped exponential where Ed(λ, z) is the attenuation coefficient with unitsof m−1, and is derived from

Ed(λ, z) = Ed(λ, 0−) exp (−Kd(λ)z) (5.34)

Reorganization of Equation (5.34) yields the following equation for Kd(λ, z) :

Kd(λ, z) = (1/z) ln[Ed(λ, 0−)/Ed(λ, z)] (5.35)

From their definitions, both Kd(λ, z) and R(λ, z) are ratios of irradiances, so that they areindependent of instrument drift.

From field observations and as cited in Mueller (2000), Gordon and McCluney (1975)show that 90% of the water-leaving radiance originates within the first e-folding depth, orwithin the depth z−1 defined by

Ed(λ, z−1) = Ed(λ, 0−) exp (−1) (5.36)

From (5.36),

Kd(λ, z) = 1/z−1 (5.37)

where the depth z−1 is a function of λ derived from examination of the depth-dependence ofthe irradiance profiles. For water containing suspended and dissolved organic and inorganicsubstances, Mueller (2000) replaces Kd(λ, z) with Kd(λ), which is its average over the e-folding depth. For clear water, Smith and Baker (1981, Table 1) show that Kd(λ) is equal tothe sum of a(λ) and a small forward-scattering term, so that, to first order, Kd(λ) a(λ).

From a regression analysis using seawater data, Mueller (2000) finds that

Kd(490) = KW(490) + 0.15645

[[LW(490)]N

[LW(555)]N

]−1.5401

(5.38)

where KW(490) = 0.016 m−1 is the clear-water value discussed by Mueller and Trees(1997) and derived from Pope and Fry (1997). Mueller et al. (2002) rank Kd(490) as anessential quantity of remote sensing.


5.5 Reflection from foam 135

5.5 Reflection from foam

The problem of reflection from the sporadic foam patches generated by breaking waves isa current topic of field and laboratory research. From Gordon and Wang (1994b), foam isgenerally assumed to be a Lambertian reflector with an irradiance reflectance RF(λ). Withinan instrument pixel, the determination of the irradiance reflected from foam is the productof RF(λ) and the foam areal extent.

Frouin et al. (1996) and Moore et al. (2000) show that RF(λ) decreases with increasingwavelength. This occurs because foam consists of small volumes of air contained on thesurface within a fine lattice of seawater and of bubbles entrained into the near-surfacewater column (Section 2.2.2), so that reflection from foam has both surface and subsurfacecomponents. In the visible, both contribute to the reflectance. In the infrared, because ofincreased seawater absorption, the subsurface contribution is greatly reduced. From fieldobservations in the surf zone, Frouin et al. (1996) find that RF(λ) = 0.40 for 400 nm λ

650 nm, while RF(λ) is reduced by 40% to 0.25 at λ = 850 nm, by 50% at 1.02 µm,and by 85% at 1.65 µm. From instruments deployed on a 6000-km ship traverse across theequatorial Pacific Ocean, Moore et al. (2000) confirm this result. They also show that inthe visible, on the scale of a satellite pixel and for a wind speed range of 9–12 m s−1, theadditional satellite reflectance associated with foam lies in the range 0.001–0.002, with noapparent dependence on wind speed. These foam properties are incorporated into the oceancolor algorithms described in the next chapter.


6

Ocean color

6.1 Introduction

This chapter reviews the retrieval of organic and inorganic, dissolved and suspended materialin the water column. While the last chapter discussed the properties of clear water anddefined the irradiance reflectance, water-leaving radiance and the radiance received at thesatellite, this chapter shows how the presence of dissolved and suspended material alters thewavelength-dependence of the water-leaving radiances from their clear-water values. Asthe following shows, satellite observations in the visible and near infrared allow retrievalof the oceanic chlorophyll a (Chl-a), the principal photosynthetic pigment associated withoceanic plant life.

Most oceanic plants are microscopic single- or multi-celled free-floating plants calledalgae or phytoplankton, from the Greek phyton, meaning plant, and planktos, meaning wan-dering (Jeffrey and Mantoura, 1997). Phytoplankton use photosynthesis to fix inorganic car-bon into organic forms of carbon such as carbohydrates. They reproduce asexually, are glob-ally distributed, consist of tens of thousands of species and make up about 25% of the totalplanetary vegetation (Jeffrey and Mantoura, 1997). Jeffrey and Vesk (1997) and Lalli andParsons (1993) provide an introduction to the kinds and variety of phytoplankton species.

Siegel et al. (2012) show that the phytoplankton production associated with photosyn-thesis that occurs in the sunlit upper layer of the ocean is the dominant source of organicmaterial for the marine food web. Phytoplankton make up about half of the total landand ocean net primary production. On average each day, phytoplankton transform onehundred million tonnes (1011 kg) of carbon in the form of carbon dioxide into organicmaterial, where, on a regional basis, these rates depend on the availability of nutrientsand sunlight. Every two to six days, the entire global mass of phytoplankton is consumed(Behrenfeld et al., 2006a).

Globally, phytoplankton play at least two roles. First, as stated above, phytoplanktonare the base of the marine food web. Small oceanic animals called zooplankton derivetheir energy by grazing on the phytoplankton. In turn, larger species of fish and mammalsconsume the zooplankton. Second, phytoplankton contribute to the global carbon cycle. Asphytoplankton increase in number and mass, they fix carbon, meaning that, in the upperwater column, the incident solar energy allows them to convert inorganic CO2 to organic

136


6.1 Introduction 137

carbon. Their rate of growth and of carbon fixation is called primary production and ismeasured using radiocarbon techniques, with typical units of (µg of carbon) m−3 s−1, wherethe net primary production is defined from the 14C uptake (Behrenfeld and Falkowski, 1997).

As the phytoplankton die, they sink into the abyss and sequester carbon in the deepocean, in a process called the biological pump. Because of fossil fuel consumption, thecarbon cycle is out of balance, with the excess CO2 transported into the ocean and atmo-sphere. In the atmosphere, CO2 increases the opacity of the thermal-infrared windows, thuscontributing to global warming. Carbon fixation by phytoplankton transfers some of thisexcess atmospheric carbon from the upper to the deep ocean. Given the concerns aboutthe imbalance of the carbon cycle, and about feeding the growing human population anddetermining the carrying capacity of the planet, there is an immediate need to determinethe oceanic global and regional distribution of chlorophyll and primary production.

Measurements of ocean color from space depend on the small-scale nature ofphotosynthesis. Most oceanic carbon is inorganic; the photosynthetic pigments withineach phytoplankton cell make possible the reduction or fixation of carbon dioxide intoorganic carbon, so that solar energy is converted to chemical energy with oxygen as aby-product. These pigments consist of the ubiquitous chlorophyll a, the accessory pig-ments chlorophyll b and c, and the photosynthetic carotenoids. The annual production ofoceanic chlorophyll is about 1012 kg (Jeffrey and Mantoura, 1997). For cells growing inenvironments with strong sunlight, additional photoprotectant carotenoids protect the cellfrom photo-oxidation (Trees et al., 2000). All of these pigments account for about 95%of the light absorbed by phytoplankton (Aiken et al., 1995). Because chlorophyll a is theonly photosynthetic pigment that occurs in all phytoplankton, it provides a measure ofphytoplankton abundance and biomass.

Jeffrey and Vesk (1997) summarize the species of phytoplankton, which include diatoms,dinoflagellates and cyanobacteria. At temperate and high latitudes, diatoms are generallythe dominant class of phytoplankton (Lalli and Parsons, 1993). Figure 6.1 shows severaldiatoms; the central diatom belongs to the chaetoceros species, which consists of a chain ofsilica-shelled single cells with spines protruding from each cell and from both ends of thechain. The figure shows that within each cell the pigments are not distributed uniformly,rather they are located within small packages called chloroplasts. These pigments area mixture of the green chlorophyll and the brownish yellow carotenoids. Because thepigment packaging differs from species to species, the response to incident light can differby species even for the same chlorophyll concentrations.

One goal of biological remote sensing is to use observations of ocean color in modelsof the global distribution of primary production. As the following sections show, insteadof primary production, measurements of ocean color are used to derive chlorophyll con-centrations that are proportional to biomass or to the standing phytoplankton stock. Whilechlorophyll is a measure of biomass, primary production is a measure of phytoplanktongrowth and the two are not necessarily related. It is impossible to tell from satellite imagesalone whether a change in observed chlorophyll concentration occurs because of increasedgrowth, or because the phytoplankton are being grazed less or are closer to the surface


138 Ocean color

Fig. 6.1. Diatoms from the coastal Pacific off Washington state. The diatom positioned diagonallyacross the picture center is a member of the chaetoceros species; it consists of a chain of silica-shelledsingle cells with spines protruding from each cell and from both ends of the chain. For this species,the width of each cell is 20–25 µm. Inside each cell, the chloroplast contains the photosyntheticpigments, a mixture of green chlorophyll and the brownish yellow carotenoids. Other diatom speciesare adjacent, including a chain of cells below the chaetoceros. (Courtesy of Rita Horner; used withpermission.) See color plate section.

(Balch and Byrne, 1994). For example, in the North Pacific, when the primary productivityincreases, zooplankton can graze the phytoplankton at such a rate that the phytoplanktonstanding stock is unchanged, and the productivity increase is represented by an increasein zooplankton (Lalli and Parsons, 1993). In contrast, in the North Atlantic, the productiv-ity increase is accompanied by an increase in both phytoplankton biomass and observedchlorophyll.

Because primary production varies with the availability of nutrients and sunlight, growthoccurs in regions of upwelling that bring nutrients to the surface. Such regions occur alongthe west coast of continents, in the equatorial Atlantic and Pacific during La Nina. Incontrast, in the equatorial regions away from the immediate vicinity of the equator, thewarm surface layer yields a stable upper ocean with little upwelling, so the productivity issmall. The model frequently used to calculate net primary production from the observedchlorophyll is the Vertically Generalized Production Model (VGPM) (Behrenfeld et al.,2006b; Behrenfeld and Falkowski, 1997). In addition to the observed chlorophyll, theinputs to the VGPM include variables such as cloud-corrected estimates of daily surfacesolar irradiance, the oceanic optical depth and the physiological variables governing theability of the organisms to take up carbon.

As this chapter shows, determination of the global distribution of primary productivity,species distribution and the inherent optical properties associated with organic and inorganic


6.2 Absorption and scattering 139

material is based on three different inputs: satellite observations of ocean color, in situobservations of the regional distribution of nutrients and species, and numerical modelsthat combine the satellite and in situ observations. Except for a few regions of clear water,ocean water can be described as “a stratified witches’ brew” (Dickey et al., 2011, p. 44).Namely, in the modeling of the absorption and scattering of light within the ocean, thefollowing substances must be considered: phytoplankton, chlorophyll, dissolved organicmaterial, and suspended organic and inorganic particulate matter.

As the previous chapter discussed, the scattering and absorption of sunlight by clearseawater yields a blue upwelled light. In contrast, because chlorophyll a preferentiallyabsorbs in two peaks located in the red and the blue, as its concentration within thewater column increases from zero, the water becomes less blue and more green. Also, forthe reasons discussed below, because the absorption of dissolved and suspended matterfalls off exponentially across the visible spectrum, this material yields a brownish yellowcolor to the water (Hoepffner and Sathyendranath, 1993). Historically, these easily viewedcolor changes suggested that visible sensors on aircraft and satellites could be used tosurvey large oceanic regions for biological activity. Retrieval of ocean color is a complextask. First, ocean color radiances in the blue–green can be upwelled from depths as greatas 100 m. Second, because, in the visible, aerosol and molecular scattering dominateatmospheric attenuation, the water-leaving radiances are at most about 10% of the totalreceived radiance. This means that determination of the water-leaving radiances requiresthe precise measurement of all other radiances.

In the following discussion, Section 6.2 summarizes how the presence of phytoplanktonand suspended and dissolved material alter the scattering, absorption and reflectance proper-ties of seawater from their clear-water values. Section 6.3 discusses the choice of wavelengthbands for the ocean color sensors. Section 6.4 describes the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), the Moderate Resolution Imaging Spectroradiometer (MODIS),the Visible/Infrared Imager/Radiometer Suite (VIIRS) and their calibration schemes. Sec-tion 6.5 discusses the atmospheric correction algorithms. Section 6.6 describes the surfacevalidation data sets and their use in the vicarious calibrations. Section 6.7 discusses thechlorophyll reflectance and fluorescence properties. Section 6.8 describes the NASA dataarchive and three different kinds of ocean color algorithms, namely the empirical or band-ratio algorithms, the semi-analytic Garver–Siegel–Maritorena (GSM) algorithm, and theNASA Ocean Biogeochemical Model (NOBM). Section 6.9 concludes with a discussionof the 2019 Pre-Aerosol, Clouds and ocean Ecosystem (PACE) mission that should correctsome of the shortcomings in the current missions.

6.2 Absorption and scattering by phytoplankton, particulates anddissolved material

The sources of color change in seawater include phytoplankton and its pigments, dissolvedorganic material and suspended particulate matter. Specifically, the color depends on thedistribution and sizes of particles and on the concentrations and properties of dissolved


140 Ocean color

materials (Zaneveld et al., 2006). The dissolved organic material, called chromophoricdissolved organic matter (CDOM), is also called gelbstoff, yellow substance and coloreddissolved organic matter (McClain, 2009). CDOM is derived from terrestrial and oceanicsources. Terrestrial CDOM, sometimes called tDOM (terrigenous DOM), consists of dis-solved humic and fulvic acids that are primarily derived from land-based runoff containingdecaying vegetable matter.

Oceanic CDOM is produced when the phytoplankton are degraded by grazing or pho-tolysis (Carder et al., 1999). The organic particulates, called detritus, consist of phyto-plankton and zooplankton cell fragments and zooplankton fecal pellets (Roesler et al.,1989). The inorganic particulates consist of sand and dust formed by erosion of land-basedrocks and soils. These enter the ocean through river runoff, by deposition of wind-blowndust on the ocean surface or from suspension of bottom sediments by waves or currents(Mobley, 1994).

Given the geographic distribution of this dissolved and suspended material, Morel andPrieur (1977) divide the ocean into case 1 and case 2 waters. In case 1 waters, phytoplanktonpigments and their covarying detrital pigments dominate the seawater optical properties,where Ca is the concentration of chlorophyll a in units of (mg of pigment) m−3. In case 2waters, other substances that do not covary with Ca such as suspended sediments, organicparticles and CDOM predominate. Even though case 2 waters occupy a smaller area of theworld ocean than case 1 waters, because they occur in coastal regions with large river runoffsand high densities of human activities such as fisheries, recreation and shipping, they areequally important. Based on the magnitude of Ca , the oceanic biological activity or tropicregimes have the following definitions: oligotrophic (Ca < 0.1 mg m−3), mesotrophic (0.1mg m−3< Ca<1.0 mg m−3) and eutrophic (Ca > 1.0 mg m-3). Clear water is oligotrophic,while the terms mesotrophic and eutrophic describe greater amounts of biological activity(Bailey and Werdell, 2006). Because the global ocean has a median Ca value of about0.2 mg m−3, it is largely oligotrophic (Dierssen, 2010).

Scattering in the water column depends in part on the size distribution of the suspendedliving and inert particulate matter. Following Stramski and Kiefer (1991) and Mobley(1995), the smallest living organisms are viruses, with diameters of 10–100 nm and withoceanic concentrations of 1012–1015 m−3. Because of their small size, viruses tend to beRayleigh scatterers. Next are bacteria, with diameters of 0.1–1 µm and concentrations aslarge as 1013 m−3; these can be significant absorbers of light in the blue. Third, phytoplank-ton range in size from 2 µm to 200 µm, where the larger sizes consist of collections ofcells. Because phytoplankton are larger than the visible wavelengths, they tend to be Miescatterers. Fourth, the zooplankton that graze on phytoplankton have scales of 100 µm to20 mm.

The relative concentrations of these organisms depend on their size, where large organ-isms occur less frequently than small ones. The concentrations of organisms with diametersin the range 30 nm to 100 µm have an inverse fourth-power-law dependence on diameter(Stramski and Kiefer, 1991). This relation approximately holds at larger scales, so that,even though the ocean contains fish and marine mammals with characteristic sizes of



0.1–10 m, they occur so infrequently that, at the satellite observational scales, they do notaffect scattering or absorption. Inert organic particles are comparable in size to phytoplank-ton. Because any photosynthetic pigments in this inert material are rapidly oxidized, theorganic particles lose their characteristic Chl-a absorption properties. The inorganic partic-ulates consist of fine sands, mineral dust, clay, and metal oxides, and have scales rangingfrom much less than 1 µm to of order 10 µm.

The importance of these scattering and absorption properties to remote sensing followsfrom Equation (5.32), where the remote sensing reflectance Rrs(λ) is a function of the IOPsbb(λ) and a(λ). For other than clear water, Maritorena et al. (2002) show that the absorptionand backscatter coefficients in Equation (5.31) are replaced by the total absorption andbackscatter, aT (λ) and bbT(λ), written as

aT(λ) = aw(λ) + aph(λ) + aCDOM(λ) (6.1)

bbT(λ) = bbw(λ) + bbp(λ) (6.2)

where (6.1) describes the absorption properties and (6.2) the backscattering properties.In these equations, the subscript w refers to clear-water values, ph to phytoplankton andp to particulates. Because the spectral absorption of the organic CDOM that of and theinorganic particulates have similar spectral shapes, their contributions to absorption aregrouped together under aCDOM(λ). For clear water, Pope and Fry (1997) give the absorptioncoefficient and Equations (5.19) and (5.23) give the backscatter coefficient, so that threeadditional terms describe the remote sensing properties of seawater: the phytoplanktonabsorption aph(λ), the CDOM absorption aCDOM(λ)and the particulate backscatter bbp(λ).

The spectral dependence of the water-leaving radiances on the organic and inorganicmaterial in the water column allows retrieval of the variables in Equations (6.1) and (6.2).In the following, Section 6.2.1 describes the wavelength-dependence of the absorptionproperties of phytoplankton and CDOM; Section 6.2.2 describes the scattering propertiesof particulates, then briefly discusses chlorophyll fluorescence.

6.2.1 Absorption

This section describes the spectral absorption of CDOM and phytoplankton as derived fromempirical relationships based on observations.

CDOM and particulates. For different concentrations of CDOM and particulates, rang-ing from water that is nearly clear to water heavily dominated by these substances, Figure 6.2shows the wavelength dependence of aT(λ). As the amount of CDOM increases, the uppercurves show that the absorption is greatest in the blue, then decreases exponentially towardlonger wavelengths. From the observations of Roesler et al. (1989) and Hoepffner andSathyendranath (1993) for 350 nm < λ < 700 nm, and following the notation of Mari-torena et al. (2002), aCDOM(λ) can be expressed as the following empirical relation:

aCDOM(λ) = aCDOM(λ0) exp[−S(λ − λ0)] (6.3)


142 Ocean color

400 450 500 550 600 650 700λ (nm)

0

0.05

0.01

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Baltic

IndianOcean

Near Bermuda

Increasingconcentration

aT

(λ)

(m–1

)

Fig. 6.2. Field observations of the λ-dependence of the total absorption coefficient as observed inthree locations with different concentrations of CDOM and particulate matter. (Data from Mobley(1995), Table 7, courtesy of Curtis Mobley.)

In (6.3), aCDOM(λ0) is the concentration-dependent absorption with values of order10−1 –10−3 m−1 (PACE-SDT, 2012), where λ0 is generally set equal to 443 nm, and Sis a species-specific constant (Maritorena et al., 2002; Garver and Siegel, 1997). In Equa-tion (6.3), S ranges over an order of magnitude from 0.006 to 0.02 (Roesler et al., 1989;Garver and Siegel, 1997). From tuning their absorption model against a large numberof case 1 water observations, Maritorena and Siegel (2006) find that S = 0.0206 nm−1.Equation (6.3) shows that the mathematical form of the CDOM absorption consists ofa functional dependence of the absorption on wavelength times a value of the CDOMabsorption at a specific wavelength. As shown below, the other inherent optical propertiesin (6.1) and (6.2) have similar forms.

Phytoplankton: Compared with that of CDOM, the phytoplankton absorption has amore complicated wavelength dependence. It is described as the product of the chlorophyllconcentration, Ca , times the empirically derived a∗

ph(λ), which is the chlorophyll specificabsorption coefficient with units of m2 mg−1,

aph(λ) = Ca a∗ph(λ) (6.4)

From case 1 waters in the summer North Atlantic, Figure 6.3 shows the specific absorptioncurves for chlorophyll a and the carotenoids, where each curve is normalized on its respec-tive pigment concentration Ca . The carotenoid curve includes contributions from both



0.06

0.05

0.04

0.03

0.02

0.01

0400 450 500 550 600 650 700 750

Wavelength (nm)

Nor

mal

ized

abs

orpt

ion

(m

2 (m

g pi

gmen

t)–1

)

Fig. 6.3. The normalized absorption for Chl-a (solid line) and the carotenoids (dashed line). Eachcurve is normalized by division of the measured absorption by the respective pigment concentrationin units of (mg of pigment) m−3. (Figure 9 from Hoepffner and Sathyendranath (1993), C© 1993American Geophysical Union, reproduced/modified by permission of AGU.)

photosynthetic and photoprotective carotenoids. Because the concentrations of chlorophyllb and c are generally much smaller than that of Chl-a, they are omitted from this figure.

Examination of the Chl-a curve shows that it has two major absorption peaks, in theblue near 440 nm, called the Soret band (Trees et al., 2000) and in the red centered at665 nm, where, in most cases, the blue peak is about three times greater than the red (Mob-ley, 1994). Between 550 and 650 nm, the absorption approaches zero, giving chlorophyll-rich water its characteristic green color (Kirk, 1996). The dashed curve shows the carotenoidabsorption, with its peak shifted toward 500 nm and its bandwidth extending from about450 to 550 nm. PACE-SDT (2012, Table A-1) shows that field observations of Ca rangefrom 0.015 to 40 mg m−3 or vary by about three orders of magnitude.

From samples taken in the North Atlantic during September, Figure 6.4 shows the spe-cific absorption minus the contribution of clear seawater for three cases: the upper panelshows the total specific absorption; the middle panel, CDOM absorption; the lower panel,phytoplankton absorption. The figure shows the characteristic Chl-a peaks at 440 and665 nm, the exponential decay with increasing λ of the CDOM absorption, and the vari-ance in the normalized phytoplankton absorption associated with differences in species,packaging and accessory pigments.

6.2.2 Scattering

The final unknown term in Equation (6.2) is the particulate backscatter bbp(λ)that includesscattering from both CDOM and particulates. Recent papers and a video that describe themeasurement and importance of backscatter include Dickey et al. (2011), RaDyO (2009)and Sullivan and Twardowski (2009).


144 Ocean color

400 500 600 700

400 500 600 700

400 500 600 700Wavelength (nm)

0.20

0.15

0.10

0.05

0

0.20

0.15

0.10

0.05

0

0.20

0.15

0.10

0.05

0

0.25

Nor

mal

ized

abs

orpt

ion

(

m2

(mg

Chl

-a)–

1 )N

orm

aliz

ed a

bsor

ptio

n

(m

2 (m

g C

hl-a

)–1 )

Nor

mal

ized

abs

orpt

ion

(

m2

(mg

Chl

-a)–

1 )

(a)

(b)

(c)

Fig. 6.4. Dependence of the specific absorption on wavelength from measurements made in thewestern North Atlantic. In each case, the clear-seawater absorption is subtracted. (a) total absorption.(b) particulate and CDOM absorption; (c) phytoplankton absorption. (Figure 3 from Hoepffner andSathyendranath (1993), C© 1993 American Geophysical Union, reproduced/modified by permissionof AGU.)

In general, the presence in the water column of even a small amount of particulatematter generates a strong forward scatter and increases the scattering coefficient by anorder of magnitude (Mobley, 1995, p. 43.33). Scattering from small particles tends towardthe Rayleigh solution with a smaller forward-scattering peak and a strong wavelength-dependence; scattering from larger particles tends toward the Mie case with a large forwardscatter and a weak wavelength-dependence.



0 15 45 90 105 120 135 150 165 180

–4

0

4

3

2

1

–1

–3

–2

Angle (degrees)

Vol

ume

scat

terin

g fu

nctio

n (m

–1 s

r–1 )

Forward Backward

Turbid harbor

Coastal ocean

Clearocean water

Pure seawater

30 60 75

Fig. 6.5. The dependence of the volume scattering function on angle for pure seawater (dashed line)and three different natural waters at 514 nm. The arrows at the bottom of the figure mark the directionsof forward and backward scatter. (Data from Petzold (1972), as listed in Mobley (1994), Table 3.10,courtesy of Curtis Mobley).

To show the effect of this forward scatter, for three different water masses, Figure 6.5compares some early measurements of the angular dependence of the total volume Scatter-ing function βT(α, λ) with the clear-seawater case. Each scattering function was measuredat a single wavelength of 514 nm; for the same wavelength, the clear-seawater values aretaken from Equation (5.19). The measurements are from turbid water in San Diego Harbor,coastal water from the Santa Barbara Channel and clear water from the Tongue of theOcean in the Bahamas. Even though these scattering functions are derived from differentwaters and locations, they have similar shapes. Comparison of the curves shows that theaddition of suspended materials increases the forward scattering by four to five orders ofmagnitude and the backscatter by up to one order of magnitude. Because of the strong for-ward scatter, the particulate backscatter is relatively small, being only about 2% of the total(Carder, 2002).

From Equation (5.23), the backscatter coefficient bb(λ) is the integral of the volumescattering function β(α, λ) over 90 ≤ α ≤ 180, where 180° is the backscatter direction.Through use of an innovative instrument called Multi-angle Scattering Optical Tool (MAS-COT), Sullivan and Twardowski (2009) collect and analyze several million measurementsof the particulate backscatter function. MASCOT measures the particulate volume scatter-ing function βp(α, λ) at a wavelength of 658 nm and for α at 10° intervals between 10° and


146 Ocean color

90 100 110 120 130 140 150 160 170

0.13

0.16

0.19

0.22

0.25

Angle (deg)

p

(θ)/b

bp (s

r–1 )

β

Fig. 6.6. The normalized particulate backscatter function taken from measurements made usingMASCOT (Multi-angle Scattering Optical Tool) from ten different coastal and oceanic environments.See the text for further description. (From Sullivan and Twardowski (2009), Figure 2c, copyrightAmerican Optical Society, used with permission.)

170°. From MASCOT, they collected backscatter measurements from ten different coastaland oceanic environments, ranging from the surf zone to the Southern Ocean.

For measurements from each of their ten sites, and for angles of 90° to 170°, Figure 6.6shows the average of βp(α, 658) normalized by the backscatter coefficient bbp(658). Giventhe diversity of the sites, the figure shows the consistency in the shape and magnitude of thenormalized backscatter. Even though these scattering functions are derived from differentwaters and locations, they have similar shapes, with the majority of the radiance scatteredin the forward direction.

For clear seawater and from Equation (5.21), the backscatter coefficient has a strongpower-law dependence and is described by bbw (λ) ∼ λ−4.32. But for suspended particu-lates, this strong wavelength-dependence disappears. Instead, the particulate backscattercoefficient becomes

bbp(λ) = bbp(λ0)[λ/λ0]−Y (6.5)

where λ = 443 nm and Y is a power-law exponent (Maritorena et al., 2002). The magnitudeof Y depends on whether the scattering is from large or small particles. For particles thatare large relative to λ0, the scattering has a strong forward peak and a weak wavelength-dependence(λ−0.3), while, for small particles, the scattering is more nearly symmetric, witha stronger wavelength-dependence (λ−1.7) (Kopelevich, 1983; described in Mobley, 1994).


6.3 Ocean color satellite instruments 147

Similarly, in their more general modeling of the backscatter from an arbitrary collectionof particles applicable to case 2 waters, Carder et al. (1999) find that, for large particlesand Mie scatter, Y 0, while for small particles Y > 0 (Carder et al., 1999). Also, fromcomparison of Equation (6.5) with the observed backscatter in primarily case 1 waters,Maritorena and Siegel (2006) find that Y = 1.0337.

Finally, as Section 6.6.2 discusses further, a feature that does not occur in the absorp-tion spectra but is important in the reflectance is the presence of a Chl-a fluorescencepeak at 683 nm, adjacent to the 665-nm absorption peak. At the fluorescence peak, thephytoplankton emit radiation that is detectable by satellite.

The above discussion shows that, to observe CDOM, phytoplankton and fluorescence,ocean color instruments need to employ the following wavelengths. Determination of thechlorophyll and CDOM concentrations involves observations at the chlorophyll absorptionpeak of 443 nm and at a CDOM-dominated wavelength such as 410 nm. Measurementsmust also be made in the range 500–550 nm where the chlorophyll absorption is zero andcarotenoid absorption dominates. Fluorescence requires observations in the vicinity of the683-nm peak. These absorption, scattering and emission properties provide the basis forthe choice of instrument wavelengths described in the next section.

6.3 Ocean color satellite instruments

Satellite observations of ocean color began in 1978 with the launch of the Coastal ZoneColor Scanner (CZCS) on the NIMBUS-7 satellite (Mitchell, 1994). CZCS observationscontinued through about June 1986, although, in its later years, the instrument sufferedsensor degradation (Evans and Gordon, 1994). The next instruments were the JapaneseOcean Color and Temperature Sensor (OCTS) on the ADEOS-1 satellite that operatedfrom August 1996 to June 1997 and the German Modular Optical Scanner (MOS) on theIndian Remote Sensing Satellite IRS-P3 that operated from 1996 to 2006.

The SeaWiFS instrument that was launched in August 1997 with a nominal five-yeardesign life operated until December 2010, yielding 13 years of observations. It was oneof the most successful of the ocean color missions. Because of its design and calibrationscheme that Section 6.4.1 describes below, it produced some of the best-quality ocean colordata. In March 2002, the European Medium Resolution Imaging Spectrometer (MERIS)was launched on ENVISAT. MERIS was a pushbroom instrument in a 1000 descendingSun-synchronous orbit with 15 observing bands between 400 and 900 nm that continuedto operate until May 2012.

As Section 6.3.2 describes, the MODIS instrument was launched on TERRA in Decem-ber 1999 and on AQUA in May 2002. As of 2013, AQUA continues to produce oceancolor data while TERRA does not. In October 2011, the launch of the VIIRS instrument onSuomi-NPP provides an additional source of biological data. One important difference withVIIRS versus SeaWiFS and MODIS is that VIIRS is operated by NOAA and lacks some ofthe NASA heritage. Table 1.1 lists other ocean color missions by China, India and Korea.


148 Ocean color

Table 6.1. Comparison of the location of the ocean color bands for the VIIRS, MODIS,SeaWiFS and CZCS instruments. See the text for further description.

Bandwidth (nm)VIIRS/MODIS/SeaWiFS bands

λ0

(nm) VIIRS MODIS SeaWiFS CZCS

M1/8/1 412 402–422 405–420 402–422 –M2/9/2 443 436–454 438–448 433–453 433–453M3/10/3 490 478–498 483–493 480–500 ––/–/4 510 – – 500–520 510–530–/11/– 531 – 526–536 – –M4/12/5 555 545–565 546–556 545–565 540–560M5/13/6 670 662–682 662–672 660–680 660–680M5/14/– 678 662–682 673–683 – –M6/15/7 765 739–754 743–753 745–785 –M7/16/8 865 846–885 862–877 845–885 700–800

1 With the exception of MODIS bands 11, 14 and 15, the center wavelengths λ0 correspond to theSeaWiFS bands.

2 SeaWiFS and CZCS data from Gordon and Voss (1999), Table 1; O’Reilly et al. (1998), Table4; MODIS data from MODIS-specifications, 2013; VIIRS data from Hsu (2010). See the text forfurther description.

For all these instruments, the International Ocean Colour Coordinating Group (IOCCG)website provides descriptions and specifications of current and pending ocean color mis-sions, and gives access to a series of reports on mission design and algorithms (IOCCG,2013). IOCCG provides a forum for international calibration and validation and for ensuringthat the in situ observations conform to common standards. It also encourages its membersto produce their data in a common format for the purposes of exchange, and, under CEOS,promotes the maintenance of a virtual ocean color constellation.

Given the biological, oceanographic and atmospheric constraints discussed in this chap-ter, each of these instruments uses similar wavelength bands. Because SeaWiFS and MODIShave generated a program of research cruises and surface observations as well as extensiveseries of papers, reports and conferences concerning the instruments and their algorithms,the following concentrates on these instruments and on VIIRS. For the four instruments,VIIRS, MODIS, SeaWiFS and CZCS, Table 6.1 lists the wavelength bands used for oceancolor observations, where MODIS bands 13 and 14 both lie within VIIRS band M5. Animportant difference between MODIS and SeaWiFS is that the MODIS bands are narrowerby factors of one-half to one-quarter, while the VIIRS bands have about the same width asthe SeaWiFS bands. Also, the VIIRS and MODIS data are 12-bit digitized while SeaWiFSis 10-bit digitized.

Between SeaWiFS and MODIS, the largest shift in band locations was that MODISband 11 at 531 nm replaced the 510-nm SeaWiFS band. The purpose of this move wasto improve the instrument response to accessory pigments and to match the 531-nm laser



2.5

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O2 H2O H2O

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Wavelength (nm)

Irra

dian

ce (

GW

m–3

)

(c)

8 10 11 12 13 14 15 16

M4, 5 7 M7, 8

9

M5, 6M1, 1 M2, 2 M3, 3 4 M6

Fig. 6.7. The solar irradiance, the atmosphere transmittance, and the surface irradiance shown withthe locations of the SeaWiFS, VIIRS and MODIS bands. (a) The solar irradiance at the TOA withlabels on the Fraunhofer lines, where Hα, Hβ and Hγ are the different hydrogen lines (locations fromPhillips (1992), Table 3.2); (b) the transmittance from the MODTRAN 1976 standard atmospherewith the absorption lines labeled; (c) the surface irradiance for the sun at zenith, where the gray barsand the numbers above the frame show the VIIRS (M) and SeaWiFS bands; the lower numberedblack bars, the MODIS bands. For clarity in the lower figure, SeaWiFS band 4 is slightly offset in thevertical. See the text for further description.

wavelength used in aircraft remote sensing (Esaias et al., 1998). Another change was theaddition of MODIS band 14 at 678 nm for detection of fluorescence. As Section 6.6.2shows, MODIS bands 13, 14 and 15 permit the retrieval of the florescence emitted by thephytoplankton, where VIIRS omits these channels. Finally, none of these instruments havebands in the ultraviolet at wavelengths less than 400 nm, even though such measurementswould help separate the CDOM and phytoplankton signal (PACE_STD, 2012, Figure 2.2).The locations of all these bands depend on two constraints: the optical properties of thephytoplankton and suspended and dissolved oceanic material discussed in Section 6.2, andthe locations of the atmosphere and solar absorption bands that are next discussed.

To illustrate the constraints imposed by atmospheric and solar absorption, Figure 6.7compares the locations of the SeaWiFS, MODIS and VIIRS bands with the solar irradianceat the TOA, the atmospheric transmittance and the solar irradiance at the Earth’s surface.Figure 6.7(a) shows the TOA solar irradiance from Figure 3.9; the chemical symbols


150 Ocean color

mark the location of the major Fraunhofer absorption lines generated in the solar corona(Phillips, 1992).

Figure 6.7(b) shows the atmospheric transmittance for the MODTRAN 1976 standardatmosphere, where the oxygen, oxygen-A and water vapor absorption bands are marked;Figure 6.7(c) shows the solar irradiance at the surface for normal incidence, where theupper horizontal bars give the location of the VIIRS medium (M) resolution bands and theSeaWiFS bands; the lower bars, the MODIS bands. The figure shows that the SeaWiFS745–785-nm band overlaps the oxygen-A band, while MODIS and VIIRS avoid all of themajor Fraunhofer and atmospheric absorption bands.

Table 6.1 and Figure 6.7 show that SeaWiFS has a similar set of bands to MODIS andVIIRS, where only MODIS has a band at 678 nm, used for the detection of florescence. TheMODIS visible bands have characteristic widths of 10 nm, compared with 20 nm or greaterfor SeaWiFS and VIIRS. For comparison, Table 6.1 shows that CZCS had only three bandsin the blue–green, one band in the red and a single band in the NIR (not listed), which hadinsufficient gain for aerosol removal. The purpose of these bands is as follows: the 412-nmband detects the presence of CDOM and suspended sediments; the 443-, 490-, 510- and555-nm bands determine chlorophyll concentrations. For MODIS, band 13 at 670 nm, band14 at 678 nm and band 15 at 765 nm allow determination of the height of the chlorophylla fluorescence peak at 683 nm; the reason why MODIS band 14, SeaWiFS band 6 andVIIRS band M5 are located at a slightly shorter wavelengths than the fluorescence peakis to avoid the oxygen absorption band at 687 nm. For all three instruments, the 765- and865-nm bands are used for atmospheric aerosol correction. For CZCS, only the 670-nmband was used for this purpose.

For the four instruments, Table 6.2 gives an example of the magnitudes of thereceived radiances and their instrument-associated uncertainties. The radiances are frommeasurements in a region of low pigment concentration in the summer Sargasso Sea andare taken near the scan edge to maximize their uncertainty (Gordon and Voss, 1999). Thefirst five columns in the table list the instrument band number, the center wavelength λ0,the maximum total radiance LTmax received at the satellite, a more typical total receivedradiance LT and the corresponding values of the water-leaving radiances [LW]N. The lastfour columns list the values of the noise-equivalent delta-radiance NEL defined in Section3.5.4, where the VIIRS, MODIS and SeaWiFS values are from preflight specifications; theCZCS values, from in-orbit measurements. Because for each wavelength, as Chapter 1discusses, the number of VIIRS sensors decreases with look angle, the VIIRS values ofNEL are the aggregate of the sensor noise (Turpie et al., 2012).

Examination of Table 6.2 shows that VIIRS and MODIS are typically two to three timesmore sensitive than SeaWiFS, which is about twice as sensitive as CZCS. The exceptionsare MODIS bands 13 and 14, which are six times more sensitive than SeaWiFS and aboutten times more sensitive than CZCS. At 443 nm, Table 6.2 also shows that [LW]N makesup only 13% of LT, so that as Section 6.4 shows, about 90% of LT consists of contributionsfrom atmospheric Rayleigh and aerosol scattering. From McClain (2009), the goal of theseinstruments is to determine the water-leaving radiances to within 5% and the chlorophyll



Table 6.2. Comparison of the measured and derived radiances and their uncertaintiesfor VIIRS, MODIS, SeaWiFS and CZCS, with a solar zenith angle of θS = 60° and for

measurements near the scan.

LT max LT [LW]N NEL (µW cm−2 nm−1 sr −1)VIIRS/MODIS/SeaWiFS bands

λ0

(nm) (µW cm−2 nm−1 sr−1) VIIRS MODIS SeaWiFS CZCS

M1/8/1 412 13.6 9.3 1.1 0.003 0.005 0.019 –M2/9/2 443 13.8 8.7 1.1 0.006 0.005 0.013 0.033M3/10/3 490 11.1 7.1 0.7 0.004 0.004 0.010 ––/–/4 510 8.9 5.6 0.3 – – 0.0109 0.017–/11/– 531 8.9 5.6 0.3 – 0.004 – –M4/12/5 555 7.4 4.5 0.12 0.003 0.003 0.008 0.019M5/13/6 670 4.1 2.6 0.10 0.001 0.001 0.006 0.012M5/14/– 678 4.1 2.5 0.01 0.001 0.001 – –M6/15/7 765 2.9 1.6 – 0.002 0.002 0.004 –M7/16/8 865 2.0 1.1 – 0.0005 0.001 0.002 –

See Table 6.1 for data sources and text for further description.

400 500 600 700 800 900Wavelength (nm)

0.00

0.02

0.04

0.06

0.08

0.10

Radi

ance

(W m

–2 s

r–1 n

m–1

)

Fig. 6.8. Illustration of the relative contributions of the water-leaving radiance (dashed line at bottom),the radiance reflected at the surface (thin solid line), the atmospheric path radiance (upper dashedline) and the radiance received at the satellite (upper solid line). (Reprinted with permission fromFigure 1.2 in NRC (2011), courtesy of the National Academies Press, Washington, DC, copyrightNAS.)

concentrations to within 35%. To achieve this goal, Hooker and McClain (2000) show thatthe sum of the other radiances must be determined to within 1%.

As an example of the relative size of the water-leaving radiance to that received at thesatellite, Figure 6.8 compares the relative contributions of four radiances: the water-leaving


152 Ocean color

radiance, the radiance generated by reflection at the surface, the atmospheric path radi-ance and the radiance received at the satellite. As NRC (2011, pp. 8–9) describes, thecurves are calculated at a 10-nm wavelength resolution from a numerical simulation usinga program called HydroLight for in-water processes and MODTRAN radiative transfermodels for atmospheric processes, along with input from typical oceanic and atmosphericproperties. Figure 6.8 shows that, consistently with Table 6.2, the water-leaving radi-ances in the blue/green (400–555 nm) are at most 10% of the radiance received at thesatellite.

6.4 SeaWiFS, MODIS, VIIRS and their calibrations

This section describes the operations of SeaWIFS, MODIS and VIIRS, with particularemphasis on their calibration. Each of these instruments experienced sensor drift and decaythat without a detailed calibration would have greatly reduced the value of the data. In thefollowing, Section 6.4.1 discusses the SeaWiFS instrument; Section 6.4.2 gives a detaileddescription of its calibration. Section 6.4.3 and Section 6.4.4 respectively describe theMODIS and VIIRS instruments and their calibrations.

6.4.1 SeaWiFS

Because SeaWiFS was specifically designed for ocean color retrieval, it is one of themost important ocean color sensors and, of all the satellites discussed in this chapter, itproduced the highest-quality data (McClain, 2009). The private company Orbital SciencesCorporation built and launched the SeaWiFS sensor and its OrbView-2 spacecraft. In August1997, the instrument was launched from an altitude of about 15 km using an L-1011 aircraftas the first stage. SeaWiFS occupied a Sun-synchronous orbit at an altitude of 705 km witha descending equator-crossing time of 1200 local.

SeaWiFS (2012a, 2012b) provide a pictures and a detailed description of the instrumentand spacecraft. The instrument is a cross-track scanner with a scan-angle range of ±58.3°,corresponding to a 2800-km swath width, and near global coverage at two-day intervals.At nadir, its resolution of 1.6 mr yielded a surface resolution of 1.1 km. In December 2010,the mission ended, yielding 13 years of operation, or more than 2.5 times its expected5-year lifetime.

Figures 6.9 and 6.10 respectively show a drawing and photograph of the SeaWiFS cross-track optical scanner and electronics module. Relative to the satellite, the scanner consistsof a rotating folded off-axis telescope and a non-rotating optical bench. In the cross-track direction, the telescope rotates at six revolutions per second, providing continuouscoverage at nadir. The SeaWiFS output is compatible with the existing AVHRR directbroadcast format described in Chapter 7. From Figure 6.9, the primary mirror collects thesurface radiance and reflects it from a polarization scrambler into the half-angle mirror,which focuses the radiance into the non-rotating Aft Optics Bench. The half-angle mirror


Flight direction

View direction

Direction of scan (West to East)

Polarization Scrambler

Aft Optics Bench

–20o, 0, +20o

Tilt axis (+20o isaft-looking)

Primary Mirror

Solar Diffuser PlateHalf-Angle Mirror

Cut-away viewof rotating telescopeand housing

Entering sunlight

SolarCalibrator

(Sunlight reflects fromthe Solar Diffuser Platethrough the circularaperture to the instrument)

Fig. 6.9. Cutaway drawing of the SeaWiFS instrument. The instrument attaches to the bottom of thespacecraft by the four top mounting points. (Figure 7 from Hooker et al. 1992, not subject to UScopyright, courtesy William Barnes, Orbital Science Corporation and the NASA SeaWiFS program.)

Fig. 6.10. Photograph of the SeaWiFS instrument with a caliper for scale. The view direction isupward, the solar calibrator is to the back right, the Aft Optics Bench is not visible. See the text andFigure 6.8 for further information. (Figure courtesy of Raytheon Co., Santa Barbara Remote Sensing,used with permission.)


154 Ocean color

rotates at half the rate of the telescope, and uses alternate sides on successive telescopescans. To avoid sun glint, the entire instrument could be tilted in the along-track directionto angles of +20°, 0° and −20°.

6.4.2 SeaWiFS calibration

For all the instruments, the purpose of the calibration was to provide good-quality environ-mental and climate data records (EDRs and CDRs). Because the mirrors and lenses thatmake up these instruments degrade with time, for SeaWiFS and the other instruments, thereare four kinds of calibrations. The first three are instrument calibrations that correct for thetemporal degradation of the lenses, mirrors and sensors; the fourth is a vicarious calibrationthat uses in situ oceanic observations to adjust for systematic bias of the combination ofthe instrument and atmospheric algorithm.

The first calibration is a prelaunch laboratory calibration performed against standardstraceable to the National Institute of Standards and Technology (NIST). The second isthe transfer-to-orbit calibration, which determines any changes that occur between theprelaunch calibration and the start of on-orbit operations; the third is the on-orbit calibration.As Barnes et al. (2001) describe, the on-orbit calibration divides into three parts. First, atapproximately daily intervals, the instrument is calibrated against the Sun. This solarcalibration takes place when the satellite passes over the South Pole, at which time theinstrument is tilted by 20° so that it views the attenuated solar reflection in the SolarDiffuser Plate. Because this plate deteriorates slowly, it cannot be used for long-termcalibrations and is intended only for detection of abrupt changes.

Second, because radiances reflected from the Moon at night have about the same magni-tude as the daytime ocean radiances, monthly lunar observations of the full moon provide alonger-term calibration. In this calibration, during the full moon and on the nighttime seg-ment of its orbit, the spacecraft rolls 180° along its flight axis from its normal Earth-orientedposition to point at the Moon. This means that the SeaWiFS instrument observes the Moonnear nadir along the same optical path as is used for the ocean. The lunar brightness isdetermined from the US Geological Survey (USGS) Robotic Lunar Observatory (ROLO)model of the radiometric lunar properties (Eplee et al., 2012).

For the entire SeaWiFS mission, Figure 6.11 shows the results of the lunar calibrationfor each band in a time plot of the individual radiances normalized by their initial value.All of the bands decay with time. As Eplee et al. (2012) describe, for bands 1–4 (412–510 nm), the degradation decreases with increasing wavelength, which is probably causedby yellowing of the instrument optics. In contrast, for bands 5–8 (555–865 nm), the degrada-tion increases with increasing wavelength, the cause of which is charged-particle damage tothe photodiodes. Over the instrument lifetime of the instrument, the 865-nm band decayedby 19%, the 765-nm band by 8%, and the other bands by 1%–3%.

The importance of these lunar observations is that they not only permit calibrationof the visible bands, where the blue and green bands can also be calibrated by in situobservations, but also provide for calibration of the red and NIR bands, for which the in situ


6.4 SeaWiFS, MODIS, VIIRS and their calibrations 155

1.00

0.95

0.90

0.85

0.80

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mal

ized

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ianc

e

98 0900 1099 05 07 0804030201 06Year (ticks denote 1 January)

Band

Band

Band

Band

Band

Band

Band

Band

1 2

3 4

5 6

7 8

Fig. 6.11. The change in the sensitivity of the SeaWiFS bands derived from the lunar calibration forthe mission duration of 1 August 1997 to 11 December 2010. The diamonds represent bands 1 and6; the squares represent bands 3, 4 and 5, where these two sets of bands have similar degradationprofiles. Bands 2, 7 and 8 have unique degradation profiles, and are respectively represented bycrosses, triangles and asterisks. (Figure derivation described in Eplee et al. (2012), courtesy of GeneEplee and Charles McClain, used with permission.)

observations lie beneath the noise floor. For SeaWiFS, the aggregate of these calibrationsyields an estimated uncertainty in the top-of-the-atmosphere radiance measurements of3%–4% (Eplee et al., 2001). As Figure 6.8 shows, because about 90% of the radiancereceived at the satellite is generated from either Rayleigh or aerosol scatter, a 1% error inthe received radiance yields a 10% error in the blue–green water-leaving radiance; a 4%error in the received radiance yields a 40% error (Barnes et al., 2001). Over the missionlifetime, production of CDRs requires an on-orbit calibration stability of 0.1%, which canbe assessed retrospectively (Turpie et al., 2011).

The fourth, vicarious calibration, differs from the other three in that it calibrates thesatellite-retrieved radiances against in situ measurements. While the on-orbit calibrationremoves the time-dependent changes of the instrument, the vicarious calibration removesthe systematic bias. Because of the importance of understanding the atmospheric correctionsbefore discussion of the vicarious calibration, its discussion is postponed to Section 6.6.

6.4.3 MODIS

MODIS is the principal visible/infrared instrument on the TERRA and AQUA satellites(Barnes and Salomonson, 1993; MODIS, 2012; MODIS, 2013b). MODIS is a hybrid cross-track scanner with a scan-angle range of ±55° yielding a swath width of 2300 km, wherethe swaths are nearly contiguous at the equator and provide global coverage every 1–2 days(see Figure 4.2 for an example of single-day coverage). In the Appendix, Table A.2 lists


156 Ocean color

Solar diffuser

Scan mirror

Aperture cover(open in flight)

Nadir

Blackbody

Thermal blanket Space

view

Electronics

Radiative cooler

Cooler door

Fig. 6.12. The MODIS instrument. The instrument measures approximately 1 m × 1 m × 1.6 m andweighs 250 kg; the length of the scan mirror is 0.58 m. (Courtesy of NASA and William Barnes.)

the bands and their resolutions; the instrument has 36 bands with a spectral range of 0.4–14.4 µm. MODIS makes simultaneous observations of ocean color and SST, where theocean color and thermal bands have a 1-km nadir resolution, the land/cloud bands (bands3–7) have a 500-m nadir resolution and the land/cloud boundary discrimination bands(bands 1 and 2) have a 250-m resolution.

MODIS operates differently than SeaWiFS. First, instead of the SeaWiFS rotating tele-scope, MODIS uses a fixed telescope that is focused on a double-sided rotating-paddle-wheel mirror (Figure 6.12). The mirror rotates at 20.3 rpm, where its two sides (called 1 and2) alternately collect the surface scans. The scan mirror reflects the Earth radiances ontoanother mirror, then into a telescope that transmits them to an optical bench. At the opticalbench, the radiance for each band is focused onto linear strips of sensors that subdivide thealong-track scan into multiple pixels.

For the 1-km bands, 10 sensors subdivide the 10-km-wide swath into 1-km pixels;for the 500-m bands, 20 sensors are used; for the 250-m bands, 40 sensors are used. AsSection 1.6.4 discusses, the use of these sensor strips instead of the single sensors usedwith SeaWiFS means that the mirror rotation speed can be reduced below that required fora single sensor, increasing the dwell time and yielding a better signal-to-noise ratio. UnlikeSeaWiFS, MODIS does not tilt. Instead, the expectation was that, despite sun glint, twonon-tilting MODIS instruments would provide better coverage than one tilting instrument.

Like SeaWiFS, the TERRA and AQUA MODIS on-orbit calibrations use lunar and solarobservations. For each revolution of the mirror, and for different angles and mirror sides,the telescope views a space view port that is used for the lunar views, a solar diffuserthat is monitored for stability and, for the reflective bands, an interior calibrator called


6.4 SeaWiFS, MODIS, VIIRS and their calibrations 157

the Spectral Radiometric Calibration Assembly (SRCA). This means that, for the MODISreflective bands, there are three on-orbit calibrations taken at different scan angles. In asimilar manner, a blackbody and the space view port are used to calibrate the thermal bands.

The solar diffuser is illuminated when the satellite is near the North Pole; an attenuationscreen reduces the incident light by about 92%. The diffuser is protected by a door thatopens about once every two weeks (Turpie et al., 2011). Lunar calibrations occur wheneverthe Moon fills the space view port (these are called opportunistic calibrations) and atapproximately monthly intervals when the spacecraft engages in a partial roll for a plannedcalibration. Those MODIS bands that do not saturate on the lunar radiance (bands 1–4 and8–12) are calibrated through the view port (Eplee et al., 2009). In the planned lunar view,the Moon is full such that, in the scan and along-track directions, it occupies about seven1-km MODIS pixels; in the opportunistic view, the Moon is at a variety of phases. For bothAQUA and TERRA, the MODIS band degradation is a function of band, mirror side, lookangle and detector.

Because the solar and lunar observations occur at different angles, the look-angle depen-dence of the instrument calibration can be determined. Given the geometry of the rotatingmirror and telescope, MODIS views the Moon through the space port at an angle of inci-dence corresponding to the beginning of the Earth scan of 55°, views the solar diffuser atan angle close to nadir and views the SRCA at an intermediate angle (Turpie et al., 2011).

A joint calibration between SeaWiFS and AQUA MODIS provided a direct intercom-parison of the two instruments. On 14 April 2003, both satellites simultaneously performedan 180° roll and viewed the full Moon at angles close to nadir. This maneuver showed thatthe biases between the two sets of instrument bands were 1%–5%. For both TERRA andAQUA MODIS, these calibrations permit determination of the sensor changes, the angulardependence of the system response and the difference in reflective properties of the twosides of the mirrors (Sun et al., 2007). Finally, before SeaWiFS ceased to operate, AQUAMODIS used its observations as another calibration source (NRC, 2011, p. 40).

The results of the calibration are as follows. From Sun et al. (2007, Figures 13–16),for the two MODIS instruments, the band sensitivity decreases with time, where shorterwavelengths experience a greater decrease. For AQUA MODIS in 2006, the dependence onmirror side is small, where the greatest decrease in sensitivity occurs with band 8 (412-nm)that experiences a gain factor decrease from 1.0 to about 0.8. Compared with TERRAMODIS, the mirror side dependence is small, but there is a dependence on viewing angle.For the MODIS AQUA 412 nm band, this dependence affects the gain by 20%. All of theseeffects are incorporated into lookup tables.

6.4.4 VIIRS

The VIIRS instrument on the Suomi NPP spacecraft is modeled on SeaWiFS, with a rotatingtelescope that reflects radiances into a two-sided half-angle mirror. The telescope rotatesat 33.3 rpm; to eliminate rotation of the image, the half-angle mirror rotates at half thatspeed and reflects the received radiances into a fixed optical bench (Welsch et al., 2001).


158 Ocean color

M4 (555 nm)

Time in days since 1 January 2012

M5 (672 nm)

M6 (746 nm)

M7 (865 nm)

Rel

ativ

e re

spon

se

1.00

0.95

0.90

0.80

0.75

0.85

–50 500 100

Fig. 6.13. Preliminary results of the VIIRS solar and lunar calibrations. The black dots are the lunarcalibrations, the names and wavelengths of the VIIRS moderate (M) resolution bands are written ontheir respective curves. See the text for further description. (Figure courtesy of NASA, redrawn fromVIIRS (2013a.)

The instrument measures 1.3 m × 1.4 × 0.8 m and weighs about 275 kg (VIIRS, 2012c).Section 1.6.4 describes the scheme that the instrument uses for reduction of the bowtieeffect.

Similarly to MODIS, VIIRS observes the Earth through a ±56° Earth scan for a 3000-km swath width. For on-orbit calibration and relative to its half-angle mirror, VIIRS viewsat the same angle both the solar diffuser and the Moon through its space port that lies justoutside of the Earth scan. The use of the same view angle for the solar and lunar imagingmeans that the on-orbit calibration cannot determine whether the instrument gain dependson view angle. The lunar calibration depends on both scheduled and opportunistic lunarviews. Unless they are cancelled owing to operational concerns, the calibrations occur atapproximately monthly intervals when the Suomi NPP spacecraft rolls about 10° to viewthe Moon at a constant lunar phase (F. Patt, 2013, private communication).

Examination of the VIIRS performance reveals a number of problems. For example, asingle instrument band has difficulty obtaining the same measurement when viewing anidentical radiance, while adjacent spectral bands view different radiances. These spectralperformance issues “could affect the ability to consistently calibrate the instrument to alevel commensurate with heritage performance” (Turpie et al., 2011, p. 81530M-5). Anadditional problem is that, during construction, tungsten oxide contaminated four of theVIIRS mirrors (VIIRS, 2013a; Turpie et al., 2012). When exposed on orbit to ultravioletlight, this contamination darkened the mirrors.

As an example derived from the lunar and solar calibration, Figure 6.13 shows theeffect of this darkening that caused an initial rapid degradation at wavelengths in the red


6.5 Atmospheric correction and retrieval 159

and NIR. The solar diffuser monitor also yellowed at a rapid unexpected rate; this wasapparently due to its lack of a protective cover. These initial rapid calibration changesslowed to manageable levels as the mission progressed (Turpie et al., 2012). Even thoughthe calibration is changing, at one year into its lifetime, its behavior is better than thatof MODIS or SeaWiFS at the same time into their operation. Also, the combined jointNOAA and NASA engineering and science efforts that are focused on VIIRS exceed thoseexpended on MODIS and SeaWiFS in their early days.

Another problem with VIIRS is that, unlike with SeaWiFS and MODIS, NOAA managesVIIRS with an algorithm development that is independent of NASA. Initially at least, theydid not take advantage of the work done by the NASA Ocean Biology Processing Group(OBPG) that oversaw CZCS, SeaWiFS and MODIS and emphasized the production of bothoperational and climate data records. Instead, the NOAA work emphasizes the productionof operational data records and not CDRs. Given the requirements for CDRs described inSection 1.7.3, Turpie et al. (2012) expressed concern that, for VIIRS, there was a lack ofsupport for reprocessing and that its atmospheric correction algorithms were not consistentwith MODIS and SeaWiFS.

At the time of writing, the OBPG is producing in-house versions of VIIRS ocean colordata. Given that time will resolve the problems discussed above, further speculation asto whether VIIRS will produce and continue the existing NASA CDRs is useless. If theOBPG can apply the same standards and procedures for VIIRS as are used for MODIS andSeaWiFS, the instrument may provide ocean color CDRs. If not, there may be at least atwo-year gap in the ocean color CDRs until the next VIIRS or the Japanese OCI beginsoperation (NRC, 2011).

6.5 Atmospheric correction and retrieval of the water-leaving radiance

Given the amount of analysis and algorithm development invested in the SeaWiFS instru-ment and observations since its launch in 1997, and because SeaWiFS, MODIS, MERIS andthe other existing and proposed instruments use similar bands for atmospheric correction,the retrieval of the water-leaving radiance follows the SeaWiFS algorithm. The first stepis to determine whether every oceanic pixel in the image under investigation is cloud-free.The SeaWiFS cloud detection test uses the 870-nm band. For this band, because the water-leaving radiance is near zero and clouds are reflective, pixels with a reflectance greater thana preset threshold are classified as cloud. Because the MODIS cloud algorithms depend onboth the visible and infrared bands, their description will be delayed until Section 7.6.3,after discussion of the infrared SST algorithms.

Assuming cloud-free conditions, the retrieval of LW(λ) depends both on the removalof all other radiances from the total radiance LT(λ) received at the satellite and on thecalculation of the beam and diffuse transmittances. In the following, Section 6.5.1 discussesterm-by-term the contributions to the total radiance and their evaluation. For SeaWiFS andMODIS, Sections 6.5.2 and 6.5.3 discuss the aerosol retrieval; Section 6.5.4 describes thespecial case of the CZCS aerosol correction.


160 Ocean color

Wind

Sensor

Ozone

Foam

(CZCS assumes a flat ocean surface)

Sun

SeaWiFS and CZCS

SeaWiFS only

Phytoplankton

Water molecule

Aerosol molecule

Air molecule

Fig. 6.14. Schematic drawing of the radiance received at the satellite from direct reflectance, the pathradiance, the reflected path radiance and the water-leaving radiance for VIIRS, MODIS, SeaWiFSand CZCS. (Adapted from Figure 4, McClain et al. (1992), not subject to US copyright.)

6.5.1 Contributions to the total radiance

Retrieval of the water-leaving radiance is described in terms of both the radiances andthe extraterrestrial reflectances defined in Equation (5.31) (Esaias et al., 1998). Becauseradiances are the quantity measured by field and satellite instruments, they are used in thefollowing discussion. Given that, for any λ, the reflectances and radiances differ by only amultiplicative constant, the equations for the reflectances have a similar form.

The corrections include the determination and removal from LT(λ) of the ozone atten-uation, the radiances associated with sun glint and foam, the Rayleigh path radiances and,most computationally difficult, the aerosol path radiances. Because, as Table 6.2 shows,the total of these radiances makes up about 90% of the retrieved signal, their removal iscritical to the accuracy of the LW(λ) retrieval. Figure 6.14 illustrates the contributions tothe total radiance received at the sensor and shows the terms included in the CZCS andSeaWiFS/MODIS/VIIRS algorithms. Each algorithm corrects for ozone attenuation andthe Rayleigh and aerosol path radiances. The CZCS algorithm assumes a flat surfaceand single molecular and aerosol scattering; CZCS avoided sun glint by tilting at angles of±10° and ±20°. The SeaWiFS/MODIS/VIIRS algorithm assumes a rough ocean surface,multiple molecular and aerosol scattering, and accounts for reflection from foam.



From Hooker and McClain (2000), the total radiance LT(λ) received at the satellite iswritten as

LT(λ) = tD(λ)[LW(λ) + LF(λ)] + t(λ)LG(λ) + LR(λ) + LA(λ) (6.6)

In Equation (6.6), tD(λ) is the diffuse transmittance, LF(λ) is the radiance reflected byfoam, LG(λ) is sun glint, and LR(λ) and LA(λ) are respectively the atmospheric Rayleighand aerosol path radiances, where it is assumed that LA(λ) also contains the contributionfrom any Rayleigh–aerosol interaction. For simplicity, the θ -dependence of all variablesis omitted. As described below, each of these terms is corrected for ozone attenuationusing Equation (4.52). Because Fresnel reflection from wave facets is the source of thesun glint term LG(λ), it is attenuated by the beam transmittance t(λ). In contrast, becauseLambertian reflection is the source of LF(λ) and LW(λ), they are attenuated by the diffusetransmittance tD(λ). An alternative way to look at these radiances follows Hooker andMcClain (2000), who show that the contributions to LT(λ) divide into the path radiancesgenerated in the atmosphere [LR(λ) + LA(λ)], the foam and sun glint radiances generatedat the ocean surface [tD(λ)LF(λ) + t(λ)LG(λ)], and the diffuse attenuated water-leavingradiance tD(λ)LW(λ). These terms are evaluated as follows.

Ozone. For wavelengths between 500 and 700 nm, Figure 4.12 shows that the attenuationhas a small but non-negligible seasonal dependence on ozone. From Gordon and Voss(1999) and for the SeaWiFS bands, the ozone attenuation τOZ(λ) 0.035, where ozone isassumed to be absorbing and non-scattering. Because all terms in LT(λ) depend on the solarirradiance, they are each reduced by a seasonally and latitudinally dependent downwardand upward passage through the ozone layer. For MODIS and SeaWiFS, the spatial andtemporal distribution of ozone and τOZ is determined by observations provided from theNational Centers for Environmental Prediction (NCEP) and taken by the METOP-B andAURA satellites, where AURA is an ozone- and atmosphere-specific satellite in the A-Train(Keyser, 2012).

Sun glint. As Figure 5.7 shows, the angular distribution of the solar radiances generatedby Fresnel reflectance from wave facets is a function of Sun angle and vector wind speed.As an example, the white arrows in Figure 4.2 mark the stripes of sun glint along theindividual MODIS swaths. For each SeaWiFS and MODIS image, the combination of theCox and Munk (1954) wave facet model described in Sections 2.2.4 and 5.2.3 with vectorwind speeds derived from NCEP numerical weather prediction models allows calculationof a sun glint mask (Wang and Bailey, 2001). Although the data from the forecast modelsare available at intervals of 3–6 hours, this procedure unavoidably neglects the effect oflocal wind gusts. An additional check on sun glint is provided by examination of the NIRradiances, where, if they exceed a preset threshold, sun glint is assumed and the pixel ismasked.

Foam. There is an important difference between the spatial and angular distribution ofthe reflected radiances due to foam and sun glint. The reflected sun glint radiances aredescribed by geometric optics and are distributed around the solar conjugate angle, so that,


162 Ocean color

b

2

Sun

a

1

c

3

Sensor

Surface

Fig. 6.15. The sources of the solar-generated single-scattering path radiance. (a) The path betweenthe sensor and surface, with a scattering location shown at 1; (b) the atmospheric path radiancegenerated at locations such as 2, which is reflected into the sensor; (c) the contribution to the pathradiance along (a) generated at locations such as 3 by the reflected solar radiance. Path radiances areshown as dashed lines; solar irradiances as solid lines. The points 1, 2 and 3 are illustrative only andare symbolic of an integration across the atmosphere.

depending on wind velocity, these radiances may affect only a fraction of the image, whichcan be masked. The foam coverage also depends on wind speed, but, because the foamreflectance is more nearly Lambertian, it has a much weaker dependence on solar angle, sothat LF(λ) can be nearly uniform across an image. In the processing, LF(λ) is estimated,then subtracted from LT(λ); or, if LF(λ) is too large, the image is discarded. Estimationof LF(λ) follows the model of Frouin et al. (1996) and Moore et al. (2000) described inSection 5.5. In almost all cases, the correction for foam is small, perhaps because cloudsoften accompany strong winds.

Rayleigh path radiances. At the shorter wavelengths, the Rayleigh path radiance isgenerally the largest term in the received radiance. The single-scattering Rayleigh pathradiance LR(λ) is from Equation (4.53), where the Rayleigh optical thickness τR(λ) isderived from Equation (4.24) with the surface pressure p taken from a numerical weatherprediction model. In addition to the direct path radiance and for both Rayleigh and aerosolscattering, there are two additional smaller path terms, so that the total path radiance dividesinto the following three parts (Figure 6.15):

(a) the dominant path radiance generated by the scattering of the downward solar irradianceinto the sensor look direction, from Equation (4.53);

(b) the path radiance generated along the conjugate path to the sensor look direction thatis then reflected at the surface into the sensor direction;

(c) the path radiance in the sensor direction generated by the reflected solar radiance.



Because the Fresnel surface reflectivities are small, the first term is dominant. Includ-ing multiple scattering further complicates these terms, but does not affect their relativemagnitudes. Also, because wind waves alter the magnitudes of the reflected radiances in(b) and (c), these radiances are functions of wind speed (Wang, 2000). Finally, the anglesand reflectances in the above three terms are generally incorporated into an expanded phasefunction (Gordon and Wang, 1992). Each of these terms is removed numerically.

Aerosol path radiances. The retrieval of the aerosol path radiances and diffuse trans-mittance are complicated and at the heart of the LW(λ) retrieval. As the following shows,for the case of small values of chlorophyll and CDOM, the NIR observing bands at 748and 870 nm permit retrieval of the aerosol radiances and their dependence on wavelength.Given the complexity of this retrieval, it is discussed twice, first in a brief summary, thenmore extensively in the next sub-section.

Although the magnitudes of the aerosol path radiances LA(λ) strongly depend on theaerosol type and concentration, their determination and removal is conceptually straightfor-ward. First, because the Rayleigh, foam and sun-glint terms can be calculated and removed,if the water-leaving radiance is zero, the remaining radiance equals the aerosol contribution.For clear water, Figure 5.15 shows that, in the NIR, the reflectance approaches zero, wherethe addition of small chlorophyll concentrations should not change this behavior. There-fore, one way to calculate the aerosol radiance is to work in the NIR, where the receivedradiances are assumed to have no water-leaving contribution. For the 748- and 870-nmbands, this means that, under most conditions, LW(λ) is set equal to zero. The magnitudeof the 870-nm band radiance and the ratio of the radiances at the 748- and 870-nm bandsprovide information on the aerosol type and permit the modeling of the aerosol radiancefor all of the visible wavelengths, where the modeled aerosols are then removed.

For the case of zero water-leaving radiance in the NIR, estimation of the aerosol radiancesproceeds as follows. First, the ozone attenuation, sun glint, foam reflection and Rayleighscattering terms are removed from all bands. For the two NIR bands where LW(λ) isassumed equal to zero, this means that, in the NIR,LT(λ) yields values of LA(748) andLA(870). The wavelength-dependence of the observed radiances is compared with radiancesthat are numerically calculated from many different aerosol models. If the observed andcalculated radiances agree, this comparison provides an estimate of the aerosol type andconcentration, which allows the observed NIR aerosol radiances to be extrapolated to thevisible. Removal of these extrapolated radiances from LT(λ) leaves only the attenuatedwater-leaving reflectance tD(λ)LW (λ). The final step in the recovery of LW(λ) is theestimation and removal of tD(λ).

Diffuse transmittance. As Section 4.9.1 discusses, tD(λ) describes the attenuation ofa radiance that is generated at an extended surface and propagates through a scatteringatmosphere. In the treatment of tD(λ), two factors are considered: its contribution to landcontamination and its method of calculation. First, for a scattering atmosphere and anextended surface, the received radiance has contributions not only from the instrumentFOV, but also from the surrounding area. Thus, when the FOV in question is close to land,the received radiance becomes land-contaminated, so that the ocean color algorithms break


164 Ocean color

700 800 900 1000 1100 1200 13000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1A

bsor

ptio

n de

pth

(m)

M6,15 16 M8, 5

1400

Wavelength (nm)

M7

87

Fig. 6.16. The absorption depth in the NIR, where the horizontal bars show the location of the MODIS,VIIRS and SeaWiFS bands.

down within a few pixels of the coast. For example, in Puget Sound, the color retrieval breaksdown within about three pixels of the coast (B. Sackmann, 2000, private communication).This contamination can also occur adjacent to an ice edge or to any location where thesurface reflectances change abruptly, such as adjacent to reflective clouds. Second, forsingle scattering and the assumption of a Lambertian distribution of radiance at the surface,Equation (4.55) describes tD(λ). For multiple scattering, tD(λ) is numerically determinedfrom the choice of aerosol model.

For large concentrations of sediment, CDOM or chlorophyll in the surface waters, thisassumption of zero-water leaving radiance in the NIR is violated. Figure 6.16 shows theabsorption depth derived from Equation (3.13) plotted versus wavelength for 700–1400 nm,and the location of the 748-, 865- and 1240-nm bands (MODIS bands 15, 16 and 5;SeaWiFS bands 7 and 8, VIIRS bands M6, M7, M8). From the figure, the absorption depthsat 748 and 870 nm lie between 0.1 and 0.4 m. This suggests that highly productive case 1waters or waters with large concentrations of sediment or CDOM will have water-leavingradiances in the 745- and 865-nm NIR bands (Wang and Shi, 2005). Figure 6.16 also showsthat, for λ1000 nm, the absorption depth approaches zero. In oceanic regions with high



sediment loads or large chlorophyll concentrations, Wang et al. (2009) recommend use ofan alternative correction algorithm that depends on radiances measured in the short-waveinfrared (SWIR), represented by MODIS band 5 on Figure 6.16.

6.5.2 Determination of the aerosol path radiances

Determination of the aerosol and mixed Rayleigh–aerosol scattering terms in Equation (6.6)divides into the single- and multiple-scattering cases. The single-scattering approximationis valid for thin layers of marine aerosols that occur in oceanic regions far from land, butbreaks down for thick aerosols where multiple scattering becomes important.

There are several different kinds of aerosols. Over the open ocean and at low levels in theatmosphere, the marine aerosols are non-absorbing and consist of a mixture of sea salt andwater produced from breaking waves. On land, coal power plants in Europe, Asia and NorthAmerica produce anthropogenic aerosols such as sulfates, while automobiles and trucksproduce black and organic carbon that are advected over the oceans at higher altitudes thanthe sea salt aerosols. These are often called tropospheric aerosols. Other anthropogenictropospheric aerosols consist of smoke produced by biomass burning in Africa and the sootproduced by industrial processes. Finally, winds advect dust from the Sahara and Gobideserts over the ocean (Ahmad et al., 2010). The marine aerosols consist of large particles,the tropospheric aerosols consist of small particles and the dust storms are often opaque. Thissection reviews the methods used to retrieve the aerosol properties and radiances, definesthe terminology used in single and multiple scattering, and discusses the global aerosoldistribution.

For single scattering and in the visible, when the sun glint, foam and Rayleigh pathradiances are removed from each band, the remaining terms are the aerosol path and water-leaving radiances. In the NIR and assuming a zero water-leaving radiance, the remainingterm is the single-scattering aerosol radiance from Equation (4.53):

LA(λ) = ωA(λ)τA(λ)F ′S(λ)PA(λ, θ, θS)/(4π cos θ ) (6.7)

In Equation (6.7), θS is the solar zenith angle, θ is the look angle, ωA(λ) is thesingle-scattering aerosol albedo defined in Equation (4.46) and PA (λ, θ, θS) is the aerosolphase function expanded to include the contributions from the reflected path radiances inFigure 6.14.

Estimation of the aerosol type and concentration proceeds by division of the LA(λ) at765 and 865 nm by their respective ozone-attenuated F ′

S(λ) from Equation (4.52), thentaking their ratio. Following Gordon and Castano (1987), this ratio becomes

ε(λ, λ0) = LA(λ)F ′S(λ0)

LA(λ0)F ′S(λ)

= ωA(λ) τA(λ)PA(λ, θ, θS)

ωA(λ0) τA(λ0)PA(λ0, θ, θS)(6.8)

where λ0 = 870 nm.Ahmad et al. (2010) describe the current aerosol correction procedure and classification

of aerosols that replaces the earlier classification of Gordon and Wang (1994a) and Gordon


166 Ocean color

and Voss (1999). These Two procedures use the same code, but with different lookuptables for the aerosol properties. In the atmospheric correction procedure, for each pixel,ε(748, 870) is calculated then compared with values of ε derived from known aerosols andlisted in lookup tables.

The Ahmad et al. (2010) model is based on field measurements of aerosol types, opti-cal thicknesses and particle size distributions made from the Aerosol Robotic Network(AERONET) stations, where the deployment of these stations began in the late 1990s. Theimportance of the AERONET observations is that, for the different aerosol types, they yieldthe actual size distributions. For oceanic purposes, Ahmed et al. (2010) used measurementsfrom island and coastal stations such as Lanai, Midway and Tahiti in the Pacific Ocean,Cape Verde, Ascension Island and Bermuda in the Atlantic, Kaashidhoo Island in the Mal-dives and the coastal town of Darwin in the Indian Ocean. These observations show thatthe ocean aerosols could be described as a mixture of fine particles with radii 0.1 µm andcoarse particles with radii 3 µm. This means that the oceanic aerosols could be repre-sented as a function of relative humidity and as a weighted sum of fine and coarse particles,where the fine particles originate from the continents and the coarse particles from theocean.

These aerosol properties were calculated for relative humidities of 30%, 50% and at 5%intervals between 70% and 95%. For each relative humidity, there are 10 different aerosols,leading to 80 possible aerosol solutions. For each relative humidity, the values of ε aredesigned to span the observed data, so that data points that lie between the models canbe determined by interpolation, not extrapolation. Because of the proposed design of thePACE instrument described in Section 6.9, the curves extend into the ultraviolet; at 870nm, the curves are normalized to 1.

As an example of the aerosol solutions for a relative humidity of 80% and seven of the tenmodel curves, Figure 6.17 shows a plot of the dependence of ε(λ, 870) on wavelength. Tothe left of each curve, the pairs of numbers are respectively ε(443, 870) and the average oreffective radius of the aerosol, reff in units of µm. Proceeding upward from the lowest curve,reff decreases from a value typical of a maritime radius to, at the top-most curve, a radiuscharacteristic of a continental aerosol. The magnitude range of reff extends across that of thewavelengths used in Figure 6.17. The lower three curves show a Mie scattering dependence;for the upper curves and the aerosol with the largest particles, LA(443) is approximatelytwice LA(870). For comparison, the Rayleigh path radiances give LR(443) 15LR(870), sothat the Rayleigh dependence on wavelength is much greater than the aerosol dependence.

Comparison of the observed value of ε(765, 865) with lookup tables derived from thesolution curves allows the observed NIR aerosol radiances to be extrapolated into the visibleand permits calculation of the diffuse transmittance. If the observed value of ε(748, 870)equals that of a model aerosol, then ε is assumed to equal the model result in the visible; ifε lies midway between two model aerosols, it is also assumed to lie midway between thesame two model results. Consequently, once the aerosol type or ε is determined, a solutionfor LA can be found in the visible, so that, for example at 443 nm,

LA(443) = ε(443, 870)LA(870)[F ′S(443)/F ′

S(870)] (6.9)



300 400 500 600 700 800 900

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

443 870748

NIRVISUV

0.12, 2.79

0.14, 2.12

0.44, 1.56

0.79, 1.08

1.20, 0.67

1.73, 0.32

2.02, 0.18ε

(λ, 8

70)

Fig. 6.17. The wavelength dependence of ε(λ, 870) for a relative humidity of 80%, a solar zenithangle of 30°, an instrument look angle of 60°, and a relative azimuth angle with respect to the Sun of130°. For each aerosol, the numbers on the curves show the values of ε(443, 870) and reff . See thetext for further description. (Figure courtesy of Ziauddin Ahmad, used with permission.)

The use of (6.9) for each band allows removal of the aerosol radiances from LT(λ),leaving the term tD(λ)LW(λ). For single scatter, tD(λ) is from Equation (4.55); for multiplescatter, tD(λ) is from lookup tables.

Aerosols are described in terms of two variables, the aerosol optical thickness τA and theAngstrom exponent α, determined as follows. Given the aerosol type from the procedurenext described, the scattering albedo ωA and the aerosol phase function PA in Equation(6.7) can be estimated in the NIR, which allows retrieval of the aerosol optical thicknessτA(λ) at 748 and 870 nm. The ratio of these τA(λ) can be written as follows:

τA(748)/τA(870) = (748/870)−α (6.10)

For particles that are large relative to λ, Mie scatter occurs so that τA is nearly constant andα is approximately zero, while, for small particles, the scattering tends toward Rayleighscattering and α is larger. For the aerosols, the magnitude of the optical thickness τA(870)is proportional to the concentration while α characterizes their size.

The global oceanic distribution of aerosols can be derived from the NIR bands. For Apriland October 1998, Figure 6.18 shows the global oceanic distribution of α and τA(870)(Wang et al., 2000). On the figure, land is black and regions with no data are gray. To thenorth and south, the gray regions correspond to sea ice; to the west of Africa, to opticallythick dust blowing off the Sahara desert (April), or to biomass burning in southern Africa(October). The upper images show that most of the global oceanic aerosols have a smalloptical thickness (τ 0.1, 0.2). The lower images show that, in the Southern Hemisphere


168 Ocean color

Fig. 6.18. A monthly global composite SeaWiFS image of the aerosol optical thickness τA(865) forApril (a) and October (b) 1998, and the Angstrom exponent α for the same periods, (c) and (d).The color bars show the scales; land is black and regions with no data are gray. See the text forfurther description. (Figure 1 from Wang et al. (2000), C© 2000 American Geophysical Union, repro-duced/modified by permission of AGU, courtesy of Menghua Wang; OrbView-2 Imagery provided byORBIMAGE, the SeaWiFS Project and NASA/Goddard Spaceflight Center.) See color plate section.

and away from land, α is small, implying large marine particles. In contrast, off the eastcoast of North America, around Europe and on the east coast of Asia, α 1, implyingthe presence of what are probably small sulfate particles characteristic of coal-fired powerplants.

6.5.3 CZCS atmospheric correction algorithm

Because CZCS had no bands in the NIR, its atmospheric correction proceeded as follows.For each image, an operator determined the values of ε from the 670-nm band using oneof two different methods. In the first, the operator estimated the aerosol type by guessingthe values of ε(λ, 870). These were generally assumed to be close to unity and were basedon the particular geographic region. The aerosol concentrations and resultant water-leavingradiances varied with this guess. In the second, the operator searched each image for a clear


6.6 Surface validation data sets and calibration 169

water pixel, defined as a pixel containing only clear seawater for which LW(λ) could becalculated. For this pixel, the LW(λ) and the Rayleigh radiances were removed from LT(λ),yielding the aerosol radiances at all wavelengths. These aerosol radiances were then usedto calculate the values of ε(λ, 870), which were assumed constant across the entire image.As long as the aerosol composition remained constant, then, even though its concentrationvaried from pixel to pixel, both procedures removed the aerosol radiances. This assignmentof ε or search for a clear-water pixel meant that each image had to be individually processed,which was both time-consuming and a source of uncertainty.

6.6 Surface validation data sets and the vicarious calibration

Because of the dominance of the aerosol radiances in the retrieval algorithms, the instru-ments cannot be calibrated from on-orbit measurements alone. Instead, while the on-orbitmeasurements remove the effects of the instrument degradation with time, the vicariouscalibration removes the wavelength-dependent systematic bias associated with the atmo-spheric correction (Eplee et al., 2001; Bailey et al., 2008). Section 6.6.1 discusses the typesof in situ data sets used in the vicarious calibration; then following Franz et al. (2007),Section 6.6.2 discusses the nature and results of this calibration.

6.6.1 Surface validation data sets

The following discusses the types of in situ calibration data used in the vicarious calibra-tion: moored buoys, radiances from areas of open ocean in the Southern Hemisphere andindividual stations taken by ship. The buoy used in the NASA vicarious calibration is theMarine Optical Buoy (MOBY) off Hawaii.

Regarding the MOBY location, Gordon (1998) and Eplee et al. (2001) give the require-ments for the vicarious calibration site: homogeneous waters with an extended area of case1 waters containing low concentrations of chlorophyll and an atmosphere that is relativelycloud-free containing an optically thin aerosol of constant known properties. The watershould be sufficiently clear that in the NIR bands, the water-leaving radiance is essentiallyzero. Based on these conditions, MOBY was placed 20 km west of Lanai in Hawaii (Baileyet al., 2008). Since July 1997, MOBY has been continuously deployed by NOAA, andduring monthly visits serviced to remove biofouling. At three-month intervals, the buoyis brought to shore for additional service while a duplicate buoy is deployed in its place(McClain et al., 2006). MOBY provides in situ direct measurements of the water-leavingradiances at the satellite wavelengths and of chlorophyll. For the wavelength range of 340–955 nm, MOBY measures the water-leaving radiance upwelling radiance with a spectralresolution of 0.6 nm.

There is a second buoy in the Mediterranean called Bouee pour l’acquisition de SeriesOptiques a Long Terme (BOUSSOLE) (Bailey et al., 2008; Antoine et al., 2008). TheBOUSSOLE location is in the northwestern Mediterranean between France and Cyprus,


170 Ocean color

where during monthly visits, it is maintained by the French weather agency. The waters inthis area are predominantly case 1 where a strong bloom in spring, followed in summerby a stable period of oligotrophic conditions, provides a variety of conditions for sensorcalibration. Because of its proximity to the European landmass and the resultant land-based aerosols as well as the variable chlorophyll, NASA does not use BOUSSOLE in itscalibrations.

The SeaWiFS Bio-optical Archive and Storage System (SeaBASS) provides anotherdata set for instrument calibration and algorithm development. Beginning in 1997, theNASA-sponsored SeaWiFS Bio-optical Algorithm Mini-Workshop (SeaBAM) under thedirection of the NASA OBPG began collection of the SeaBASS global surface radianceand chlorophyll data set. SeaBASS contains simultaneous in situ measurements of radi-ance and chlorophyll, and less-frequent simultaneous in situ observations of chlorophyll andsatellite-observed radiances, as well as atmospheric properties such as aerosol thicknesses(SeaBASS, 2013; SeaDAS, 2008). In 1997, the data set consisted of 919 different stations,containing a range of chlorophyll of 0.019 mg m−3 < Ca < 32.79 mg m−3 (O’Reilly et al.,1998).

In about 2005 and specifically for validation of the satellite algorithms, the OBPG defineda subset of SeaBASS called the NASA bio-Optical Marine Algorithm Dataset (NOMAD).NOMAD consists of high-quality surface observations of water-leaving radiances, watertemperatures and salinity, inherent optical properties and chlorophyll, along with metadatasuch as the time, date, water depth and coordinates of individual stations (Werdell andBailey, 2005).

In early 2013, from 2529 field campaigns conducted by 112 national and internationalcontributors, SeaBASS contained 71,302 data files and 422,472 individual stations withlocations ranging from coastal to offshore regions. At the same time, version 2 of NOMADcontained 4459 records, again from a variety of coastal and offshore regions. In NOMAD-2,the concentrations of chlorophyll range from 0.017 to 70.2 mg m−3, with a median valueof around 0.54 mg m−3, so that most of the samples are from oligotrophic and mesotrophicwaters. Although NOMAD has more than 4000 stations, only several hundred of thesecontain the combination of water-leaving radiances, pigment concentrations, absorptionand backscatter coefficients (J. Werdell, 2013, private communication).

6.6.2 The vicarious calibration

In the ocean color retrieval, the aerosol correction dominates the algorithm and is mostsubject to error. The purpose of the vicarious calibration is to remove any systematicbias in the instrument/atmospheric algorithm that exists after the on-orbit calibration. ForSeaWiFS, it is based on the ratio of the NIR band 7 to band 8 aerosol radiances, which is thenextrapolated into the shorter, visible wavelength bands. These values are then comparedwith the predicted radiances measured at the satellite.

Franz et al. (2007) give the details of the calibration. The goal is to adjust the responseof the sensor/algorithm system to maximize the agreement between the satellite-retrievedand the measured in situ water-leaving radiances. This calibration assumes that the on-orbit


6.7 Chlorophyll reflectance and fluorescence 171

calibrations remove the time-dependent changes in the instrument, so that over the missionlifetime, the bias removed by the vicarious calibration is constant. Eplee et al. (2012)describes the iterative approach used for the vicarious calibration.

As Section 6.5 describes, application of the atmospheric corrections to the retrievedradiances produces the water-leaving radiances LW(λ). In the vicarious calibration, theratio of the simultaneous in situ and satellite-retrieved water-leaving radiances LW(λ) iscalculated. This ratio is the vicarious gain, which is used to bring the satellite and surfaceradiances into agreement. The procedure divides into two parts, first the NIR bands arecalibrated, then the retrieved aerosol radiances are used to calculate the satellite LW(λ),which is then compared with the in situ value.

It takes 2–3 years to gather sufficient data for a successful vicarious calibration. For Sea-WiFS, it required two years to obtain about 30 cloud-free and sun-glint-free simultaneouscomparisons with MOBY; for the MODIS instrument, with its inability to tilt to avoid sunglint, it took about three years (McClain et al., 2006). In this calibration and for the NIR,the first assumption is to set the gain of the 865-nm band to 1. The second assumption is thatthe aerosol type is known, so that the aerosol radiances for the 765- and 748-nm SeaWiFSand MODIS bands can be calculated. At the recommendation of the OBPG, this calculationis done at clear-water sites in the South Pacific and in the South Indian Ocean, where bothlocations have zero water-leaving radiances and known, thin aerosol types. With the gainof the 765-nm band determined, the algorithm is applied for all of the visible bands fromthe MOBY site.

In the data screening, if there are clouds, stray light or aerosol optical thicknesses greaterthan 0.15, or if Ca > 0.2 mg m−3, the data are discarded. For nine years of SeaWiFS data,there were 1450 potential match-ups, of which 150 passed the screening test. For the gaincorrection, 150 of these match-ups were aggregated to produce a mean and a standarddeviation of the mean. To minimize the effects of outliers, the points used in the calculationlie within the central 25%–75% of the data. For SeaWiFS and MOBY, and for the 443-,555- and 765-nm bands, Figure 6.19 shows an example of the gain coefficients calculatedfrom the ratio of the in situ to the satellite radiances determined at the top of the atmosphere.Specifically, at 443 nm, the gain is 1.014 ± 0.0007; at 765 nm, 0.9720 ± 0.0011. For allSeaWiFS bands, the changes were less than 4%.

6.7 Chlorophyll reflectance and fluorescence

In the following, Section 6.7.1 describes the response of the subsurface reflectance at thedifferent observational bands to increasing values of chlorophyll; Section 6.7.2 describesthe retrieval of chlorophyll florescence.

6.7.1 Reflectance

From the scattering and absorption behavior described in Section 6.2 and for seawatersamples taken at sites off the Oregon coast, in the Gulf of Maine and from Puget Sound,


172 Ocean color

1998 1999 20012000 20032002 200620052004Year

1.05

1.00

0.95

1.05

1.00

0.95

0.90

765 nm

443 nm

1.05

1.00

0.95Gai

n co

effic

ient

555 nm

Fig. 6.19. From September 1997 to March 2006, the vicarious gains derived from MOBY for SeaW-iFS bands 443, 555 and 765 nm. The black circles show the individual gain measurements; the solidlines show the derived averaged gain. See the text for further description. (Redrawn from Figure 3,Franz et al. (2007).)

Figure 6.20 shows the dependence on wavelength and chlorophyll concentration Ca ofthe subsurface reflectance R(λ) defined in Equation (5.22). On the figure, the horizontalbars show the location of the SeaWiFS and MODIS bands where the black bars iden-tify the bands used in the empirical Chl-a algorithms discussed below. Examination ofFigure 6.20 shows that, as Ca increases, the reflectances have the following wavelength-dependent behavior. First, for λ < 550 nm, R decreases as Ca increases; for λ 550nm, R increases as Ca increases; while at λ = 550 nm, R is approximately indepen-dent of Ca. Second, the radiance emitted at the 683-nm fluorescence peak increases withincreasing Ca.

As discussed below, the empirical algorithms discussed in Section 6.7.2 make use ofthe reflectance behavior shown in Figure 6.20 for λ 550 nm to retrieve the chlorophyllconcentrations. At the 443-nm absorption peak and for Ca 1 or nearly clear-water, thefigure shows that R(443) 0.08. As Ca increases, R(443) decreases dramatically and themaximum reflectance shifts toward 500 nm, so that the water-leaving radiances becomemore green and less blue. For Ca greater than about 1–2 mg m−3, R(443) becomes sosmall that it approaches the noise floor of the instruments, while, at 490 and 530 nm,the presence of accessory pigments with the weaker dependence of their absorption onCa means that R decreases more slowly with increasing concentration. Consequently,the algorithms discussed in Section 6.7.2 depend not only on the radiances measured atthe 443-nm Chl-a absorption peak, but also on radiances in the 490–550-nm range that aredominated by carotenoid absorption.


6.7 Chlorophyll reflectance and fluorescence 173

400 450 550 600 650 700500Wavelength (nm)

Ref

lect

ance

0.07

0.09

0.6

1.3

2.8

8.7

8 10 11 12 13 14

10–1

10–2

10–3

10–4

1 3 4 5 62

9

Fig. 6.20. The subsurface reflectance R(λ) plotted versus wavelength, for several values of Ca shownto the left and adjacent to each curve in units of mg m−3. The lower horizontal bars show the MODISbands; the upper, the SeaWiFS bands. For clarity, SeaWiFS band 4 is vertically offset. For each setof bands, the black bars identify those used in the SeaWiFS and MODIS Chl-a empirical algorithmsdiscussed in Section 6.8 (Data from Roesler and Perry (1995), courtesy of Collin Roesler.)

For the algorithms to be successful, the concentrations of carotenoids and accessorypigments must covary with Chl-a in all parts of the ocean. Trees et al. (2000) showthat, even though the ratios of the accessory pigments to the Chl-a concentrations varylocally, globally the concentrations covary. They find that a log-regression of the measuredaccessory pigments against Chl-a yields a correlation coefficient of 0.934 with a root-mean-square error of 28%. This strong correlation in part explains the success of the algorithms.Finally, although, at small Ca, R(412) is sensitive to changes in Ca, its companion sensitivityto CDOM and suspended particles means that the 412-nm band cannot be used in achlorophyll algorithm without an accompanying CDOM algorithm.

6.7.2 Fluorescence

Figure 6.20 also shows that the magnitude of the 683-nm chlorophyll fluorescence peakincreases with Ca. Fluorescence is generated from re-emission in the red of a portionof the solar radiation that is absorbed at the visible wavelengths by the phytoplanktonchlorophyll. Of the absorbed radiation, about 85% is lost as heat, up to 12% is converted tochemical energy through photosynthesis and about 3% is re-emitted as fluorescence (Esaias


174 Ocean color

et al., 1998). Measurement of the fluorescence emission provides an alternative method forestimation of Ca as well as for determination of other phytoplankton properties. Letelierand Abbott (1996) and Esaias et al. (1998) show that determination of the fluorescencemagnitude requires radiance measurements at the triplet of 10-nm-wide bands centeredat 667, 678 and 748 nm, where the 678-nm measurement determines the fluorescenceand the 667- and 748-nm measurements allow removal of the background contribution.Because of the 687-nm atmospheric oxygen absorption line shown in Figure 6.7, the 678-nm band was located slightly below the 685-nm florescence peak. Measurements at thistriplet allow determination of the chlorophyll-generated fluorescence line height (FLH).Behrenfeld et al. (2009) summarize the properties of the fluorescence mechanism and givethe results of global surveys.

Although VIIRS lacks the florescent bands and SeaWiFS band 6 is too wide to observethe details of the fluorescence peak, ocean color instruments that carry this observingtriplet include MODIS, MERIS and the Japanese Global Imager (GLI) on the short-livedADEOS-2. The advantage of this measurement is that the fluorescence is produced onlyby chlorophyll and is independent of CDOM and particles. From measurement of FLHand by making assumptions about the absorbed light and the species-specific fluorescencequantum efficiency, Ca can be calculated. Alternatively, knowledge of the species and itsconcentration yields the fluorescence quantum efficiency. In summary, there are at leasttwo kinds of Chl-a algorithms: those that function in the blue–green (400–550 nm), where,as Ca increases, the reflectances at 440, 490 and 530 nm decrease relative to 550 nm,and those in the vicinity of the 683-nm fluorescence peak where the reflectances increasewith Ca.

6.8 The empirical, semi-analytic and biogeochemical algorithms

In the following, Section 6.8.1 describes the NASA data archive called Giovanni (Ackerand Leptoukh, 2007), then, in order of their increasing complexity, three algorithms forbiological retrievals, where the Giovanni archive contains the algorithm products, arediscussed. First, Section 6.8.2 describes the empirical bio-optical algorithms for SeaWiFSand MODIS with an emphasis on chlorophyll retrieval. These algorithms depend only on theratio of pairs of water-leaving radiances at two different wavelengths, and retrieve individualquantities such as chlorophyll, the diffuse attenuation coefficient K(490), CDOM, calciteand particulate carbon (McClain, 2009).

Second, Section 6.8.3 discusses the semi-analytic algorithms, specifically the Garver–Siegel–Maritorena (GSM) algorithm (Maritorena et al., 2002). The semi-analytic algo-rithms combine observational models of the various absorption and scattering IOP coef-ficients discussed in Section 6.2 with the observed radiances to retrieve ocean propertiessuch as chlorophyll concentration, CDOM and the particulate scattering coefficient. Third,Section 6.8.4 describes the data assimilation models, with the specific example of theNASA Ocean Biogeochemical Model (NOBM) (Gregg, 2008). The NOBM combines the


6.8 The algorithms 175

daily chlorophyll data retrieved from the empirical algorithm with other satellite data suchas SST, clouds and radiation with numerical models of the ocean circulation and biogeo-chemical processes to retrieve the distribution of four species of phytoplankton, the totalchlorophyll and a variety of nutrients.

6.8.1 The NASA data archives

The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC)contains a wealth of tutorials, data and graphic tools (NASA, 2013a). Within this center,the GES DISC Interactive Online Visualization ANd aNalysis Infrastructure (Giovanni)provides tools for data access, analysis and visualization (Giovanni, 2013). In its oceanportal, Giovanni contains a variety of biological and radiative data, including productsfrom the empirical, GSM and NOBM algorithms. Using the Giovanni programs, these datacan be displayed as images or in a variety of time and space displays, such as histograms andwaterfall plots. Also within GES DISC, the Laboratory for Ocean Color Users (LOCUS)provides references, examples and Giovanni tutorials (LOCUS, 2013).

6.8.2 Empirical bio-optical algorithms

The empirical algorithms are derived from regression of coincident ship and satellite obser-vations of LW(λ) against the SeaBASS shipboard observations of Ca (O’Reilly et al., 1998;Carder et al., 1999). The inputs to these algorithms are ratios of satellite observations ofLW(λ) or equivalently Rrs(λ) at several wavelengths; the output is chlorophyll concentrationand other oceanic variables such as CDOM, where each variable is calculated separately.

This section concentrates on the empirical chlorophyll algorithms, which provide conti-nuity within the almost 40-year record of ocean color satellite observations. Dierssen (2010)provides a review and critique of these algorithms. In Giovanni, the empirical algorithmsuse Rrs(λ) as input, where, from Equation (5.31),

Rrs(λ) = T 2R(λ)/(n2Q) (6.11)

From (6.11), Rrs(λ) is a linear function of subsurface reflectance R(λ). Because Figure6.20 shows that R(555) is approximately independent of chlorophyll concentration, theradiances or reflectances used in the empirical algorithms are expressed as ratios relativeto their value at 555 nm, so that, from Equation (6.11),

Rrs(λ)

Rrs(555)= R(λ)

R(555)(6.12)

As Equations (6.11) and (6.12) show, an advantage of working with ratios instead ofwith the individual radiances or reflectances is that the uncertainties associated with lightpropagation across the interface represented by n2, T2 and Q cancel out. For this reason,the empirical algorithms are also called band-ratio algorithms.


176 Ocean color

In the chlorophyll retrievals, the band-ratio algorithms use ratios of Rrs(λ) based on thewavelength pairs 443/555, 490/555 and 510/555. The CZCS algorithm uses the first andthird pair, SeaWiFS uses all three and MODIS uses the first two. From field data, Figure6.21 shows the dependence of the Rrs ratios on Ca. The figure shows that, as Caincreases,the 443-ratio decreases most rapidly, and the 490- and 510-ratios respectively decreasemore slowly. This means that the 443-ratio is largest for small Ca, then, as Ca increases, the490-ratio becomes the largest, followed by the 510-ratio. This behavior provides the basisfor the empirical algorithms, which employ what is called a maximum band ratio approach.

From the SEABASS data described in Section 6.5, O’Reilly et al. (1998) tested twosemi-analytic and fifteen empirical regional and global algorithms, where global refers toa single algorithm that provides reasonable results for tropical, subtropical and temperatewaters. The SeaWiFS global algorithm that provided the best fit to the SeaBAM data wasthe maximum band ratio Ocean Chlorophyll-4 (OC4) algorithm, which is version 4 of therecommended algorithm. As this section describes, MODIS uses a similar maximum bandratio algorithm with another proposed for VIIRS (VIIRS, 2011b).

The reason why they are called maximum band ratio algorithms is that there is nofixed value of Ca at which the algorithm switches ratios. Instead, the algorithm uses thelargest of the following Rrs-ratios (443/555, 490/555, 510/555). As Caincreases, the OC4algorithm first uses the 443-ratio, then, when the 490-ratio is greater than that derived fromthe 443-ratio, OC4 switches to the 490-ratio, and finally to the 510-ratio. The advantage ofthis approach is that, over a broad range of Ca , the signal-to-noise ratio remains as large aspossible. The current form OC4 version 6 (v6) algorithm gives the best polynomial fit ofthe remote sensing reflectances to the in situ observations from the NOMAD data set.

For SeaWiFS, the OC4 v6 algorithm consists of the following fourth-order polynomial(Band ratio algorithms, 2010):

RMAX = Maximum of [Rrs-ratio (443/555, 490/555, 510/555)]

RL = log10 (RMAX)

log10 (Ca) = 0.3272 − 2.994RL + 2.722R2L − 1.226R3

L − 0.568R4L (6.13)

For the OC4 v6 algorithm, Figure 6.22 shows the dependence of Ca on RMAX. Thefigure shows that Ca increases as RMAX decreases. At small values of Ca , the 443-ratiodominates; at intermediate values, 490 dominates; at large values, 510 dominates. Becausethe range of the dominant bands overlaps by 10%–30%, the algorithm experiences smoothtransitions as RMAX varies. Following Dierssen (2010, Figure 1), the sloping bars show theapproximate range and slope for each dominant band.

As Ca increases, the polynomial in Equation (6.13) has three different slopes: gentle(−1.6) corresponding to the 443-ratio; intermediate (−2.4), the 490-ratio; steep (−3.6),the 510-ratio. The importance of these slopes is that those parts of the curve with steepslopes are more sensitive to errors than those with smaller slopes, where steep slopes leadto large errors in the retrieved chlorophyll concentration (Dierssen, 2010). This suggeststhat the smallest errors in the model occur for the lowest chlorophyll concentration, where,



100

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0.10.01 0.10 1.00 10.00 100.00

100

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0.01 0.10 1.00 10.00 100.00

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R rs(

510)

/Rrs

(555

)R

rs(4

90)/

Rrs

(555

)R r

s(44

3)/R

rs(5

55)

Fig. 6.21. The dependence of Rrs(λ)/Rrs(555) on Ca for λ = 443, 490 and 510 nm. The straightlines are the linear least-square fits to the data. (Adapted from Aiken et al. (1995), not subject to UScopyright.)


178 Ocean color

0.1 1.0 10.0RMAX

10–3

10–2

0.1

1

10

102

Ca

Fig. 6.22. A comparison of the in situ NOMAD observations and satellite Chl-a for the OC4 v6maximum band algorithm. The gray tilted bars are adapted from Dierssen (2010, Figure 1); the uppervertical bar shows the factor of 5 range of the modeled data, the lower vertical bar shows the factor of2 range, the dashed horizontal line shows the oceanic median value of chlorophyll at 0.2 mg m−1. Seethe text for further description. (Figure courtesy of NASA, ocean color reprocessing, 2010. The dataused in this effort were acquired as part of the activities of NASA’s Science Mission Directorate, andare archived and distributed by the Goddard Earth Sciences Data and Information Services Center(GES DISC).)

for waters with Ca< 0.2 mg m−3, the satellite values fall within a factor of 2 of the observedvalues, while large values of Ca are correct to within a factor of 5. For the low and highvalues of chlorophyll concentration, the vertical bars represent factors of 2 and 5.

In another comparison, Figure 6.23 compares the in situ values of the NOMAD v2 dataand OC4 v6 satellite-retrieved values of Ca , where the central 45° straight line is the line ofperfect agreement and the two dashed lines respectively show the 1:5 and 5:1 ratios (Bandreprocessing, 2010). Following Szeto et al. (2011), the algorithm uncertainty for the figureis written in terms of the variable i , defined as

i = log10(Xi) (6.14)

where the chlorophyll ratio Xi = Csat, i/Cin situ, i and the subscript i refers to the individualobservations. From Equation (6.14), the mean of i is the bias; the root-mean-square (rms)is the uncertainty. For the data shown in Figure 6.23, the bias is 0.000, the correlationcoefficient is 0.861 and the rms is 0.250. On the assumption that is normally distributed,the chlorophyll ratio X has a log-normal distribution. For Figure 6.23, this means that 68%of the values lie within of 10±rms, or, for a median value of 1, between 0.56 and 1.78,

Figure 6.23 shows that, except for a slight disagreement between the two data sets forCa < 0.05 mg m−3 and a scatter that increases with concentration, the in situ and modeldata sets are in agreement. For carefully selected data, better agreement is possible. For the



10–2 0.1 1 10 102

Cain situ

10–2

0.1

1

10

102

Cam

odel

r 2: 0.861rms: 0.250bias: 0.000

Fig. 6.23. A log–log comparison of the SeaWiFS OC4 algorithm with the in situ NOMAD data. Ineach panel, the solid line shows Ca from Equation (6.15); the data points show the dependence ofthe chlorophyll concentration on the Rrs-ratios. The dashed lines show the factor of 5 range of themodeled data; the inset shows, for the data set, the r2-coefficient, the rms and bias. See the text forfurther description. (Figure courtesy of Jeremy Werdell, see legend of Figure 6.20 for credit.)

special case of SeaWiFS, ocean water depths greater than 1000 m and a carefully filtereddata set, Bailey and Werdell (2006) show that, for coincident field and satellite observations,the accuracies of the retrieved radiances lie within 6%–12% of the observed, or 1–2 timesthe desired 5% accuracy. From Werdell (2013, private communication), the sources of thiserror are about half from the surface radiometers and half from the satellite.

Because MODIS lacks the 510-nm band used in the OC4 SeaWiFS algorithm, theMODIS maximum band ratio algorithm uses three bands instead of four. The algorithm,called OC3M v6 for MODIS, is the successor to the SeaWiFS empirical algorithms, iscurrently used for AQUA MODIS processing and is written as follows (Band reprocessing,2010):

RL = log10 (max[Rrs-ratio (443/551, 488/551)])

log10(Ca) = 0.2424 − 2.742RL + 1.802R2L + 0.002R3

L − 1.228R4L (6.15)

For OC3M, the relation between Rrs and chlorophyll was parameterized with the sameSeaBAM data as used with OC4. Examination of the figures given at Band reprocessing(2010) shows that OC3M has similar statistics to the OC4. For SeaWiFS and MODISAQUA, Giovanni (2013) contains monthly and 8-day averages of the band-ratio products ata 9-km resolution, with some MODIS products given at a 4-km resolution, posted at abouta one-month delay.

The BOUSSOLE site permits a direct comparison of satellite-retrieved data with in situdata. Figure 6.24 compares the monthly in situ measurements with the MERIS, AQUAMODIS and SeaWiFS retrieved values of chlorophyll. The monthly servicing of the buoy


180 Ocean color

0.1

1

Chl

-a (

mg

m–3

)2003 2004 2005 2006

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 6.24. For 2003–2008, comparison of the seasonal cycles of the surface chlorophyll measuredat the BOUSSOLE site. The black circles are the average surface (<10-m depth) values determinedfrom monthly field samples; the diamonds are satellite chlorophyll concentration determinations fromMERIS, SeaWiFS and MODIS-AQUA. The thin curve shows a fit to the satellite data; the thick curveis a fit to the in situ values, where the changes in time are derived from the satellite curve. The satellitedata are from a 3×3 km cloud-free box centered at the buoy. The vertical line with the crossbars showsthe factor of 2 range of the modeled data. See the text for further description. (From Antoine et al.(2008), Figure B1, C© AGU.)

includes collecting in situ data; the satellite data are from a 3 km × 3 km area centered onthe buoy, which is filtered for clouds and sun glint. Figure 6.24 shows that the field andin situ curves are in approximate agreement, with the peaks in both data sets occurringduring the spring bloom, followed by a quiescent period. The error bar shows the range ofthe 1:2 and 2:1 ratio, and suggests that the satellite values agree with the observed within afactor of 2–3.

Another comparison is in the application of the OC4 band ratio algorithm to the coastalwaters of British Columbia, Washington and Oregon. For 1 September 1999, Figure 6.25shows the total radiances LT(λ) for the wavelengths of 865, 765, 670, 555, 443 and 412 nmand illustrates the effect of Rayleigh scattering. The gray scales to the right of each imageare in radiance counts. For the images at 765 and 865 nm where LW is near zero, land andclouds are bright, and except for the radiances associated with the sediment plumes at themouths of the Columbia and Fraser Rivers, the ocean is dark. The 865-nm image showshow, at this particular wavelength, the clouds stand out against the ocean background.Both the Columbia River and Fraser River carry large sediment loads, which from personalobservation generate a brownish yellow color in the surface waters. At 670 nm, the riverplumes remain visible and there is a suggestion of a large vortex or jet off the Strait ofJuan de Fuca. For shorter wavelengths, examination of the remaining images shows thatRayleigh scatter progressively obscures the land and ocean surface.



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Fig. 6.25. The total radiances received at the SeaWiFS instrument for the northeast Pacific adjacentto British Columbia, Canada and Washington and Oregon, United States on September 1, 1999.The channels include the two NIR channels at 865 and 765 nm, the 670-nm channel spanning thefluorescence peak, and three channels in the blue-green at 555, 443 and 412 nm. On the figure, VIis Vancouver Island; FR, Fraser River; JdF, Strait of Juan de Fuca; PS, Puget Sound; CR, ColumbiaRiver. (OrbView-2 imagery provided by ORBIMAGE, the SeaWiFS Project and NASA/GoddardSpaceflight Center, processing courtesy of Brandon Sackmann and Miles Logsdon.)


182 Ocean color

Figure 6.26 shows the normalized water-leaving radiances [LW(λ)]N for 670, 555, 510,490, 443 and 412 nm. Because their water-leaving radiances are zero except at the rivermouths, the 865- and 765-nm images are omitted. The radiance scales are to the right ofeach image; these vary from image to image and are chosen to maximize the contrast. Thelength of these scales is proportional to the range of radiance values; the shorter the bar, themore sensitive the measurement. Examination of the image for the 670-nm band shows thatthe productive regions adjacent to the coast are bright, the river outflows are very bright,and the offshore waters are dark. This suggests that, at 670 nm, the bright radiances awayfrom the river mouths are generated by fluorescence; adjacent to the rivers, they are causedby reflection from CDOM and sediments. At 555 nm, which is used in the denominatorof the Rrs -ratios, the image does not have a uniform brightness, rather the river mouthsremain bright. Away from these regions, the 555-nm radiances generally follow the Chl-adistribution but with less contrast.

At 510 and 490 nm, the river mouths remain bright, while, away from these areas, theradiance pattern is reversed from the 670-nm fluorescence image, in that the water-leavingradiance is now less bright in the high Chl-a water adjacent to the coast than in the lessproductive, offshore water. At 443 nm, [LW(λ)]Nis zero in the high-Chl-a waters adjacentto the coast, and there is only a slight hint of a bright region off the Fraser River delta.Finally, at the 412-nm absorption maximum for suspended material and CDOM, the onlybright pixels in the image occur in the offshore region of low concentrations of Chl-a. Thisshows that the radiances at the river mouths become smaller at those wavelengths where theenhanced attenuation associated with CDOM and particles predominates. In summary, ona band-by-band basis, the images are consistent with the algorithms and with the regionaloceanography. The above images also illustrate the difficulties that the empirical algorithmshave with sediment-laden waters.

Figure 6.27(a) shows a true color image of the region, obtained by a red–green–blue(RGB) mixing of the 670-, 555- and 410-nm bands, with Rayleigh scattering removedand the colors enhanced. The image shows green land, snow in the mountains and whiteclouds off the coast. Away from the coast, the water is blue; closer to the coast, it is darkerblue with hints of green. The image also shows the sediment plumes off the mouths ofthe Columbia and Fraser Rivers. For comparison, Figure 6.27(b) shows the OC4 Chl-aconcentrations in units of mg m−3. The land and clouds are masked in black, the coastis outlined in red. Because the processing of this image depends on the assumption of azero water-leaving radiance at 865 and 765 nm, the results are invalid adjacent to the rivermouths. Figure 6.27(b) shows enhanced biological activity adjacent to the coast, a numberof plumes and jets extending into the Pacific and the absence of biological activity in theoffshore waters. The image also shows that, at the Pacific entrance to the Strait of Juande Fuca, a plume of a high-chlorophyll water flows into the low-chlorophyll Pacific water.The overall chlorophyll distribution is consistent with field observations, in that coastalupwelling generates the productive regions adjacent to the coast, while the offshore regionsremain inactive. Because of land contamination from diffuse attenuation, there is littleusable data from the interior of Puget Sound.


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184 Ocean color

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Fig. 6.27. Composite SeaWiFS image of the northeast Pacific adjacent to British Columbia, Canadaand Washington and Oregon, United States on September 1, 1999. (a) A true color image, mixed fromSeaWiFS bands at 410, 555 and 670 nm, with Rayleigh scattering removed. (b) The Chl-a distributionfor the same region in mg m−3. Black corresponds to land and to cloud mask. (OrbView-2 Imageryprovided by ORBIMAGE, the SeaWiFS Project and NASA/Goddard Spaceflight Center; processingcourtesy of Brandon Sackmann and Miles Logsdon.) See color plate section.

6.8.3 The Garver–Siegel–Maritorena (GSM) semi-analytic algorithm

In contrast to the band ratio algorithms, the semi-analytic algorithms combine theoreticalmodels of the relation of Rrs(λ) on the backscatter and absorption coefficients, with empiri-cal models of the dependence of the absorption and backscatter on the oceanic constituentsdescribed in Section 6.2. For the semi-analytic models, as Carder et al. (1999) review,combination of the measured Rrs(λ) with the theoretical and empirical models yields a setof simultaneous equations for quantities such as Ca, the combined dissolved and detritalabsorption coefficient and the particulate backscatter coefficient. For case 2 waters, thisapproach allows chlorophyll to be retrieved in the presence of CDOM.



The Garver–Siegel–Maritorena (GSM) model archived in Giovanni combines theoret-ical models of the Rrs(λ) dependence on the backscatter and absorption coefficients withempirical formulas that allow the retrieval of three quantities: CDOM, Ca and the particulatebackscatter coefficient (Maritorena et al., 2002; Maritorena and Siegel, 2006).

When the total absorption and scattering from Equations (6.1)–(6.5) replace the clear-water absorption and scattering terms in Equation (5.31), it becomes

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aw(λ) + aCDOM(λ) + aph(λ) + bbw(λ) + bbp(λ)

)i

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In Equation (6.16), the clear-water absorption and backscatter are known; the absorptionof CDOM and chlorophyll, and the particulate backscatter coefficient, are unknown.

These three unknowns divide into two parts: their functional forms given in Equations(6.3)–(6.5) as specified by values of Y, S and a∗

ph(λ), and their unknown magnitudes,aCDOM(443), Ca and bbp(443). In the retrieval of these unknowns, one runs for Equation(6.16) a nonlinear least-squares regression that minimizes the mean square differencebetween the measured and modeled values ofRrs(λ) at wavelengths of 410, 440, 490, 510and 555 nm. Because CDOM, chlorophyll a and particulate backscatter have differentfunctional dependences on wavelength, with chlorophyll having a peak at 443 nm, theCDOM having an exponential decay and the scattering having a nearly flat response, theseunknown terms are separable.

The retrieval yields not only the desired terms, but also, because the errors in theradiances can be propagated through the equations, the errors in the retrieved variables.Maritorena et al. (2010, their Figure 10) show the daily and monthly average percenterror for February 2, 2009 and February 2009. Their daily errors are 20–70%; theirmonthly errors are 15%–45%. From a large oceanic data set consisting of primarily case1 waters, Maritorena and Siegel (2006) derive the values of S, Y and a∗

ph(λ). For SeaWiFS,S = 0.0206 nm−1, Y = 1.0337, and Figure 6.28 shows the wavelength-dependence of a∗

ph(λ).For a global comparison of the band-ratio and GSM algorithms, Figure 6.29 shows

for 2011 the global annual distribution of four quantities: the empirical and semi-analyticdistributions of Chl-a, the CDOM absorption at 443 nm and the normalized fluorescence lineheight (FLH), as derived from Giovanni. Because this is a global algorithm applied to case1 and case 2 waters, Maritorena et al. (2010) show that the errors are greater in the coastalregions, as well as in high-latitude regions for which the algorithm was not designed. AsMaritorena and Siegel (2006) state, the algorithm can also be tuned against coastal waters,yielding a more suitable algorithm for case 2 waters. For these quantities, the empiricalChl-a is from Equation (6.15), the semi-analytic distributions of Chl-a and aCDOM are fromthe GSM algorithm, and FLH is derived from the fluorescence triplet algorithm discussedin Section 6.7.2. For the GSM algorithm, the Giovanni archive provides the monthly valuesof the derived quantities at a 9-km resolution and at about a 10-month time lag.


186 Ocean color

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The two Chl-a distributions and the FLH image show that, along the equator in thePacific, there is a band of enhanced chlorophyll associated with the equatorial upwelling.This band is bounded to the north and south by large biologically unproductive areasthat lie within the subtropical gyres. Because the surface solar heating stabilizes the upperocean and limits the nutrient upwelling, these areas have low biomass. Regions of enhancedchlorophyll concentration associated with wind-driven upwelling exist along the west coastsof equatorial South America and Africa, near the tip of eastern South America in the vicinityof the Falkland Islands and around Antarctica, and in the marginal seas of the North Pacific.Comparison of the band-ratio and GSM values of Chl-a shows that, at high latitudes, theGSM values are greater than the empirical. Also, even though the FLH is derived verydifferently, it shows similar features to the other estimates, with strong fluorescence alongthe equator and at mid to high latitudes.

The CDOM absorption image shows that, because of river runoff, CDOM has a maximumin the river-rich Northern Hemisphere. In regions of biological productivity, the distributionis although enhanced by the presence of detritus and CDOM. This occurs in the equatorialPacific and in other regions of biological productivity such as around Antarctica. The imagealso shows the absence of CDOM absorption in the mid-ocean gyres where there is littledetritus or biological activity. Although these images vary from one another, they show thesame general features and are consistent with ship-based oceanographic investigations.

6.8.4 The NASA Ocean Biogeochemical Model (NOBM)

The band-ratio algorithms retrieve chlorophyll, and, as McClain (2009) describes, canalso retrieve a few species such as coccolithophores and harmful algal blooms (HAB).But, because many different species have similar spectral shapes in their water-leaving


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188 Ocean color

radiances, ocean color data alone cannot be used to identify them. Even though theymay have similar spectral responses, because certain phytoplankton species differ in theirbiogeochemical and physical behavior, the NASA Ocean Biogeochemical Model (NOBM)can retrieve their distributions.

In contrast to GSM and the band-ratio models, the NOBM is a data assimilation modelthat combines numerical models of the physical and biogeochemical ocean processes, wherethe satellite-observed chlorophyll from the band-ratio models constrains these models. Theoverall model combines the physical behavior and interaction of four phytoplankton groupswith nutrients, sunlight, SST, currents and winds to describe the changes in the species andnutrient distributions with time (Gregg et al., 2003; Gregg, 2008).

The numerical models contain the physics, radiative fluxes, oceanic currents, the dynamicheight observed by satellites, and the equations governing the exchange and develop-ment of the ocean biology, geology and chemistry. From Giovanni (2013), Gregg et al.(2003) and Gregg (2008), the data products from the NOBM model include total chloro-phyll, concentrations of nutrients and the concentrations of four phytoplankton species:diatoms, coccolithophores, cyanobacteria and chlorophytes. These species have differ-ent responses to nutrients and incident radiation and different growth and sinking rates.Although the concentrations and distributions of these species are model outputs andare not directly based on remote sensing observations, the constraint on these speciesis that the sum of their chlorophyll must equal the observed. The model also includesiron concentration, mixed layer depth, nitrate and sea ice cover. Figure 6.30 shows aschematic diagram of the coupled general circulation, radiative and biogeochemical model.The figure shows that atmospheric forcing from winds, SST, cloud cover, solar radiation,ocean circulation, advection/diffusion and the atmospheric deposition of iron drives themodel.

The source of iron is atmospheric entrainment from deserts such as Gobi, Sahara andthree deserts in India. The iron dust is transported over the ocean, with its depositiongreatest in the North Atlantic west of the Sahara, in the ocean south of India, and, to a lesserextent, in the western North Pacific east of China (Gregg et al., 2003, Figure 6). The ironhelps drive the biogeochemical model and growth of the different species. The four speciesrespond differently to this iron input; diatoms are the most sensitive and coccolithophoresare the least. The species also have different responses to the other nutrients, SST andincident solar radiation.

Figure 6.31 shows a schematic diagram of the biogeochemical processes model (Gregg,2008, Appendix A). On the right, the figure shows the four modeled phytoplankton species.These four species interact with the four nutrient groups to the left, which are dissolvednitrate, ammonium, silica that regulates the diatom growth and the iron that is externallyprovided from atmospheric deposition. The middle circle shows the deitrital pools thatcontain solid material; the lower oval shows the herbivores; the arrows show the flux ofmaterial. The circulation of the nutrients is as follows. On death of the phytoplankton,the ammonium immediately returns to the nutrient pool while the other nutrients first



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Fig. 6.30. A schematic diagram of the coupled general circulation, radiative and biogeochemicalmodel, NASA Ocean Biogeochemical Model (NOBM). See the text for further description. (Figurefrom Gregg (2008), Figure 1, C© Elsevier, used with permission.)

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Fig. 6.31. A schematic diagram of the NOBM biogeochemical processes sub-model shown in Figure6.22. See the text for further description. (Adapted from Gregg et al. (2003), Figure 1.)


190 Ocean color

remineralize, then return to the pool. The herbivores indiscriminately ingest all of thephytoplankton groups, then through excretion directly contribute ammonium and iron tothe nutrients. After the herbivores die, they dissolve, returning silica and nitrate to thenutrients. In the center, the detrital pools represent the material derived from diatoms andother species. When this material dissolves, it enters the nutrient pool and serves as anothersource for growth.

The behavior of the species and their different responses to nutrients and sunlightcontribute to the success of the model (Gregg et al., 2003). Diatoms have the fastest growthrate; cyanobacteria, the slowest. Diatoms have a sinking rate of 1 m d−1; cyanobacteriado not sink. Diatoms have the greatest sensitivity to iron, coccolithophores the weakest.Because of their faster growth rates, diatoms outcompete the other groups in the competitionfor available nutrients.

The NOBM produces daily gridded values of the four species, the total chlorophylland the four nutrients. For January 1, 1998 through December 31, 2007, Giovanni providesdaily and monthly values of these products. Using the optimal interpolation models for SSTdescribed in the next chapter, the NOBM also interpolates and fills any cloud-induced gapsin the satellite chlorophyll data. LOCUS (2013, Tutorial 8) provides additional informationon the data assimilation and gap-filling schemes. Comparison with in situ data shows thatthe calculated distributions of diatoms, cyanobacteria and coccolithophores qualitativelyagree with in situ data, while the chlorophytes did not (Gregg et al., 2008). The diatomspredominate at high latitudes, in coastal and equatorial upwelling regions, and are associatedwith regions of high nutrient availability. Cyanobacteria occurred in regions with low levelsof nutrients; coccolithophores are a transitional species.

Coccolithophores are an unusual class of phytoplankton. When they bloom, they growand shed external plates or shells, consisting of micrometer-scale white platelets madeup of calcium carbonate (calcite). Moore et al. (2012) review the literature; Holliganet al. (1993) describe a field study of a bloom of the most widespread coccolithophore,Emiliania huxleyi (E. huxleyi). E. huxleyi occurs in the mid to high latitudes, where itsblooms take place in one-month periods over areas of order 105 km2 and produce morecalcite than any other single organism. The importance of these blooms is two-fold. First,they generate large fluxes of dimethyl sulfide (DMS) to the atmosphere, which can triggercloud formation. Second, because each bloom generates of order 109 kg of calcite, theyenhance the absorption of atmospheric CO2. The presence of the white shells in the surfacewaters changes the water color to a milky blue. In contrast to the phytoplankton pigments,which strongly decrease the radiance in the blue while only slightly increasing it in thegreen, coccolithophores increase the water-leaving radiance uniformly in the blue and green(Balch et al., 1999).

From Giovanni and for June 2007, Figure 6.32 shows the monthly average distributionof the four species (Gregg et al., 2003). The images show that diatoms are abundant at highlatitudes. In the model, diatoms occur where iron deposition and nutrients are abundant,such as regions of coastal and equatorial upwelling where turbulent mixing supplies the


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Fig. 6.32. The June 2007 average of the NOBM monthly average distribution of diatoms, coccol-ithophores, cyanobacteria and chlorophytes. See the text for additional description. (Acknowledge-ments are provided in the caption of Figure 6.27.) See color plate section.


192 Ocean color

nutrients. Coccolithophores also occur at high latitudes, especially in the North Atlantic.Although, under favorable growth conditions, cyanobacteria cannot compete with diatoms,because of their low sinking rates and their energy uptake efficiency, they are abundantin mid-ocean gyres with sluggish circulation, where the lack of nutrients prevents themfrom reaching large concentrations. Comparison of the diatom and cyanobacteria imagesshows that their distributions mirror each other; diatoms occur in nutrient-rich waters,while cyanobacteria occur in nutrient-poor regions. Finally, chlorophytes are a transitionalspecies between diatoms and cyanobacteria. Chlorophytes inhabit regions with low lightand nutrient availability where diatoms cannot thrive, but not regions where levels ofnutrients are so low that the chlorophyte losses by sinking exceed their growth.

6.9 The Pre-Aerosol, Clouds and ocean Ecosystem (PACE) mission

Given the difficulties with the biological and aerosol retrievals described in the previoussections, a future NASA mission called Pre-Aerosol, Clouds and ocean Ecosystem(PACE) is being planned, with a tentative launch date of 2019 (PACE-STD, 2012). PACEemphasizes ocean ecology, biogeochemistry and aerosols; specifically, it is designedto deal with such issues as the identification of different species, CDOM, processes incoastal waters, and, probably most importantly, identification, classification and removalof aerosols from the received radiances. For the future mission, the report sets forth severaldifferent design strategies.

The PACE report divides into two parts: a description of the Ocean Color Instrument(OCI) and of the mission concept or architecture. The proposed OCI is a well-calibratedinstrument designed to cover the spectral range of 350–800 nm with a 5-nm resolution.For the purpose of distinguishing CDOM from chlorophyll, the instrument will include aband in the ultraviolet at 350 nm. It will also include the existing NIR and visible bands,and three short-wave infrared bands at 1240, 1640 and 2130 nm for atmospheric correctionover waters that contain large amounts of chlorophyll or CDOM. The basic instrument willhave a nadir resolution of 1 km2; for use in coastal waters, one of its variants has a nadirresolution of 250–500 m.

Second, the proposed mission architecture builds on that of the SeaWiFS and MODISprograms. PACE will include a program of on-orbit lunar and solar calibration and an in situprogram of vicarious calibration. It will also include algorithm development, reprocessingof data once new algorithms are available and product validation from measurements madeby buoys and ships. Given the importance of aerosols, both to atmospheric and radiativeprocesses and in the accurate retrieval of ocean color and ocean biology, the retrieval ofaerosols is a critical part of the mission.

While the SeaWiFS and MODIS instruments were designed to address the shortcomingsof CZCS, PACE addresses the shortcomings of SeaWiFS and MODIS, by extending theobservational bands into the ultraviolet, and in part by incorporating bands with finer spatialresolution into the instrument such that it can be used in coastal waters. By addressing


6.9 The PACE mission 193

the question of aerosol composition, distribution and its role in radiative transfer, PACEshould significantly improve the current retrievals. If the concept is successful, PACEshould continue the ocean color time series of the past forty years, allow continuationand expansion of the work illustrated by models such as GSM and NOBM, and provideexpanded observations in coastal waters.


7

Infrared observations of sea surface temperature (SST)

7.1 Introduction

Satellite SST observations contribute to an understanding of regional variability and globalclimate change and permit the visualization of a wide variety of oceanic flows. Theseobservations are important for the following reasons. First, because the upper 3 m of thewater column has about the same heat capacity and the upper 10 m has about the same massas the overlying column of atmosphere, the upper ocean moderates the global climate systemwhere SST is proportional to the upper ocean heat storage (Gill, 1982). SST varies fromabout −1.8 °C near the edge of the polar sea ice to about 30 °C near the equator. Second,the spatial and temporal distributions of the atmospheric fluxes of water vapor and heatare functions of surface temperature. Third, the patterns of surface temperature gradientsassociated with current systems, eddies, jets and upwelling regions make these processesvisible in SST imagery. Given the importance of SST to the global heat budget, the GlobalClimate Observing System (GCOS, 2011) describes SST as an essential climate variable.

In 1981, satellite infrared observations of SST began with the launch of the AVHRR/2 onNOAA-7, so that there now exist three decades of satellite SSTs. These SST observationscontribute to studies of multiyear global climate change and to short-time-period regionalsupport of fisheries, ship routing, hurricane forecasting, and delineation of ocean fronts,upwelling regions, equatorial jets and ocean eddies (Walton et al., 1998; Gentemann et al.,2009). For numerical weather prediction (NWP) models, SST serves as a critical surfaceboundary condition. The applications of SST data sets range from regional studies ofupwelling at the eastern boundaries of the ocean to large-scale studies of the variabilityassociated with the phenomenon of El Nino Southern Oscillation (ENSO) in the equatorialPacific.

Changes in SST accompany shifts in global weather. An example is the change in SSTpatterns that occur with such interannual climate variations as the cycle involving La Ninaand El Nino in the equatorial Pacific and Atlantic. Identification and tracking of frontal, eddyand upwelling features require accuracies of at least 0.5 K and frequent revisits (Waltonet al., 1998). The accuracy requirement is at present being met, but, because the acquisitionof cloud-free images has only a 10%–20% success rate, the revisit requirement is met bythe optimal interpolation of in situ and satellite data sets. For studies of oceanic climate

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7.1 Introduction 195

change, given that the anticipated trends are 0.2 K/decade, the requirement is for at leasttwenty years of consistent SSTs with uncertainties less than 0.3 K. The NWP requirementis less stringent at 0.5 K and, as Section 7.7 discusses, this error approximately equals theobserved (Minnett, 2010).

The SST data sets come from two sources, satellite and in situ observations. Beginningin 2001, because of the importance of SST and problems with incompatible formats andunknown errors among different national sources of SST (Australia, Canada, France, Japan,UK, United States), the GODAE program organized a series of meetings to form theGODAE High Resolution SST project (GHRSST) (Gentemann et al., 2009; Donlon, 2010).The purpose of GHRSST is to encourage different countries and agencies to produceSST products in a common format (Martin et al., 2012). These data come from sets ofinfrared and passive microwave observations made by the six Sun-synchronous and fourgeosynchronous satellites in the SST constellation (SST-VC, 2013) in situ measurementsmade from moored and drifting buoys and ships. As Martin et al. (2012) discuss, varioussubsets of these data are combined into different GHRSST national products (Section 7.8).Some of these are ensemble-averaged in near real time into the GHRSST MultiproductEnsemble (GMPE) to produce a daily Level 4 SST gridded product.

The GHRSST goals are first, to have the products produced by different countriesplaced into a common format with documented algorithms; second, to provide uncertaintyestimates and ancillary data such as bias, standard deviation and wind speed on a pixel-by-pixel basis; third, to place the data in an L2, L3 or L4 format. In 2013, there are 61GHRSST data products available at the JPL Physical Oceanography Distributed ArchiveCenter (PO.DAAC); GHRSST (2013a) provides a comprehensive list of these data setsand their properties. Because the infrared SST retrievals need cloud-free pixels to observethe surface, for each instrument, GHRSST also requires a documented cloud-filteringscheme. The US contribution to GHRSST is under the direction of the interagency NationalOceanographic Partnership Program (NOPP). Its product is the Multi-Sensor Improved SST(MISST), which combines SST measurements from a combination of in situ and infraredand microwave satellite observations. GHRSST (2012b) gives the GHRSST version 2 dataspecifications with which the retrieved SSTs must be compliant; GHRSST (2011) providesan introduction to working with these data sets.

Satellite SST measurements use both infrared and microwave bands. For polar orbitingsatellites, the infrared instruments include the Advanced Very High Resolution InfraredRadiometer (AVHRR) flown on the midmorning METOP series, including METOP-A, thatwas launched in 2008, METOP-B, launched in 2012, and METOP-C, proposed for launchin 2017. The early-afternoon NOAA-19 launched in 2009 also carries an AVHRR; in about2013 NOAA-19 will be replaced by VIIRS on the early-afternoon Suomi NPP (NOAA,2012c). Other polar orbiting instruments include the US MODIS on AQUA and a varietyof instruments flown by India, Japan and China.

In geosynchronous orbit, the instruments include Spinning Enhanced Visible andInfrared Imager (SEVIRI) on the Meteosat Second Generation-2(MSG-2) satellite, theJapanese MTSAT visible/infrared imager and the Advanced Baseline Imager (ABI) on the


196 Infrared observations of SST

EQ

30N

60N

30S

90N

60S

30E 60E 150E120E90E 180 150W 120W 30W60W90W 0 30E

Fig. 7.1. Location of ships reporting near-surface ocean temperatures during December 1993 to theJapan Meteorological Agency (JMA). (Figure 21–1 from the Japan Meteorological Agency MonthlyOcean Report, December 1993 (No. 12), courtesy of JMA, used with permission.)

2015 GOES-R. These have resolutions of 1–4 km. The polar orbiters (NOAA-19, METOP-B, NPP) sample the global ocean over many orbits at the same local time, where the data mustbe filtered for clouds. The geosynchronous satellites (GOES, Meteosat, MTSAT) sample thesame area at approximately 30-min intervals, but need to be corrected for surface curvatureand clouds. The advantage of the geosynchronous satellites is that they allow investigationof the diurnal cycle in surface temperature. As discussed below in Chapters 8 and 9, passivemicrowave instruments such as Advanced Microwave Scanning Radiometer-EOS (AMSR-E) and AMSR2 view the surface through non-raining clouds. From RSS (2013a), althoughthe resultant SST cannot be used within 75 km of land, it is mapped to a 0.25-degree(30-km) grid, so that, compared with the thermal infrared, it provides a lower-resolutionbut cloud-independent product. Donlon et al. (2007, Table 1) summarize the different kindsof SST retrievals, their coverage and accuracies; Donlon (2010, Appendix) lists the varioussatellite instruments and their wavelength bands and resolutions.

Commercial ships and arrays of moored and drifting buoys take the equivalent surfacemeasurements of SST. For December 1993, Figure 7.1 shows the locations of ships reportingseawater intake temperatures to the Japan Meteorological Agency (JMA) and other nationalweather services. The intakes are at depths of 3–10 m below the surface. Figure 7.1 showsthat the ship positions are heavily biased toward the Northern Hemisphere and are primarilylocated on the great circle routes connecting the United States, Europe and Asia. Mooredand drifting buoys provide additional SST observations; as Section 7.5.4 describes, theseare deployed both globally and in regions of climatic importance such as the equatorialPacific.

The following sections describe the infrared retrieval of SST. Section 7.2 discusses howthe upper-ocean properties affect the SST; Section 7.3 describes the AVHRR, MODIS and


7.2 What is SST? 197

VIIRS bands used in the SST retrieval and the various forms of the AVHRR data. Section7.4 discusses the atmospheric emission properties, the emission and reflection propertiesof the ocean surface and the problem of sun glint. Section 7.5 describes the operationalAVHRR, MODIS and VIIRS algorithms, as well as the AVHRR Pathfinder algorithm,which is a non-operational climate data record. The section continues with discussion ofthe surface match-up data sets used to calibrate the satellite observations, and discusses theproperties of the temperatures collected by the ships, moored and drifting buoys that makeup the in situ match-up data. It also discusses the Reynolds and the Operational SST andSea Ice Analysis (OSTIA) gridded Level 4 SSTs, and the dual-look Advanced Along-TrackScanning Radiometer (AATSR). Section 7.6 describes cloud-detection algorithms and theAdvanced Clear-Sky Processor for Oceans (ACSPO) used in the operational AVHRRretrievals; Section 7.7 discusses the errors and biases in the data sets. Section 7.8 discussesthe GHRSST SST products, their archives and the merged GMPE data set; Section 7.9concludes with examples of AVHRR and MODIS imagery.

7.2 What is SST?

Because the AVHRR, MODIS and VIIRS SST retrievals remove the atmospheric radiancesgenerated by tropospheric water vapor but not by aerosols, their SSTs must be calibratedagainst in situ observations. Consequently, the various SST products are a hybrid of surfaceand satellite observations. The AVHRR and VIIRS SST combine satellite-retrieved surfacetemperatures with in situ temperatures; the MODIS SST combines satellite with buoy andship-based SST observations. Given that the SSTs depend on a combination of atmosphericproperties and near-surface measurements, two sets of processes must be considered. Thefirst is the effect of the surface, atmosphere and Sun on the received radiances; the secondis the effect of the ocean surface and near surface processes on the measured SST.

Figure 7.2 illustrates the radiances and atmospheric properties involved in the retrievalof the ocean surface radiances. On the figure, T is a characteristic temperature of thelower atmosphere, Tint is the surface interface temperature, or temperature at the top ofthe water column, and Tf is the foundation temperature measured at depths of 0.3–5 m.At the interface, the heat loss to the atmosphere generates a surface cool skin layer with athickness of 0.01–1 mm that conduction and viscosity dominates (Gentemann and Minnett,2008; Minnett, 2010). This means that Tint is 0.1–0.3 K cooler than the temperature at thebase of the skin layer. Because Tint is impossible to measure, the best approximation to it isthe surface temperature TS that an infrared radiometer retrieves operating at those infraredwavelengths between 3 and 13 µm that are used by the satellite instruments. As Section7.4.1 shows, these wavelengths have penetration depths between 10 and 100 µm, so thatthe retrieved TS is a measure of the temperature at the base of the skin layer (Donlon et al.,2007).

The processes that govern the surface and skin temperatures divide into those applicableduring day and night, and those applicable only in daytime. First, during daytime andas Section 7.4.2 discusses in detail, the reflection of sunlight into the instrument must be



TS

Upwelled atmospheric radiance

Emitted surface radiance

T

Sensor

Troposphere

Water vapor

Stratosphere

OceanSun glint

Clouds

Sun

Stratospheric aerosols

Day Day and night

Tropospheric aerosols

BuoyTf

Tint

Fig. 7.2. A schematic drawing of the radiances and atmospheric and oceanic properties involved inthe infrared SST retrieval. See the text for further description.

avoided. This reflection dominates the shorter thermal wavelengths (4 µm), but at the longerwavelengths (11–12 µm) can be ignored except when the instrument looks directly at thesub-solar spot. This means that the 4-µm window can be used only at night. Second, forday/night SST retrieval with the polar orbiters, the interfacial diurnal heating and coolingmust be minimized.

A variety of surface and near surface processes determines the upper-ocean temperatureprofile. As Figure 7.3 shows, these include solar heating and nighttime radiative cooling,evaporative cooling and wind and wave mixing. In the near-surface layer, the deepestupper-ocean temperature is the foundation temperature Tf , defined as the temperaturemeasured at a depth where there is no diurnal variability (Donlon et al., 2007). The term“foundation” means that it is the temperature at the depth from which the diurnal thermoclinedevelops, or at the foundation of the diurnal thermocline. It is sometimes called the bulk orbuoy temperature Tb. The foundation temperature can be measured only from moored anddrifting buoys or by ships using thermometry. The lack of diurnal temperature changes atthis depth does not mean that Tf is constant, rather that it responds to turbulent mixing andadvection of warm and cold water into its vicinity that is independent of diurnal heating andcooling.

For the case of weak winds and strong solar radiation, Figure 7.4 shows the differencebetween the night and day upper-ocean profiles of temperature and the effect of the diurnalvariability on these profiles. The figure also shows the standard GHRSST notation forthe various temperatures, SSTint for the interface temperature, SSTskin for the infrared,


Latentheat flux

Mass fluxby evaporation

Sensibleheat flux

Mean wind profile

Atmospheric shear stress

Oceanic shear stress Wave orbital

motion

TurbulenceMean drift current

Precipitation

Clouds

Incoming solar radiation Downwelling

longwave

Radiative fluxTS

ΔT

Capillary waves

~1 m depth

Temperature

Wave breaking

Tf

Fig. 7.3. The factors that determine the surface temperature and the upper-ocean interior temperatures,where T is the temperature difference between the foundation and skin temperatures. (Adapted fromFigure 1, Katsaros (1980).)

TS

T11μm

T10 GHz

Tf (b)

10 μm

100 μm

1 mm

10 mm

100 mm

1 m

10 m

TS

T11μm

T10 GHz

Tf

Temperature

Dep

th

(a)

ΔT

Night Day

ΔT

Tint–0.4 –0.2 0 0 0.2 0.4 0.6 0.8

Tint

Fig. 7.4. Comparison of characteristic temperature profiles for day and night conditions. Depth ison a log scale. (a) Nighttime weak- or strong-wind case and daytime strong-wind case. (b) Daytimeweak-wind and strong solar insolation case. On the figure, TS is the surface temperature, the barmarked T11µm shows the depth range that contributes to the infrared 11-µm SST; the bar markedT10 GHz shows the depth range that contributes to the microwave surface temperature, Tf is the buoyor bulk temperature, T is the difference between the interface and foundation temperature. See thetext for further description. (Adapted from un-numbered figure in Donlon et al. (2007).)



SSTsubskin for the microwave and SSTfnd for the foundation temperature (Donlon et al.,2007). Because the depth range over which the remote sensing temperature is measureddepends on the observational wavelength, different instruments measure SST over differentdepths. The infrared surface temperature TS represents the temperature within the top 10–100 µm. As discussed in Chapters 8 and 9, the temperature T10 GHz is that measured inthe microwave at frequencies of 7–11 GHz. At these frequencies, T10 GHz is the radiativetemperature emitted from the top 1–2 mm of the water column, where this measurement isrepresentative of the temperature immediately below the cool skin layer called the subskintemperature (Donlon et al., 2007).

The temperature TS responds to changes in the evaporative, conductive and radiativebalance within a few seconds; because viscous processes dominate T10 GHz, it respondson time scales of order minutes. In Figure 7.4(a), T ranges from 0 to 0.8 K, while,under the daytime conditions shown in Figure 7.4(b), T varies from 0 to 4 K (Donlonet al., 2007; Gentemann and Minnett, 2008). Figure 7.4(a) is characteristic of both thenighttime retrievals and the strong-wind case discussed in the next paragraph. Figure 7.4(b)shows that, for weak winds and strong solar surface heating, a warm bulge develops in thesubsurface profile, so that the measured TS can be much warmer than Tf . The figures showthat the cool skin feature is always present, while the diurnal heating increases with theincident solar radiation and decreases with wind speed (Gentemann and Minnett, 2008).

In the calibration of the infrared satellite retrievals of SST, Tf serves as a surrogate for TS.As Donlon et al. (2002, 2007) describe, T in Figure 7.4(a) decreases with wind speed.From infrared radiometer measurements, they show that, for wind speeds greater than6 m s−1, the effect of diurnal heating is minimized for both day and night conditions,where the surface is cooler than the interior and T equals −0.17 ± 0.07 K. In some SSTretrievals, this value of T is used to adjust the observed TS to Tf . At smaller wind speeds,the daytime thermal stratification of the upper layers means that T is larger (Figure 7.4(b).Because the comparison of satellite-retrieved SST and the in situ Tf depends on keepingthe difference between the two as small as possible, in most SST retrievals, the daytimecomparison is rejected if the wind speed U as determined from numerical models is lessthan 6 m s−1 (Martin et al., 2012).

7.3 Properties of AVHRR, MODIS and VIIRS bands used in the SST retrieval

As Chapter 1 and Cracknell (1997) describe, the AVHRR is a whiskbroom scanner, with itsscanning rate determined by a mirror rotating at six scans per second around an axis parallelto the Earth’s surface. The AVHRR has a swath width of 2700 km, an angular resolution of1.4 mr and a nadir resolution of 1.1 km. Since the satellite velocity is about 6 km s−1, theFOVs overlap between scans.

The AVHRR instrument is mounted on the NOAA and METOP series of satellitesdescribed in Chapter 1. Beginning with the launch of the five-channel AVHRR/2 on theNOAA-7 satellite in 1981, replacement satellites have been launched at intervals of 2–3 years, depending on the satellite lifetime. In 2012, the AVHRR that operated on the


7.3 Properties of AVHRR, MODIS and VIIRS bands 201

Table 7.1. The properties of the AVHRR/3, MODIS and VIIRS bands used in SSTalgorithms. For each instrument, the bands used in the SST retrieval are in bold face.

AVHRRband

Wavelength(µm)

NET(K)

MODISband

Wavelength(µm)

NET(K)

VIIRSband

Wavelength(µm)

NET(K)

1 0.58–0.68 10 0.483–0.493 M4 0.54–0.562 0.725–1.0 16 0.862–0.877 M7 0.85–0.883A 1.58–1.64 1.58–1.643B 3.55–3.93 0.1 I4 3.55–3.93 0.07

20 3.660–3.840 0.05 M12 3.66–3.84 0.0722 3.929–3.989 0.07 M13 3.97–4.13 0.0823 4.020–4.080 0.07

4 10.3–11.3 0.1 31 10.78–11.28 0.05 M15 10.3–11.3 0.0405 11.5–12.5 0.1 32 11.77–12.27 0.05 M16 11.5–12.5 0.070

From Zhou (2011) and MODIS (2013); NET for thermal bands from VIIRS (2011c); the NETare determined at 300 K.

NOAA-19 satellite in an early-afternoon orbit was replaced in the same orbit by theVIIRS observations on Suomi-NPP. In the late-morning orbit, the AVHRR observationson METOP-B are scheduled to continue on METOP-C through 2021 (CEOS, 2013). Thefollowing two subsections discuss the properties of the AVHRR, MODIS and VIIRS bandsused in the SST retrieval and the different kinds of AVHRR data. Chapters 1 and 6 discussthe MODIS and VIIRS instruments.

7.3.1 AVHRR, MODIS and VIIRS thermal bands

The current AVHRR/3 version of AVHRR has six bands, five of which operate at any time.Henceforth, the AVHRR/3 will be referred to as the AVHRR. The bands consist of one inthe visible, two in the near infrared and three in the thermal-infrared. Table 7.1 lists all ofthe AVHRR bands and those MODIS and VIIRS bands used in the SST retrieval. TableA.2 in the Appendix lists the MODIS bands; Table A.3, the VIIRS bands. For each band,Table 7.1 lists its wavelength range and, for the thermal bands, NET.

Beginning with AVHRR, Table 7.1 shows that band 1 is located in the visible at 0.58–0.68 µm, where this wavelength range was chosen to minimize the effect of Rayleighscattering (K. Engle, private communication, 2002). Band 2 is in the NIR at 0.725–1.0 µm.Because this band is located in a region of negligible oceanic thermal emission and verylow water-leaving radiance, it provides good discrimination of the land/ocean boundaryand clouds. Band 3A is at 1.58–1.64 µm and operates only day-time when it is used forreflectance discrimination of snow, ice and clouds, and for detection of forest fires. It is notused in the SST retrieval. Band 3B is at 3.55–3.93 µm and operates only at night when itis used for SST retrievals. Beginning with the launch of NOAA-15 in 1998, the AVHRR



can measure bands 3A and 3B simultaneously. Finally, bands 4 and 5 at 10.3–11.3 µm and11.5–12.5 µm are used for both day and night SST retrievals.

Table 7.1 also lists the MODIS bands used for SST retrieval; these consist of one band inthe range 3.6–4.1 µm and two in the range 10.7–12.3 µm. MODIS band 21, which occupiesthe same wavelength interval as band 22, is omitted because it is specifically designed formonitoring of forest fires and has a much lower gain than band 22. Finally, the table showsthat the location of the VIIRS thermal-infrared bands matches the AVHRR bands.

AVHRR began as a four- and five-band instrument, using bands 1, 2, 3B (previouslycalled 3), 4 and sometimes 5, where band 5 was omitted on NOAA-6, 8 and 10. As Section7.4.2 shows, because wavelengths in the vicinity of 4 µm are easily overwhelmed by sunglint, band 3 is only used for nighttime SST retrievals. Band 3 is also noisier than the otherthermal bands. Consequently, beginning with the launch of NOAA-15 in 1998, the AVHRRwas upgraded from five bands to the current six-band AVHRR/3.

On each rotation, the AVHRR infrared bands are calibrated by sequentially viewing aconstant-temperature blackbody and cold space, which is assigned a nominal temperatureof 3 K. Bands 1, 2 and 3A are calibrated before launch, but not in space. The units ofthe calibrated AVHRR data are as follows: bands 3B, 4 and 5 have units of brightnesstemperature in K. Bands 1, 2 and 3A have units of albedo, which is defined as the ratio ofthe solar radiance normally incident on the Earth to the radiance received at the instrument(NOAA, 2012b, Section 7.1). As Section 7.6 describes, these three bands are used toidentify daytime clouds, and bands 3B, 4 and 5 are used to identify nighttime clouds. Incontrast, MODIS uses 17 bands for cloud identification.

7.3.2 Forms of AVHRR data

There are several ways to obtain AVHRR data. As the satellite orbits the Earth, the dataare broadcast continuously in real time to local ground stations and are also recordedonboard for later broadcast to a US ground station. The simplest way to obtain these data isfrom the Automatic Picture Transmission (APT) mode, which broadcasts the local visibleand infrared imagery in an analog format with a 4-km pixel size to any receiving station.The inexpensive APT receivers require only an omnidirectional antenna and produce fax-like images. The other source of direct broadcast data is the High Resolution PictureTransmission (HRPT) mode, which broadcasts digital data with 1-km pixels. The HRPTstation and its tracking antenna are about an order of magnitude more expensive than anAPT station.

For regions inaccessible to direct broadcast, such as in the vicinity of Kerguelen Islandin the South Pacific that is assumed not to have a ground station, there are two options. First,to obtain 1-km data, the user must request Local Area Coverage (LAC) data from NOAA,where, if data storage on the satellite permits, the HRPT coverage of the region is recordedfor later transmission to a US ground station. LAC data must be requested and paid forby the user ahead of time; the satellite can store about ten minutes of LAC data per orbit.Second, the user can obtain lower-resolution Global Area Coverage (GAC) data. GAC is a


7.4 Atmosphere and ocean properties in the infrared 203

2 6 10 12 14 16Wavelength (μm)

Pen

etra

tion

dept

h (μ

m)

102

10

1

103

104

84

3B

4

5

Fig. 7.5. The dependence of the absorption depth da on wavelength in the infrared. The horizontalbars show the locations of the AVHRR channels.

reduced data set that is recorded only during one out of every three mirror rotations. Duringthe data-gathering rotation, the data are averaged into blocks of four adjacent samples, thenthe fifth sample is skipped, the next four are averaged, and so forth so that the data volumeis reduced by an order of magnitude.

GAC data are recorded continuously around the globe, have a nominal 4-km pixel size,and are downloaded and archived by NOAA. Third, METOP provides Full Resolution AreaCoverage (FRAC) data at 1.1-km resolution; this data set began with the launch of METOP-A in October 2006. In 2013, these data are available from the AVHRR on METOP-A andB. GAC provides global coverage every 1–2 days; GAC, FRAC and VIIRS imagery can beviewed and retrieved at the NOAA Comprehensive Large Array-Data Stewardship System(CLASS) archive (NOAA, 2012a).

7.4 Atmosphere and ocean properties in the infrared

In the following, Section 7.4.1 examines the properties of radiances that are emitted orreflected from the ocean surface in the TIR, with particular emphasis on the AVHRR,MODIS and VIIRS bands. The section shows that in the TIR, the radiance is emitted fromthe top 1–100 µm of the water column, where for θ less than about 40°, the emissivity isapproximately constant. Section 7.4.2 discusses solar reflection, with particular emphasison the ratio of the reflected solar to the thermally emitted radiation. Because of sun glint,thermal bands with λ 4 µm are usable only at night.

7.4.1 Thermal emission and reflection

The wavelengths used in the SST retrieval lie between 3 and 13 µm. For this range and fromEquation (3.1), Figure 7.5 shows the dependence of the absorption depth da on wavelength.



Incidence angle (deg)

0 10 20 30 40 50 60 70 80 900.0

0.1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

1.0

Ref

lect

ance

0.0

0.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

Em

issi

vity

V-pol

H-polUnpolarized

Fig. 7.6. The unpolarized and vertically (V) and horizontally (H) polarized reflectance and emissivityversus incidence angle for λ = 10 µm. (Derived from Equation (5.7).)

For 2–6 µm, da is between 10 and 100 µm; for 10–12 µm, it is between 1 and 10 µm.Consequently in the IR the radiance is entirely emitted from the top 1–100 µm of the watercolumn. Since at these wavelengths energy cannot be transmitted through the water column,this also means that r = 1 − e, where, following Section 5.2.3, r and e are respectively theunpolarized reflectance and emissivity, with similar relations for the polarized terms.

Figure 7.6 shows the dependence on viewing zenith angle θ of the reflectance andemissivity for V-pol, H-pol and unpolarized radiation. This figure differs slightly but sig-nificantly from Figure 5.6. For θ less than about 45°, e is nearly constant at about 0.99,corresponding to r = 0.01. Because this θ -dependence approximately holds throughoutthe TIR, and because e ∼= 0.99 in this wavelength range, the ocean is approximated as aLambert surface. Since for θ less than about 45°, e is nearly constant, this means that evenfor a rough ocean surface, the emitted radiances are about the same as for a specular surface(Wu and Smith, 1997). The treatment of foam is more complicated. According to Wu andSmith (1997), even though foam is made up of air bubbles surrounded by a thin water film,the detailed physical processes by which foam affects the emissivity are not well enoughunderstood for one to include its effects. In summary, for moderate look angles and exceptfor large wind speeds, the emissivity is assumed independent of surface roughness.

For normal incidence and using the Segelstein (1981) data from Figure 3.3, the λ-dependence of the unpolarized values of r and e are derived from Equation (5.6) and dis-played in Figure 7.7. On this figure, the horizontal bars show the average values of r and e atthe locations of the MODIS and AVHRR bands. For 3.6–4 µm, r = 2.2 × 10−2 and e = 0.98,for 10.8–11.3 µm, r = 3.5 × 10−3 and 0.996, and for 11.8–12.3 µm, r = 1.8 × 10−3 and



2 6 10 12 14 160.00

0.01

0.02

0.03

0.04

Nor

mal

ref

lect

ance

3B

4,

5,32

23

31

22

Nor

mal

em

issi

vity

1.00

0.99

0.98

0.97

0.96

Wavelength (μm)

84

M15 M16,

20,M12

Fig. 7.7. The normal reflectance (left-hand scale) and emissivity (right-hand scale) in the infrared.The horizontal bars show the average reflectance and emissivity for the MODIS bands (20, 22, 23,31, 32), the AVHRR bands (3B, 4, 5) and the VIIRS bands (M13, M15, M16) listed in Table 7.1and used in the SST retrieval. For clarity, the bars showing the wavelength ranges of MODIS bands22 and 23 are exaggerated by 50%, and the gray bar showing the location of MODIS band 20 andVIIRS band M12, which occupy the same wavelength range, are displaced downward. See the textfor further description.

e = 0.998. At 4 µm, the magnitude of r is approximately six times its value at 11 µm, and,at all IR wavelengths, the emissivities are approximately equal to 1.

As Section 4.8.1 describes, the or absorption–emission approximation governs radiativetransfer in the IR. Because the temperatures of the atmosphere and surface are both about300 K, the radiation received at the TOA is not only reduced by atmospheric absorption,but also enhanced by atmospheric emission. For observations of an ocean with a surfacetemperature of 288 K corresponding to that of the Standard MODTRAN atmosphere,Figure 7.8 compares the 288-K blackbody irradiance with the ocean-emitted irradiancemodified by a vertical passage through the atmosphere. The upper solid curve is the 288-K blackbody irradiance; the lower solid curve shows the same irradiance after passagethrough an absorbing and emitting atmosphere; the dashed curve is the contribution fromatmospheric emission as measured at the TOA. When the dashed curve equals the lowersolid curve, the surface irradiance is completely attenuated. The symbols on the surfaceirradiance curve mark the O3 and CO2 absorption regions; the numbered horizontal blackbars show the location of the AVHRR, MODIS and VIIRS bands used for SST retrieval.

Figure 7.8 shows that the irradiance observed at the TOA nearly equals the blackbodyirradiance in three windows, which are located at approximately 3–4 µm, 8–9 µm and 10–12 µm, and are called the 4-µm, 8-µm and 11-µm windows. For λ less than 2–3 µm, thesurface emission is negligible and solar reflection and atmospheric scattering are dominant.For 4 µm, the TOA irradiances are at least an order smaller than at 11 µm, which lies near thepeak of the 288-K blackbody curve. Figure 7.8 also shows that the water vapor absorptionis much less important at 4 µm than at the other windows. Finally, the reason why the 8-µmwindow is not generally used for SST retrieval is that the received radiance from the surface



4

5

10

15

20

25

Spe

ctra

l irr

adia

nce

(MW

m–3

)

10 12 143 11 13 15Wavelength (mm)

O3

CO220

22

23

3B

31 32

5 6 7 8 90

M12

4, M15 5, M16

29, M14

Fig. 7.8. The 288-K surface blackbody irradiance (upper solid line), the same blackbody curve at theTOA after a vertical passage through the standard MODTRAN atmosphere (lower solid line), andthe atmosphere emission at TOA (dashed line). The numbered bars show the location of the AVHRR,MODIS and VIIRS bands used in the SST retrieval; O3 and CO2 identify the regions of ozone andcarbon dioxide absorption. (Data from MODTRAN, location of absorption regions courtesy of RobertCahalan.)

is less than that at 11 µm, but remains sensitive to changes in atmospheric water vapor. AsSection 7.6.3 discusses, the 8-µm bands are used primarily for cloud identification.

7.4.2 Contribution from reflected solar radiation

This section discusses the λ-dependence of the ratio of the reflected solar and thermallyemitted radiation. In the TIR, the foam reflectances and water-leaving radiances are negli-gible (Section 5.6 and Chapter 6), so the analysis considers only Fresnel surface reflectionof the incident solar radiance.

The magnitude of the solar reflectance is calculated by combination of the r (λ) inFigure 7.7 with the assumption that a given area of wave facets reflects the solar radiancedirectly into the sensor. In this calculation, the reflecting facets are assumed to occupy only0.001% or 10 m2 of a 1-km2 FOV. Because the relative magnitudes of these emitted andreflected radiances are not affected by an additional atmospheric passage, they are evaluatedjust above the surface. For this fractional area, Figure 7.9 compares the 288-K blackbodyradiance with the reflected solar radiance after a downward passage through the StandardMODTRAN atmosphere; for the AVHRR, MODIS and VIIRS bands, Table 7.2 lists theratio of the reflected solar to the emitted blackbody radiances.



Table 7.2. The relative contributions to theMODIS, AVHRR and VIIRS thermal bands from

normal solar reflectance, where the reflectingfacets occupy 0.001% of the FOV.

MODISband

AVHRRband

VIIRSband

Relative solarcontribution (%)

20 3B M12 1222 M13 623 4

4 M15 0.00231 0.00132 5 M16 0.0004

10–1

1

10

10–2

10–3

10–4

10–5

Wavelength (μm)3.5 4 6 8 10 11 12 13 14 15

2022

2331 32

5, M163B 4, M15

Rad

ianc

e (M

W m

–2 s

r–1 )

95 7

M12

Fig. 7.9. Comparison of the 288-K blackbody radiance (dashed line) with a normal solar radiance thatpasses through the Standard MODTRAN atmosphere, then is reflected by the surface wave facets.The reflected radiance (solid line) is evaluated just above the surface for the case when the reflectingfacets occupy 0.001% of the surface. The horizontal numbered bars show the location of the AVHRR,MODIS and VIIRS bands used in the SST retrieval. See the text for further description.

Even for this relatively small area of reflecting facets, Table 7.2 and Figure 7.9 showthat, for the 4-µm bands, the solar contribution ranges from 12% to 4%. In contrast, for the11- and 12-µm bands, the solar contribution ranges from 0.002% to 0.0004%. This meansthat, even if the reflecting area were increased by an order of magnitude, solar reflectancewould dominate the 4-µm bands, but would still make only a small contribution to the11- and 12-µm bands. Because of this sensitivity to solar reflectance, the 4-µm bands areused only at night, while, except in the immediate vicinity of the sub-solar spot, the 11-and 12-µm bands are used during both day and night.



In summary, the relative advantages of the two groups of bands are as follows. The 11-µm bands are used during day and night and their radiances are an order larger than those ofthe 4-µm bands. The width of the 11-µm bands is also greater than that of the 4-µm bands,yielding a greater received power. In contrast, and as Figure 4.15 shows, the 4-µm bandsare used only at night and are much less sensitive to water vapor than the 11-µm bands.Also, from the definition of the Planck function, it is easy to show from calculation of

1

L

dL

dT

∣∣∣∣λ

that the 4-µm bands are more sensitive to changes in surface temperature (Stewart, 1985).

7.5 SST algorithms

The AVHRR thermal infrared SST retrievals consist of the daily operational SSTs andPathfinder SSTs, where the Pathfinder SSTs are a climatological data set (Casey et al., 2010;Pathfinder, 2013). MODIS, VIIRS and the various infrared geosynchronous instrumentsuse similar algorithms. These algorithms consist of three parts: the theoretical algorithm,the tuning of the algorithm against ship and buoy temperatures, and a cloud mask. Thesealgorithms are designed to account for and minimize the effects of atmospheric water vapor.Given that the 4-µm bands cannot be used during daytime, different algorithms are used forday and night, where day is defined as a solar zenith angle θS < 90° and night as θS 90° (Mayet al., 1998; ASCPO, 2010). Because, in a simple model, the equations governing the SSTretrieval depend on two variables, surface temperature and atmospheric water vapor, SSTretrievals require observations in at least two bands. Although this model ignores the effectsof aerosols, these can be accounted for in the comparison with in situ data. In the following,Section 7.5.1 gives the theoretical background for the algorithms; Section 7.5.2 describesthe general form of the algorithms based on the AVHRR bands; Section 7.5.3 describes theVIIRS, MODIS and Pathfinder algorithms. Section 7.5.4 discusses the temperatures fromships and buoys used in the in situ match-up data sets; Section 7.5.5 describes the Reynoldsand OSTIA gridded SSTs used in the algorithms; Section 7.5.6 describe the operation ofthe dual-look Advanced Along-Track Scanning Radiometer (AATSR).

7.5.1 Background

Because the dependence of attenuation on water vapor differs from band to band, theMODIS, AVHRR and VIIRS SST algorithms use pairs of bands to remove its effect.The derivation is based on Equation (4.5), which is the integrated across-the-atmosphere,constant-coefficient form of the Schwarzschild equation, written as

L (λi, zH) = L0 (λi) t sec θi + fP

(T , λi

) (1 − t sec θ

i

)(7.1)

In (7.1), the index i refers to different bands, the left-hand term is the radiance receivedat the satellite, the first term on the right is the attenuated surface radiance, and the second


7.5 SST algorithms 209

is the atmospheric path radiance, where the 1 − t factor is the atmospheric emissivity andθ is the viewing zenith or look angle. In the third term, fP is the Planck function fromEquation (3.21). Additionally, the lower troposphere is assumed to be characterized by amean temperature T , so that t = t

(T , V , λi

).

Because, at a particular λ, the attenuation associated with other atmospheric gases isconstant, their contribution to the attenuation is neglected, although it could easily beincluded in the analysis. The relatively small term generated by reflection of the down-welling atmospheric radiance is also neglected. The analysis further neglects aerosols andassumes that variations in t are caused only by the water vapor concentrated in the lowertroposphere (Section 4.2.1). Although this procedure ignores processes such as the injec-tion of volcanic aerosols into the stratosphere, as Section 7.7.2 shows below, in situ SSTobservations correct for them.

If the radiances are written in terms of the Planck function, Equation (7.1) is furthersimplified. With the assumption that e = 1, the radiance L0 emitted by the surface isL0 = fP (TS, λi), where TS is the surface temperature defined in Section 7.2. Similarly,at the satellite, L (λi) = fP (Ti, λi), where Ti is the blackbody temperature correspondingto the received radiance. Substitution of the Planck function into Equation (7.1) and forconvenience omitting the superscript sec θ on t yields

fP (Ti, λi) = fP (TS, λi) ti + fP(T , λi

)(1 − ti) (7.2)

Equation (7.2) shows that the received radiance L or blackbody temperature Ti is afunction of the three unknowns, T , TS and t, where t is a function of the columnar watervapor V.

Application of Equation (7.2) to the instruments proceeds as follows. Beginning withAVHRR, the daytime algorithms use bands 4 and 5; the nighttime algorithms use bands3B, 4 and 5. The following analysis is initially restricted to daytime, where i represents theAVHRR bands, so that T11 and T12 are the band-4 and -5 radiances received at the TOA,and in addition are proxies for the 11- and 12-µm bands on the other Sun-synchronous andgeosynchronous satellites. With the addition of the 4-µm band 3B, the nighttime algorithmshave similar forms.

Following McClain et al. (1985), who derived the initial form of the AVHRR algorithm,the daytime algorithm is derived as follows. As justified below, T11, T12, T and TS are ofthe same order. Consequently, in Equation (7.2), each value of fP can be linearized asa first-order Taylor series around the blackbody radiance at TS, so that for T11, and withsimilar equations for T4, T12 and T ,

fP(T11) ∼= fP(TS) + dfP

dT

∣∣∣∣TS,λ11

(T11 − TS) (7.3)

Also from McClain et al. (1985), the dependence of the transmittance t on V and θ is

ti = exp (−mi V sec θ ) (7.4)



In (7.4), the subscript i on the constants mi indicates that the dependence of transmittanceon water vapor is a function of wavelength. For later use, εi is defined as

εi = mi V sec θ (7.5)

If Mi = 1 − ti , then substitution of (7.3), (7.4) and Mi into (7.2) yields

T11 − TS = (T − TS)M11

T12 − TS = (T − TS)M12 (7.6)

In Equation (7.6), if the upper equation is multiplied by M12 and the lower by M11, thensubtraction of the lower equation from the upper and reorganization of terms gives

TS = T11 + (T11 − T12) , where = (1 − t11) / (t11 − t12) (7.7)

Equation (7.7) is called the split window form of the SST algorithm. The definition of

is from Walton et al. (1998), where is sometimes written as γ (Barton, 1995). Becausethe 12-µm band is more affected by water vapor than is the 11-µm band, the leading termin all of the daytime equations is T11. If is expanded in terms of small values of εi , theleading term in the expansion is

0 = m11/ (m12 − m11) (7.8)

A typical value of 0 is about 2.5 (Barton, 1995). For small εi , Equations (7.7) and(7.8) show that TS is independent of V and θ , so that it is only a function of T11, T12 andthe water vapor absorption properties of the two bands. The nearly linear relation betweentemperature and water vapor described by these two equations is the basis for several SSTalgorithms. As an example of the observed dependence of T11 − T12 on columnar watervapor, Figure 7.10 shows that, for small look angles, its dependence is nearly linear, withthe deviations from linearity occurring at low values of the water vapor.

Equation (7.7) contains three temperatures, T11, T12 and TS and the temperature differenceT = T11 − T12. For moist tropical atmospheres and under cloud-free conditions, T11 issmaller than TS by a maximum amount of about 9 K. For the range of MODTRANatmospheres, T ranges from a minimum of about 0.5 K to a maximum of about 4 K, sothat T11, T12 and TS are approximately equal (Walton et al., 1998). Similarly, because T isrepresentative of the lower troposphere, it is also of order TS.

7.5.2 AVHRR operational algorithms

The first AVHRR SST algorithm was the Multi-Channel SST (MCSST), which McClainet al. (1985) derived from the equivalent of Equation (7.7). In their derivation, was firstestimated from a data set consisting of radiosonde profiles of temperature and humiditymeasured over the ocean. After substitution of this value of into Equation (7.7), the derivedTS were compared with a set of buoy-derived surface temperatures taken at positions andtimes that closely matched the satellite observations. These surface data are called the



10 2 543 6

1

0

2

3

Total column water vapor (g cm–2)

T 11

– T 1

2 (K

)

(d)

(c)

(b)

(a)

Fig. 7.10. Brightness temperature difference between AVHRR channels 4 and 5 as a function ofcolumnar water vapor derived from SSM/I. Trend lines are for satellite zenith angles of (a) 0–15°, (b)15°–30°, (c) 40°–45° and (d) >45°. (Redrawn from Kilpatrick et al. (2001), Figure 3, points are notshown on the original, copyright American Geophysical Union.)

match-up data set. The comparison showed, however, that the satellite-derived TS had largebiases relative to the buoys.

Motivated by this lack of agreement, they next tried an empirical approach by rewritingEquation (7.7) as

SST = a0 + a1T11 + a2 (T11 − T12) (7.9)

In (7.9), a0, a1 and a2 are constants. On the left-hand side of the equation, the replacementof TS by SST indicates that the retrieved surface temperature now includes contributionsfrom the foundation temperatures and does not necessarily equal the surface temperature.A least-squares regression of the SSTs derived from satellite observations of T11 and T12

against the in situ match-up observations determines the coefficients in Equation (7.9),which is the simplest form of the two-channel SST retrieval. As an example of the coeffi-cients, for daytime and NOAA-14, Walton et al. (1998, Table 2) show that Equation (7.9)becomes

SST = −261.68 + 0.95876T11 + 2.564 (T11 − T12) (7.10)

where T11 and T12 are in K and SST is in °C. In Equation (7.10), the first term convertsK to °C; the second term is T11 multiplied by a constant nearly equal to unity so that itapproximates the surface temperature; the second removes the effect of water vapor, whichis proportional to the difference between the 11- and 12-µm brightness temperatures. For a



look angle of θ < 30°, McClain et al. (1985) and Brown and Minnett (1999) show that thelinear approach described by Equations (7.8)–(7.10) gives results of the desired accuracy.

Because Equation (7.10) is valid only for small values of εi , several methods are used toaccount for larger values of θ and V. Three of these are briefly described: the water vaporSST (WVSST), a revised MCSST and the nonlinear NLSST.

First, regarding the WVSST, Emery et al. (1994, Appendix 1) find that, to second orderin ε,

= [m11/ (m11 − m12)

][1 + (m11V sec θ ) /2 + · · ·] (7.11)

Substitution of Equation (7.11) into (7.7) yields the WVSST equation with an explicitdependence on V and θ , and allows direct incorporation into the SST algorithms of valuesof V derived from radiosonde or passive microwave observations.

Second, beginning in about 1989, to introduce the effect of variable θ or path length intoEquation (7.9), the daytime MCSST equation was rewritten as

SST = a0 + a1T11 + a2 (T11 − T12) + a3 (T11 − T12) (sec θ − 1) (7.12)

In (7.12), the additional sec θ term gives the increase in path length with θ , and includesthe water vapor effect through the T11 − T12 term. The values of the coefficients dependon the specific satellite instrument and are again determined by comparison with the buoymatch-up data set. The equivalent nighttime algorithm is discussed below (Walton et al.,1998). Unlike the NLSST, the advantage of the MCSST is that, once its constants havebeen determined, the equation is invariant.

Third, the currently used NLSST algorithm improves on MCSST by implicitly account-ing for V. As Walton et al. (1998) describe, a numerical study of the behavior of overa large range of SSTs and marine atmospheric profiles shows that, for 0 °C < SST <

30 °C, increases nearly linearly with SST. The reason for this dependence is that moistatmospheres generally occur over warm oceans, so atmospheric humidity increases withSST. To account for this dependence, a field of surface reference temperatures TR is addedto the formulation:

SST = a0 + a1T11 + a2TR (T11 − T12) + a3 (T11 − T12) (sec θ − 1) (7.13)

In (7.13) the as are constants and TR is the daily high-resolution Reynolds SST discussedin Section 7.5.5. The coefficients in Equation (7.13) are determined by comparison of theretrieved SSTs with match-up data. For NOAA-14, the daytime NLSST has the form

SST = −255.16 + 0.9398T11 + 0.0761TR(T11 − T12) + 0.8015(T11 − T12)(sec θ − 1)

(7.14)

In (7.13) and (7.14), T11 and T12 are in K, TR and SST are in °C. Petrenko et al. (2010)show that, in the NOAA ACSPO SST processing, the NLSST equation is used in daytimewhile the MCSST is used at night.

With a suitable choice of coefficients, the MCSST and NLSST algorithms describedabove are also used at night. Alternatively and to take advantage of band 3, the nighttime



forms of the MCSST and NLSST use all three thermal bands in what is called a triple-window algorithm, where the difference between T4 and T12 is proportional to attenuationby water vapor. With arguments similar to those used in the daytime derivation and fromWalton et al. (1998, Table 4), the NOAA-14 NLSST nighttime algorithm is

SST = −266.19 + 0.980T11 + 0.0319TR(T4 − T12) + 1.818(sec θ − 1) (7.15)

In (7.14) and similar to the daytime algorithm, the T11 term provides the basic SSTestimate, with the corrections and conversion to °C provided by the other terms. Becausethe third term in (7.15) lacks the product of (T4 − T12) with the sec θ term, the nighttimeequation is simpler than the daytime. The advantage of the 4-µm band over the 11- and 12-µm bands is that it is less sensitive to water vapor, so that over a broad range of atmospheresT4 is reduced from the SST by at most 2 K, as opposed to a 9-K reduction for the 11-µmband (Walton et al., 1998).

Following Petrenko et al. (2010), the current AVHRR nighttime algorithm used inACSPO is as follows:

SST = b0 + b1T4 + b2T11 + b3T12 + [b4(T4 − T12) + b5](sec θ − 1) (7.16)

where the bs are the nighttime coefficients again determined from match-up data.

7.5.3 Pathfinder, MODIS and VIIRS algorithms

Even though the SSTs from the operational algorithms are archived, the Pathfinder algorithmprovides an SST climate data record (CDR) (Kilpatrick et al., 2001; Casey et al., 2010). Thisdata set differs from the operational algorithms in that it is not produced in near real time;rather it is the CDR for the NOAA SSTs that is intended for long-term climate studies. It isproduced in compliance with GHRSST specifications and is available as gridded Level 3product with gaps caused by clouds (K. S. Casey, private communication, 2013).

One difference between Pathfinder and the algorithms described in Section 7.5.2 is thatPathfinder, MODIS and VIIRS use a “stratified” algorithm, which consists of one set ofcoefficients for dry atmospheres and another for moist or wet atmospheres. The Pathfinderalgorithm uses the same stratified algorithm for both day and night, whereas MODISand VIIRS use stratified algorithms only in daytime (B. Petrenko, private communication,2013). As Figure 7.10 shows, the nonlinearity in the dependence of T on columnar watervapor increases with viewing zenith angle θ . From their investigations of the dependenceof T on water vapor, Kilpatrick et al. (2001) find that there is a “consistent positive bias”for T < 0.7 K. To correct this, they introduce the stratified algorithm with one set ofcoefficients for T < 0.7 K, and another set of coefficients for T 0.7 K. To avoid adiscontinuity at T = 0.7 K, for 0.5K < T < 0.9K, they use a linear interpolation of thetwo solutions.

The Pathfinder algorithm is written as

SST = c0 + c1T11 + c2TR (T11 − T12) + c3 (T11 − T12) (sec θ − 1) (7.17)



For NOAA-14 and T < 0.7 K, the coefficients are 0.640, 0.952, 0.121 and 1.145; forT 0.7 K, the coefficients are 1.457, 0.942, 0.075 and 0.758. In (7.17), SST is in K and TR

is the Reynolds SST (Pathfinder, 2001). As Casey et al. (2010) describe, similar algorithmsare used with the daily Reynolds SST for both day and night observations.

As Table 7.1 shows for MODIS, it employs two sets of thermal bands for SST retrieval,three at 4 µm (bands 20, 22 and 23) for nighttime retrievals, and one each at 11 and 12 µm(bands 31 and 32) for daytime retrievals. The 11-µm algorithm is identical in form to theabove Pathfinder algorithm, and is written as

SST = c0 + c1T31 + c2TR (T31 − T32) + c3 (T31 − T32) (sec θ − 1) (7.18)

MODIS (2006) describes the MODIS stratified algorithms and provides the coefficients.As an example, for MODIS on AQUA and if T = T31 − T32, then, for T 0.7 K,typical values of the coefficients c0 through c3 in Equation (7.18) are 1.101, 0.9470, 0.1710and 1.4210; for T > 0.7 K, they are 1.8820, 0.9350, 0.1230 and 1.3720. Between 0.5 and0.9 K, the SST is again derived from a linear interpolation between the two solutions. Theseequations are used primarily for day retrievals; Figure 7.18 later in this chapter shows anexample of a MODIS image processed with this algorithm.

MODIS uses a different form of the nighttime algorithm than AVHRR. At 4 µm, theMODIS nighttime SST retrieval, called SST4, is an unstratified dual-wavelength algorithmbased on measurements at 3.9 and 4.0 µm (bands 22 and 23), written as

SST4 = c0 + c1T22 + c2 (T22 − T23) + c3 (sec θ − 1) (7.19)

This equation is used only at night and involves one set of coefficients. For MODIS onAQUA, typical values of the coefficients are 0.529, 1.030, 0.499 and 1.458 (MODIS, 2006).Compared with (7.18), Equation (7.19) is simpler, has one set of coefficients and lacks theTR term. Equation (7.19) shows the advantages of working at 4 µm, where water vapor isless important than at 11 µm.

To summarize the differences between the day and night algorithms, the advantages ofthe MODIS 11-µm algorithm are that it is usable at all times and continues the AVHRRSST time series with an improved accuracy. Its disadvantages are that it is more sensitive towater vapor and is also sensitive to volcanic and tropospheric aerosols. The SST4 algorithmis simpler, less sensitive to water vapor and slightly more accurate. Its problems are that,because of sun glint, it is usable only at night, has a lower signal level compared with theday/night 11-µm retrieval, has a similar sensitivity to aerosols and lacks continuity with theAVHRR SSTs.

The current VIIRS algorithm, (VIIRS, 2011e) uses an identical stratified daytime algo-rithm to Equation (7.18), with a switch point at 0.8 K and different coefficients for the tworegimes, where, between 0.6 and 1.0 K, the results from the two algorithms are linearlyinterpolated. With different coefficients, the VIIRS nighttime algorithm is identical in formto Equation (7.15).



ATLAS TRITON Subsurface ADCP

30oN

30oS

20oS

20oN

10oN

10oS

120oE

0o

140oE 160oE 180o 100oW160oW 140oW 120oW 80oW

Fig. 7.11. The Pacific TAO/TRITON array. The ATLAS and ADCP (Acoustic Doppler Current Pro-filer) buoys are US; the TRITON buoys are Japanese. (Courtesy of NOAA/PMEL/TAO Project Office,Dr. Michael J. McPhaden, Director.)

7.5.4 Surface match-up data set

As stated in Section 7.1, the retrieved SST is a hybrid of satellite and in situ measurements.The in situ data are used in two ways. First, the coefficients in the SST algorithms aredetermined by comparison of the satellite with the in situ observations; second, for griddedproducts such as the Reynolds SST described in the next section, the in situ data are usedto fill those gaps in the satellite SST that are generated by clouds.

To determine the coefficients, at daily intervals the satellite-derived SSTs are comparedwith temporally and spatially coincident surface temperatures taken by ships and mooredand drifting buoys in the ice-free ocean. These match-up temperatures determine the coef-ficients in the retrieval algorithms, which are reset as frequently as at monthly intervals. Forthe operational AVHRR, there are four sources of match-up temperatures: those taken byships, drifting buoys, and tropical and coastal moorings. The buoys use the NOAA satellitesto transmit their temperatures and positions to the National Environmental Satellite, Data,and Information Service (NESDIS) and to other national weather services; the ship dataare transmitted via the Global Telecommunications System (GTS).

Within the match-up data, the tropical moorings include the equatorial PacificTAO/TRITON array shown in Figure 7.11 (McPhaden et al., 1998; TAO, 2012), andthe PIRATA array in the tropical Atlantic (Bourles et al., 2008). These tropical mooringsprovide the algorithms with validation in the warm equatorial waters, which are associatedwith the largest atmospheric humidities.

Figure 7.12 shows the US coastal moorings that include the National Data Buoy Center(NDBC) buoys located off the east and west coasts of the United States, in the Gulf ofMexico and Gulf of Alaska, and around Hawaii (Hamilton, 1986; Meindl and Hamilton,1992; NDBC, 2012). The United States and its international partners have deployed about1000 of these moored buoys that measure wind direction and magnitude, air and water



180 o W 150 o W 120 o o 0o W

60o N

45o N

30o N

15o N

Alaska

Canada

United StatesPacific Ocean

Hawaii

WW 90

Fig. 7.12. The locations of the NDBC buoys in September 2001; see the text for further description.

60

30

0

60 120 180 –60–120 0

3564 Floats05-Oct-2012

–30

–60

Fig. 7.13. The black dots show the locations of the surface drifters from the Global Drifter Programon October 1, 2012. (Figure courtesy of Mayra Pazos, Global Drifter Program, AOML, NOAA, usedwith permission.)

temperature, and in some cases, salinity. For the moored buoys, the water temperature ismeasured at a depth of about 1 m.

The Global Drifter Program sponsors the drifting buoys that measure water tempera-ture at depths of about 0.3 m and have lifetimes of 1–2 years. The Drifting Buoy DataAssembly Center (DAC) at the NOAA Atlantic Oceanographic and Meteorological Lab-oratory build and deploy the US buoys (AOML, 2012; see Figure 7.13). NATO and theCanadian Maritime Environmental Data Service (MEDS) also deploy drifters. Finally, the



ship water-temperature measurements come from ships of opportunity that report theirengine intake water temperatures, or the temperature from a sensor at depth or the temper-ature measured from seawater collected in an insolated bucket. As Section 7.7.1 discusses,the ship measurements are the least accurate of the observations. All of the observationsare quality controlled and sorted into day or night observations. The US processed data setis available through NESDIS.

Each month, SST is reported by about 1500 ships, 1300 drifting buoys and 300 mooredbuoys, of which 100 are in the tropics and 200 are in coastal areas (Xu and Ignatov, 2010).The number of monthly SST reports consists of about 100,000 from ships and 1,000,000from buoys. For an ice-free ocean divided into 1°× 1° latitude/longitude boxes, the spatialmonthly coverage for ships and drifting buoys is about 4%; and for moored buoys, thecoverage is about 0.4%.

Regarding quality, a major difference between the in situ and satellite data is that, forsatellites, the instruments few, are well-calibrated, and designed for the retrieval of SST,where their observations are functions of cloud cover, aerosol variability and satellite lookangles. In contrast, from Xu and Ignatov (2010), the in situ data are collected by manyinstruments with variable quality and negligible calibration after deployment, and wheremuch of these data is not specifically intended for use in satellite SST validation. Beforedeployment, the buoy sensors are calibrated to 0.1 K, but they are rarely recovered andrecalibrated after deployment (Minnett, 2010). Because of the potential problems with dataquality, before the in situ data are used for validation, they are quality controlled and theoutliers removed (Ignatov et al., 2009).

There are two additional sources of SST data used in the calibration. The first is ship- andaircraft-mounted infrared radiometers that measure the same SST as is observed by satellite(Minnett, 2010). These instruments have the advantage that they observe the same quantityas the satellite and they are calibrated. Minnett (2010) describes such an instrument calledMarine-Atmosphere Emitted Radiance Interferometer (M-AERI) that has been deployedon research vessels since 1998 and is used in the MODIS validation.

The second is a set of surface temperature observations from the vertically profiling Argofloats (Argo, 2012). These consist of approximately 3500 profiling buoys across the globalocean at north–south and east–west intervals of approximately 300 km (Figure 7.14). Thebuoys operate as follows. From their initial position at the surface, the buoys take profilesdown to depths of about 2 km, drift at depth for about 10 days, then return to the surfaceand report their position and profile data via satellite. The buoys have a design life ofabout 4 years; they are deployed from ships of opportunity, aircraft and research vessels.The data are publically available at Argo (2012). Although the Argo data are not used inthe match-ups, as Martin et al. (2012) describe for the GHRSST Multi-Product Ensemble(GMPE) data set in Section 7.8, they are used as an independent data set in the GMPE erroranalysis.

The US NCEP stores the temperatures and positions of all these buoys, then once per dayextracts buoy and satellite measurements that are coincident within 4 hours and 20 km, andadds them to the match-up data base (Dash et al., 2010; 2012; SQUAM, 2013). At monthly



60

30

0

45 90 135 180 –90–135 –45

IQUAM 2012.10

Ship Drifter Mooring

–30

–60

Fig. 7.14. Positions of Argo profiling drifters on 5 October 2012. These data were collected and madefreely available by the International Argo Program and the national programs that contribute to it(From http://www.argo.ucsd.edu, http://argo.jcommops.org; the Argo Program is part of the GlobalOcean Observing System.)

intervals and for day, night and different geographic areas, the iQUAM (2013) websitegenerates statistics such as the standard deviation and bias of the difference between thebuoy and satellite temperatures. If these statistics are too large, the MCSST and NLSSTcoefficients are recalculated. As Section 7.7.1 discusses further, cloudiness reduces theannual successful match-ups to about 10%–20% of the total possible. Examination ofthe monthly distribution of the match-up data given in iQUAM (2013) shows that thesurface measurements are unevenly distributed, especially those measurements by shipsand moored buoys, which have a strong bias toward the northern hemisphere and patchycoverage south of about 15° N.

7.5.5 The Reynolds and OSTIA SST data sets

There are at least two important near-real-time SST data sets used to validate the algorithmsand in the cloud filtering. The first is the Reynolds SST produced by National ClimateData Center (NCDC) (Reynolds et al., 2007); the second, the Operational SST and SeaIce Analysis (OSTIA) produced by the UK Met Office (Donlon et al., 2012). Both areGHRSST-compliant; both are derived from a combination of satellite SST retrievals andin situ data; both produce monthly, weekly and daily products. These SSTs are used in theretrievals described above, in the cloud masks that Section 7.6 describes, in some of themicrowave retrievals described in Chapters 9 and 11, and in the numerical weather andocean forecasting models.

For the Reynolds data sets, Reynolds et al. (2002) describe the weekly and monthlyaveraged global SSTs, which are derived from in situ and AVHRR observations that are

http://www.argo.ucsd.edu

http://argo.jcommops.org



optimally interpolated to a 1-deg latitude/longitude grid. These data sets are referred toas the OI SST, version 1 and version 2 (OI.v1 and OI.v2), and, using AVHRR data, arederived from 1981 to the present. The OI.v2 is the current weekly Reynolds SST; it isGHRSST-compliant and described and archived in OI-SST (2012).

The daily Reynolds SST is derived from an optimally interpolated combination of satel-lite and in situ SSTs and has a 0.25-deg (30-km) latitude/longitude resolution (Reynoldset al., 2007). Chelton and Wentz (2005) inspired the development of this data set; theyshowed that, compared with passive microwave retrievals, the OI.v2 severely underesti-mated the gradients associated with features such as the Gulf Stream. The daily ReynoldsSST covers the period 1985 to the present, and, through comparison with a spatiallysmoothed seven-day average of surface observations, it adjusts for the bias induced by thediurnal signal. Its formal name is the GHRSST Level 4 AVHRR_OI Global Blended SeaSurface Temperature Analysis. There are two daily products, one using AVHRR and in situdata; the other, a mix of AVHRR and AMSR-E SSTs that ended in 2011 when AMSR-Eceased to operate. For the AVHRR-only data set, the rms error is about 0.6 K; for theblended AVHRR/AMSR-E data, it is about 0.4 K.

Because the Reynolds daily product is available from 1981 to the present, it is used inclimate studies and for TR in the SST algorithms described in Sections 7.5.2 and 7.5.3.The difference between the Reynolds and the satellite-derived SST is that the ReynoldsSST combines the satellite and in situ derived SST and applies a regional and seasonal biascorrection to produce a gap-free Level 4 product. In contrast, the satellite SST are derivedfor clear skies from application of the various algorithms to the observations, where in situdata are used only to set the coefficients in the algorithms.

The second important blended product is the OSTIA SST. It is optimally interpolatedfrom a variety of GHRSST infrared and microwave products, as well as from in situ data(Donlon et al., 2012, Table 1). Its output is a daily, weekly and monthly L4 product ofSSTfnd at a grid resolution of 0.05 deg (6 km). In a series of experiments, the use ofthe OSTIA SST fields over the old low-resolution AVHRR and in situ fields in numericalweather prediction models yields forecast improvements for periods of 6 days into thefuture. Also, comparison of the OSTIA results with SST fields not used in the model showsthat its mean rms error is about 0.5 K and the bias is negligible.

7.5.6 Advanced Along-Track Scanning Radiometer

In contrast to the AVHRR and MODIS split window retrieval, the Along-Track Scan-ning Radiometer (ATSR) on ERS-1 and ERS-2 and the Advanced ATSR (AATSR) onENVISAT enhances the multichannel retrievals with a dual-look-angle technique to removeatmospheric attenuation (Llewellyn-Jones and Remedios, 2012). This technique works asfollows: imagine being able to view the same element of surface area at two differentlook angles, for example at nadir and at 60°. With the assumption that the atmosphericproperties are identical along each path and that the observed surface temperature does not



NLSST

12 NOAA-14NOAA-11

SST Equation:

MCSST CPSST

Equation Updates:

MT. PINATUBO

Satellite

Scatter Bias

0.5

0

–0.5

–1

–1.51989 1990 1991 1992 1993 1994 1996 1997 1998

Year of comparison

Glo

bal b

ias

and

scat

ter

(K)

Fig. 7.15. A schematic diagram of the ATSR and AATSR operation. See the text for furtherdescription.

vary because of the larger FOV associated with the longer path, the nadir view correspondsto a passage through one atmosphere; the 60° view, to a passage through two atmospheres.

The difference in received brightness temperatures between the two paths equals theattenuation and emission associated with a single vertical passage through one atmosphere.Subtraction of this difference from the nadir brightness temperature yields an accuratemeasurement of TS. The advantage of the dual-look retrieval is that it removes all of theattenuation along the path, including contributions from tropospheric water vapor and fromtropospheric and stratospheric aerosols.

Minnett (1995a, 1995b) describes the ATSR in detail; Birks et al. (1999), O’Carroll(2006) and Embury and Merchant (2012) describe the AATSR dual-look and multibandalgorithms. Because of the dual look, the algorithm coefficients can be determined theoret-ically and do not require tuning against a match-up data set. This provides an SST that isindependent of in situ observations. Figure 7.15 shows a schematic drawing of the ATSRand AATSR operation. The instruments are conical scanners that observe the surface ina 500-km wide swath, which is narrow compared with the AVHRR swath width of 2600km and the VIIRS swath width of 3000 km. One side of the cone intersects the surface atnadir; the other at a 55° look angle. Approximately two minutes separate the forward andnadir views of the same area; the nadir FOV has a 1-km diameter. For each path, using theprocedures described in Section 7.6, clouds are separately identified.

ATSR has four bands that are identical to AVHRR bands 3A, 3B, 4 and 5; the purposeof band 3A at 1.62 µm is to identify clouds and land. AATSR has a total of seven bands,


7.6 Cloud-detection and masking algorithms 221

including the four ATSR bands and three additional bands at 550, 670 and 870 nm. FromMinnett (2010, Table 14.7) and compared with buoys, the AATSR SSTs have a standarddeviation of about 0.4 K in daytime and 0.3 at night. The successor to AATSR is the Sea andLand Surface Temperature Radiometer (SLSTR), which will operate in a similar mannerand is scheduled for launch on Sentinel 3 in 2014 (ESA, 2012d).

7.6 Cloud-detection and masking algorithms

There are many kinds of clouds: warm liquid water clouds, high thin ice clouds that arepartially transmissive, thick opaque ice or liquid water clouds, warm low stratus or semi-transparent fog decks, and broken sub-pixel clouds (Pavolonis et al., 2005). The basis ofcloud detection depends on several factors, first, compared with the oceanic background,clouds are generally more reflective but colder; second, the wavelength dependence of theemitted and reflected radiances differ as a function of cloud type; third, arrays of sub-pixelbroken clouds exhibit more spatial variability than the background.

McClain et al. (1985), May et al. (1998), Pavolonis et al. (2005) and Petrenko et al.(2010) describe the cloud tests, and, for many of the tests, Saunders and Kriebel (1988)give the theoretical background. Ackerman et al. (2010) give the physical and observationalbackground of many of the AVHRR and MODIS tests; Petrenko et al. (2010) give the detailsof the NOAA Advanced Clear-Sky Processor for Ocean (ASCPO) operational algorithmdiscussed in Section 7.6.2. Over open ocean, these tests depend on two factors: the cloudsbeing colder and more reflective than the ocean surface, and, for spatial scales of order 100km, the ocean surface being nearly uniform in temperature and reflectance (Rossow, 1989).

For the ice-free ocean, the number of cloud-free pixels amounts to 10%–20% of thetotal. The process of identification and removal of clouds from the satellite observationsdepends on whether it is day or night and on whether the ocean surface is ice-free. Ingeneral, because of the different reflectance and emissive properties of clouds and openwater, cloud discrimination over open ocean is easier than over land or ice. Section 7.6.1discusses the general concept of cloud algorithms, in particular, those that use the observedreflectances and brightness temperatures to discriminate clouds from ocean. Section 7.6.2describes a different approach used by the ACSPO algorithm that compares the calculatedbrightness temperatures from a hypothetical clear-sky ocean surface with the observed.Finally, Section 7.6.3 briefly describe the MODIS and VIIRS cloud tests. For the ocean,the day/night AVHRR cloud tests use all five bands, while, as Section 7.6.3 discusses,VIIRS and MODIS respectively use as many as 16 and 17 bands. Because of the GHRSSTrequirements, cloud algorithms are currently in a state of transition, so the proceduresdescribed below are subject to change.

7.6.1 Basis for the cloud-detection algorithms

The accurate retrieval of SST from infrared satellite observations requires that the oceanpixels be cloud-free. In any cloud-filtering scheme, the first task is to mask the land, seaice and sun-glint pixels. For a particular geographic location, prediction of sun glint useswind speed from numerical weather models, the Cox and Munk (1954) algorithm and



the solar zenith angle. Because the amount of water vapor and aerosol along the viewingpath increases with zenith incidence angle, angles greater than about 55° are discarded(Kilpatrick et al., 2001). Then for AVHRR, the pixels within a 24-hour period are placedinto day and night files (Casey et al., 2010).

After these steps, tests remove clouds from the data. The tests divide into those appliedto single pixels and those applied to pixel arrays. The simplest single-pixel tests involvethe removal of thick clouds. Because, in daytime, these clouds are more reflective than theocean surface, and in day and night, they are colder, they can be identified using a reflectionor temperature threshold. In daytime, these tests are more difficult because, the reflectiondepends both on the satellite viewing zenith angle and on the solar zenith angle, while thebrightness temperature tests depend only on the viewing zenith angle.

Another single-pixel test is the daytime reflectance ratio contrast test, where thereflectance ratio is defined as the ratio CR of the band-1 visible reflectance to the band-2NIR reflectance. Because the atmospheric Rayleigh scatter is greater in the visible thanin the NIR, and because clouds generally occur above the aerosol-laden marine boundarylayer, under cloud-free conditions, the band-1 reflectance is about twice that at band 2. Incontrast, under cloudy conditions, the reflectances are nearly equal (Saunders and Kriebel,1988). This means that, if CR is less than a look-angle-dependent threshold, the pixel isclear. A third single-pixel test for clouds uses the retrieved SSTs. If the retrieved SSTsdepart significantly from either the Reynolds SST or climatology, the pixels are flagged ascloudy.

This climatology test can present problems. Donlon et al. (2012) describe the BritishOperational SST and Sea Ice Analysis (OSTIA) system, which, before 2008, was designedsuch that, if the SST variation from climatology exceeded a threshold, the observationwas replaced with climatological SST. During the extreme melt-back of the Arctic icecover in September 2007, the system rejected the retrieved SSTs in the newly exposedopen water and replaced them with erroneous climatological SSTs, which led to incorrectforecasts.

There are also single-pixel tests that use pairs of infrared bands to detect uniformthin fog or stratus layers. These tests depend on the wavelength-dependent emissivity ofclouds. For clouds consisting of water droplets, the cloud emissivities ec are functionsof λ, the droplet size distribution and the cloud physical and optical thicknesses. In thethermal infrared, Hunt (1973) shows that, as the cloud thickness increases, ec increases andits transmittance decreases, so that, depending on λ and cloud thickness, ec varies fromnear zero to about 0.97. For thick clouds, Hunt (1973) shows that ec is generally smaller at4 µm than at 11 or 12 µm; specifically, at 3.5 µm, ec is about 0.80; at 11 µm, ec is about 0.97.Because of this dependence of ec on λ, there is a class of nighttime tests called “three minusfive tests (TMFT)”, where, for AVHRR, T35 = T3B − T5, which is the brightness tem-perature difference between the 4- and 12-µm bands. In the presence of clouds, T35 < 0.In contrast, for cloud-free conditions, because for both bands the seawater emissivity isnearly constant at about 0.99 and the water vapor attenuation is greater for band 5 than forband 3B, T35 ≥ 0.



Another example is the detection of high thin cirrus clouds. These clouds consist ofthin, semi-transparent layers of ice crystals that are associated with the penetration ofconvectively active rain cells into the upper troposphere. At these altitudes the ice crystalsspread rapidly and laterally over distances of hundreds of kilometers and persist for hours(Prabhakara et al., 1988). Because cirrus clouds are thin and semi-transparent, they aredifficult to identify from satellite observations; because they are very cold, they introducesignificant errors into the SST retrieval. As Prabhakara et al. (1988) show from aircraftobservations, the presence of these crystals tends to reduce both T11 and T12, but with agreater attenuation of T12 than of T11.

The result is that, in the presence of cirrus, T11,12 = T11 − T12 tends to increase,reducing the retrieved SST below TS, so that T11,12 is more positive than for cloud-free conditions. From May et al. (1998), the day/night operational criterion used for highcirrus clouds is to accept a pixel as cloud-free only if T11,12 is less than or equal to alook-angle-dependent threshold.

Next, the retrieved SST is used in a spatial uniformity test that examines the varianceof an array of SST pixels. This test is applied to a 3 × 3 array of GAC pixels, or to a 5 ×5 array of LAC or FRAC pixels, where the test determines the status of the central pixel.If the standard deviation of the array exceeds a threshold, it may indicate the presenceof sub-pixel clouds. This test needs to be carefully applied, particularly in the presenceof gradients in surface temperatures associated with upwelling, fronts or currents. FromMartin et al. (2012), such tests are the cause of increased error in regions of rapid oceanicvariability, such as mesoscale eddies, and the edges of the Gulf Stream, Kuroshio andupwelling regions.

7.6.2 The Advanced Clear-Sky Processor for Ocean (ACSPO)

For the operational SST derived from AVHRR, the ACSPO cloud tests employ GAC,LAC and FRAC pixels. ACSPO uses very different cloud filters than those described inthe previous section. Instead of using the retrieved brightness temperatures to search forclouds, ASCPO calculates the brightness temperatures and SSTs for a sky that is assumedto be cloud-free, compares these quantities with the observed and defines the cloud maskin terms of their differences (Petrenko et al., 2010). Ignatov and Petrenko (2010) show thatan algorithm similar to ACSPO is used in the VIIRS retrieval and is proposed for the 2015Advanced Baseline Imager (ABI) on the GOES-R satellite.

Following the code described in Petrenko et al. (2010, 2013), the tests are applied asfollows. The daily collections of pixels are grouped into day and night bins, then filtered forsea ice and land. Pixels contaminated with sun glint are not immediately rejected, insteadthe reflectance tests described below eliminate them. The pixels that pass sea ice and landtests are subjected to a series of four single-pixel and three-array tests. As input to theclear-sky model, ACSPO uses, as a first guess, the daily Reynolds or OSTIA SST from theprevious day, atmospheric profiles of temperature and water vapor from numerical weathermodels and the solar zenith and satellite viewing zenith angles. From these data and for all



bands, ACSPO calculates the clear-sky radiance from the Community Radiative TransferModel (CRTM). These predicted clear-sky radiances are compared with the observed, andthe presence of clouds is determined by how well the observed and predicted radiancesagree. From these tests, ASCPO classifies the pixels into three categories: clear, probablyclear and cloudy.

Petrenko et al. (2010, 2013) describe seven tests, the first three of which are day/nighttests used to identify the presence or absence of cloud cover. The first is a single pixel testthat examines the differences between the observed and calculated brightness temperatures;the second is a single pixel “static” anomaly test that compares the observed and calculatedSSTs. Both tests search for pixels that are too cold. The third is called an adaptive SST test,which uses the array method described below to search for cloud edges. The fourth andfifth tests are daytime tests that examine the single-pixel reflectances and search for pixelsthat are bright compared with the ocean surface. If the pixel fails any one of these five tests,it is cloudy. The final two tests are array tests, sometimes called texture tests. The first isa day/night test that examines the standard deviation of the retrieved SSTs using a medianfilter; the second is a daytime test that examines the correlation between the reflectance andthe SST, where the correlations of cold temperatures with large reflectances may indicatethe presence of sub-pixel broken clouds. If the pixels fail either of these tests, they areclassified as “probably clear”.

Here is a detailed description of the ACSPO tests.

1. Brightness temperature (BT) test (day/night). During nighttime, this gross cloud test isthe root-mean-square comparison of the 4-, 11- and 12- µm band brightness temperatureswith those calculated from the daily Reynolds or OSTIA SSTs; during daytime, the testis a similar comparison for the 11- and 12- µm band temperatures. The test eliminatescold pixels that fall below a threshold.

2. SST static anomaly test (day/night): This test examines the difference between theday/night SST retrievals and the daily Reynolds or OSTIA SST. If the retrieved differenceis greater than a latitude/longitutde threshold, the pixel is cloudy.

3. The adaptive SST filter (day/night). This test is applied to the results of the static anomalytest, and is designed to search for cloud boundaries. This test is applied to a 7 × 7 GACarray or a 21 × 21 LAC array, and is the most computationally intensive operation withinASCPO. It works by analyzing the statistics of TS − TO where TS is the Reynolds orOSTIA SST and TO is the observed. Within the window surrounding a central pixel,separate statistics are generated for the sets of pixels classified as clear and cloudy inthe static test, then compared. Based on this comparison, some of the clear pixels arereclassified as cloudy. This process continues until either the central pixel is classifiedas cloudy or the classification of pixels within the array stabilizes.

4. Reflectance gross contrast test (RGCT) (day). This gross cloud test examines the AVHRRchannel 2 reflectance. If this reflectance is less than a threshold that is dependent onviewing zenith angle and solar zenith angle, the pixel is clear.



5. Reflectance ratio contrast test (RRCT) (day). This test examines the ratio CR of theband-1 to band-2 reflectances. Because atmospheric Rayleigh scatter is greater in thevisible than in the NIR, and because clouds generally occur above the aerosol-ladenmarine boundary layer, for cloudy conditions, the reflectances are approximately equal.If CR is less than a threshold, the pixel is clear.

If the observations fail any one of these five tests, the pixel is cloudy.The next two tests examine the spatial uniformity of the retrieved SSTs around a central

pixel. Under ASCPO, these are applied to arrays of GAC or LAC pixels; the purpose ofboth these tests is to search for the presence of sub-pixel broken clouds. If the results ofthe previous tests yield clear skies, but the pixels fail either one of these spatial uniformitytests, then the pixel is classified as probably clear.

6. SST uniformity test (day/night) This test searches for the presence of sub-pixel scaleclouds within a 3 × 3 sliding window through examination of the SST variability. Asdescribed in the previous section, one problem with this test is that, if the pixel is locatedin a region of thermal gradient, as occurs at the edge of an upwelling region or theGulf Stream, the test could classify these regions as cloudy. To reduce its sensitivityto oceanic thermal fronts, instead of using the standard deviation as described in theprevious section, the ACSPO uses a median filter similar to a standard deviation butwhich is based on an analysis of SST minus the median SST, which is the median of allvalid pixels within the window. If the filter yields a result less than a threshold, the pixelis clear, otherwise it is classified as probably clear (Petrenko et al., 2010, 2013).

7. SST/albedo cross-correlation (CC) filter. Ignatov and Petrenko (2010) describe thesecond uniformity test, which is a daytime cross-correlation of the SST with thechannel 2 reflectance. Because the presence of scattered sub-pixel clouds means thatthe cloud-affected pixels are more reflective and colder than the clear pixels, negativeSST fluctuations correlate with positive fluctuations in the band-2 reflectance, so that across-correlation that exceeds a threshold indicates the presence of these clouds. Thisfilter can detect clouds that pass the SST uniformity test.

Petrenko et al. (2013) describe the application of these tests. If the data fails any one oftests 1–5, the pixel is “cloudy”. For pixels that pass each of the first five tests, the two spatialuniformity tests are then applied. If the pixel passes both of these tests, it is classified asclear; if it fails either one, the pixel is classified as “probably clear”. From Petrenko et al.(2010), for METOP AVHRR observations on 1 August 2008 and using an earlier versionof ASCPO, the brightness temperature test rejects about 55% of the pixels, the static SSTrejects an additional 16%, and the adaptive test in the neighborhood of cloud boundariesrejects, an additional 6%. Finally, the uniformity test rejects an additional 7% as probablyclear, leaving 16% as clear. The daytime sequence yields similar results.

Table 7.3 shows the percentage of clear pixels derived from ACSPO for three NOAAsatellites and METOP-A. The table shows that the percentage of clear pixels is about 15%.



Table 7.3. For AVHRR on foursatellites, the percentage of clear pixels

derived from ACSPO, for 100 orbitsduring 1–7 August 2008 (adapted from

Petrenko et al. (2010), Table 5).

Satellite Percentage of clear pixels

NOAA-16 17.24NOAA-17 14.83NOAA-18 15.20METOP-A 14.88

As another example, Pathfinder (2001) provides annual lists of possible versus cloud-freematch-ups through 1999. For 1999, they find a success rate of 14%. In aggregate, thesestatistics suggest a cloud-free match-up rate of 10%–20%.

7.6.3 MODIS and VIIRS cloud algorithms

The MODIS and VIIRS instruments have many more bands than the AVHRR. The VIIRStests for clouds over ocean use 16 bands (VIIRS, 2011a); the MODIS tests use 17 bands(Ackermann et al., 2010). In spite of the increased number of bands, MODIS and VIIRSuse many of the single- and multiple-pixel tests described in the previous sections. Also, asSQUAM (2013) describes, NOAA has adapted ASCPO for use with MODIS and VIIRS.

For MODIS, the cloud algorithms are designed not only to mask clouds for SST andocean color retrieval, but also to classify the clouds for radiative balance calculations(Ackerman et al., 2010). In the Appendix, Table A.2 and Table A.3 respectively list theMODIS and VIIRS bands. MODIS bands 1 and 2 have a 250-m resolution; bands 3–7have a 500-m resolution; all other bands have a 1-km resolution. The better resolution ofthe 250-m and 500-m bands provides daytime reflectances and reflectance ratios for usein threshold and uniformity tests at a finer resolution than the AVHRR, which helps in theidentification of cloud edges, aircraft contrails and small broken clouds. Bands 18 and 26occur in strong water vapor absorption bands and, as shown below, serve in the daytimediscrimination of thin cirrus. Band 19 is used for detection of cloud shadow, band 27 isused for cloud discrimination in the polar regions and band 29 is used in combination withthe 11- and 12-µm bands for cloud identification.

For VIIRS, all of the imaging-resolution (I) bands are used in the cloud algorithm,where each of these bands is approximately co-located with an AVHRR band. For themoderate-resolution (M) bands, with the exception of M9, M10 and M11 that lie between0.378 and 2.25 µm, and band M14 at 8.55 µm, the bands are nearly co-located with eitherthe AVHHR or SeaWiFS bands. The clouds are classified into the same four categories asMODIS, although ACSPO has been adapted for VIIRS. For both MODIS and VIIRS, the


7.7 Error and bias of the data sets 227

high-resolution bands are used in spatial uniformity tests; band I5 (11.45 µm) for night andband I2 (0.865 µm) for day. For both instruments, the high-resolution bands allow betterdefinition of cloud edges.

One important difference between AVHRR and the other two instruments occurs in thetwo bands with strong water vapor absorption shown in Figure 4.9: the MODIS band at0.936 µm and the VIIRS and MODIS bands at 1.375-µm. For the 1.375 µm band, Gao et al.(1993) show that, as long as V > 4 mm, the surface and near-surface reflected radiances arecompletely attenuated. This provides a simple reflectance threshold test for daytime highcirrus clouds. Because these clouds occur in the upper troposphere and lower stratosphere,they appear bright in contrast to the completely attenuated surface reflectances from thesurface and from clouds in the lower troposphere. At night, the high cirrus is identifiedusing the T11,12 test described in Section 7.6.1.

Another difference between AVHRR and the other instruments is that MODIS and VIIRShave bands in the wavelengths 6–9 µm, where MODIS has three such bands and VIIRS hasone. Following Ackerman et al. (2010) and Liu et al. (2004), the bands in this range aresensitive to moisture in the mid-level atmosphere, in contrast to the 11–12 µm bands, whichare sensitive to conditions at the surface. The brightness temperature difference betweenthese two bands is used to detect mid-level clouds. With the addition of the 1.375 µm test,and tests involving the 8-µm bands, the single-pixel tests and multiple-pixel uniformitytests are identical to those used with the AVHRR.

7.7 Error and bias of the data sets

One problem with discussion of the bias and errors associated with the satellite SSTsis its accuracy can be calculated only relative to another data set that also has potentialinaccuracies, such as the surface match-up data set. With the exception of the limitedM-AERI data set described in Minnett (2010) and Section 7.5.4, there is no absolute data setwith which to compare either the satellite retrieved or in situ SSTs. Section 7.7.1 describesthe errors associated with the ACSPO retrieval; Section 7.7.2 describes the longer-termerrors associated with volcanic eruptions and sandstorm outbreaks from the Sahara.

7.7.1 Determination of the errors in the SST data sets

As an example of the AVHRR accuracy, for October 2012, Table 7.4 compares in situobservations with the daily Reynolds SST, where, in this case, the input to the Reynoldsdata set consists only of the AVHRR data. For this month, the table shows that the driftersprovide 75% of the match-up data, the coastal moorings, 15%, and the ships and tropicalmoorings, the remaining 10%. The ship temperatures have the largest bias and are warmrelative to the satellite SST; this is because many of these temperatures are measured fromengine intake water that is heated in the engine room (Reynolds et al., 2010). Similarly,the ship observations have the largest standard deviations, while the coastal and tropicalmoorings have the smallest at 0.3 K.



Table 7.4. Comparison of the accuracy of the coincident in situ match-up observationswith the same day 0.25-deg Reynolds OI SST derived using only AVHRR as an input for

October 2012 modified from iQUAM (2013).

PlatformNumber of quality-controlled observations

Number ofmatch-ups

Percentageof total (%)

Bias(K)

Standarddeviation (K)

Ship 76,000 68,000 6.8 0.2 0.96Drifter 748,000 745,000 74.5 0.04 0.33Tropical mooring 34,000 34,000 3.4 0.03 0.32Coastal mooring 189,000 152,000 15.2 −0.03 0.48

Total 1,047,000 999,000 – – –

For a variety of instruments, Minnett (2010) summarizes their biases and standarddeviations relative to the buoys and to M-AERI. For AVHRR, the statistics for the period1985–1999 yield a bias of 0.02 K and a standard deviation of 0.5 K. In the M-AERIcomparison, the bias is 0.14 K and error is 0.4 K, where, at night, the error drops to±0.3 K. The improved nighttime behavior is due to the use of 4-µm band and to thephysical behavior of the ocean surface. One reason that nighttime measurements are moreaccurate than daytime, is that, in the day, solar heating can increase the skin temperaturewithout changing the atmospheric temperature and humidity profiles. Because for constantatmospheric properties, T11 has a greater response to an increase in TS than T12, T11,12 alsoincreases, which reduces the retrieved SST. For these reasons, nighttime SST observationshave a greater accuracy than those retrieved in daytime. The MODIS errors are slightlylarger than the AVHRR; the AATSR errors are smaller.

7.7.2 Impact of volcanoes and sandstorms

Volcanic eruptions and Saharan dust generate serious problems for the algorithms. Sincethe beginning of the AVHRR SST time series, two major eruptions have injected largeamounts of sulfuric acid droplets into the stratosphere. These were the Mexican El Chichoneruption in April 1982 (Bernstein and Chelton, 1985), and the Philippine Mount Pinatuboeruption in June 1991. The stratospheric aerosols from the Pinatubo eruptions persistedfor about two years, first spreading around the globe in the tropical regions, then laterallyinto the temperate latitudes (Walton et al., 1998). This distribution of aerosols meantthat the globally averaged satellite SSTs were 0.5 °C colder than the buoy SSTs, withtropical negative biases exceeding 2 °C. The nighttime algorithm had a similar but smallernegative bias. For both day and night, adjustment of the algorithm coefficients removed thisbias. Similar tropospheric aerosol events such as Saharan dust storms that occur at muchshorter time scales have a similar effect, and are a concern for observations in the NorthAtlantic.


7.8 Other GHRSST data sets and merged products 229

Swath width(500 km)

55o

AATSR sensor

900 km or 2 minutes

780

km

FOV

23.5o

Flight direction

FOV

Fig. 7.16. A 9-year time series of the statistics of the monthly global difference between the match-upsatellite and buoy SSTs. See the text for further description. (Figure 9 from Walton et al. (1998),published 1998 American Geophysical Union, not subject to US copyright.)

For the 9-year period 1989–1998, Figure 7.16 shows the monthly time series of theglobal mean and standard deviation of the difference between the satellite SSTs and thebuoy temperatures. On the figure, the means are called biases; the standard deviationsare called scatter. The lower part of the figure lists the satellites used in these measurements,NOAA-11, -12 and -14, and the algorithms used to compute the SST, where CPSST is thebriefly used Cross-Product SST (Walton et al., 1998). The diamonds on the bottom linemark the times when either the algorithm or its coefficients were updated. A large increasein cold bias occurs during the period when the Pinatubo aerosols affected the SST retrieval;following this period, the standard deviation approaches 0.5 K and the bias approaches 0K. The behavior of the nighttime algorithm, which is omitted, is similar and is described inWalton et al. (1998).

Another similar problem occurs with the outbreaks of Saharan dust blown over the NorthAtlantic. For the peak months of June, July and August, Vazquez-Cuervo et al. (2004) andReynolds et al. (2010) discuss the effect of the Saharan dust over the North Atlantic. Thesedust outbreaks tend to bias the data in a manner similar to the volcanoes and particularlyaffect the SEVIRI retrieval.

7.8 Other GHRSST data sets and merged products

The success of the GHRSST products and procedures is next demonstrated by discussion ofthe various national data sets and of a blended product called the GHRSST Multi-ProductEnsemble (GMPE) SST. In the following, Section 7.8.1 describes the variety of GHRSSTproducts and their archives. As the section shows, SST users are now provided with a broad



choice of SST analyses that before GHRSST would have been unavailable. Section 7.8.2discusses the blended Level 4 GMPE produced by the UK Met Office.

7.8.1 Products and archiving

As of 2013, a variety of countries or agencies including Australia, Canada, ESA, France,Japan, the UK and the United States produce a total of 61 GHRSST L2, L3 and L4 products.The GHRSST, L2 product is often referred to as the L2P (pre-processed) product; this isa specific GHRSST product designed for ease of data handling (GHRSST, 2013b). In theUnited States, all of the GHRSST-compliant data sets are ingested at the PO.DAAC GlobalData Assembly Center (GDAC), where the ESA Global Monitoring for Environment andSecurity (GMES) is a mirror site (GHRSST, 2013a). At GDAC, the GHRSST data areavailable in a 30-day rolling storage and then sent to the NODC Long Term Stewardshipand Reanalysis Facility (LTSRF) for permanent storage.

Of these 61 data sets, there are currently 29 L2, 11 L3 and 21 L4 data sets, where mostof these are EDRs. Their temporal resolutions range from 15 min to daily with the majoritybeing daily. For swath data (L2), the spatial resolution ranges from 1 to 25 km; for grid data,from 0.01 to 0.25 deg. Examples include the 15-min temporal resolution GHRSST Level2P Atlantic regional skin SST from SEVIRI on the MSG-2 satellite with an approximately5-km spatial resolution. The SEVIRI time series began in November 2009 and continuesto the present. The daily Reynolds AVHRR analysis described in Section 7.5.5 began inSeptember 1981, continues to the present, and is a CDR designed for climate studies.

Third, for short-term high-resolution use, JPL has developed the Multi-scale Ultra-highResolution (MUR) that provides daily global SST at a spatial resolution of 0.01 deg (about1 km) where MUR is available from June 2002 to the present. MUR is a blend of active andpassive SST retrievals with in situ data designed for the study of upwelling, Gulf Streamrings and other high-resolution features. There are also a variety of passive microwavelow-resolution GHRSST data sets that Chapter 9 discusses. For all 61 data sets, GHRSST(2013a) gives detailed descriptions; the NOAA SST Quality Monitor website (SQUAM,2013) describes these products, as well as providing near-real-time intercomparisons, errorstatistics and quality monitoring.

7.8.2 GHRSST Multi-Product Ensemble (GMPE)

From all of the L4 GHRSST data sets, the UK Met Office produces a daily GMPE L4gap-free gridded SST from an ensemble average. As Martin et al. (2012, Tables 1, 2)describe, the data sets used as input are from infrared and microwave observations takenby AVHRR, AASTR, AMSR-E, the GOES, SEVIRI and MTSAT sensors and from thein situ observations. These satellite instruments provide a mix of the high-resolution butcloud-encumbered infrared sensors and the lower-resolution but cloud-free microwaveobservations. The GMPE SSTs are restricted to wind speeds greater than 6 m s−1, andprovide estimates of foundation temperatures.


7.9 Illustrations and examples 231

The GMPE errors and biases are evaluated as follows. Since none of the individual datasets use Argo data in their production, an independent determination of the GMPE biasesand standard deviations compares the GMPE SSTfnd with the in situ Argo temperaturestaken at depths of 2–4 m. This is not an ideal comparison; as Figure 7.14 and Martinet al. (2012) show, Argo data are sparse in the South Pacific, around Indonesia and in theCaribbean. For the annual global ice-free ocean and relative to the Argo measurements, theGMPE has a mean bias of 0.03 K and a standard deviation of 0.4 K (Martin et al., 2012).These results are an improvement over the errors of the individual data sets, which typicallyhave a standard deviation of 0.5 K.

The GMPE data set has several problems. First, on a daily basis, the various infraredobservations encounter approximately the same cloud cover, so that the gaps in the separatedata sets occur at about the same locations. Second, near the ice edge, uncertainty in itsposition causes problems in the adjacent SSTs. Third, because the interpolation techniquesused to fill these gaps tend to smooth the data, larger errors and biases occur at thelocation of oceanic features with strong temperature gradients, such as fronts, eddies and theedge of currents such as the Gulf Stream. For example, Martin et al. (2012) show that,because of the variability of the Gulf Stream, the errors are greatest in the North Atlantic,and their Figure 12 shows in a Gulf Stream case study that the different national modelsproduce slightly different temperature distributions. In spite of these minor problems, thestrength of the GHRSST ensemble is that it has better error statistics while keeping thecoherent features that the individual models observe.

7.9 Illustrations and examples

The following sections discuss three examples of AVHRR and MODIS imagery. Section7.9.1 examines each band of an AVHRR image, Section 7.9.2 describes a global MODISSST image and Section 7.9.3 uses AVHRR and ocean color data to examine the transitionbetween El Nino and La Nina conditions in the equatorial Pacific

7.9.1 Examination of an AVHRR image

Figure 7.17 shows the five AVHRR bands used in the SST retrieval and the resultant cloud-and land-masked SST image. This image is from the same day and region of the Washingtonand British Columbia coast as the SeaWiFS image in Figure 6.27. Although the AVHRRand SeaWiFS images show similar features, the images are derived very differently; theSST is derived in the infrared from the top 10–100 µm of the water column, while the Chl-adistributions are derived in the visible from water-leaving radiances from the top 10–40 m.On Figure 7.17, the upper two panels show the solar reflectance bands 1 and 2. The band-1image shows the visible reflectance; clouds and land are reflective or white, water is darker.The oceanic pattern of water-leaving radiance shown in Figure 6.27 is faintly visible in thisimage, and, at the lower left, some sun glint is visible. The band-2 image shows the NIRreflectance, where seawater is black or non-reflective and clouds are gray or white. The


10

191817161514131211

0

5

% a

lbed

o

15

0

5

10

10

191817161514131211

C

EU

10

191817161514131211

FR

CR

VI

PS

JdF

10

191817161514131211

Band 3 Band 4

Band 2Band 1

Band 5%

alb

edo

(oC)

3.55–3.93 μm 10.3–11.3 μm

(oC)

NLSST

(oC)

11.5–12.5 μm

(oC)

0.725–1.0 μm0.58–0.68 μm

Fig. 7.17. Daytime AVHRR image of the Washington and British Columbia coast from NOAA-14,September 1, 1999, 2300 UTC, 1559 Pacific Daylight Time, or nearly coincident with the SeaWiFSimage in Figure 6.27. The sub-images show bands 1 through 5 and the SST distribution. On the band-1 figure, VI is Vancouver Island; FR, Fraser River; JdF, Strait of Juan de Fuca; PS, Puget Sound; CR,Columbia River. The letters C,eand U mark oceanographic features explained in the text. (Courtesyof Kate Edwards, used with permission.)



–2 0 5 10 15 20 25 30 35

Temperature (oC)

ab

c

d

gf

e

Fig. 7.18. One-month average for May 2001 of the MODIS-derived SST. Black is land, the colorscorrespond to the temperature scale. The letters identify physical features discussed in the text.(Courtesy of MODIS Ocean Group, NASA GSFC and the University of Miami.) See color platesection.

sharp contrast between land and water in this image shows why band 2 is used to identifythe land/water boundary.

The next four images show the three thermal bands and the derived SST. For each ofthese images, darker shades of gray are warm, lighter grays are cold. The scan lines in theband-3 image are caused by its increased noise relative to the other images. Also, eventhough the clouds are colder than the seawater, the direct reflection of solar radiation fromthe clouds and wave facets means that, at band 3, solar reflectance overwhelms thermalemission, so that the brightness temperatures in the region marked C are warmer than itssurroundings. Examination of bands 4 and 5 shows that, in contrast to band 3, thermalemission dominates, so that the clouds are colder and less noisy than at band 3. The lastpanel shows the SST distribution, which is derived from the NLSST Equation (7.13), whereTR is from the MCSST Equation (7.12) and the cloud and land mask in the SST image isbased on a band-2 threshold. All of the thermal images show the oceanic eddy off VancouverIsland, marked byein the SST image, and the cold upwelling adjacent to the coast markedby U, both of which are associated with the biological productivity shown in Figure 6.27.

7.9.2 A global MODIS SST image

For May 2001, Figure 7.18 shows the average global SST distribution derived from MODIS.The image is processed using nighttime data and the 11-µm SST algorithm in Equa-tion (7.18). On the image, the broad zonal distributions of SST are illustrated by thedark blue boundaries of the sub-polar fronts, and by the warmer red-to-green boundariescloser to the equator. There are also some specific non-zonal features. These include thenorthward-flowing plume of warm water along the east coast of North America associated



SST (oC) Chlorophyll-a concentration (mg m–3)<0.01 0.05 502010.1 0.5 2 105+15 +30

AVHRR SeaWiFSJa

nuar

y 19

98Ju

ly 1

998

Fig. 7.19. Comparison of AVHRR SST with SeaWiFS ocean chlorophyll for El Nino conditionsin January 1998 and La Nina during July 1998. See the text for further description. (Courtesy ofFrancisco Chavez, reprinted with permission from Chavez et al. (1999), Figure 1; C© 1999 AAAS;OrbView-2 Imagery provided by ORBIMAGE, the SeaWiFS Project and NASA/Goddard SpaceflightCenter.) See color plate section.

with the Gulf Stream (a) and a similar plume adjacent to the Japanese coast generated by theKuroshio (b). Along the east coast of South Africa, the southward-flowing Agulhas currentextends south of the Cape of Good Hope (c). The image also shows a region of cold-waterupwelling adjacent to the west coast of South America and the La Nina band of equatorialcold-water upwelling in the Pacific (d). A similar cold band extends along the equatorialAtlantic (e). Finally, adjacent to Central America, strong winds flowing through the moun-tain gaps that Chapter 11 discusses generate two localized regions of upwelling (f and g).

7.9.3 Transition from El Nino to La Nina

El Nino occurs when the equatorial trade winds weaken and allow warm, less biologicallyproductive Pacific water to replace the cold equatorial La Nina upwelling. For the PacificOcean in January and July 1998, the four panels in Figure 7.19 compare the monthly



averages of the AVHRR SST and SeaWiFS band-ratio chlorophyll at a 4-km resolution(Chavez et al., 1999). The SeaWiFS images also show the normalized land differencevegetation index (LDVI). The shift from El Nino to La Nina is the cause of the differencesbetween the two sets of panels. The January 1998 images occur toward the end of the1997–98 El Nino, while July 1998 shows the return to La Nina conditions. The JanuarySST and chlorophyll images show that, for El Nino, the equator is characterized by warmwater and low chlorophyll concentration.

In January 1998, the SST anomalies exceeded 5 K and were close to the largest observedfor this event, while the equatorial chlorophyll concentrations were the lowest on record.For La Nina, the July SST image shows that the easterly trade winds at the equator generateupwelling, which forms an equatorial tongue of cold water extending from the coast of SouthAmerica across the Pacific. The accompanying Chl-a image shows that this cold tongueis accompanied by a dramatic equatorial phytoplankton bloom with enhanced values ofchlorophyll. This behavior has important consequences for global climate studies, regionalfisheries and for understanding the oceanic uptake of carbon.


8

Introduction to microwave imagers

8.1 Introduction

Passive microwave radiometers provide a powerful, nearly all-weather technique forretrieval of a wide variety of ocean, sea ice and atmospheric geophysical variables. In con-trast to the lenses and mirrors used in the VIR, antennas are used with passive microwaveradiometers to receive the Earth-emitted radiances, and with radars to transmit and receiveenergy pulses. The present chapter describes the radiometer antennas and their terminology,discusses how radiometers work and summarizes the properties of the past, present and near-future operational passive microwave imagers. The next chapter describes the atmospherictransmissivity in the microwave, discusses the dependence of the surface emissivity on avariety of geophysical variables, gives examples of the retrieval algorithms and concludeswith examples.

Microwaves occupy that part of the electromagnetic spectrum between 1 and 500 GHzin frequency, or between 0.3 m and 1 mm in wavelength. The microwave band is bounded atlow frequencies by the television broadcast bands, the presence of which makes Earth obser-vations difficult, and at high frequencies by the far-infrared wavelengths where alternativemethods exist for detection. The frequency dependence of the atmospheric transmissiv-ity and interference from other users restricts the frequencies used in retrieval of oceanicvariables to specific windows in the range 1–90 GHz. The importance of microwave obser-vations is that the ocean surface emissivities and atmospheric transmissivities depend bothon frequency and on geophysical variables such as atmospheric water vapor and liquidwater, rain rate, sea surface temperature and salinity, wind speed, and sea ice type andextent. As Chapter 9 discusses in detail, to retrieve these variables, the instruments mustobserve the ocean at several different frequencies.

Compared with the VIR, the microwave has advantages and disadvantages. First andas Chapter 9 shows, because the atmosphere is much more transparent than in the VIR,especially in the range 1 GHz < f < 10 GHz, microwave instruments can view the surfacethrough clouds and gather data under almost all weather conditions except heavy rain.Second, with the exception of certain extraterrestrial sources of radiation such as the Sun,the brightness temperatures of the surface and of the atmosphere are less than or order of300 K. At these temperatures and in the microwave, the Rayleigh–Jeans approximation

236


8.2 General antenna properties 237

to Planck’s law applies, so that the radiative transfer equation can be written in termsof brightness temperatures instead of radiances. Third, the long microwave wavelengthsrelative to those in the VIR cause certain disadvantages. From the Rayleigh criterion inSection 3.5.1, these long wavelengths mean that, to obtain the same spatial resolution as inthe VIR, the antenna aperture must be much larger. Also, because the Earth approximatelyradiates as a 300-K blackbody with its maximum radiance at a wavelength of about 10 µm,from Planck’s equation, the emitted microwave radiances are much smaller than in theVIR. Thus, for an antenna to receive the same radiant flux as an optical instrument, itrequires either a larger aperture or a larger FOV. At present, because the size constraintsimposed by launch vehicles restrict the diameters of passive microwave antennas to 1–4 m,the microwave resolution is in the range 5–100 km. Finally, because the ocean surfacemicrowave emissivity strongly depends on look angle, a whiskbroom scanner cannot beused. Instead, most microwave imagers employ a conical scanner that observes the surfaceat a constant angle.

In the following, Section 8.2 discusses the properties of antennas. Although this dis-cussion primarily applies to passive imagers, some of it also applies to the active radarsdiscussed in Chapter 10. Section 8.3 describes how passive microwave antennas retrieve thesurface radiances; Section 8.4 describes the design of the conical scanner and the depen-dence of the surface emissivity on incidence angle; Section 8.5 describes the process ofantenna pattern correction. Finally, Section 8.6 describes the design and characteristics ofseveral of the past and present microwave imagers used for retrieval of oceanic properties.

8.2 General antenna properties

Ulaby et al. (1981, p. 93) define an antenna as “a region of transition from electromagneticradiation propagating in free space, to a guided wave propagating in a transmission line”.Figure 8.1 shows three common antennas, including a horn, a front-feed Cassegrain dishantenna and a front-feed paraboloid. For a transmitting antenna, the energy from the waveg-uide is radiated into space with a non-uniform directional distribution; for receiving, theantennas collect the incident radiation and focus it into a waveguide. The reciprocity theo-rem (Balanis, 1982, Sections 3.8.0 and 3.8.1) states that the directional distribution of theenergy transmitted and received by the same antenna is identical. Because of this reciprocitybetween transmission and reception, the antenna discussion begins with the derivation oftheir directional properties during transmission, then continues with the application of theseproperties to the receiving case.

Figure 8.2 shows an idealized radiating two-dimensional antenna of aperture width D,where D > λ. The antenna is illuminated by an electric field E, written as

E(x, t) = f (x)eiωt (8.1)

In Equation (8.1), f (x) is the antenna illumination pattern. On Figure 8.2, r is range, θ

is elevation angle, φ is azimuth angle and the exitance M(r, θ, φ) is the power density. At


238 Introduction to microwave imagers

Horn

Mainreflector

Line feed

Cassegrain antenna

Feed

Reflector

Front feed paraboloid

Sub-reflector

Fig. 8.1. Different kinds of antennas used in satellite applications. (Adapted from Figure 3.1, Ulabyet al. (1981).)

2

2–

f (x)

rθ

φ

M (θ,φ, r)

Boresight direction

+

D

D

Fig. 8.2. A diagram of an idealized antenna.



any given r, the boresight direction is that direction, generally located at θ = 0 and φ = 0,along which M is a maximum.

For transmission and in the far field where r > 2D2/λ, M decreases as r−2, so that itcan be written as

M(r, θ, φ) = I (θ, φ)/r2 (8.2)

where the intensity I (θ, φ) is independent of r (Balanis, 1982). If T is the total radiantflux transmitted by the antenna, then

T =∫4

∫π

I (θ, φ)d (8.3)

where d = sin θ dθ dφ and the integration is over the entire sphere. From these definitions,and as the next sections show, the power pattern, the pattern solid angle, the main beamand sidelobe solid angles, the main beam efficiency and the gain characterize the antennaproperties.

8.2.1 Power pattern

One of the differences between antennas and the lenses used in the VIR is that antennashave sidelobes, which means that they transmit and receive energy at angles well away fromthe boresight direction. Following Ulaby et al. (1981), the sidelobe properties are definedin terms of the normalized power or radiation pattern Fn(θ, φ), given by

Fn(θ, φ) = I (θ, φ)/I0 (8.4)

where I0 is the maximum intensity, which is in the boresight direction. For a particularantenna, Fn is either calculated numerically or analytically, or is determined experimentallyin an antenna test facility. From the reciprocity theorem described above, the power patternFn for receiving and transmission is identical, so that theFn of a receiving antenna can bedetermined from its transmission properties.

For the 85-GHz H-pol channel on the SSM/I microwave imager, Figure 8.3 shows thepower pattern, which consists of the dominant main lobe, smaller sidelobes and, althoughthe figure does not show these, much smaller back lobes. As the figure shows, the widthof the main lobe is given by the angular distance between the minima closest to theboresight direction; the sidelobe widths are similarly defined by their respective minima.The magnitude of Fn is given in terms of decibels or dB as defined in Equation (4.7), andthe half-power points are those angles at which the radiated power is reduced by a factorof 1/2 from its peak value, or where Fn = −3 dB. From Ulaby et al. (1981, Section 3.11),the half-power beamwidth θ1/2 is the angle between the two half-power points and isapproximated by

θ1/2 ∼ λ/D (8.5)



–2 –1 –0.5 0 0.5 1–3 3–40

–30

–20

–10

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Half-power points

Bor

esig

ht

Degrees from boresight direction

Main lobe

Nor

mal

ized

pow

er p

atte

rn (

dB)

Sidelobes

Sidelobes

2

Fig. 8.3. Power pattern for the SSM/I 85-GHz, H-pol antenna, plotted around the boresight directionfrom −2° to +2°, and showing the main and sidelobes. The half-power beamwidth is 0.35°. (Datacourtesy of Gene Poe.)

In Figure 8.3, the power pattern consists of a sharp peak between −2° and +2° and ahalf-power beamwidth of 0.35°. The narrow beamwidth and small sidelobes are typical ofsatellite antennas. The shape of the power pattern means that the antenna receives powernot only within θ1/2 but also from solid angles outside this beamwidth. For example, ifa very bright object such as the Sun fills one of the sidelobes, its radiance can overwhelmthe contribution from the main lobe.

For a microwave antenna, θ1/2 defines the size of the surface half-power field-of-view,or, equivalently, the 3-dB FOV, which is also called the surface footprint. Equation (8.5)shows that, the smaller the wavelength or the greater the frequency, the better the resolution.However, because the surface radiance is very small, it is frequently necessary to average thereceived radiances over a period of time to enhance the signal-to-noise ratio. As Sections1.6 and 8.6.1 describe in greater detail, because of this averaging, the FOV discussiondivides into the instantaneous FOV (IFOV) or the FOV determined at any instant and itstime-averaged value, the effective FOV (EFOV).

The power pattern has two limiting cases. The first corresponds to an optical telescopeor to what is called a pencil-beam antenna, which lacks sidelobes and gathers radiance onlyfrom within a specified solid angle around the boresight direction. For this case, the powerpattern becomes

Fn(θ, φ) =

1, θ ≤ θ/2, 0 ≤ φ ≤ 2π

0, otherwise(8.6)



The antenna pattern shown in Figure 8.3 is nearly a pencil beam.The second case is the ideal isotropic antenna, which transmits or receives uniformly at

all angles around the sphere, so that its power pattern is

Fn(θ, φ) = 1, for all angles (8.7)

For this isotropic case, the average normalized intensity is

Iave = T/(4π ) (8.8)

Even though it is impossible to build an isotropic antenna, it is a useful limiting concept.

8.2.2 Solid angles associated with the power pattern

Various solid angles describe the antenna properties, including the pattern solid angle, themain beam solid angle and the sidelobe and backlobe solid angles. The pattern solid angleP is a measure of the width of the antenna pattern and is defined as the integral of thepower pattern over all solid angles,

P =∫4

∫π

Fn(θφ) d (8.9)

For an isotropic antenna, P = 4π , and, for the pencil-beam antenna described in (8.6),

P = 2π θ2/8 (8.10)

Similarly, the main beam solid angle M is defined as the integral of Fn over the main lobe,as in

M =∫

main

∫lobe

Fn(θφ) d (8.11)

The sidelobe and backlobe solid angles S and B have similar definitions. From (8.9) and(8.11), the main beam efficiency ηM is defined as

ηM = M/P (8.12)

Generally speaking, the closer ηM is to 1, the smaller the sidelobes and the larger the con-tribution from the half-power beamwidth. As the following sections show for the differentchannels on the microwave imagers, in most cases ηM > 0.9. For example, for the antennapattern shown in Figure 8.3, ηM = 0.92.

8.2.3 Gain

The gain G(θ, φ) describes the antenna directionality, and is defined as the ratio of theintensity received from a given direction I (θ, φ) to the average intensity Iave in (8.8),

G(θ, φ) = I (θ, φ)/Iave (8.13)



Division of the top and bottom of this equation by Imax and use of Equations (8.3), (8.4),(8.8) and (8.9) transforms (8.13) to

G(θ, φ) = 4πFn(θ, φ)/P (8.14)

The maximum gain, called G0, occurs for Fn = 1, where

G0 = 4π/P (8.15)

From (8.15), G0 is the ratio of the solid angle occupied by a sphere to the pattern solidangle. Since a large gain implies a small P, a pencil-beam antenna has high gain.

8.3 Measurement of a surface radiance with an antenna

This and the next two sections describe the method to determine the surface brightnesstemperature TB within the half-power beamwidth. First, the present section discusses howa microwave antenna retrieves TB, where this retrieval includes contributions both fromthe main beam FOV and the from various sidelobes. Second, Section 8.4 describes whymicrowave imagers operate as conical scanners. Third, Section 8.5 discusses antennapattern correction (APC), which uses the values of TB taken from the adjacent FOVsproduced by the scanner to remove the sidelobe contributions and to improve the accuracyof the retrieved TB. In the following, the V-pol and H-pol brightness temperatures arewritten as TBV and TBH, or as TB(V,H), where the subscript can be either V or H.

Consider the relation between the solid-angle distribution of radiances incident on anantenna and the received radiant flux. The derivation assumes that there are no losses withinthe antenna, and that the antenna is sensitive to radiation at a center frequency f0 with abandwidth f f0. From Ulaby et al. (1981, Section 4.2), if L(θ, φ, f ) is the angulardistribution of radiance observed by the antenna and Fn(θ, φ) is the power pattern, thenthe received radiant flux F(V,H) is approximately given by the product of L and the powerpattern Fn integrated over the entire sphere:

(V,H ) = 1

2Ae f

∫4

∫π

L(θ, φ, f0)Fn(θ, φ) d (8.16)

In (8.16), φ(V,H) is the polarization-dependent radiant flux received by the antenna.Because antennas operate at only one polarization, then, depending on the instrumentdesign, the subscript on is either V or H. This means that the antennas receive only halfthe incident power, explaining the factor of 1/2 in front of the integral (Ulaby et al., 1981).Also in (8.16), Ae is the effective aperture area, which depends on the nature of the antennaand the properties of the incident radiation. For example, an antenna made up of a wire gridcan have an effective area nearly equal to that of a solid antenna. Finally, f is assumedsufficiently small that the integral over f can be linearized.

For an antenna located within a black box, the received radiant flux is calculated from(8.16) for two cases: the inner surface of the box at a uniform temperature and at spatiallynon-uniform temperature. For the first case, Figure 8.4 shows the antenna penetrating


8.3 Measurement of a surface radiance 243

ΦOUT

TB

Fig. 8.4. An antenna extending into a black box held at a constant temperature.

through the wall of a black box with its inner surface held at a constant temperature TB.The Rayleigh–Jeans law is assumed valid, so that

L (f0) = 2kBTBf 20 /c2 = 2kBTB/λ2

0 (8.17)

wheref0λ0 = c and λ0 is the center wavelength. After substitution of (8.17) into (8.16) anddropping the polarization subscript to simplify the resultant equation, the radiant flux OUT

from the antenna becomes

OUT = 1

2Ae f

∫4

∫π

(2kBTB/λ2

0

)Fn(θ, φ) d (8.18)

Integration of (8.18) and substitution of the definition of P from (8.9) gives

OUT = (Aef kBTB/λ20)

∫4

∫π

Fn(θ, φ)d = Aepf kBTB/λ20 (8.19)

From (8.19) and assuming that the antenna properties Ae, f , λ0 and P are known,measurement of OUT permits solution for the unknown TB.

Assume next that the inner wall of the box has a non-uniform surface or scene temperatureTsc(θ, φ). For this case,

OUT = (Ae f kB/λ2

0

) ∫4

∫π

Tsc(θ, φ)Fn(θ, φ) d = AeP f kBTA/λ20 (8.20)

For the non-uniform temperature distribution, Equation (8.20) shows that the box interiorappears to have a uniform temperature TA, where

TA = 1

P

∫4

∫π

Tsc(θ, φ)Fn(θ, φ) d (8.21)

The temperature TA is called the antenna radiometric temperature or simply the antennatemperature, and is the weighted integral of Tsc(θ, φ), with either V or H polarization.Despite its name, it is not the physical antenna temperature; in fact, because antennas are



θ

φ

Flight direction

Scan direction

Sub-satellite track

Sw

ath

wid

th

Sensor

Fig. 8.5. The geometry of the conical scanner and its surface scanning pattern. The figure shows theincidence angle θ , azimuth angle φ, the swath width and a few representative half-power FOVs.

designed to be highly reflective with correspondingly low emissivities, their brightnesstemperatures are small.

For a specific antenna, there are great advantages to being able to correct the measuredTA such that it corresponds only to the brightness temperature that is emitted from withinthe half-power FOV. Because the APC procedure depends on the nature of the radiometerscan, Section 8.4 next describes why conical scanners are frequently used in the microwave.

8.4 Conical scanners and the surface emissivity

Because the microwave emissivities of the atmosphere and ocean strongly depend onincidence angle, many of the current operational imagers are conical scanners. AsFigure 8.5 shows, these instruments view the surface at a fixed incidence angle θ androtate at a constant rate about their nadir axis so that their FOVs lie along successive arcs.For the reasons discussed in Section 9.4.2 and for all conical scanners, the incidence anglesare in the range 50°–55°.

For the representative observational frequencies of 6, 18, 37 and 85 GHz, and for aspecular fresh-water surface, Figure 8.6 shows the θ -dependence of the V- and H-polvalues of the reflectivity and emissivity. The curves are derived by substitution of the fresh-water index of refraction into the Fresnel equations (Equations (5.7) and (5.8)). Althoughthis figure neglects the ocean salinity, as Section 9.4.1 shows, for f > 5 GHz, the emissivityis independent of surface salinity. Figure 8.6 also shows the 50°–55° range of the scannerincidence angles. Examination of the figure shows that the emissivity and reflectivity


8.5 Antenna pattern correction (APC) 245

0

0.1

0.2

0.3

0.4

0.6

0.7

0.8

0.9

1.0

0.5

Em

issi

vity

H-pol

Con

ical

sca

nner

Incidence angle (degrees)

Ref

lect

ance

V-pol

0

0.2

0.4

0.6

0.8

1.00 20 30 40 60 70 9050 55 8010

Fig. 8.6. The dependence on incidence angle of the microwave emissivity and reflectivity of a specularfresh-water surface. The figure shows the emissivity (left-hand scale) and reflectivity (right-handscale) for 6 GHz (solid line), 18 GHz (dashed line), 37 GHz (dot-dash line), and 85 GHz (dotted line)and for V- and H-polarization. The vertical lines show the 50°–55° operating range of the conicalscanners. See the text for additional description.

have a very different and stronger θ -dependence than the infrared properties shown inFigure 7.6. For θ = 50°–55°, the reflectivities are on the order of the emissivities. Theselarge reflectivities mean that unlike the infrared, the radiative transfer model must includethe reflected atmospheric and extraterrestrial radiances. Figure 8.6 shows that, at the viewangle of the conical scanner, the V-pol emissivity is about 0.5 and the H-pol emissivity isabout 0.3, so that, for a surface temperature of 300 K, the V-pol brightness temperature isabout 150 K and the H-pol is about 90 K, yielding a 60-K difference. Neglecting all othersources of radiance, the brightness temperature of a flat ocean surface is cold and stronglypolarized. Finally, even though the conical scanner avoids the problems associated withθ -dependent emissivities, small spacecraft oscillations alter θ and the surface emissivities,creating uncertainties in the received brightness temperatures.

8.5 Antenna pattern correction (APC)

This section describes how the combination of the antenna scanning pattern and the receivedantenna temperatures permits retrieval of the surface or atmospheric brightness temperatureTB from within the half-power FOV, while minimizing unwanted radiances. As Wentz(1992) and Colton and Poe (1999) show, these unwanted radiances include the following:



(1)

(2)

(3)

TB(V,H)

Ocean

Sw

ath

edge

Scandirection

Coast

Land

Flight direction

(n – 1)(n + 1)

(n)

Fig. 8.7. The surface pattern of the main beam FOV for a conically scanned microwave antenna. Seethe text for further description.

(1) surface radiances originating from outside the half-power FOV, called sidelobe con-tamination;

(2) reflected extraterrestrial sources of radiance;(3) radiances generated by cross-polarization coupling within the instrument called

crosstalk, so that a radiance at one polarization has contributions from the oppositepolarization.

Depending on the antenna design and on the magnitude of the brightness temperatureswithin the surrounding FOVs, these additional radiances can cause the antenna temperaturesto differ significantly from the desired TB.

The APC procedure uses the antenna properties in combination with the surface FOVsto reduce the contributions of the unwanted radiances, and to reformat the retrieved datainto regularly spaced Earth-located grid cells. Njoku et al. (1980a) review the general APCprocedure and apply it to SMMR; Wentz (1992) briefly describes the application of APCto the SSM/I; Colton and Poe (1999) describe this application in more detail. This analysisfollows the treatment of Colton and Poe, which is valid for antennas with main beamefficiencies ηM 0.9. For this case, the concentration of most of the received power withinone or two beamwidths of the boresight direction simplifies the APC.

Figure 8.7 shows a series of circles representing the half-power FOVs from three suc-cessive radiometer scans. The figure illustrates three cases: (1) an ocean FOV with itssurrounding FOVs completely inside the swath; (2) an ocean FOV at the swath edge; (3) an


8.5 Antenna pattern correction (APC) 247

ocean FOV adjacent to land. For the first case, the TA measured at the surrounding FOVsare used to estimate the sidelobe radiances. Following Colton and Poe (1999) and for thenth FOV shown in Figure 8.7, it is assumed that TB(V,H) (n) is the desired surface brightnesstemperature and TA(V,H) (n) is the measured antenna temperature. For the H-pol radiances,the solution for TBH can be written as

TBH(n) = c0TAH(n) + c1TAV(n) + c2TAH(n − 1) + c3TAH(n + 1) (8.22)

with a similar solution for TBV. On the right-hand side of (8.22), the first term is the correctedmeasurement from within the FOV; the second is the crosstalk term; the third and fourthterms are sidelobe contributions from the surrounding FOVs. For the sidelobe contributions,the derivation implicitly assumes that the radiances at the (n − 1)th and (n + 1)th FOVs arerepresentative of the surrounding FOVs. For the 85-GHz H-pol antenna pattern in Figure8.3, typical values of the coefficients in (8.22) are c0 = 1.03, c1 = 0.013 and c2 = c3

= 0.0015, where these coefficients were determined in an antenna measurement facility(Colton and Poe, 1999, Table II). The reason why c0 is greater than 1 is to compensate forthe falloff in the power pattern around the boresight direction.

Estimation of the magnitude of the corrections generated by Equation (8.22) proceedsas follows. For a physical surface temperature of 300 K, a non-interfering atmosphere andfrom the emissivities in Figure 8.6, TAH is approximated as 120 K and TAV as 160 K.Substitution of these values and the coefficients listed in the previous paragraph into (8.22)shows that the first term on the right-hand side yields a temperature increase of 3.6 K, thesecond term yields an increase of 2.1 K, and the third and fourth terms yield increases of0.2 K. Summation of these terms yields TBH = 125.9 K, which is 5.9 K larger than TAH. Thesize of this correction verifies that the APC procedure must be applied in order to obtainthe desired accuracy of 0.5–1 K.

Because under most conditions the surface TB distribution varies negligibly over thescale of the FOV diameter, combining C2 and C3 into C0 further simplifies Equation (8.22),in which case the APC is applied only to the FOV of interest. This simplification means that,even for FOVs adjacent to the swath edge, the APC is still applicable. Alternatively, for theswath-edge case, when ηm is less than 0.9, as occurred with the SMMR 6.6-GHz channel,the sidelobe radiances from beyond the swath edge are accounted for with a classificationmap. This consists of a mean climatology or lookup table of ocean surface brightnesstemperatures that are used to estimate the sidelobe contributions, where the temperaturesare functions of location and season. The third case that is not amenable to correction occurswhen the FOV is adjacent to land or to an ice edge, ocean storm, or any region with a stepor strong spatial gradient in surface brightness temperature. Because the APC smooths outsuch steps, the correction is not applied in these cases. Instead, the FOVs adjacent to thesegradient regions are discarded or masked, so that the imager data are used only at distancesof at least one FOV away from a land or ice edge boundary. As in the discussion of thediffuse transmittance in Section 4.9.1, such data are described as contaminated.



Table 8.1. Comparison of the frequencies, polarizations and incidence angles (θ) for theSMMR, SSM/I, TMI, GMI, AMSR-E and AMSR2.

Instrument Frequencies and polarization (GHz, V, H) θ (deg)

SMMR 6.6 V, H; 10.7 V, H; 18.0 V, H; 21.0 V, H; 37.0 V, H; — 51SSM/I —; —; 19.3 V, H; 22.2 V; 37.0 V, H; 85.5 V, H 53TMI —; —; 10.7 V, H; 19.3 V, H; 21.3 V; 37.0 V, H; 85.5 V, H 53GMI —; —; 10.7 V, H; 18.7 V, H; 23.8 V; 36.5 V, H; 89.0 V, H 53AMSR-E 6.9 V, H; 10.7 V, H; 18.7 V, H; 23.8 V, H; 36.5 V, H; 89.0 V, H 55AMSR2 6.9/7.3 V, H; 10.7 V, H; 18.7 V, H; 23.8 V, H; 36.5 V, H; 89.0 V, H 55WindSat 6.8 V, H; 10.7 V, H, 3, 4; 18.7 V, H, 3, 4; 23.8 V, H; 37.0 V, H, 3, 4; — 49.9–53.5

The numbers 3, 4 stand for the third and fourth Stokes vector. Adapted from Wentz and Meissner(1999), Maeda et al. (2011), PPS (2010), GPM (2010) and Gaiser et al. (2004, Table 2).

8.6 Passive microwave imagers

The series of research and operational passive microwave satellite imagers began withthe US Electrically Scanned Microwave Radiometer (ESMR), which was a single-channel19-GHz cross-track scanner that operated from 1973 to 1976. Since ESMR, all of theimagers operate as either conical or pushbroom scanners. The first conically scannedinstrument was the US Scanning Multichannel Microwave Radiometer (SMMR) that oper-ated on SEASAT for 3 months in 1978, and on the NASA NIMBUS-7 spacecraft from 1978to 1987; the second is the US Special Sensor Microwave/Imager (SSM/I) and its successorthe Special Sensor Microwave/Imager Sounder that with a number of replacements hasoperated on the US Department of Defense DMSP satellites since June 1987.

The third is the US/Japanese TRMM Microwave Imager (TMI) that was launched onthe Tropical Rainfall Measuring Mission (TRMM) in November 1997 and in 2013 isstill operating. The fourth is its successor, the Global Precipitation Measurement (GPM)Microwave Imager (GMI) scheduled for launch in 2014. The fifth is the Japanese AdvancedMicrowave Scanning Radiometer-EOS (AMSR-E) that was launched on AQUA as part ofthe A-Train constellation in May 2002 and is a modified version of the AMSR launched onthe Japanese short-lived ADEOS-2 in December 2002. As Chapter 1 describes, the AMSR-E antenna ceased to rotate in November 2011 and in 2012 was replaced in the A-Train byits successor AMSR2 on the GCOM-W1 satellite.

For these instruments, Table 8.1 compares their operating frequencies and incidenceangles, and shows that they employ similar, but not identical channels. As the next chapterand Section 8.6.4 describe, the atmospheric transmissivity, the frequency sensitivity ofthe desired atmosphere and ocean variables and the necessity to avoid those bands thatexperience RFI determine the choice of frequencies. The largest change in band frequenciesoccurs between SMMR and SSM/I, where the SSM/I eliminated the 6.6- and 10.7-GHzchannel, and, because of the reassignment of the 18-GHz channel for commercial use,


8.6 Passive microwave imagers 249

Table 8.2. Properties of the SMMR bands.

Frequency (GHz) 6.6 V, H 10.7 V, H 18 V, H 21 V, H 37 V, H

3-dB beamwidth (deg) 4.5 2.9 1.8 1.5 0.9Bandwidth f (MHz) 250 250 250 250 250NET at 300 K (K) 0.9 0.9 1.2 1.5 1.5Integration time τI (ms) 126 62 62 62 30Main beam efficiency ηM 0.82 0.85 0.87 0.85 0.893-dB EFOV (km × km)

(along-scan × along-track)148 × 95 90 × 60 45 × 30 40 × 25 20 × 15

From Stewart (1985), Gloersen and Barath (1977) and Njoku et al. (1980b).

shifted the location of the 18-GHz channel to 19.3 GHz. Also, for reasons discussed inthe next chapter, the SSM/I shifted the position of the 21-GHz channel that is close to the22.235-GHz water absorption peak to 22.2 GHz, and added high-frequency channels at85 GHz. As the next chapter shows, because the SST retrieval requires at least one of the6.9- and 10.7-GHz channels, the SSM/I cannot retrieve SST. These low frequency channelsremained absent until the 1997 launch of TMI with its 10.7-GHz channel, and of AMSR-Eand AMSR2 with their 6.9- and 10.7-GHz channels. The next sections briefly survey theinstruments listed in the table.

8.6.1 Scanning Multichannel Microwave Radiometer (SMMR)

SMMR was launched on the NIMBUS-7 satellite and provided data for the period 1978–1987. NIMBUS-7 was in a noon–midnight Sun-synchronous orbit at an altitude of 955 km.Before its launch, in 1978 another SMMR on the SEASAT satellite operated for a 99-dayperiod. Gloersen and Barath (1977), Massom (1991) and Gloersen et al. (1992) describethe instrument; Table 8.2 lists its properties. The instrument consisted of an oscillating1.1 m × 0.8 m elliptical antenna that reflected the Earth radiances into fixed microwavefeedhorns. The antenna was the only part of SMMR that rotated relative to the spacecraft.On NIMBUS-7 the antenna scanned in the forward direction across a swath width of 780km. The scanning was sinusoidal, in that over a period of 4.096 s, the reflector swung toone side of the flight path, paused, swung back to the other side and paused again.

For each frequency and polarization, Table 8.2 lists the SMMR 3-dB beamwidth, thebandwidth f, the NET, the integration time τi, the main beam efficiency ηm and theEFOV. As described earlier, the EFOV consists of the IFOV averaged over the integrationtime, where the purpose of this integration is to reduce instrument noise. From Stewart(1985, Section 9.3), the noise reduction is calculated as follows: for a bandwidth f , thecorrelation time τc of the received radiance is given by τc ∼ f −1. For f = 250 MHz,τc 4 × 10−6 ms, so that an integration over τi = 126 ms is equivalent to averagingover N = 6 × 107 independent observations. Since the uncertainty is proportional to

√N ,



the integration reduces the noise by a factor of 104. As Table 8.2 shows, this integrationalso makes the along-scan axis of the EFOV ellipse larger than the along-track. Since theswath width is only 780 km, at 6.6 GHz, the swath contains only 5 EFOV. Table 8.2 alsoshows that, for all frequencies, ηm < 0.9. Because ηm = 0.82 at 6.6 GHz, the sidelobecontributions meant that SST could not be retrieved within 1–4 EFOV or within about 600km of the ocean/land boundary, which greatly reduced its value (Njoku et al. 1980a).

There were several problems with the SMMR design. First, the combination of thefixed feedhorns and rotating antenna generated crosstalk between different polarizations.Second, because NIMBUS-7 was in a Sun-synchronous orbit with a local noon and midnightequator-crossing time, daytime heating and nighttime cooling generated instrument noise.Also, as the satellite passed over the South Pole, SMMR experienced severe transientsgenerated by the Sun shining directly into the feedhorns. Third, because SMMR operatedon alternate days to conserve power, near-global coverage was achieved only at six-dayintervals. Fourth, when the instrument was turned on, there was a 1-hour transient duringwhich the data had to be discarded; fifth, the SMMR was inadequately calibrated. In spiteof these problems, the SMMR served as a testbed for future instruments and began the timeseries of the extent of polar sea ice.

8.6.2 Special Sensor Microwave/Imager (SSM/I)

The SSM/I corrected many of the problems associated with SMMR, and provided the basisfor the TMI and AMSR design. Hollinger et al. (1990) and Massom (1991) describe theSSM/I; on June 19, 1987, the first SSM/I was launched on the US Air Force DMSP satelliteand, with occasional replacements, remains in orbit. The DMSP is in a dawn–dusk Sun-synchronous orbit at an altitude of 860 km and a period of 102 minutes. This orbit providescomplete Earth coverage except for two circular areas of 2.4° centered at the poles. SSM/Iwas supported by the US Department of Defense through 2003. In late 2003, the SSM/Iwas replaced by the Special Sensor Microwave Imager/Sounder (SSMI/S) that combinesthe SSM/I imager and the temperature and humidity sounder into a single instrument thatuses the present SSM/I antenna. As part of JPSS, the SSMI/S will continue to operate onthe morning DMSP satellites.

Figure 8.8 shows a photograph of the SSM/I; it consists of an offset parabolic reflectorof dimensions 0.61 m × 0.66 m that focuses microwave radiation into a seven-port antennafeedhorn. In a design feature common to TMI and AMSR, SSM/I is mounted on top of theDMSP satellite. Relative to the spacecraft, the reflector and feedhorns rotate with a uniformperiod of 1.90 s, where the data pass through a set of slip-rings into the spacecraft body.SSM/I has two non-rotating calibration sources, a cold space reflector and a hot referenceload held at a temperature of about 300 K. These sources are fixed to the spacecraft, sothat, for instrument calibration, once per scan, their radiances are sequentially observed bythe feedhorns. The hot load is independently measured with precision thermometry andthe cold space temperature is assumed constant at the 2.7K background temperature of theUniverse (Colton and Poe, 1999).



Fig. 8.8. A photograph of the SSM/I. (Figure 3 from Hollinger et al. (1990), C© 1990 IEEE, courtesyof Gene Poe.)

Figure 8.9 shows the scan geometry; surface observations are taken during a 102.4° arcwhen the SSM/I is looking aft. The arc is centered on the spacecraft track and correspondsto a swath width of 1394 km. During the antenna rotation period of 1.90 s, the spacecraftadvances 12.5 km along the surface. The ellipses on the surface show the IFOVs; theybecome progressively smaller with increasing frequency. The scans divide into A- andB-scans that alternate in time; the A-scan includes all channels, the B-scan includes only85 GHz. For both scans, the 85-GHz channels are sampled 128 times over the arc, whereeach sample is integrated over 3.89 ms, during which time the antenna boresight movesabout 12 km on the surface in the along-scan direction. Because of their larger resolution,the three lower-frequency channels are sampled only during the A-scan, where they are



Table 8.3. Properties of the SSM/I bands.

Frequency (GHz) 19.35 V, H 22.235 V 37.0 V, H 85.5 V, H

3-dB beamwidth (deg) 1.9 1.6 1.0 0.42Bandwidth NEF (MHz) 100 100 200 600NET (K) 0.8 0.8 0.6 1.1Integration time τI (ms) 7.95 7.95 7.95 3.89Main beam efficiency ηM 0.96 0.95 0.93 0.923-dB EFOV (km × km)

(along-scan × along-track)45 × 70 40 × 50 30 × 37 13 × 15

From Hollinger et al. (1990) and Wentz (1992).

Fig. 8.9. The SSM/I scan geometry. (Figure 20 from NASA Science Working Group (1984).)

averaged into 64 EFOVs along the arc. Table 8.3 lists the instrument properties and the 3-dBEFOVs for the individual channels. Because the SSM/I integration times are much shorterthan for SMMR, the SSM/I EFOVs are ellipses with their long axis in the along-trackdirection and their short axis in the along-scan direction, which is the reverse of the SMMRcase. The offset antenna with the 53°–55° incidence angle and the 360° uniform rotation ischaracteristic of the rest of the scanning radiometers described in this chapter.



The SSM/I design corrected many of the problems that occurred with SMMR. First,the SSM/I dawn–dusk orbit minimized the SMMR diurnal heating and cooling prob-lems. Second, because the SSM/I feedhorns and antenna rotate together, the position ofthe feedhorns relative to the reflector is fixed, which eliminates the rotation-dependentcrosstalk between polarizations that occurred with SMMR. Third, because SSM/I operatescontinuously, there are no start-up transients. Fourth, because the SSM/I swath width istwice as large as the SMMR, and since the SSM/I operates continuously instead of onalternate days, it has much greater coverage and produces about four times as much data.Fifth and as the next chapter discusses, the use of a dawn–dusk orbit greatly reduces sunglint. Its major disadvantage occurs because SSM/I lacks channels at frequencies lowerthan 19 GHz, 50 it cannot retrieve SST.

8.6.3 TRMM Microwave Imager (TMI) and the GPM Microwave Imager (GMI)

TMI is a nine-channel radiometer designed to investigate tropical regions of heavy precip-itation. TMI is mounted on the TRMM satellite, where TRMM is a joint mission betweenNASA and the Japan Aerospace Exploration Agency (JAXA). TRMM is in a low-inclinationcircular orbit at an altitude of 350 km and an inclination angle of 35°, which covers anarea slightly greater than half the globe. The orbit is not Sun-synchronous, rather it waschosen so that, over a month, it samples the tropics at uniform intervals throughout the day.This permits determination of the rainfall dependence on the local time-of-day. Its lowerinclination orbit also means that its surface sampling rate is roughly twice that of a polarorbiter.

As Table 8.1 shows, the locations of TMI 19-, 21-, 37- and 85-GHz channels are almostidentical to the SSM/I (Kummerow et al., 1998). Differences between the two instrumentsinclude the addition of TMI channels at 10.7 GHz V and H, and a shift of the 22.235- GHzchannel to 21.3 GHz. The purpose of this shift was to move the channel onto the lowershoulder of the 22.235-GHz water vapor absorption line described in Section 9.2 so that theobservations would not saturate in the tropical atmosphere. Similarly to SSM/I, the rotatingpart of the TMI includes the antenna and feedhorns. These rotate uniformly about the nadiraxis with a period of 1.9 s, during which time the satellite advances 13.9 km along thesurface. The TMI antenna is an offset 61-cm-diameter parabolic reflector that takes surfaceobservations within a 130° arc, yielding a swath width of 786 km. Because the entireTRMM spacecraft is occasionally rotated by 180° about its nadir axis to maintain thermalstability, the instrument points either forward or backward relative to the flight direction.To calibrate the TMI, once per rotation the feedhorns are moved to point sequentially ata hot load and a cold space reflector that are fixed to the spacecraft. Unlike SSM/I, TMIdoes not divide the scans into A- and B-scans, but instead, accepts the gaps in the 85-GHzEFOVs. Table 8.4 lists the TMI characteristics and shows that because of the lower TRMMaltitude and at any specific frequency, the TMI EFOVs have about half the area of theSSM/I EFOVs.



Table 8.4. Properties of the TMI bands.

Frequency (GHz) 10.65 V, H 19.35 V, H 21.3 V 37.0 V, H 85.5 V, H

3-dB beamwidth (deg) 3.7 1.9 1.7 1.0 0.42Bandwidth f (MHz) 100 500 200 2000 3000NET (K) 0.6 0.5 0.7 0.3 0.7Integration time τI (ms) 6.6 6.6 6.6 6.6 3.3Main beam efficiency ηM 0.93 0.96 0.98 0.91 0.833-dB EFOV (km × km)

(along-scan × along-track)37 × 63 18 × 30 18 × 23 9 × 16 5 × 7

Adapted from Kummerow et al. (1998) and GPM (2010, Table 14).

The replacement for TRMM is the Global Precipitation Measurement (GPM) MicrowaveImager (GMI), a joint US/Japanese project scheduled for launch in 2014. The GPM coremission is the center of the GPM constellation, which has the goal of providing near-globalmeasurements of precipitation at intervals of about 3 hours. The NASA contribution toGPM is the GPM Core Observatory (GPM, 2012). The GPM Core Observatory is a jointmission with JAXA, and carries the GPM Microwave Instrument provided by NASA andthe JAXA Dual-Frequency Precipitation Radar (DPR). The GPM Core will fly at an altitudeof 400 km with an orbit inclination of 65° and is scheduled for launch in 2014. This is nota Sun-synchronous orbit, instead, at the equator, the crossing time of the GPM Core variesover 24 hours of local time with a 46-day cycle.

There will be at least seven other satellites in the GPM constellation of satellites. Fora mission to join the constellation, it must carry a passive microwave radiometer andsubmit data to the GPM Precipitation Processing System (PPS) at NASA Goddard. Currentmembers of the GPM constellation include TRMM, the ISRO/CNES Megha-Tropiquesmission that was launched in 2010 and carries the microwave radiometer named MicrowaveAnalysis and Detection of Rain and Atmospheric Systems (MADRAS), the SSMI/S on theDMSP satellites, the AMSR2 and the WindSat radiometer described in Section 8.6.5.Potential mission contributors include Brazilian and ESA missions. The purpose of GMIon the Core satellite is not only to gather data, but also to serve as a calibration standardfor other instruments in the constellation.

Table 8.5 lists the observing frequencies and characteristics for the GMI on the GPMCore satellite (GPM, 2012). The GPM Core satellite acquires data using a parabolic reflectorwith a diameter of 1.22 m, which is twice the diameter of the TMI antenna. It rotates at32 rpm. The reflector surface is accurate to the design specifications to within 50 µm(0.05 mm). The temperatures of the hot and cold load are carefully controlled. Because ofthe size and precision of the reflector surface, as Table 8.5 shows, the beam efficienciesrange from 0.92 to 0.97, an improvement on TMI.



Table 8.5. Properties of the GMI bands.

f (GHz) 10.65 V, H 18.7 V, H 23.8 V 36.5 V, H 89 V, H

3-dB beamwidth (deg) 1.2 0.65 0.75 0.35 0.15Bandwidth f (MHz) 100 200 400 1000 6000NET (K) 0.96 0.84 1.05 0.65 0.57Main beam efficiencyηM 0.92 0.92 0.92 0.97 0.96EFOV (km × km)

(along-scan × along-track)19 × 32 11× 18 10 × 16 16 × 9 7 × 4

From GPM (2010, Table 2), Newell et al. (2010, Table 1) and PPS (2010, Table 1.1).

8.6.4 The Advanced Microwave Scanning Radiometer-EOS (AMSR-E)and its successor AMSR2

AMSR-E is a NASDA instrument launched on the AQUA satellite in May 2002; the com-panion AMSR instrument was launched in December 2002 on the Japanese Advanced EarthObserving Satellite-2 (ADEOS-2), which failed prematurely in October 2003 (AMSR-E,2013). In October 2011, the instrument failed when the AMSR-E antenna stopped rotat-ing. The AMSR-E design is slightly modified from AMSR; the difference between thetwo instruments is that AMSR has two additional V-pol channels at 50.3 and 52.8 GHzdesigned for atmospheric sounding. AQUA is in a 1330- ascending Sun-synchronous orbitat an altitude of 705 km, where it is part of the A-train constellation.

On AQUA, the AMSR-E instrument rotates continuously around its nadir axis with a1.5-s period, during which time the spacecraft travels 10 km along its surface track. AMSR-E measures the upwelled radiances over a range of ±61° about the sub-satellite track, fora swath width of 1445 km. AMSR-E is a twelve-channel, six-frequency conically scannedradiometer similar to SSM/I; the major differences are that AMSR-E has more channels,a larger 1.6-m diameter parabolic reflector, and a slightly different choice of frequencies(Table 8.6). The AMSR-E parabolic reflector focuses the surface radiances into an arrayof six feedhorns that are amplified by twelve separate receivers. The 18.7- and 23.8-GHzreceivers share a feedhorn. To avoid having A- and B-scans, two offset feedhorns are usedfor the 85-GHz channels, which produce two 85-GHz FOVs that are separated in the along-track direction by 5 km. This gives the 85-GHz FOVs an along-track separation of 5 km;at the other channels, the FOVs are separated by 10 km.

Two non-rotating external sources provide the AMSR-E calibration (AMSR-E, 2013).The first is a hot reference load maintained at a physical temperature of about 300 K; thesecond, a mirror that reflects the cold space brightness temperature into the instrument. Themirror and reference load are fixed to the spacecraft so that, once per rotation, they pass insequence between the feedhorn array and the parabolic reflector and provide a calibration.The view angle of the parabolic reflector is fixed at 47.4°, which results in an incidence



Table 8.6. Properties of the AMSR-E bands.

f (GHz) 6.9 V, H 10.7 V, H 18.7 V, H 23.8 V, H 36.5 V, H 89.0 V, H

3-dB beamwidth (deg) 2.2 1.4 0.89 0.9 0.4 0.18Bandwidth f (MHz) 350 100 200 400 1000 3000NET (K) 0.3 0.6 0.6 0.6 0.6 1.1Integration time τI (ms) 2.6 2.6 2.6 2.6 2.6 1.3Main beam efficiency ηM 0.95 0.95 0.96 0.96 0.95 0.96EFOV (km × km)

(along-scan × along-track)43 × 75 27 × 48 16 × 27 18 × 31 8 × 14 4 × 6

From AMSR-E (2013).

Fig. 8.10. Image of the AMSR-2 instrument mounted on the GCOM-W1 spacecraft; the antennadiameter is 2 m. (Figure C© Japan Aerospace Exploration Agency (JAXA), used with permission.)

angle of 55° ± 0.3°. The small variation in θ is due to the slight eccentricity of the orbitand the oblateness of the Earth.

Text citationmissing of Fig.8.10.

AMSR2, the AMSR-E replacement, was launched on the first Global Climate Observa-tion Mission-Water (GCOM-W1) in 2012 and has a similar design to AMSR-E. Table 8.7describes its band properties. It is the only Earth observation instrument on GCOM-W1,



Table 8.7. Properties of the AMSR2 bands.

f (GHz) 6.9/7.3 V, H 10.7 V, H 18.7 V, H 23.8 V, H 36.5 V, H 89.0 V, H

3-dB beamwidth (deg) 1.8 1.2 0.65 0.75 0.35 0.15Bandwidth f (MHz) 350 100 200 400 1000 3000NET (K) <0.3/0.4 <0.7 <0.7 <0.6 <0.6 1.33-dB EFOV (km × km)

(along-scan × along-track)35 × 60 24 × 42 14 × 22 15 × 26 7 × 12 3 × 5

From GPM (2010, Table 6) and Maeda et al. (2011).

Fig. 8.11. Photograph of the WindSat instrument; the satellite is not shown. (Image courtesy of NavalResearch Laboratory, not subject to US copyright.)



Anti-clockw

ise

WindSat

Forward Swath (950 km)

Aft Swath (350 km)

Fig. 8.12. Geometry of the WindSat scan. (Redrawn from Khan (2009), Figure 16.)

and will continue the existing AMSR-E measurements. Compared with AMSR-E, AMSR2has an improved calibration system. To alleviate RFI problems experienced with the 6.9-GHz channel, it carries an additional channel at 7.3 GHz. The 6.9- and 7.3-GHz channelsshare the same feedhorn; the 6.9-GHz channel is kept for intercomparison of the AMSR-Eand AMSR2 data. The major differences between the two missions are that AMSR2 has a 2-m-diameter antenna compared with a 1.6-m-diameter antenna for AMSR-E, and, as Section9.3.3 discusses, because of the RFI problems experienced at 6.9 GHz, the instrument hasan additional observing band at 7.3 GHz (Imaoka et al., 2007). Its rotation rate is 40 rpm.The GCOM-W1 is part of the A-Train constellation, and is positioned just ahead of theAQUA satellite in the same orbit (Maeda et al., 2011). This is the largest passive microwaveantenna to be flown in orbit.

8.6.5 The WindSat radiometer

The WindSat instrument on the Coriolis satellite launched in January 2003 is a microwaveradiometer designed to retrieve vector winds from multifrequency V- and H-pol measure-ments, as well as from measurements of all four of the Stokes parameters described inSection 3.2.4 (St. Germain et al., 1998; St. Germain and Gaiser, 2000). Such instrumentsare called polarimetric radiometers. NPOESS and the Naval Research Laboratory jointlyfunded WindSat (WindSat, 2013a). It operates at an altitude of 830 km in a Sun-synchronous



Table 8.8. WindSat frequencies, Stokes parameters, incidence angles, noise, bandwidthand spatial resolution.

Frequency(GHz) V-pol H-pol

ThirdStokes

FourthStokes

Bandwidth(MHz)

NET(K)

Incidenceangle (deg)

Spatialresolution(km × km)

6.8 Y Y N N 125 0.63 53.5 39 × 7110.7 Y Y Y Y 300 0.44 49.9 25 × 3818.7 Y Y Y Y 750 0.44 55.3 16 × 2723.8 Y Y N N 500 0.60 53.0 20 × 3037 Y Y Y Y 2000 0.42 53.0 8 × 13

For each frequency, the Ys mean that the parameter is acquired, the Ns, not acquired; the spatialresolution is given as cross-scan by along-scan. From WindSat (2013) and Gaiser et al. (2004,Table 2).

0600 dawn–dusk descending orbit designed to minimize solar reflectance (Gaiser, 1999;Gaiser et al., 2004). WindSat consists of a conically scanned radiometer mounted on top ofthe Coriolis satellite with a 1.83-m-diameter antenna where the different channels observethe ocean surface at look angles in the range of 50°–55°. Figure 8.11 shows a photographof the instrument; it has a forward swath of 950 km and an aft swath of about 350 km(WindSat_payload, 2013), see Figure 8.12.

For the WindSat observational frequencies, Table 8.8 lists the polarizations and Stokesparameters. The table shows that the 6.8- and 23.8-GHz channels are V-pol and H-pol,while the 10.7-, 18.7- and 37.0-GHz channels are fully polarimetric. The incidence angleslie within the range 50°–54°, which is similar to those of the other passive microwaveinstruments. The reason why incidence angles differ as a function of frequency is that thereceiving horns could not be placed such that they all received at a common angle. Instead,the 37-GHz horn is located at the focal point of the antenna, while the other horns areslightly offset (Gaiser et al., 2004). The antenna rotates at 31.6 rpm; the reflector diameteris 1.8 m. Once per revolution, the antenna samples a hot and cold load. The pitch and roll ofthe antenna mounting changes the observation angle by a total of about 1.5 deg (Meissnerand Wentz, 2009). Table 8.8 also gives the spatial resolution of each frequency, where, inthe processing, the brightness temperatures are resampled to a common grid that measures40 km × 60 km.

As Sections 9.4.4 and 9.4.5 describe, WindSat is designed to retrieve vector winds intwo ways: first, following Wentz (1992), from a combination of two HH and VV looksat the same surface area from ahead and behind the satellite; second, from a single lookusing all four Stokes parameters. Chapter 9 describes the use of these measurements toretrieve vector wind speeds; Chapter 11 describes the role of WindSat in the calibration ofthe scatterometer observations.


9

Passive microwave observations of theatmosphere and ocean surface

9.1 Introduction

The importance of the multifrequency passive microwave imagers is that, irrespective ofcloud cover, they can retrieve a large variety of surface and atmospheric variables. Figure 9.1shows the atmospheric and surface variables that affect the transmissivities and emissivities,and are retrievable by passive microwave. In the atmosphere, these include columnar watervapor, the cloud liquid water and the surface rain rate. At the surface, they include sea iceextent and type, sea surface temperature (SST) (TS) and salinity (SS) and the scalar andvector wind speeds.

As this chapter shows, because the emissivity or transmissivity associated with eachatmosphere or oceanic constituent has a different frequency dependence, the variablesare retrieved from a set of multifrequency, multivariable simultaneous equations. Thedisadvantage of this formulation is that in most cases the solutions are not separable, sothat if, for example, the only variable of interest is TS, then by necessity many of the othervariables must also be retrieved. An advantage of the microwave is that except in regionswith heavy rain the retrievals are independent of cloud cover. In the following, Section9.2 discusses the frequency dependence of the atmospheric absorption and transmission,and shows that, for frequencies less than 10 GHz, the effects of clouds and water vaporare negligible. Section 9.3 discusses the microwave form of the radiative transfer equation,the problem of sun glint, radio-frequency interference and Faraday rotation. Section 9.4describes the effect on the surface emissivity of ocean waves, surface roughness and foamand shows how the azimuthal distribution of capillary and gravity waves relative to the winddirection permits retrieval of the vector wind speed. Section 9.5 describes the effect of seasurface temperature and salinity on the emissivity; Section 9.6 describes the multichannelalgorithms for retrieval of the different oceanic and atmospheric variables; Section 9.7describes the WindSat retrieval of vector winds; Section 9.8 discusses the sea ice algorithms.

9.2 Atmospheric absorption and transmissivity in the microwave

The next three sub-sections describe the contributions of oxygen, water vapor and liquidwater droplets to the atmospheric microwave attenuation and transmissivity. The resultsshow that the best conditions for viewing the surface occur at the lower frequencies.

260


9.2 Atmospheric absorption and transmissivity 261

Sea iceSS TS Wind-roughened

surface Foam frombreaking waves

Ice clouds

Non-rainingcloud liquid water Oxygen,

Water vapor

RainWind speed and direction

Sensor

Fig. 9.1. The properties of the sea surface and the atmosphere that affect the atmospheric attenuationand emission and the surface emissivity in the microwave.

9.2.1 Atmospheric absorption by oxygen and water vapor

The oxygen absorption κoxy and water vapor absorption κvap are functions of the air tem-perature Ta and pressure p; κvap additionally depends on the vapor density ρv. From Ulabyet al. (1981, Section 5.5) and for p = 1013 mb and Ta = 270 and 300 K, Figure 9.2 showsthe dependence of κoxy on f.

On the figure, κoxy is given in units of Np (neper) km−1, where nepers are a dimensionlessquantity frequently used in the microwave literature to describe atmosphere absorption.The word “neper” is derived from “Neperian”; the name comes from the fact that thetransmissivity t is proportional to exp(−κDz), where Dz is a length scale, so that to recoverκ from t involves taking the natural or Neperian log of t. Neper is dimensionless, its onlypurpose is to designate that the quantity in question is atmospheric microwave absorption.Absorption is also described in units of dB km−1, where Np km−1 and dB km−1 are linearlyrelated (Ulaby et al., 1981, Section 5.6).

Examination of Figure 9.2 shows that κoxy has two absorption peaks; the first is the60-GHz oxygen complex, which consists of the large number of absorption lines in therange 50–70 GHz; the second is a single line at 119 GHz. The figure also shows that κoxy

increases with Ta and suggests that the best observing windows occur at 1–40 GHz and80–105 GHz.

For water vapor, Figure 9.3 shows a plot of κvapversus f at Ta = 300 K and p = 1013 mband for several values of ρv (Ulaby et al. (1981, Section 5.4). As Section 4.2.1 and Equation(4.2) describe, at sea level ρv0 ranges from near zero in the polar regions to a maximum ofabout 30 g m−3 in the tropics; the values of ρv0 on the curves lie within this range. For 0 < f< 130 GHz, Figure 9.3 shows that the frequency dependence of κvap divides into two parts,a strong absorption peak at 22.235 GHz and a general increase of κvap with frequency that is


Frequency (GHz)0 20 40 60 80 100 120

10

1

10–1

10–2

10–3

Abs

orpt

ion

coef

ficie

nt (

Np

km–1

)

270 K

300 K

Fig. 9.2. The dependence of the oxygen absorption κoxy on f for p = 1013 mb and for the twodifferent temperatures on the curves, from formula in Ulaby et al. (1981, Section 5.5). See the textfor additional description.

Frequency (GHz)0 20 40 60 80 100 120

10–1

10–2

10–3

10–4

10–5

10–6

100

Abs

orpt

ion

coef

ficie

nt (

Np

km–1

)

1 g m–3

5

10

20

Fig. 9.3. The dependence of the water vapor absorption κvap on f for p = 1013 mb, Ta = 300 K, andon several values of ρv from a formula in Ulaby et al. (1981, Section 5.4). The numbers on eachcurve give ρv0 in units of g m−3; the arrow marks the absorption peak at 22.235 GHz. See the text forfurther description.



generated by water vapor lines at 183.31 GHz and higher frequencies. Because the 22-GHzabsorption peak occurs for water vapor but not for liquid water, the presence or absenceof this peak makes it possible to distinguish water vapor from the liquid. Figure 9.3 showsthat κvap has a strong dependence on ρv and that, as in Figure 9.2, the most transparent partof the atmosphere occurs for f less than about 10 GHz.

9.2.2 Atmospheric transmissivity of oxygen and water vapor

Integration of κoxy and κvap vertically across the atmosphere yields the respective contribu-tions of oxygen and water vapor to the atmospheric transmissivity. Figure 9.4 shows theresultant oxygen and water vapor transmissivities, and their total. For three MODTRANatmospheres, Sub-arctic winter, Standard and Tropical, Figure 9.4(a) shows the dependenceof the oxygen transmissivity toxy on frequency, where toxy is derived by integration of κoxy

across the first 25 km of the atmosphere. Because κoxy increases with temperature, thetropical case is slightly less transmissive.

Figures 9.4(b) and (c) show the dependence of the transmissivity on water vapor withthe addition of a case derived from running the MODTRAN Sub-arctic winter case forV = 0.5 mm. Figure 9.4(b) shows the dependence of the water vapor transmissivity tvap onthe columnar vapor density V; Figure 9.4(c) shows the sum of toxy and tvap. Because watervapor is primarily concentrated in the lower troposphere, tvap is derived by integration ofκvap across the first 10 km. As expected, the transmissivity decreases with increasing V;this is most apparent at high frequencies and in the vicinity of the 22-GHz absorption peak.In Figure 9.4(c) and for all cases, the most transmissive frequencies occur for f < 10 GHz,where t is nearly independent of water vapor, and for the arctic dry atmosphere, where, forf < 40 GHz, t > 0.9.

Figure 9.4(c) also shows the location of several frequencies used for oceanographicmicrowave radiometry that are described in the previous chapter, namely 1.4, 6, 10, 18,21, 37 and 85 GHz. With the exception of 18 and 21 GHz, these frequencies occur in theminima of the absorption curves. In contrast, the 21-GHz band is very close to the 22-GHzabsorption peak and the 18-GHz band lies on its shoulder, so that, at small concentrations ofwater vapor, 21 GHz is used for its retrieval, while at large concentrations 18 GHz is used.In summary, while regions of strong oxygen absorption are avoidable by a proper choiceof frequencies, for f > 10 GHz the effect of atmospheric water vapor must be included inmodels of atmosphere attenuation.

9.2.3 Transmissivity of water droplets

The liquid water droplets in clouds and rain affect the transmissivity by scattering theincident radiation. Ulaby et al. (1981) and Petty (2006, Section 7.4.4) show that non-rainingcloud liquid water droplets have radii between 5 and 15 µm, while droplets with radii oforder 100 µm or greater fall out of the clouds as rain. For rain, the droplet radius can be


264 Passive microwave observations

0.5

1

0

0.5

1

0

Tra

nsm

issi

vity

Tra

nsm

issi

vity

Oxygen

Water vapor

48 mm

17

5

0.5

(a)

(b)

0.8

0.6

0.4

1

0

0.2

Tra

nsm

issi

vity

48 mm

17

5

0.5Total

(c)

18 21 37 85 GHz61.4 10

10 20 30 40 50 60 70 80 90 100Frequency (GHz)

Fig. 9.4. The atmospheric transmissivity for (a) oxygen, (b) water vapor, and (c) the sum of theoxygen and vapor transmissivity. Several typical observing frequencies are shown at the bottom ofthe figure; the numbers on the curves in (b) and (c) give the columnar water vapor V in mm. See thetext for further description.

as large as 3 mm. Because of the large difference in droplet size between cloud liquidwater and rain, liquid water attenuation occurs from two kinds of scatter; cloud dropletsare Rayleigh scatterers, while, especially at higher observational frequencies, the largerrain droplets are Mie scatterers (Wentz and Spencer, 1998; Hilburn and Wentz, 2008). Thisdifference in scattering behavior allows microwave discrimination of clouds and rain rate.

Volume scattering from raindrops has two effects: the desired radiance is attenuated byscattering out of the beam; and the scatter of reflected or solar radiances in the direction ofthe sensor generates an additional, unwanted radiance. As Section 4.2.2 discusses, cloud



1.0

0.75

0.5

1.0

010 20 30 40 50 60 70 80 90 100

Frequency (GHz)

Tra

nsm

issi

vity

Tra

nsm

issi

vity

Cloud liquid water

Rain rate

10 mm h–1

5

2

1

0.5

0.2 mm18 21 37

85 GHz

61.4 10

0.25(b)

0.15

0.1

0.05(a)

0.9

0.8

0.85

0.95

0

0.75

0.25

Fig. 9.5. The effect of (a) non-raining cloud liquid water L and (b) rain rate RR on the transmissivity.In (a), the curves are labeled in mm of columnar liquid water; in (b), in mm h−1 of rain rate. Toseparate the liquid water curves from each other, the vertical scale of the upper figure extends from0.75 to 1.05 and is four times the scale of the lower figure. See the text for additional description.(Curves derived from formula in Wentz and Meissner (1999).)

liquid water is described in terms of the columnar liquid water L. The range of L is muchsmaller than that of V and varies from 0 to 0.25 mm. Rain is described in terms of therain rate RR with units of mm h−1. Over the ocean, only 3% of the SSM/I observations ofRR exceed 2 mm h−1; the maximum observed rain rate is about 25 mm h−1 (Wentz andSpencer, 1998).

Figure 9.5(a) shows the frequency dependence of transmissivity on L, and Figure 9.5(b)shows its dependence on RR, where the curves are derived from a formula based on theAMSR range of frequencies in Wentz and Meissner (1999). The curves for RR > 2 mm h−1

lie outside the range of their solution and are only qualitatively correct. Since Rayleighscattering is proportional to λ−4, or equivalently to f 4, in Figure 9.5(a), the transmissivityassociated with cloud liquid water decreases as L and f increase. In contrast, for f < 10 GHzor long wavelengths, the effect of L on the transmissivity is negligible. For the larger raindroplets, Mie scattering becomes increasingly important at high frequencies and at largedroplet concentrations. Consistently with this behavior, Figure 9.5(b) shows that, for f <

10 GHz and RR < 1 mm h−1, rain attenuation can be neglected, while for f > 10 GHz thetransmissivity decreases dramatically with both f and RR. At high frequencies, the increase



in attenuation with increasing RR shows why the rain rate must be determined or the datamust be masked. Finally, for frequencies less than 10–15 GHz, both parts of Figure 9.5show that the transmissivity is unaffected by light rain and clouds.

Because cirrus clouds are composed of ice crystals with characteristic radii r < 0.2 mminstead of liquid water, they have a negligible effect on the transmissivity (Ulaby et al.,1981, Section 5.11). In the microwave, ice crystals also have a smaller index of refractionthan water droplets, so that, for constant f, the attenuation associated with the crystals isan order of magnitude smaller than that for droplets. Given that columnar concentrationsof these crystals are also about an order of magnitude less than that of cloud liquid water,the attenuation associated with cirrus crystals is generally neglected. This is very differentfrom the retrieval of SST in the infrared, where, as Section 7.6 describes, thin cirrus cloudsmust be identified and masked.

In summary, comparison of Figures 9.4(b) and 9.5 shows that the transmissivities ofwater vapor, cloud liquid water and rain each have a different frequency dependence.The water vapor absorption peak at 22 GHz does not occur for rain and cloud liquidwater. Also, because of their respective derivations from Mie and Rayleigh scattering, thetransmissivities of rain and cloud liquid water differ both from that of the vapor and fromeach other. These differences make possible their retrieval from microwave observations.

9.3 Radiative transfer in the microwave

The next four sub-sections describe the radiative transfer in the microwave and the factorsthat affect the retrieval. These include reflection of Light from the Sun into the instrument,radio-frequency interference (RFI) at certain bands from surface and geosynchronous satel-lite broadcasts, and, at low microwave frequencies, Faraday rotation of the energy propa-gating across the ionosphere.

9.3.1 The radiative transfer equation

For small rain rates and for frequencies less than about 25 GHz, Figure 9.5 shows thatscattering is negligible in the microwave. For these conditions, the radiative transfer equation(RTE) can be approximated as an absorption–emission balance similar to that used in theinfrared (Section 4.8.1). The difference between radiative transfer in the infrared andmicrowave windows is that, as Figure 8.6 shows for the microwave, a large range ofincidence angles exists for which the surface reflectivity cannot be neglected. Consequently,the reflection at the surface of the downwelled atmospheric and extraterrestrial radiancesmakes significant contributions to the received radiance.

The derivation of the microwave RTE assumes that, for a constant look angle θ , theocean has an emissivity e and a reflectivity 1 − e, where e depends on the sea surfacesalinity (SSS), SST and roughness. The atmosphere is assumed to be plane parallel, so that,from Equation (4.30), the transmissivity is given by t(θ ) = t sec θ . Given that θ is constantfor the conical scanner, the superscript on t is dropped. Finally, because the Rayleigh–Jeans


9.3 Radiative transfer in the microwave 267

TS , SS

Extraterrestrialradiances

Upwelled atmospheric radiance

Surface radiance plus reflected downwelled radiances

Downwelled atmospheric radiance

T

Sensor

Text

TA

Sun glint

Solar radiance

TSun

Fig. 9.6. The solar, extraterrestrial and atmospheric radiances, their reflection from the rough oceansurface, and the emission and attenuation of the surface brightness temperature.

approximation applies to the microwave, in the RTE, brightness temperatures can replacethe radiances.

Following Stewart (1985, Section 9.4) and as Figure 9.6 illustrates, the absorption–emission form of the RTE can be written as

TB = etTS + (1 − t)T + (1 − t)(1 − e)t T + (1 − e)t2(TSun + Text) (9.1)

In Equation (9.1), TB is the brightness temperature observed at the satellite, TS is thesurface temperature, T is the vertical average of the tropospheric temperature profile, TSun

is the solar brightness temperature, and Text is the extraterrestrial brightness temperatureexclusive of the Sun. Except for heavy rain and at the higher frequencies where the equationbreaks down, Equation (9.1) shows that TB can be written as the sum of the following:the upwelled surface radiance, the upwelled atmospheric radiance, and the reflection ofthe downwelled atmospheric, extraterrestrial and solar radiances. The upper boundaryon the RTE is cold space; the lower is the rough ocean surface. As shown below, thesurface emissivity and reflectivity are determined by TS, SS, sea foam and the isotropic anddirectional distributions of the wind-induced surface waves and roughness.

The upwelled and downwelled atmospheric radiances and the extraterrestrial terms inEquation (9.1) merit further discussion. First, although Equation (9.1) does not include thiseffect, because the atmospheric temperature decreases with height, the T associated withthe downwelled atmospheric radiance is generally 1–2 K warmer than that associated withthe upwelled radiance. This occurs because the warmer, lower atmospheric layers make agreater contribution to the downwelled radiance, while the colder upper layers similarlycontribute to the upwelled radiance (Wentz, 1992). Second, the extraterrestrial radiance Text

consists of two terms:

Text = Tuniv + Tgal (9.2)



where Tuniv is the nearly isotropic 2.7 −K background temperature of the Universe and Tgal

is the temperature of the Milky Way galaxy. The temperature Tgal has a strong directionaldependence and is strongest in the plane of the zodiac. Ulaby et al. (1981, Section 5.6.2)show that the galactic radiance decreases approximately as f −3, and, for f > 5 GHz, Tgal canbe neglected relative to the atmospheric downwelling radiance. For f 1 GHz, however,Tgal is relatively large, with a strong angular dependence relative to the galactic plane (LeVine and Abraham, 2002).

Le Vine et al. (2005) show that, at the L-band radio astronomy window of 1.41 GHzused for Aquarius, brightness temperature changes of 1–3 K are observed for measurementstaken across the galactic plane, so the salinity retrieval must consider the surface reflectionof the galactic radiance. In addition, because of the RFI and Faraday rotation discussedbelow and because of the ionospheric attenuation emission, all of which increase withdecreasing frequency, remote sensing observations are rarely made at f < 1 GHz (Ulabyet al., 1981, Section 5.6.2; Le Vine and Abraham, 2002).

9.3.2 Solar interference

The ratio of the magnitude of the solar brightness temperature TSun to the temperature Tsol

received at the antenna by reflection from the ocean surface depends on four factors: thesurface roughness, the solid angle S subtended by the solar disk, the antenna pattern solidangle p and the frequency. If the antenna points directly at the Sun, then, from Equation(8.21),

Tsol = TSun[S/p] (9.3)

In (9.3), TSun is assumed independent of location on the solar disk. If, away from the Sun, theblackbody sky temperatures can be neglected, then the ratio S/p determines the relativeimportance of Tsol (Ulaby et al., 1981). Although, for f > 37 GHz, TSun is approximately5900 K, for f 37 GHz, the solar brightness temperature is no longer constant. Instead,as Table 9.1 shows, because the frequency dependence of TSun is driven by synchrotronradiation, it increases dramatically as f decreases, so that both the direct and the reflectedsolar contribution are larger at lower frequencies (Meissner et al., 2011b). At 1.4 GHz,which is the Aquarius operating frequency, the large solar brightness temperature, whichvaries between 105 and 106 K depending on solar activity, means that considerable caremust be taken to avoid reflection of light from the Sun into the instrument (Reul et al.,2007). Because, in our range of interest, the solar brightness temperature decreases withfrequency, the restrictions on the view angle also decrease.

Satellite instruments vulnerable to sun glint in the microwave include those that are notin dawn–dusk orbits, and, even though it is in a dawn–dusk orbit, the L-band radiometer onAquarius (Dinnat and Le Vine, 2008). For satellites such as SMMR, AMSR-E, AMSR2,TMI and GMI that are not in dawn–dusk orbits, Ulaby et al. (1986) review the microwavesun glint algorithms, Wentz (1978, 1981) describe a sun-glint model based on observationaldata, and, for SMMR with its noon equator crossing, Wentz et al. (1982) describe its sun



Table 9.1. Solar brightnesstemperatures as a function of

frequency.

f (GHz) TSun (K)

1.4 105–106

6.6 2.2 × 104

10.7 1.5 × 104

18 1.1 × 104

21 1.0 × 104

37 7 × 103

Adapted from Wentz (1978, 1981),Reul et al. (2007 Meissner et al.)(2011b, Section 11.3.2).

θ

θΔθS

θS

Sensor

Ocean surface

0

Sun

Fig. 9.7. The coordinate system used in the discussion of the microwave sun glint mask.

glint mask. Figure 9.7 shows the coordinate system from Wentz et al. (1982); they definethe relative solar or sun-glint angle θS as the angle between the conjugate solar zenithangle θ0 and the instrument look angle θ . For θS < 15° and U < 15 m s−1, they observemore sun glint than at larger velocities. The result is consistent with Figure 5.7, whichshows that, although the angular extent of the reflected radiances increases with the windspeed, there is less reflection into any given direction. Consequently, their sun glint filterhas two parts. If θS < 10°, a pixel is masked for all values of U; if θS < 15°, it is maskedfor U < 15 m s−1.

For the newer instruments such as AMSR and TMI, at 6.6 and 10.7 GHz, Meissneret al. (2011b, Section 11.3.2) mask all data for θS < 25°, and at higher frequencies for



θS < 10°, where these masks were determined from examination of the data. For instru-ments in dawn–dusk polar orbits such as the SSM/I where θS is close to 90° or near grazing,with the exception of Aquarius with its 1.41-GHz channel, problems with solar reflectivityare minimized.

9.3.3 Radio-frequency interference (RFI)

There are two kinds of radio-frequency interference (RFI) that occur for Earth observingsatellites: the first is the reception of the geosynchronous broadcasts that are reflectedfrom the ocean surface; the second is the reception of the surface-to-space transmissionsfrom ship and land sources. Gentemann et al. (2010c, Section 2.6.3) describe RFI as thefastest growing source of errors in the retrieval of microwave products. The direct broadcastsatellites use the 10.7- and 18.6-GHz bands; the 6.9-GHz band is shared with bands usedin ground-to-satellite communications (RSS, 2013b; Maeda et al., 2011).

The microwave instruments and bands most affected by RFI from the geosynchronousdirect broadcast satellites are the AMSR-E and WindSat 10.7- and 18.6-GHz bands.These frequencies are used for satellite TV broadcasts over Europe, the United States andthe Mediterranean (Gentemann et al. 2010c, Table 2.4). Further, the 6.9-GHz band is theprimary band for ground-to-satellite communications (Maeda et al., 2011). For these threebands, the 6.9- and 18.7-GHz bands are not protected and the AMSR 10.65-GHz band withits 100-MHz bandwidth is only partially protected, with only 10.68–10.70 GHz of this bandreserved for radio-astronomy use (Gentemann et al., 2010a).

For example, the 6.9-GHz band on AMSR-E is important to microwave retrieval ofSST. Because this band is shared with ground-to-satellite communications, it suffered fromincreasing RFI throughout its lifetime. Because of this, the new Japanese AMSR-2 carriesboth 6.9- and 7.3-GHz bands. The hope is that these two bands will have a differentresponse to RFI so that the actual signal can be retrieved (Imaoka et al., 2007). Otherexamples of RFI occur because of reassignment of frequency bands. For example, althoughthe frequency band 5.3–5.6 GHz was originally allocated to satellite SAR, the US andEuropean telecommunications authorities have allocated part of this band to broadbandcommunications, so the width of the observing band is reduced to 5.35 – 5.47 GHz. Thisaffects the planning for the Sentinel-1 SAR satellite, and places limits on its total broadcastpower over the United States and Europe (Sentinel-1, 2012).

For the broadcast satellites, their location and antenna-pointing angle are designed toserve specific markets, such as Europe, North America, Asia or the Middle East. Once thebroadcast energy reaches the ocean surface, then, as for sun glint, it can be reflected to theEarth observing satellites by the wind-generated wave facets. When this reflected energylies within the instrument bandwidth, RFI results. Because of the relative pointing anglesof the Earth observation satellites and the geosynchronous satellites, the geosynchronousRFI occurs preferentially on ascending or descending passes.

For AMSR-E in the Northern Hemisphere, RFI occurs during descending passes, whereit is most intense in coastal regions. To explain this, Figure 9.8 shows a schematic diagram



Geostationary broadcast satellite

Ocean

Satellite

Ascending orbit

Geostationary broadcast satellite

Ocean

Sensor

Descending orbit

Equator

Satellite

(a)

(b)

Sensor

Fig. 9.8. The geometry of radio-frequency interference (RFI) generated by reflection from the oceansurface of transmissions from a geostationary broadcast satellite to a conceptual AMSR-E: (a)descending mode in the Northern Hemisphere, where the transmission is reflected by ocean surfaceroughness into the microwave antenna; (b) ascending mode, where the angles are such that reflectioninto the antenna is not likely.

of the radiation geometries during the AMSR-E nighttime descending (a) and daytimeascending (b) passes. The reason why the AMSR-E descending passes in the NorthernHemisphere are so vulnerable is that the geostationary satellite is looking northward andthe AMSR is looking southward, so that it is relatively easy for AMSR to view the reflectedbroadcast energy. This RFI is particularly strong around Europe and in the Mediterranean(Gentemann et al., 2010a). For this broadcast geometry, Figure 9.8 also shows that theascending passes are not vulnerable, although the opposite conditions apply in the SouthernHemisphere. In contrast, the RFI from ground-to-satellite broadcasts is independent of theascending or descending orbits.

Suggestions for reduction of RFI include narrowing the satellite bandwidths, buying upthe relevant bands and reserving them for Earth observations, rotating the satellites 180°before passing over Europe and applying RFI masks. Masking strong RFI is relatively easy;masking weak RFI is much harder (Gentemann et al., 2010a).



9.3.4 Faraday rotation

When an electromagnetic wave propagates through the ionosphere, the free electrons causea rotation of its polarization vector, called Faraday rotation, which increases as the inversesquare of the frequency. For example, this Faraday rotation means that, after a V-polradiance has crossed the ionosphere, it has both V-pol and H-pol components. In additionto its frequency dependence, the magnitude of the Faraday rotation depends on the free-electron density that is a function of solar activity, geographic location and time of day,being greater at night and smaller during the day, and on the magnitude and orientation ofthe Earth’s magnetic field. Both the free-electron density and the magnetic field propertieshave been tabulated; from these, the Faraday rotation can be calculated (Meissner andWentz, 2006a). For V-pol and H-pol observations, Faraday rotation is most important atfrequencies of about 1 GHz, so the L-band (1.4 GHz) observations of Aquarius and of theJapanese PALSAR must be corrected for this rotation. For the WindSat 10.7-GHz channel,Meissner and Wentz (2006a) show that the third Stokes vector is also affected by Faradaycorrection, and must be corrected before calculation of the wind retrievals.

9.3.5 The retrieved variables

Over the ocean, the atmospheric variables retrievable from the V- and H-pol passivemicrowave observations include the mean atmospheric temperature T , the columnar watervapor V, the columnar non-raining cloud liquid water L and the rain rate RR. At the surface,the variables include the sea surface temperature and salinity TS and SS, and the 10-m scalarand vector wind speed, where the winds are derived from the surface wave distribution. Theatmospheric parameters are viewed against the background of the ocean surface. Becausethe distributions of wind-generated capillary and gravity waves vary symmetrically withazimuth angle relative to the wind direction, the surface emissivity varies with azimuthangle, polarization and the third and fourth Stokes parameters. As the following sectionsshow, this means that, if a V- and H-pol radiometer takes two looks at the same area fromdifferent directions, it can retrieve the vector wind speed. It also means that, for polarimet-ric radiometers such as WindSat that measure all four Stokes parameters, under conditionsdiscussed in Section 9.4.5, a single look at the ocean surface can be used to retrieve thevector wind speed.

Because none of the above atmospheric and oceanic variables occur in isolation, thereare two ways to solve for an individual variable. The first is to use the received brightnesstemperatures to solve simultaneously for all of the variables. The second is, for variablesthat cannot be retrieved, either to provide masks, so that, for example, rain would be masked,or to replace them with variables derived from other sources, so that SST might be takenfrom the Reynolds SST. Once the non-retrievable variables have been masked or replaced,the remaining variables can be derived. Given that the lower boundary common to all theseretrievals is the ocean surface, the next section describes the dependence of the emissivityon surface waves, roughness and foam, and on the azimuthal look angle relative to the winddirection.


9.4 Dependence of emissivity on surface waves and foam 273

9.4 Dependence of the emissivity on surface waves and foam

As Chapter 2 describes for the ocean surface, the wind generates long waves, capillary-gravity waves and foam, all of which affect the emissivity. Additionally, from Chapter 2and Cox and Munk (1954), because the wave slopes and amplitudes are azimuthally dis-tributed around the wind direction, the emissivity dependence on U divides into two parts:an isotropic term that is independent of azimuth and depends only on U, and an anisotropicterm that depends both on U and on the relative azimuthal look angle φR. For a radiometerazimuthal look angle φ and a wind direction φW, φR is defined as

φR = φW − φ (9.4)

where φR = 0 in the upwind direction.For a flat ocean surface at U = 0, the emissivity is a function of temperature and salinity,

where the maximum in the salinity dependence occurs at about 1.4 GHz and that of thetemperature dependence occurs at about 6 GHz (Meissner and Wentz, 2004) (See Figure9.15 below). As U increases from zero, the addition of waves, roughness and foam altersthe emitted microwave radiation, and generates changes both in the isotropic and in theazimuthal-look-angle-dependent emissivities (Meissner and Wentz, 2002; Meissner et al.,2011b). Depending on wind speed and the resultant surface conditions, the emitted andreflected radiation depends on three terms: capillary waves and roughness, gravity wavesand foam. Relative to the long waves, foam and roughness occur at different locations,where the short capillary waves occur on the leading edge of the wave crest and the foamfrom breaking waves occurs behind the crest. The presence and distribution of each of thesephenomena affect the received radiance.

In order of increasing complexity, the next five sub-sections describe the effect of wavesand foam on the emissivity. Section 9.4.1 discusses the terminology used to describe theircontributions to the emissivity and the two-scale approximation. Section 9.4.2 describes theazimuthally averaged emissivity of a foam-free, two-scale surface and justifies the choiceof the 50° conical scanner look angle. Section 9.4.3 discusses the contribution of foam tothe azimuthally averaged emissivity. Section 9.4.4 discusses the azimuthal dependence ofthe V-pol and H-pol emissivity components on U, and Section 9.4.5 describes the azimuthaldependence of all four Stokes components on U. Sections 9.4.4 and 9.4.5 discuss the useof this dependence in retrieval of the vector wind speed. As in Chapter 8, V-pol and H-polbrightness temperatures are written as TBV and TBH, and the 18-GHz V-pol instrumentchannel is abbreviated as 18V, with similar notation for the other channels.

9.4.1 Contributors to the wave-induced emissivity

From Meissner et al. (2011b), the surface emissivity e can be written as the sum of threeterms:

e = e0(S, T ) + eiso(U,F ) + edir(U, φR) (9.5)



The first term is the specular sea surface emissivity e0(S, T ), which is a function ofsalinity, temperature and frequency (Meissner and Wentz, 2002). This is the dominant termin the emissivity, and as Figure 8.6 shows, at θ = 50, the flat ocean surface has a coldbrightness temperature and is strongly polarized, with its V-pol brightness temperaturesexceeding the H-pol. The second term, the isotropic emissivity eiso(U,F ), is a functionof wind speed and the fractional areal extent of foam F. The third term is the small butsignificant directional dependence of the emissivity on waves and roughness edir(U, φR),where equation (9.3) defines φR.

For the isotropic term in equation (9.5), if F is the fractional areal coverage of foamwithin the instrument FOV, eiso can be written as

eiso = (1 − F ) eW + FeF (9.6)

where eW is the wave-induced isotropic emissivity and eF is the emissivity of foam(Wentz, 1983).

In the theoretical description of the emitted and reflected electromagnetic radiation froma wave field, the ocean surface is divided into two scales. The first is the long gravitywaves, or those waves that are much longer than the radiation wavelength. The secondconsists of those capillary-gravity waves with wavelengths and amplitudes that are muchsmaller than the radiation wavelength. The presence of foam also affects the emitted andreflected radiation. As Chapter 2 describes, beginning at wind speeds of about 3 m s−1,foam formation from breaking begins, with preferential formation on the upwind face ofthe waves and with blowing spume occurring at wind speeds greater than about 9 m s−1.

For a foam-free surface, Wentz (1975, 1997) theoretically models the scattering andemission from the ocean surface through use of the two-scale scattering approximation.This approximation is applicable at low wind speeds; at high wind speeds, foam dominatesthe response. The two-scale model assumes that the ocean surface can be divided as follows(Yueh, 1997; Meissner and Wentz, 2002).

Gravity waves that are long compared with the radiation wavelength. These long waveshave a symmetric anisotropic distribution around the wind direction and can beapproximated as tilted facets that are specular reflectors. These tilted facets mix thepolarization of the reflected downwelled radiance and are a dominant signal in thewind retrieval (Yueh, 2008).

Capillary-gravity waves whose amplitudes are small compared with the radiation wave-length. These short waves also have an anisotropic distribution around the winddirection, and are treated as surface roughness that causes incoherent scatter andemission.

With the neglect of foam, Figure 9.9 shows that this surface can be described as a small-scale surface S superimposed onto a large-scale surface L, where the water wavelengththat defines the division is a function of the observing wavelength λ. Physically, L consistsof long gravity waves with surfaces that can be approximated as specular reflecting facetscharacterized by their distribution of slopes; S consists of short capillary-gravity waves



(a)

(b)

(c)

ΣL

ΣS

Fig. 9.9. The two-scale division of (a) a wave-covered surface into (b) a faceted surface L and (c)a rough surface S, where the upper surface is the sum of the lower two. The vertical amplitude isexaggerated; see the text for further description (notation from Wentz, 1975, 1997).

that generate the roughness associated with scattering. For long waves, the radius-of-curvature of L must be greater than the radiating wavelength, so that Equation (5.9) issatisfied. Additionally, with the definition that σ 2 is the mean-square slope of Land σ 2

η isthe mean-square amplitude of S, then for the two-scale approximation to apply, σ 1and ση λ, where λ is the radiation wavelength. The two scales are separated by a waterwavelength λW called the cutoff wavelength λC. The large-scale surface consists of allwaves with λW ≥ λC; the small-scale surface consists of waves with λW ≤ λC. Geometricoptics describe the scattering from the large-scale surface; perturbation theory describesthe scattering from the small-scale surface (Yueh, 1997).

From Yueh (1997), the theoretical modeling of this problem has two parts: first, therelation among the surface waves, foam and wind speed; second, the reflection, emission andscattering of the electromagnetic waves from the surface wave field. Both these problemsare important; both must be solved to allow determination of the vector wind speed fromremote sensing observations.

The amplitudes both of the long gravity waves and of the short capillary-gravity wavesare larger in the upwind/downwind direction than in the crosswind. Also, as Figure 2.5shows, the capillary waves are concentrated on the downwind, forward face of the lon-ger waves, leading to an asymmetry in the upwind/downwind distribution. Foam frombreaking waves occurs on the upwind face. This asymmetry in the distribution of foam andcapillary waves contributes to determination of the vector wind speed.

The cutoff wavelength increases with roughness and wind speed and is larger than, but oforder of, the observing wavelength λ (Wentz, 1975). Waves that are short compared with λW

do not contribute to σ 2. Because for electromagnetic radiation, λ decreases with increasingf, σ 2 increases with f, reaching its maximum value, called the optical limit, at about 37 GHz(Wentz, 1997). Because the long wavelength, lower observational frequencies exclude fromσ 2 the short 1–10 cm ocean wavelengths that are most responsive to changes in wind speedand direction, for successful wind retrievals, f must be greater than about 10 GHz (Wilheit,1978). From the foam-free, two-scale analysis and for the frequency range 7–37 GHz takenfrom TMI data, Meissner and Wentz (2002) find that the wind signal is greatest at 37 GHz,



falling to 40% of this value at 11 GHz and to about 20% at 7 GHz. This means that, for lowwind speeds, the wind signal is less for the critical 7- and 11-GHz bands used in the SSTretrieval.

From the resultant model, Wentz (1975, 1992) shows that the factors contributing to eW

are the large-scale surface tilt associated with L and the small-scale surface roughnessassociated with S. The tilted facets of L act as independent specular surfaces, mixthe horizontal and vertical polarizations and change the local incidence angles of theemitted and reflected radiances; the roughness associated with S diffracts and scatters theemitted and reflected radiances (Ulaby et al., 1982, Chapters 11 and 12). The distributionand magnitude of σ 2 and σ 2

η determine the response of the microwave emissions to windmagnitude and direction.

In addition to their frequency dependence, σ 2 and σ 2η are also functions of the azimuthal

angle, where both quantities are larger in the upwind and downwind directions than in thecrosswind. This is in part due to the preferential formation of the parasitic capillary waveson the downwind face of the wave crests, yielding an upwind/downwind anisotropy in theirdistribution and in their resultant contributions to the emissivity. Finally, the response tothe azimuthal distribution of the short capillary-gravity waves is enhanced by a resonantcephenomenon called Bragg scatter, which will be discussed further in Section 10.6.2.

9.4.2 The azimuthally averaged emissivity of a wind-roughened foam-free surface

For radiometer observations of a foam-free wind-roughened ocean surface, Wentz (1975)theoretically derives the dependence of TBV and TBH on f, U and θ . His derivation uses thetwo-scale approximation, averages over all azimuth angles to remove the directional effectsof wind and includes the scattering and reflection of the downwelled atmospheric radiance.For his solution, Figure 9.10 shows the theoretical dependence of TB on polarization and θ

for U =13.5 m s−1 and for the U = 0 m s−1 specular surface case corresponding to Figure 8.6.Figure 9.10 also shows the observed values of TB derived from field measurements at U =0.5 and 13.5 m s−1, where the 13.5 m s−1 observations were filtered to remove the effectsof foam. At θ = 0°, small-scale roughness accounts for the elevation of the 13.5 m s−1

curves above the specular curves.An important result shown in Figure 9.10 is that, at both frequencies and for θ = 50°

55°, the values of TBV at U = 0 and 13.5 m s−1 are equal, so that, given an incidence angleof about 50° and for foam-free conditions, TBV is independent of wind speed. Even thoughthis result neglects foam, the advantages associated with the decoupling of TBV from U atθ ∼= 50° mean that all of the conically scanned microwave imagers operate at incidenceangles close to 50°. In contrast, at the same incidence angle, TBH strongly depends on U.For example, at 19 GHz, as U increases from 0 to 13.5 m s−1, TBH increases by about20 K. Given a radiometer accuracy of about 0.5 K, this suggests that a wind speed retrievalalgorithm that utilizes TBH would have an accuracy of about 0.5 m s−1. Comparison withthe specular surface results in Figure 8.6 shows also that, because TBH increases with wind



220

200

180

160

140

120

100

80

60

40

220

200

180

160

140

120

100

80

60

400 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70

Incidence angle (degrees) Incidence angle (degrees)

Brig

htne

ss te

mpe

ratu

re T

B (K

)

8.36 GHz 19.36 GHz

V-pol

V-pol

H-polH-pol

Fig. 9.10. Comparison of the computed and field measurements of brightness temperatures madefrom a foam-free, wind-driven sea for V- and H-pol at 8.36 GHz and 19.3 GHz and averaged overall azimuth angles. On each panel, the dashed line corresponds to the U = 0 specular surface case,the solid line to U = 13.5 m s−1. The vertical lines mark the angles at which the V-pol curves areindependent of U. The sea surface temperature is 291 K; the surface salinity is 35 psu, where psu isthe abbreviation for precision salinity units. The ellipses show observations at 0.5 m s−1; the crosses,at 13.5 m s−1, where foam from breaking waves is excluded. See the text for further description.(Figures 3 and 4 from Wentz (1975), C© 1975 American Geophysical Union, reproduced/modified bypermission of AGU.)

speed while TBV remains roughly constant, the effect of increasing winds is to reduce thebrightness temperature difference between the two polarizations.

9.4.3 Contribution of foam

Smith (1988) discusses aircraft passive microwave observations of oceanic foam at 19V,37V and 37H. For the case when foam fills the antenna footprint, Table 9.2 summarizeshis observations and shows that, at 37H, eF is nearly twice its value at 37V and 19V.The combination of this positive emissivity change with the increase in foam extent withU means that, once foam starts to appear, eisoin Equation (9.6) increases more rapidlywith U than for waves alone, and the lack of V-pol response at look angles of about 50°no longer occurs. The result is that at low wind speeds the emissivity is dominated bythe mean-square slopes and to a lesser extent roughness; at greater wind speeds, by thefractional area of foam.

To illustrate the effect on the emissivity of waves and foam, Figure 9.11 shows theU-dependence of the V-pol and H-pol components of eiso and TB derived from co-located SMMR and SEASAT scatterometer measurements of wind speed (Wentz et al.,



Table 9.2. The emissivity increaseeF observed from passive

microwave aircraft observations offoam, where the foam patches are

larger than the beam footprint.

Channel eF

19V 0.1537V 0.1537H 0.28

Adapted from Table III of Smith (1988).

1986). Even though this figure neglects the directional dependence, it shows that, for fourfrequencies and two polarizations, the dependence of eisoon U divides into two linearcurves, separated by a slope break between 7 and 12 m s−1. The onset of significant wavebreaking and production of foam causes this slope break. The low wind speed linear regimefor U < 7 m s−1 corresponds to the foam-free case in Figure 9.10; the high wind speedregime for U > 12 m s−1, to wind speeds where the fractional area of wave breakingand foam formation increase rapidly with U. For high-speed wind phenomena such ashurricanes, the dependence of foam extent on wind speed is the dominant contributor tothe emissivity increase.

Because of the 51° SMMR look angle, for the low wind speed regime and consistentlywith Figure 9.10, the V-pol values of eiso and TB are almost independent of U, while theH-pol values have a much stronger U-dependence. Wentz (1997) models the U-dependenceof the emissivity as a linear increase for U < 7 m s−1, a quadratic increase for 7 < U <

12 m s−1, and a steeper linear increase for U > 12 m s−1. For all frequencies, Figure 9.11shows that the contributions to the emissivity of both roughness and foam are less for V-polthan for H-pol, so that the H-pol component is more sensitive to changes in U. Also forH-pol, the sensitivity to changes in U of eiso and TB increases with frequency. The foamalso increases the emissivity and reduces the polarization from the specular surface case. AsSection 9.6 shows below, these responses are the basis for the wind magnitude algorithms.

9.4.4 Azimuthal dependence of the V- and H-pol emissivities

Because conically scanned radiometers operate at a fixed incidence angle but for a largerange of φ, these instruments unavoidably retrieve the surface variables at different Laz-imuthal angels. This section discusses the observed dependence of the emissivity on polar-ization, U and φR. It then shows how this angular dependence is removed to allow retrievalof the wind speed magnitude, and how viewing the same ocean area at two different valuesof φR permits retrieval of the vector wind. Also, for the WindSat case when all four Stokesparameters are retrieved, the vector wind can be retrieved from a single look. Both these



12

8

4

0

0 5 10 15 20 25 0 5 10 15 20 25

6

4

2

0

6

4

2

0

SASS wind speed (m s–1)

6.6V

18V

18H

10.7V

37V

37H

8

4

0

6.6H 10.7H

SM

MR

win

d-in

duce

d em

issi

vity

Δe i

so (1

0–2 )

0

12

24

36

0

12

24

0

6

12

0

6

12

ΔT B

(K

)

Fig. 9.11. Dependence of the wave and foam contribution to the emissivity eiso to the left and TB tothe right on U at θ = 51° for V- (upper four figures) and H-polarization (lower four figures). The curvesare derived from co-located SMMR and SEASAT open ocean scatterometer wind measurements. Forthe brightness temperatures, the ocean surface is assumed to be at a temperature of 300 K. Solidlines show the mean values; dashed curves, the one-standard-deviation envelopes. The 37V standarddeviations are missing on the original. See the text for further description. (Redrawn from Figures9 and 10, Wentz et al. (1986), C© 1986, American Geophysical Union; reproduced/modified bypermission of AGU.)

retrievals are important because of the obvious advantages of better wind retrievals, andbecause the accuracies of the other retrieved variables improve with more accurate winds.

The dependence of the emissivity on polarization, U and φR was derived from Russianand US aircraft experiments (Irisov et al., 1991; Yueh et al., 1999) and from comparison



of satellite and buoy winds (Wentz, 1992; Meissner and Wentz, 2002). For the satellitecase, Wentz’s (1992) derivation is based on about 3000 spatially and temporally coincidentpairs of SSM/I and NDBC winds, where SSM/I data are also used to remove the effectsof atmospheric liquid water and water vapor. Later comparison with aircraft experimentsshowed that, at small wind velocities, his results were too large (Meissner and Wentz, 2002).This difference occurs because the retrieved atmospheric variables and surface emissivitiesboth depend on the same distribution of surface roughness, so that, at small wind velocities,the use of a single radiometer to retrieve these variables generates a systematic error.Meissner and Wentz (2002) eliminate this error by redoing the analysis using one satelliteradiometer for atmospheric variable retrieval and another for directional wind retrieval.Specifically, they use about 8 × 105 coincident pairs of SSM/I and QuikSCAT winds and8000 pairs of SSM/I and buoy winds for the directional wind retrieval, both with TMIfor atmospheric correction, and 106 pairs of TMI and QuikSCAT winds with SSM/I foratmospheric correction.

For 37 GHz and both polarizations, Figure 9.12 shows the resultant dependence ofTBV and TBH on φR. On the figure, TBV and TBH are grouped into 20° bins and intothree wind speed ranges: 0–6 m s−1, 6–10 m s−1, and 10–14 m s−1; the dotted, dashedand dot–dash lines show the Meissner–Wentz results, while the solid lines show Wentz’s(1992) results. Also, 0° corresponds to the upwind direction, 180° to downwind and 90° and270° to the crosswind directions. For U < 6 m s−1, the Meissner–Wentz results are muchless than Wentz’s; for U > 10 m s−1, the two approximately agree. The Meissner–Wentzobservations show that TBV and TBH increase with U and are symmetric around thewind direction. Specifically, TBV has a dominant cos φR dependence with its maximumand minimum respectively in the upwind and downwind directions, while, at the largervelocities, TBH has a cos (2φR) dependence with its minima in the upwind, downwinddirections and maxima in the crosswind directions.

For 10–14 ms−1, the upwind/downwind range of TBV is about 3 K; the crosswind/downwind range of TBH is about 4 K. Although Figure 9.11 shows that the azimuthallyaveraged values of TBH are more sensitive to changes in U than TBV, Figure 9.12shows that the two polarizations have about the same sensitivity to azimuthal changes.From Figure 9.11, the TB associated with a 0 to 12 m s−1 increase in the azimuthallyaveraged wind magnitude is about 15 K for 37 H and 3 K for 37V. This means that, for37 H and a velocity increase of 12 m s−1, the azimuthal dependence generates a small butnon-negligible perturbation in the azimuthally averaged TBH, while for 37V the azimuthalperturbation equals the azimuthally averaged increase.

Even though Wentz’s (1992) results are overstated for U < 6 m s−1, Wentz (1997)found that, if the wind retrieval algorithm did not consider the azimuthal variability, theerrors in U depended on φR. In the upwind direction, he found that the SSM/I estimateof U was 2.5 ms−1 less than the buoy estimate; in the downwind direction, the SSM/Iestimate was 1.2 m s−1 greater. Over all directions, the rms difference between the buoyand the SSM/I wind magnitudes is about 1.6 m s−1. Because the accuracies of all theretrieved variables depend on the wind retrieval, in its operational processing, the wind



SSMI/QuikSCAT TMI/QuikScat SSMI/NDBC buoys

upwind upwind Relative wind direction (deg)Relative wind direction (deg)

ΔT B

(K)

Wentz (1992)

[10, 14] m s–1[10, 14] m s–1

0 90 180 270 3600 90 180 270 360

[0, 6] m s–1

[6, 10] m s–1 [6, 10] m s–1

[0, 6] m s–1

37V GHz 37H GHz

3

–3

0

–2

–1

1

2

3

–3

0

–2

–1

1

2

3

–3

0

–2

–1

1

2

3

–3

0

–2

–1

1

2

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–3

0

–2

–1

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–3

0

–2

–1

1

2

0 90 180 270 360 0 90 180 270 360

0 90 180 270 360 0 90 180 270 360

ΔT B

(K

)Δ

T B (

K)

Fig. 9.12. Azimuthal dependence of the brightness temperature difference TB for 37 GHz, bothpolarizations and three different wind speeds, derived from a comparison between passive microwaveradiometer and NDBC winds. The upwind direction corresponds to φR = 0. The solid line shows thebest fit to Wentz’s (1992) observations; the other symbols are defined on the figure. See the text forfurther description. (Figure 1 from Meissner and Wentz (2002), C© 2002 IEEE, courtesy of ThomasMeissner, used with permission.)



direction is derived from co-located data in the NCEP forecast model, then used with thebrightness temperatures to improve the accuracies of the retrieval of wind magnitude andother variables.

The directional dependence can also be used to retrieve the vector wind speed. From theazimuthal dependence of TBV and TBH given in Figure 9.12, Wentz (1992) shows that thewind direction could be retrieved through the hypothetical use of two satellite radiometers.In this retrieval, the first radiometer looks forward and the second looks backward, so thatthe same ocean area is observed at two different times and at two values of φR separated byabout 180°. Because the WindSat instrument on the Coriolis satellite launched in January2003 tested this concept, as well as providing operational wind retrievals from measurementof all four Stokes parameters (Sections 3.2.3 and 8.6.5), the next section discusses the φR

dependence of the brightness temperatures for the Stokes parameters.

9.4.5 Azimuthal dependence of the four Stokes parameters

From aircraft observations, this section first describes the retrieval of all four Stokes param-eters as a function of the relative wind direction, and then, from WindSat data, describesthe dependence on wind speed and direction of the third and fourth Stokes parameters.

On the basis of result from a series of aircraft experiments, Yueh (1997) and Yueh et al.(1999) describe the dependence on φR and U of the four Stokes brightness temperaturesand Yueh (1997) theoretically models this dependence. The observational data were takenfrom an aircraft-mounted Jet Propulsion Laboratory (JPL) 19- and 37-GHz polarimetricradiometer that at 19 GHz measured all four Stokes parameters, and at 37 GHz mea-sured the first three parameters. In the experiments, the aircraft flew in circles around anNDBC anemometer-equipped buoy off the California coast, where the aircraft was orientedsuch that the radiometer viewed the surface at a constant incidence angle. The observa-tions acquired data at θ = 45°, 55° and 65°; for comparison with the satellite radiometerobservations, the following discusses the 55° observations.

For 19 and 37 GHz, Figure 9.13 compares the model results with observational dataand with Wentz’s (1992) V- and H-pol results, where the azimuthally averaged responseis removed from the data. Examination of the figure shows that the V-pol and H-polcurves are similar to those in Figure 9.12; they respectively show a cos φR and a cos (2φR)response. Consistently with theory, the curves for the third and fourth Stokes parameters areanti-symmetric about the wind direction. The third Stokes parameter has a mixed sin φR

and sin (2φR) dependence, while the fourth Stokes parameter has a dominant sin (2φR)dependence and a magnitude is about 25% of each of the other parameters. Given thedifferent azimuthal responses of the four Stokes parameters, then, as shown below andexcept for U < 6 m s−1 a single look with a polarimetric radiometer at any azimuthal angleprovides a unique solution for the wind speed and direction.

For the third and fourth Stokes parameters and wind speeds of 3, 6, 9, . . . 24 m s−1,Figure 9.14 shows the dependence of the mean and standard deviation of the 18.7-GHzWindSat brightness temperatures on speed and relative direction (Yueh et al., 2006).Although Yueh et al. (2006) do not show the behavior of the 10.6- and 37-GHz bands to



Relative azimuth angle (deg)

19-GHz Data37-GHz Data19-GHz (2 Scale)37-GHz (2 Scale)SSM/I (Wentz)

3.02.0

1.0

–3.0

–2.0–1.0

0.0

3.02.0

1.0

–3.0

–2.0–1.0

0.0

3.02.0

1.0

–3.0

–2.0–1.0

0.0

3.0

0.5

–1.0

–0.5

0.0

ΔT B

V (

K)

Thi

rd S

toke

s (K

)F

ourt

h S

toke

s (K

)

0 90 180 270 360

0 90 180 270 360

0 90 180 270 360

0 90 180 270 360

ΔT B

H (

K)

Upwind

Fig. 9.13. Comparison of theoretical and observed values of the Stokes parameters for JPL WIN-DRAD’94 aircraft radiometer data taken at a 55° look angle and at a 10-m wind speed of about10 m s−1. The vertical arrow at 0°marks the upwind direction. The figure shows the 19- and 37-GHzdata and model results, and, for V- and H-pol, Wentz’s (1992) results. See the text for further descrip-tion. (Figure 4 from Yueh (1997), C© 1997 IEEE, courtesy of Simon Yueh, used with permission.)

the detail of Figure 9.14, they found similar results at these frequencies. The one exceptionwas the 37-GHz fourth Stokes parameter, which had a much smaller directional responsethan at 10.7 and 37 GHz. The behavior shown in Figure 9.14, then, is typical of that at theother two frequencies.

The figures are derived from comparison of six months of rain-free WindSat data withthe wind speed and direction derived from co-located (±3 h) 6-hourly data from the NCEP


Wind direction (deg)

18.7

-GH

z th

ird S

toke

s (K

)

Wind direction (deg)

24 m s–1 24 m s–1

21 m s–1

18 m s–1 18 m s–1

15 m s–1

12 m s–1 12 m s–1

9 m s–1

6 m s–1

9 m s–1

50 100 150 3503002502000 50 100 150 3503002502000

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(K)

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3 m s–1

–0.04–0.02

0.000.02

0.04

–0.2–0.10.00.10.2

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6 m s–1

–0.04

–0.02

0.00

0.02

–0.2

–0.1

0.0

0.1

0.2

3 m s–1

upwind upwind

Fig. 9.14. The means and standard deviations of the 19.6-GHz brightness temperatures associatedwith the third (left) and fourth (right) Stokes parameters plotted versus wind speed and direction.The vertical lines show the standard deviations, the curves show the means, the insets give the windspeeds. Also shown are the best-fit sinusoid models to the data and the difference between the modelsand observed data. See the text for further description. (Adapted from Figures 4 and 5, Yueh et al.(2006), courtesy of Simon Yueh, not subject to US copyright.)


9.5 Temperature and salinity 285

Global Data Assimilation System (GDAS). The GDAS data provide wind speed, direction,SST, water vapor and cloud liquid water. These data were used in combination withWindSat data to correct for atmospheric attenuation. The resultant brightness temperatureswere binned at wind speed intervals of 1 m s−1 and at directional intervals of 10°.

On Figure 9.14, the vertical bars show the standard deviation, while the dark line showsthe mean. Unfortunately, the sign convention for third and fourth Stokes parameters isreversed from the aircraft observations in Figure 9.13. Each sub-figure also shows thecurves generated by the best-fit sine series, namely a weighted sum of sin φR and sin(2φR)for the third Stokes parameter, and sin (2φR) for the fourth. Finally, the line near the originshows the difference between the observed and the best-fit sine series. Examination ofFigure 9.14 shows that, for the different wind velocities, the amplitude of the fourth Stokesparameter is always smaller than that of the third, ranging from a factor of two smaller atthe lowest wind velocity to nearly an order of magnitude smaller at 20 m s−1. For windspeeds less than about 6 m s−1and for both Stokes parameters, the peak-to-peak signalamplitude is less than its standard deviation. For wind speeds in the range 6–20 m s−1, theamplitudes are greater than the standard deviations and the angular dependences are clearlysinusoidal.

Except for the largest wind speeds, the Stokes parameters have a similar behavior, witha peak-to-peak amplitude as small as 0.05 K for wind speeds less than 5 m s−1, and, for thethird Stokes parameter, as large as 4 K for speeds of 12–20 m s−1. Because of the paucityof wind speed observations at wind speeds greater than 20 m s−1, the reduced number ofsamples in each bin leads to a less reliable match-up and more scatter. Finally, the smallsignal and large standard deviations for wind speeds less than 6 m s−1 suggest that, for asingle-look radiometer, vector wind retrievals are impossible.

Yueh (2008) compares the WindSat third Stokes parameter against HRD wind speeds,where, for wind speeds between 20 and 60 m s−1, the winds are grouped into 10 m s−1 bins.He shows that, for the first three bins, the Stokes parameter varies sinusoidally with windspeed, with peak-to-peak amplitudes of 3–4 K. For the largest bin of 50–60 m s−1, eventhough there are fewer match-ups, the signal remains strong with a peak-to-peak value ofabout 2 K. This suggests the possibility of extending the directional retrievals to very largewind velocities.

As Section 9.7 discusses further, WindSat polarimetric observations can retrieve thewind speed and direction, although with increased directional error for wind speeds lessthan 6 m s−1 (Monaldo, 2006). The section also discusses the important extension byMeissner and Wentz (2009) of the rain-free WindSat retrieval to all-weather case of strongwinds (>20 m s−1) and heavy rain, and describes how, under these conditions, WindSatprovides a benchmark data set for the calibration of other scatterometers.

9.5 Temperature and salinity

The Klein–Swift formulation describes for a specular surface the dependence of the emis-sivity on sea surface temperature TS and salinity SS (Klein and Swift, 1977; Swift and



Frequency (GHz)40

∂TB

–1.0

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

V-pol

H-pol

∂TB

∂TS

19 21 377 111.4

∂SS

Par

tial d

eriv

ativ

es o

f TB

with

res

pect

to T

S a

nd S

S

3020100

Fig. 9.15. The partial derivatives of TBV and TBH with respect to TS and SS for a specular surface andfor θ = 53°, as derived from the Klein–Swift relations cited in the text. Solid lines are V-pol; dashedlines are H-pol. (Computer code courtesy of Gary Lagerloef.)

McIntosh, 1983; Wentz and Meissner, 1999). Following Wilheit (1978), the sensitivity ofTB to changes in TS and SS is given by the partial derivatives of TB with respect to thesevariables. For θ = 53°, TS = 293 K and SS = 30 psu (precision salinity units), Figure 9.15shows the frequency dependence of the V- and H-pol components of these partial deriva-tives. For TS, the TBV sensitivity has a peak at 5.6 GHz, with zero crossings at 1.25 and32.2 GHz. From these curves, TBH has a smaller sensitivity than TBV with zero crossings at1.5 and 24 GHz. The optimum frequency and polarization for retrieving TS while avoidingattenuation by atmospheric water occurs for V-pol at about 7 and 11 GHz. The two lowercurves in Figure 9.15 give the dependence of the sensitivity of TB on SS, and show that, forf increasing from 1 to about 5 GHz, the sensitivity decreases rapidly. This suggests that theprotected 1.41-GHz frequency is best suited for salinity retrieval.

For salinity retrieval and for f>1 GHz, the 1.41-GHz band is the lowest available obser-vational frequency. At this frequency, and for the range of open ocean surface temperaturesand salinities, Figure 9.16 shows the dependence of TBV and TBH on TS and SS (Lagerloefet al., 2008). Across this region and for an oceanic salinity range between 32 and 37 psu,the maximum change in brightness temperature occurs for TBV and is about 5 K. If the SSTis known, then the salinity can be determined from the measured brightness temperature.For the other incidence angles and polarizations, the curves are similar, but with their scalesoffset in the vertical. Figure 9.16 shows that, for the range in temperature and salinitydefined by the curves, TBV and TBH depend primarily on SS, with a weak dependence on TS.


9.5 Temperature and salinity 287

0 5 10 15 20 25 30 35108

109

110

111

112

113

114

SST (°C)

Brig

htne

ss T

empe

ratu

re (

K)

1.413-GHz V−pol Brightness Temperature, 37.8o incidence

32

33

34

35

36

37

0 5 10 15 20 25 30 3573

74

75

76

77

78

SST (°C)

Brig

htne

ss T

empe

ratu

re (

K)

32

33

34

35

36

37

1.413-GHz H−pol Brightness Temperature, 37.8o incidence

Fig. 9.16. The dependence of the V-pol and H-pol brightness temperatures as a function of SST forconstant values of surface salinity between 32 and 37 psu, where psu is the abbreviation for precisionsalinity units, for a flat ocean surface and an incidence angle of 37.8°, as derived from Klein andSwift (1977). The incidence angle corresponds to the middle beam of the Aquarius instrument (Figure5 from Lagerloef et al. (2008), C© 2008, courtesy of Gary Lagerloef, with permission of ElsevierScience.)

The figure also shows that, at a given SST, the brightness temperature decreases as thesalinity increases. Given the oceanographic requirement that surface salinity be determinedto within 0.2 psu, for retrieval purposes, the curves suggest that TB must be determined towithin about 0.1 K.

For three values of SST, Figure 9.17 shows the dependence of V-pol brightness tem-perature on salinity. For each SST, the figure shows that TBV has a linear dependence onsalinity, where the slope at 30 °C is more than twice that at 0 °C. Because the sensitivityof brightness temperature to changes in salinity is greatest for warm water, the accuracy ofthe salinity retrieval is greatest near the equator. Because the emissivity also depends onsurface roughness, which is measured with an active radar, the discussion of the Aquariussalinity retrieval is postponed until Chapter 14.



T BV

(K)

Salinity (psu)30 32 34 36 38 40

108

106

104

102

110

15 oC0 oC 30 oC

Fig. 9.17. The dependence of V-pol brightness temperature on surface salinity for an incidence angleof 34° and for the three values of SST shown on each curve, 0 °C, 15 °C and 30 °C. The figure showsthat the sensitivity to changes in salinity is greatest warm water (0.7 K psu−1) and least for cold water(0.3 K psu−1). (Figure adapted from Aquarius (2013b), courtesy of NASA.)

9.6 Open ocean algorithms

The above discussion shows that SSS is most sensitive to observations at 1.41 GHz, SSTto the V-pol observations in the range 6–10 GHz, and, from Figure 9.11, U to H-polobservations at f 10 GHz. Given the relative transparency of the atmosphere for f 10 GHz, a hypothetical instrument for retrieval of SS, TS and U could be constructed using1.41V (SS), 6.6V (TS) and 10H (U). At these frequencies where the effects of water vaporand cloud liquid water are negligible, the combined measurements yield three equationsfor three unknowns: U, TS and SS.

The further determination of the water vapor V, cloud liquid water L and rain rate RR

requires additional channels at about 19, 21 and 37 GHz. Specifically, the retrieval of smallconcentrations of water vapor depends on a V-pol measurement in the immediate vicinityof the 22-GHz absorption peak, while, for larger concentrations, the retrieval depends onchannels located on the shoulders of the peak at 18, 19 or 24 GHz. For retrieval of L,Figure 9.5(a) shows that, because the dependence of t on L increases with f, an appropriatefrequency for its retrieval is 37 GHz. Finally, by masking pixels with large attenuations ateither 37 or 85 GHz, regions of heavy rain are excluded. This qualitative discussion givesa general description of an algorithm for retrieval of all of the above variables. With this asbackground, the next sections describe the open ocean algorithms.

9.6.1 Details of the open ocean algorithms

For the SSM/I, TMI and AMSR-E instruments, Hilburn and Wentz (2008) and Gentemannet al. (2010b) describe the algorithms used to generate the open ocean data sets, while


9.6 Open ocean algorithms 289

Meissner and Wentz (2006b) describe the WindSat algorithms. With the postponement ofthe discussion of the WindSat wind direction retrieval to Section 9.7, the five ocean andatmospheric variables recoverable by these algorithms include the sea surface temperatureTS, scalar wind speed U at a height of 10 m, columnar water vapor V, columnar cloud liquidwater L and surface rain rate RR. The retrieval of these variables depends on the satelliteobservations, in situ data sets and auxiliary data sets such as the vector winds generatedby the NCEP numerical weather prediction models and, for the SSM/I retrievals, the dailyReynolds SST.

The instruments that generate the full data sets include TMI on TRMM, AMSR-E and AMSR2, WindSat, the forthcoming GMI and other instruments that include the6.7- and 11-GHz channels. Gentemann et al. (2010b) describe the SST algorithm in detail.As Figure 9.15 shows, the V-pol brightness temperature TBV is most sensitive to changesin surface temperature between 4 and 11 GHz, with a maximum at about 6 GHz and asmaller sensitivity at 11 GHz. In this retrieval, the contributions from surface roughnessand the atmospheric emission and absorption must be removed from the received brightnesstemperatures.

For the observational frequencies used by the TMI, AMSR-E, AMSR2, WindSat andGMI, however, the signatures of the surface roughness and the atmospheric emission andabsorption are sufficiently distinct that they can be removed (Gentemann et al., 2010b).In the following, Section 9.6.2 addresses the SSM/I algorithms for observations between18 and 85 GHz; Section 9.6.3 addresses the algorithms for instruments that also use the6.9- and 11-GHz bands, such as AMSR, TMI and WindSat.

9.6.2 SSM/I algorithms

Wentz (1997), Wentz and Spenser (1998) and Hilburn and Wentz (2008) describe thealgorithms used to generate the open ocean SSM/I data sets. These algorithms retrieve theocean wind speed U, atmospheric water vapor V, cloud liquid water L and rain rate RR. Foreach pixel, this retrieval uses the 19V, 22V, 37V and 37H bands, yielding four equations forL, V, U and RR. Because, as Table 8.3 shows, the 37- and 22-GHz bands have a finer surfaceresolution than the 19-GHz bands, the higher-frequency bands are spatially averaged sothat all bands have the same pixel size. Over the SSM/I lifetime, testing and refinement hasimproved the algorithm. As RSS (2013c) states, “This algorithm is a product of 20 yearsof refinements, improvements, and verifications”.

Because the SSM/I algorithm cannot retrieve SST, instead, the algorithm uses the dailyReynolds SST (Hilburn and Wentz, 2008). The reason why the Reynolds SST must be usedis that, as Figure 9.15 shows for 19–37 GHz, the dependence of TB on TS is too weak toallow retrieval of TS, but too strong to ignore (Wentz, 1997). If this brightness temperaturedependence on TS were ignored, it would produce significant errors in the other retrievedvariables.

As Section 9.2.3 discusses, liquid water in the atmosphere has three forms, water vapor,cloud liquid water and surface rain rate, where in these algorithms, the frozen forms of



water such as snow, hail and ice particles are not retrieved. Wentz and Spencer (1998) andHilburn and Wentz (2008) discuss the retrieval of these quantities. For the case of no rain,the algorithm retrieves wind, water vapor and cloud liquid water from three channels, 22V,37V and 37H. The columnar water vapor L ranges from 0 to about 0.25 mm and, at 37 GHz,a 0.1-mm change in L yields an H-pol brightness temperature change of TBH ≈ 9K(Wentz, 1997). The extension of the algorithm to include rain rate involves the replacementat 37 GHz of the transmittance of cloud liquid water with the joint transmittance of rainand cloud liquid water. The 19-GHz V-pol band also retrieves the transmittance of cloudand rain liquid water, and yields an additional equation for the four desired variables. Forlight and moderate rain, the wind is retrieved, but for rain rates greater than about 5 mmh−1, the surface is obscured and wind can no longer be retrieved.

The difference between rain and cloud liquid water lies in their drop size, where rain-drops are much larger than cloud droplets. Because the small cloud droplets are Rayleighscatterers, their transmittance has a known dependence on frequency for the 19-, 22- and37-GHz bands, while the transmittance of the rain droplets tends toward Mie scatter. AsSection 9.2.3 describes, this difference, where cloud droplets are Rayleigh scatterers andrain droplets are Mie scatterers, allows separation of the two variables. Because the rain-storm of interest may be smaller than the instrument FOV, what is called a beam-fillingcorrection is applied. The satellite rain rate is then tuned against the surface rain ratesderived from surface observations made from islands and the Goddard Profiling Algorithm(GPROF) data set (Hilburn and Wentz, 2008). From Gentemann et al. (2010c), the predictedrain rates among the SSM/I, TMI and AMSR-E agree within 3% and approximately agreewith the results from island rain gauges.

For winds and surface roughness, to eliminate the variability in the surface emissivityassociated with the angle between the instrument pointing direction and the wind direction,and to improve the accuracy of the wind speed retrieval U, the wind direction is taken fromthe NCEP numerical forecast. Thus, the use of the daily Reynolds SST and the NCEP winddirections allows solution for the four variables. In addition to the RR tuning describedabove, the values of U are tuned against buoy vector winds, while V and L are tunedagainst a global array of radiosonde measurements made from island stations. From Wentz(1997), the rms error in U is about 0.9 m s−1, that in V about 1.2 mm, and that in L about0.025 mm, with additional but smaller systematic offsets of respectively 0.3 m s−1, 0.6 mmand 0.005 mm.

As an example of these retrievals, for March 20, 2012, Figure 9.18 shows a compositeimage of U, V, L and RR for the ascending SSM/I swaths taken at 1800 local time. Theseswaths, which cover more than half the ocean, were chosen because they are closest intime to the MODIS image in Figure 4.2. The top image gives the wind magnitude U and,similarly to Figure 4.2, shows storms around Antarctica, a cyclonic storm in the Gulf ofAlaska, a strong cyclonic storm in the North Atlantic and another storm south of Iceland.The second gives the columnar water vapor V and shows that the vapor is concentrated in thetropics, especially in the vicinity of Indonesia and New Guinea, and in the storm-associatedbands of vapor extending from the equatorial region into the temperate and sub-polarlatitudes. The third image gives the cloud liquid water L and shows that the regions of



Cloud liquid water

Wind speed

Water vapor

Rain rateRain rate

30+

20

10

25

15

5

0

(m s

–1)

75

60

45

30

15

0

(mm

)

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1.5

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0.5

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(mm

)25

20

15

(mm

h–1

)

10

5

0(no rain)

Fig. 9.18. Composite image of the distribution of SSM/I wind magnitude, water vapor, cloud liquidwater and rain rate for March 20, 2012. The swaths are the ascending evening passes at 1800 localtime. The color bars to the right give the scale for the distribution of each variable; gray is land, whiteis sea ice, black is missing data or the masked rain rate. On the scales for cloud liquid water and rainrate, the color purple marks the regions with no liquid water or no rain. The letters on the cloud liquidwater figure mark features common to the same day MODIS visible image in Figure 4.2. (SSM/I dataare produced by Remote Sensing Systems and sponsored by the NASA Earth Science MEaSUREsDISCOVER Project. Data are available at www.remss.com. Used with permission.) See color platesection.

storm-associated strong winds are regions of enhanced L. Finally, the fourth panel showsthe rain rate, which is approximately correlated with water vapor and cloud liquid water. Inthis image, the white letters mark cloud patterns and storms common to this image and toFigure 4.2.

http://www.remss.com



Fig. 9.19. The V-pol brightness temperature at 7 and 11 GHz plotted against SST. The horizontal linesshow the error in SST due to a 0.5-K noise in the received brightness temperature. The sensitivityof SST to changes in TBV decreases for 11 GHz at colder SSTs, resulting in larger errors and asmall positive bias. (Figure 1 from Gentemann et al. (2010b), figure courtesy of Chelle Gentemann,copyright IEEE, used with permission.)

9.6.3 TMI, AMSR-E, AMSR2 and WindSat algorithms

Because TMI has a channel at 10.7 GHz and AMSR-E has channels at 6.9 and 10.7 GHz,these instruments retrieve a cloud-independent SST. Although the SMMR channels at 6and 10 GHz demonstrated the feasibility of retrieving SST and generated some scientificresults (Liu, 1988), because of problems with low resolution, sidelobe contamination andinstrument noise that Section 8.6.1 describes, the SST retrieval had large errors. Conse-quently, the TMI 10.7-GHz channels provided the first real opportunity to retrieve SST,with additional opportunities provided by the AMSR-E and WindSat 6.9-GHz channels.The importance of the 6.9- and 10.7-GHz V-pol channels is that they are relatively insen-sitive to atmospheric variability while having the greatest sensitivity to SST. At the sametime, the H-pol channels are less sensitive to SST, while being more sensitive to windspeed.

Figure 9.19 illustrates the problems in using the 11-GHz channel for SST retrieval(Gentemann et al., 2010b). The figure shows that, as the SST decreases, the sensitivityof the 11-GHz channel decreases, while the sensitivity of the 7-GHz channel is nearlyconstant. The standard deviation in the SST retrieval is shown by the horizontal lines andis that associated with a 0.5-K noise in the retrieved brightness temperature. Althoughthis is five times the actual AMSR-E noise, it was chosen to expand the variability in theerror. Examination of Figure 9.19 shows that the 11-GHz retrieved temperatures have larger



errors at high latitudes than the 7-GHz. Away from high latitudes, at an SST of 20 °C, andusing the actual AMSR-E noise of 0.1 K, the error for the two channels is about the sameat 0.2 K. As SST decreases, the accuracy decreases for both channels, but at a faster ratefor 11 GHz, such that, at −1 °C, the 11-GHz accuracy is 1 K, and the 7-GHz is 0.3 K.

Gentemann et al. (2010b) describe the AMSR-E SST retrieval. In combination withan atmosphere based on 42,000 radiosonde soundings from ships and small islands, theReynolds annual SST climatology and simulated wind speeds of 0–40 m s−1 with directionsranging from 0° to 360°, they use what they call a “localized” radiative transfer model. Inthis simulation, the SST is varied within ±5 K of the Reynolds climatology. Then becausethe relation between brightness temperatures and wind and SST is nonlinear, the algorithmis subdivided into 1440 local sub-algorithms that are separately valid for 38 SST intervalsbetween −3°C and 34°C and for 38 wind intervals between 0 and 37 m s−1. This largenumber of overlapping algorithms that are applicable to a small subset provides continuityover the temperature and wind range of interest and reduces the effects of nonlinearities.

Regarding the accuracy of this retrieval, for June 2002 to December 2008, comparisonof the AMSR-E SST with the Reynolds SST yields a standard deviation between the twodata sets of about 0.5 K (Gentemann et al., 2010b, Figure 4a). Larger errors occur at thelocations of the western boundary currents such as the Kuroshio and Gulf Stream, for theAntarctic Circumpolar Current and at high latitudes. In spite of the localized algorithms,the error in SST retrieval is sensitive to increasing wind speed. This is most apparent withthe 11-GHz retrieval, where the error ranges from 0.5 K at zero wind speed and an SST of30 °C, to 2 K at 15 m s−1 and 0 °C. In contrast, although the error in the 7-GHz algorithmincreases with wind speed and SST, it remains between 0.5 K and 1 K (Gentemann et al.,2010b, Figure 7).

Regarding the general accuracy of the AMSR-E retrieval, for each retrieved variable,Table 9.3 shows the relevant frequencies, the reasons for missing data, what the retrievaldoes not include, and its accuracy and spatial resolution. For the winds, the table listsboth a low- (WSPD-LF) and a medium-frequency (WSPD-MF) wind speed retrieval. TheWSPD-LF is based on frequencies that are 10.7 GHz corresponding to AMSR-E andTMI; the WSPD-MF, on frequencies that are 18.7 GHz corresponding to AMSR-E andSSM/I. Table 9.3 shows that, because of the sidelobe contamination, the algorithms breakdown within a FOV of land. Also, the SST retrieval breaks down under strong winds, heavyrain and near sea ice from sidelobe contamination; the winds and water vapor retrievalsbreak down in heavy rain.

For January 2010 and 2011, where January 2010 is in the middle of the 2009–10 ElNino and January 2011 is in the subsequent La Nina, Figure 9.20 shows a composite imageof the weekly averaged AMSR-E-retrieved values of SST, U, V, L and RR. Comparisonof the two sets of images shows the differences between El Nino and La Nina conditions.The El Nino SST image shows a warm equatorial Pacific with little upwelling off SouthAmerica. In contrast, the La Nina image shows cold upwelling along the South AmericanPacific coast with a cold equatorial tongue extending from the coast into the central Pacific.Between these images, the decrease in equatorial temperatures is about 7 K.



Table 9.3. The AMSR-E data products and their limitations. In all cases, the variables areplotted on a 0.25 × 0.25 latitude/longitude grid. WSPD-LF is wind derived at low

frequency; WSPD-MF is wind derived at the medium frequency.

VariableFrequency(GHz)

Missing dataoccurs for

Retrieval doesnot include Accuracy Resolution

SST 6.9, 10.7 U > 20 m s−1; sunglint, rain,within 75 km ofland, sea ice

– 0.5 Ka 75 km

WSPD-LF 10.7 and above Sun glint, rain,within 50 km ofland, sea ice

– 0.5 m s−1b 50 km

WSPD-MF 18.7 and above Sun glint, rain,within 50 km ofland, sea ice

– 0.5 m s−1b 30 km

V 19, 23.8, 36.5 Heavy rain, within25 km of land

– 2 – 0.5 mmb 30 km

L 19, 23.8, 36.5 Within 25 km ofland

RR, snow, iceparticles

0.025 mmc 30 km

RR 19, 23.8, 36.5 Within 25 km ofland

L, snow, iceparticles

3%d 30 km

Adapted from RSS AMSR-E (2013).a Gentemann et al. (2010b).b Gentemann et al. (2010c), from intercomparison of different satellite algorithms.c Wentz (1997).d Hilburn and Wentz (2008), from intercomparison of different models.

Along the equator in the central Pacific, the El Nino winds are weaker than La Nina,while being stronger in the North Atlantic. The La Nina winds are slightly stronger inthe central and north Pacific. The El Nino water vapor image shows a nearly uniformdistribution of large values of V slightly north of the equator and south along the SouthAmerican coast. These larger values of V are correlated with the warmer equatorial SSTs,which produce more evaporation. For La Nina, the cold equatorial SSTs mean that theevaporation and the corresponding values of V are smaller. Also for La Nina, and in partbecause of the easterly equatorial winds, the maximum values of V shift to the westernPacific and Indian Ocean. For cloud liquid water in the Pacific, both the El Nino and the LaNina images show that L is concentrated in the doldrum region located 4° N of the equator,while the equator remains cloud-free. For both sets of images, the distribution of rain rate(not shown) follows that of the cloud liquid water, where, during La Nina, stronger rainsoccur in the eastern and northern Pacific. As Boening et al. (2012) show, and as Section12.9.3 discusses, the global change in precipitation patterns that accompanied the 2012 LaNina contributed to a 5-mm decrease in the global sea level.


9.7 WindSat retrieval of wind speed and direction 295

–14

14

24

34

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T (o

C)

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20

10

30

40

Win

ds (

m s

–1)

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apor

(m

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id w

ater

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0.5

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January 2010 El Niño January 2011 La Niña

Fig. 9.20. A composite image of the weekly averaged AMSR-E-retrieved values of SST, U, V andL for weeks ending on 2 January 2010 and 1 January 2011, where the 2010 image is from themiddle of the 2009–10 El Nino and the 2011 image is from the subsequent La Nina. The winds arefrom the low-frequency AMSR retrieval. On the images, the white line marks the equator. Blackareas over the ocean are regions of heavy rain. See the text for further description. (AMSR-E dataare produced by Remote Sensing Systems and sponsored by the NASA Earth Science MEaSUREsDISCOVER Project and the AMSR-E Science Team. Data are available at www.remss.com. Usedwith permission.) See color plate section.

9.7 WindSat retrieval of wind speed and direction

As Section 8.6.5 describes, WindSat is a polarimetric microwave radiometer designed toretrieve vector winds both from V- and H-pol measurements and from measurements of allfour Stokes parameters (Table 8.8). Although the primary mission of WindSat is to retrievethe wind speed and direction, similarly to AMSR-E, it also retrieves quantities such as SST,V, L andRR (Bettenhausen et al., 2006). WindSat was designed to retrieve winds from asingle-look procedure involving all four Stokes parameters and from a two-look procedurebased on V-pol and H-pol measurements taken in fore and aft directions. Since the forwardswath width is about 950 km and the aft swath width is about 350 km, its wind retrievalsgenerally use data from the wider forward swath.




For winds, there are two kinds of WindSat retrievals, namely the rain-free and all-weather models. The rain-free case is derived from a radiative transfer model that retrievesthe desired variables for wind speeds of 0 to 20 m s−1 (Meissner and Wentz, 2006b;Bettenhausen et al., 2006). Except for wind direction, this model is based on the AMSR-Eretrievals, which use the high-frequency channels to estimate the water vapor and cloudliquid water, and the low-frequency channels to retrieve SST and wind speed. After the thirdStokes parameter has been corrected for Faraday rotation, the wind direction is retrievedusing the 10.7-GHz Stokes parameters. For validation, the wind speed and direction arecompared against the NCEP GDAS fields that are taken within 30 min of the WindSatobservations. For cloud liquid water greater than 0.18 mm, a rain mask is applied. Forvalues of both models and for U < 6 m s−1, because of the low signal levels of the thirdand fourth Stokes parameters, the algorithms provide poor directional performance.

In contrast to the rain-free approach, the all-weather algorithm uses a statistical approachthat grew out of problems with the modeling of radiative transfer in the presence of rain(Meissner and Wentz, 2009). These problems occur because of the large variability ofrainy atmospheres, which causes serious difficulties in the retrieval and modeling of thebrightness temperatures. In rain, the brightness temperatures depend on cloud type, thedroplet size distribution and the distribution of rain within the observational footprint.At higher frequencies, whether Rayleigh or Mie scatter applies depends on the unknowndroplet size distribution. Another problem is that the brightness temperature signals of rainand wind are similar, so that an increase in rain can be interpreted as an increase in windspeed. These problems strongly suggest that, in rain, a radiative transfer approach will notwork for wind retrieval.

Because of these difficulties, the all-weather wind retrievals use an innovative statisticalapproach valid for wind speeds greater than 20 m s−1 and for rain (Meissner and Wentz,2009; Ricciardulli and Wentz, 2012a). Because of the difficulties of modeling brightnesstemperatures under rainy conditions, Meissner and Wentz (2009) use a postlaunch statisticalalgorithm that combines WindSat and surface observations from hurricanes. For theseretrievals, the authors take advantage of the 6.9- and 10.7-GHz bands that are sufficientlysensitive to wind speed while being insensitive to rain.

In this approach, the algorithm is trained from a comparison of the two match-up datasets that are measured nearly simultaneously under rainy conditions: the WindSat brightnesstemperatures and the surface wind speeds. This approach forces the algorithm to use channelcombinations that respond to surface winds while reducing the signal from rain. The hopewas that the spectral differences in rain and wind signals among the different frequencybands would allow the wind retrieval, albeit at a lower accuracy than with the rain-freealgorithm.

As a source of high wind speeds, Meissner and Wentz (2009) use data from the NOAAHurricane Research Division (HRD). Specifically, they use data from 17 hurricanes thatoccurred between 2003 and 2004, where the winds are from ship, aircraft, buoy and satelliteobservations as well as from pressure maps. Although the HRD data set was not designed asa validation source, it is a useful source of high wind data. If these winds occur within 3 h ofthe satellite overpass, they treat the two observations as simultaneous. In their comparison,



Table 9.4. The bands used in the retrieval of the different WindSat products.

Frequency (GHz)

6.8(V, H)

10.7(all Stokes)

18.7(all Stokes)

37.0(all Stokes)

Resolution (km) 50 32 22 10ProductSST Y Y – –Wind speed (no rain) Y Y Y –Wind speed (rain) Ya Ya – –Wind direction – Yb – –Water vapor Y Y Y –Cloud liquid water Y Y Y YRain rate – – – Y

Adapted from Meissner and Wentz (2009) and Meissner et al. (2010).a The dominant portion of this algorithm is a linear combination of the H-pol 6.8-

and 10.7-GHz brightness temperatures.b For wind speeds >6 ms−1 s−1.

the eye of the hurricane in the surface data is visually adjusted to match the eye observedby WindSat. The data set has 48,000 co-located points; the wind speeds range from 0 toabout 45 m s−1, although with only 166 data points at speeds >40 m s−1.

Meissner and Wentz (2009) develop two models: a high wind speed retrieval modelderived from the HRD winds, and a global wind speed model that is valid for all conditions.For band combinations that exclude the 6.9- and 10.7-GHz bands, the high wind modelworks with a degraded performance; the global model requires these channels. For boththe rain and rain-free models, Table 9.4 shows the WindSat bands used in the retrieval ofthe different geophysical products. For no rain, the wind speed is retrieved by frequencies6.8 GHz; while for rain, only the 6.9- and 10.7-GHz bands are used in the retrieval. Eitherfor rain or for no rain, the wind direction is retrieved from 10.7-GHz Stokes parameters,water vapor from the 6.9-, 10.7- and 18.7-GHz bands, cloud liquid water from all fourbands, and rain from 37 GHz. For rain, the retrieval of wind speed primarily involvesthe 6.9- and 10.7-GHz bands, the retrieved wind direction involves the 10.7-GHz Stokesparameters, which as Section 9.2 shows, are among the bands least sensitive to rain. It iscritical to note, however, that the algorithm performance degrades with rain rate.

For the 6.9- and 10.7-GHz H-pol and V-pol bands, Figure 9.21 shows the dependenceof the isotropic brightness temperature difference (TB) on the HRD wind speed, wherethe TB are calculated from the observed emissivities times a nominal surface brightnesstemperature of 290 K (Meissner and Wentz, 2009, Figure 1). The range of the HRD windspeeds is between 10 and 45 m s−1; the observations are averaged into wind-speed binswith widths of 4 to 6 m s−1. For speeds less than 10 m s−1, Figure 9.11 shows the emissivitydependence.



0 402010HRD wind speed (m s–1)

30

20

10

30

0

20

10

30

0

40

50

0 402010 30HRD wind speed (m s–1)

0 402010 30 0 402010 30

T

B (K

)Δ

T

B (K

)Δ

6.8V

6.8H 10.7H

10.7V

Fig. 9.21. The wind-induced isotropic emissivities of the sea surface expressed as brightness temper-atures for the 6.6- and 10.7-GHz WindSat V- and H-pol bands as function of the HRD wind speed.The solid lines are the emissivity values from Meissner and Wentz (2006b) linearly extrapolated from18 m s–1 to higher wind speeds. The retrieved emissivities are multiplied with a nominal surfacetemperature of 290 K. The emissivities are averaged into wind-speed bins with widths of 4–6 m s−1,the dots are the averages, the vertical lines are the standard deviations. (Redrawn from Figure 1,Meissner and Wentz (2009).)

The diagonal solid lines are the emissivity values from Meissner and Wentz (2006b)that are linearly extrapolated from 18 m s−1 to the higher wind speeds; the dots showthe average emissivities, the vertical lines show the standard deviations. Within the errorbars, the dependence on emissivity is approximately linear through 45 m s−1. This linearityoccurs because of the increase in foam area with wind speed, so the emissivity alsoincreases nearly linearly, with some evidence of saturation above 35 m s−1. The calculatedemissivity is consistent with a linear extrapolation of the radiative transfer model, where,at all frequencies, the H-pol emissivities are more sensitive than the V-pol to increases inwind speed.

For wind speeds greater than 7 m s−1, the rms difference in direction between theWindSat and GDAS winds is less than 20° (Yueh et al., 2006; Meissner and Wentz, 2009).For rain rates between 0 and 10 mm h−1, and for speeds greater than 8 m s−1, the directionalaccuracy decreases nearly linearly from 10° to 30° (Meissner and Wentz, 2009, Figure 11).This accuracy decrease is due to the heavy attenuation associated with rain. Regarding theaccuracy of the wind speed retrieval, compared with the HRD winds, its accuracy rangesfrom 2 m s−1 for no rain to 3 m s−1 for rain rates between 0 and 5 mm h−1 and 4 m s−1 forrain rates of 5–10 mm h−1.



Win

dSat

win

d sp

eed

(m s

–1)

GFDex Aircraft wind speed (m s–1)

0 2520105 150

10

20

30

30

Fig. 9.22. Comparison of the WindSat HRD-winds with aircraft winds measured from a turbulenceprobe from the Greenland Flow Distortion experiment (GFDex). The different symbols are theresults from different flights; the solid line is the line of perfect agreement; the dashed line is theleast-squaress fit. The bias between the two data is 1.5 m s−1, the rms difference is 1.35 m s−1, thecorrelation coefficient is 0.94, the slope of the least-squares agreement is 0.957 and the rms differencein wind direction is 12.1°. (Redrawn from Meissner and Wentz (2012), Figure 18 (left panel); rmswind direction difference from Meissner et al. (2010).)

As a validation of the high wind speed algorithm, Figure 9.22 compares their modelresults with field observations from the Greenland Flow Distortion experiment (GFDex)aircraft meteorological flights (Renfrew et al., 2009; Meissner et al., 2010; Meissner andWentz, 2012). The GFDex flights took place between February and March 2007 in thevicinity of the Denmark Strait between Iceland and Greenland, and in the Irminger Sea southof the strait. The flights took place during cold-air outbreaks, where the wind observationswere taken with a turbulence probe at heights of 30–50 m above the sea surface, thenadjusted to the 10-m height. Over a six-day period, GFDex flew about 150 separate runs.In this comparison, the aircraft winds were the average of a 2-min run that was equivalentto a 12-km spatial average.

These 2-min averages of wind speed and direction ranged in speed from 5 to 28 m s−1 andwere matched to the surface field-of-view of the WindSat retrieval. For this comparison, theWindSat algorithm used 10.7 GHz as its lowest frequency, so that its resolution was 35 km.The comparison included one aircraft run with light rain, shown as triangles on Figure 9.22.The figure shows that an excellent correlation exists between the aircraft and WindSat datasets. The bias shows a positive offset of 1.5 m s−1; this may be associated with land or seaice contamination in the 10.7-GHz field-of-view. When the same comparison was done for arain-free algorithm based on the 18.7-GHz bands and above, the bias dropped to 0.9 m s−1



(Meissner and Wentz, 2012, Figure 18). For the two data sets in Figure 9.22, the rmsdifference in wind speed is less than 1.5 m s−1, and the rms difference in wind directionis 12.1°. The figure suggests that, for wind speeds less than 30 m s−1, the HRD WindSatalgorithm is valid.

9.8 Sea ice algorithms

The determination of sea ice extent and ice type is one of the great successes of the passivemicrowave imagers. This section discusses the form of the RTE used in the polar atmo-sphere, describes the algorithms used for the retrieval of ice properties and gives examples.

For the polar regions, the RTE in Equation (9.1) can be further simplified. First,because over winter pack ice the polar atmosphere is very dry, Figure 9.4 shows thattvap 1. Second, the extraterrestrial brightness temperature is generally neglected (Cava-lieri et al., 1984). These simplifications mean that, over winter polar pack ice, Equation (9.1)reduces to

TB = eTS (9.7)

In (9.7), e represents the emissivity of open water and the different ice types, where TS

is the water and ice surface temperature. Although the assumptions underlying Equation(9.7) break down at the ice edge where liquid water and water vapor become important, thissimple formulation permits the retrieval of many ice properties. These include time seriesof the areal sea ice extent in the Northern and Southern Hemispheres, and, in the NorthernHemisphere, the relative concentrations of open water, first-year ice and multiyear ice.

The SMMR frequencies used in this retrieval are 18 and 37 GHz; the SSM/I frequenciesare 19, 37 and sometimes 85 GHz. The advantage of the two lower frequencies is thatthey are independent of weather; the 85-GHz frequency has a better resolution but needs aweather correction. The following concentrates on algorithms derived from 19 and 37 GHz;the simplest of these is the NASA Team (NT) algorithm, this 25-km-resolution algorithm isused by the National Snow and Ice Data Center (NSIDC) for their time series of polar seaice properties, which begin in 1978 with SMMR (NSIDC, 2013a). Markus and Cavalieri(2009) describe the NASA Team-2 (NT-2) algorithm that makes use of the AMSR 85-GHzchannel and has a better resolution.

As Comiso et al. (1997) describe in detail, two of the algorithms used in this retrievalare the NASA Team and Bootstrap algorithms. Each of these algorithms uses differentinstrument channels to take advantage of the frequency-dependent emissivity differencesthat exist between open water and the pack ice. As Chapter 2 discusses, for the Arctic, thesecategories include first-year and multiyear ice, where first-year ice is less than one year oldand multiyear ice has survived one summer. For the Antarctic, the ice categories are calledtype A and type B ice, where at this time the kinds of physical ice corresponding to typesA and B are not known. The reason why the Arctic ice types have different emissivities isthat the upper surface of first-year ice is saline, while the surface of multiyear ice is nearlyfresh and contains many air bubbles.


9.8 Sea ice algorithms 301

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.24 6 8 10 20 3040 100

V

H

V

V

H

H

FY

Water

MY

Water

Frequency (GHz)

Em

issi

vity

(50

o in

cide

nce

angl

e)

SMM/I frequenciesSMMR frequencies

Fig. 9.23. Dependence of the emissivity of the Northern Hemisphere sea ice on frequency for theSMMR and SSM/I frequencies. In the figure V and H are polarization, Water refers to open water, FYto first-year ice, MY to multiyear ice. (Figure 1 from Comiso et al. (1997), C© 1997, with permissionfrom Elsevier Science.)

For both hemispheres, the large emissivity differences between open water and seaice simplify the retrieval. For SMMR and SSM/I and beginning with the Arctic, Figure9.23 shows the dependence of the emissivities of open water, first-year (FY) ice andmultiyear (MY) ice on frequency and polarization. Examination of the figure shows thatthe difference between the V-pol and H-pol emissivities of open water is much larger thanfor first-year or multiyear ice, and that the open water emissivities increase with frequency.The ice emissivities are very different. For first-year ice, the V- and H-pol emissivitiesare large, almost equal to each other and nearly independent of f. For multiyear ice, theV-pol emissivity is greater than the H-pol, where both emissivities decrease with increasingfrequency. Comparison of the first-year and open water emissivities shows that, if thesurface temperatures of open water and first-year ice are at the seawater freezing point,the open water brightness temperature is smaller than that of first-year ice. For multiyearice with the same surface temperature as open water, at low V-pol frequencies, ice has thegreater brightness temperature, but at high V-pol frequencies, open water is brighter. Thesedifferences in the responses of the emissivities to frequency and polarization form the basisfor the algorithms.

For 19V, 19H and 37V, Table 9.5 lists some characteristic brightness temperatures forthe three Arctic categories. The table also lists the values of two variables that are functions



Table 9.5. Northern Hemisphere brightnesstemperatures at various frequencies (GHz) foropen water, first-year (FY) ice and multiyear

(MY) ice used in the SSM/I algorithm. Values ofthe polarization ratio PR and gradient ratio GR

are listed too.

f (GHz) Open water FY ice MY ice

19V 177.1 K 258.2 K 203.9 K19H 100.8 K 242.8 K 203.9 K37V 201.7 K 252.8 K 186.3 KPR (×103) 275 31 45GR (×103) 65 −11 −90

Adapted from Table 1 of Comiso et al., (1997).

of the brightness temperatures, the polarization ratio PR and the gradient ratio GR, whichare used in the NASA algorithms. The variables PR and GR are defined as follows:

PR = (TB19V − TB19H)/(TB19V + TB19H)

GR = (TB37V − TB19V)/(TB37V + TB19V) (9.8)

The advantages of using PR and GR are that to first order they are independent of the icesurface temperature; further, the use of the V-pol terms in GR minimizes its wind speeddependence.

The success of these algorithms is due to the large temperature differences betweenthe different ice and water categories. For example, Table 9.5 shows that the brightnesstemperature difference TB19V between open water and first-year ice is 80 K, and thatbetween open water and multiyear ice is 30 K. Similar large differences occur at the otherfrequencies and for PR and GR. For comparison, the oceanic range of SST is about 30 K,which from Figure 8.6 corresponds to a TB19V of about 15 K. Since the TB19V betweenopen water and sea ice is four times this value, retrieval of the areal ice extent is relativelysimple.

For individual pixels, the algorithms retrieve ice concentrations in the following way.Consider the simplified case of just two ice categories, open water and first-year ice. In thiscase, the algorithm can be written in terms of the relative concentrations CW of open waterand CI of ice, where CI = 1 − CW. If TBW is the open water brightness temperature, andTBI is the sea ice brightness temperature, TB becomes

TB = TBWCW + TBICI (9.9)

If, within each pixel, the brightness temperatures of open water and ice are known, theirrespective concentrations can be calculated.



0.02 0.10 0.18 0.26 0.02 0.10 0.18 0.26

GR

PR

OW OW

0.10

0.08

0.06

0.04

0.02

0

–0.02

–0.04

–0.06

–0.08

–0.10

–0.12

FY

MY

A

B

(a) (b)Weather Weather

PR

Fig. 9.24. The PR, GR plots of data from (a) the Northern Hemisphere ice cover and (b) the SouthernHemisphere. The solid lines represent the curves used to define the ice concentrations in the NASATeam algorithm. The small numbers on the plots are the logarithms of the number of observations ateach point. See the text for further description. (Figure 2 from Comiso et al. (1997), C© 1997, withpermission from Elsevier Science.)

In a similar manner and depending on hemisphere, the NASA Team algorithm uses PR

and GR to retrieve the concentrations of open water and two classes of ice. For the Teamalgorithm and in both hemispheres, Figure 9.24 shows plots of PR and GR. On the figure,the small numbers represent the base-10 logarithm of the number of observations, whilethe curved lines make up the triangles used to define the ice concentrations. The trianglevertices are the algorithm tie-points and represent 100% concentrations of the indicatedice type or water. For the Northern Hemisphere, the tie-points consist of open water, first-year and multiyear ice; for the Southern Hemisphere, the tie-points consist of open waterand types A and B ice. In the upper portion of both figures, the many points to the left ofthe open water tie-points are a weather effect that is associated with the atmospheric watervapor and liquid water at the ice margins. This effect is often filtered out by ignoring valuesabove a fixed GR threshold (Gloersen and Cavalieri, 1986). When, for any pixel, the valuesof PR and GR lie off the triangle, their location relative to the triangle permits solution ofthe relative contribution of each type.

Problems with the algorithms are as follows. First, as the air temperature rises abovefreezing during late spring and early summer, the ice surface becomes covered with meltponds that contain nearly fresh water and above the ice the amount of atmospheric watervapor increases. The melt ponds and the associated water vapor cause the algorithm to gen-erate apparent open water in the ice interior. Second, at the ice edge that is a mixture of ice,ocean and atmospheric water vapor, the algorithm also breaks down. In the Team algorithm,the ice edge problem is dealt with by choosing the edge as the 30% open water contour.



100%

1979–2010

80%

60%

40%

20%

<12%

100%

80%

60%

40%

20%

<12%

1979–2010

1979–20101979–2010

Fig. 9.25. For the period 1979–2010, the average Arctic sea ice extent for March (maximum) andSeptember (minimum), and the average Antarctic ice extent for February (maximum) and September(minimum) as derived from passive microwave. The color bar gives the ice concentration in percent.Gray is land, light blue is open water. See the text for further description. (Antarctic image, Figure 1from Parkinson and Cavalieri (2012); Arctic image, Figure 1 from Cavalieri and Parkinson (2012);courtesy of Claire Parkinson and Donald Cavalieri, not subject to US copyright.) See color platesection.

For an example of images processed with the SSM/I Team algorithm, Figure 9.25 showsthe March and September monthly mean ice extent for the Arctic and Antarctic. In bothhemispheres, the images show the respective maximum and minimum ice extent. In winter,the Arctic images show that marginal seas such as the Bering Sea, Sea of Okhotsk, HudsonBay and the peripheral seas of the Siberian coast are ice-covered, whereas in summer, they



Southern Hemisphere

(a) Monthly averages

(b) Monthly deviations

Sea

ice

exte

nt (

106

km2

)S

ea ic

e ex

tent

(10

6 km

2 )

1978

17,100 ± 2300 km2 yr–1

Fig. 9.26. The monthly averaged series of the Northern Hemisphere sea ice extent for 1978–2010: (a)monthly averages and (b) monthly deviations from the trend line. The insert in (a) shows the annualcycle. (From Cavalieri and Parkinson (2012); figure courtesy of Claire Parkinson and Don Cavalieri,commercial use permitted under a Creative Commons attribution 3.0 license.)

are ice-free. The Antarctic images show that much less ice survives the summer, with thelargest amount occurring in the Weddell Sea.

For examples of time series of ice extent for both hemispheres, Figures 9.26 and 9.27show a passive microwave time series derived from SMMR and SSM/I imagery similarto that shown in Figure 9.25. These figures also show the mean monthly and annual timeseries of ice extent, plus a least-squares linear fit to the annual series. The small insets in thefigures show the monthly averaged annual cycle. For the time period in question, the Arcticice extent is dramatically decreasing, while that for the Antarctic is slowly increasing. AsFigure 9.25 shows, for the Arctic, the sea ice forms in an ocean surrounded by land, whereasfor the Antarctic the sea ice forms around the Antarctic ice mass. The figures show thatthe Arctic and Antarctic sea ice have a different response to the changing climate. Comiso(2010, Figure 7.13) shows that, for 1978–2009, the Arctic September minimum extentdecreased at a rate of 11 ± 1.7%/decade, while the March maximum extent decreased ata rate of 2.2 ± 0.4%/decade. For the same period, the Antarctic March minimum extent



Northern Hemisphere

(a) Monthly averages

(b) Monthly deviations

Sea

ice

exte

nt (

106

km2 )

Sea

ice

exte

nt (

106

km2 )

–51,400 ± 1900 km2 yr–1

Fig. 9.27. The monthly averaged series of the Southern Hemisphere sea ice extent for 1978–2010:(a) monthly averages and (b) monthly deviations from the trend line. The insert in the upper panelshows the annual cycle. (From Parkinson and Cavalieri (2012); figure courtesy of Claire Parkinsonand Don Cavalieri, commercial use permitted under a Creative Commons attribution 3.0 license.)

increased at a rate of 2.1 ± 2.6%/decade; while the September maximum extent increasedat a rate of 0.7 ± 0.4%/decade (Comiso, 2010, Figure 7.29), so that the Antarctic sea iceextent has remained roughly constant, while the Arctic summer extent decreased signifi-cantly.

On average, the Arctic ice extent has a March maximum of 15 × 106 km2 and a Septemberminimum of about 5 × 106 km2. Given the trend in the Arctic ice extent, the Septemberminimum is misleading. For example, as Figure 9.28 shows for September 2012, the Arcticsea ice minimum was 3.6 × 106 km2, which was 3.4 × 106 km2 less than the 1979–2000average September extent, and 0.7 × 106 km2 below the previous record minimum extent in2007 (Comiso, 2010, Figure 7.13). The summer sea ice extent has decreased by about 50%between 1979 and 2012. Given the importance of this increase in the amount of summeropen water to Arctic shipping and Northern Hemisphere climate, NSIDC maintains a blogon the Northern Hemisphere ice conditions (NSIDC, 2013b).



Fig. 9.28. The monthly average ice extent for March 2012 (left image) and September 2012 (rightimage). White is sea ice; light gray is open ocean; dark gray is land. The gray line shows the monthlymedian ice edge for the period 1979–2000. (Images courtesy of the National Snow and Ice DataCenter, University of Colorado, Boulder, CO.)

In contrast, the Antarctic has a September maximum of 19 × 106 km2 and a Februaryminimum of 4 × 106 km2. The two pack ice regions differ because the Arctic Ocean issurrounded by land and has a strong oceanic surface stratification, while the AntarcticOcean surrounding Antarctica has a weak stratification, an open ocean boundary with coldwinds flowing off the Antarctic plateau so that the ice edge is subject to divergence fromwind and currents. Thus the Antarctic ice has a greater maximum and a smaller minimumice extent. Because the Arctic and Antarctic time series are six months out of phase, theglobal sea ice extent lies approximately between 19 and 26 × 106 km2, with the maximumin the austral winter (Comiso, 2010, Figure 7.1).

For 2012, Figure 9.28 shows the March maximum (15.2 × 106 km2) and Septemberminimum (3.6 × 106 km2) extent (NSIDC, 2013a). The 2012 September minimum wasthe lowest minimum observed to that date. The image shows the large amount of openwater north of Russia and throughout the Canadian Islands, and suggests that an open waterpassage exists between the Bering Strait and Europe; and between the Atlantic and theBering Strait through the Canadian Islands.


10

Introduction to radars

10.1 Introduction

A radar is an active microwave device that transmits short directional pulses of energy,then operates as a sensitive receiver to measure the returned energy or radar echo. The termradar is an acronym for radio detection and ranging. The oceanographic value of radar isdue to its response to different surface conditions. When the pulse interacts with a surfacethat is strongly reflective, the return is strong or bright; when the surface is non-reflective,the return is weak or dark. The properties of the reflected and scattered pulse are calledbackscatter. Because of the large variety of oceanic surface phenomena that modulatethe backscatter, radars can retrieve wind speed and direction, ocean swell properties andthe presence of heavy rain. They can also make precise measurements of distance andobserve phenomena such as internal waves, sea ice, oil and biological slicks and man-madestructures such as ships and oil platforms.

Two specialized radars discussed in this and following chapters are the scatterometersand imaging radars. By transmitting a pulse, receiving the return, then correcting the returnfor atmospheric interference and instrument noise, a scatterometer makes quantitativemeasurements of the backscatter from small surface areas. With these corrections, anyradar that measures backscatter can serve as a scatterometer (Ulaby et al., 1981, pp. 9–10).In oceanography, the backscatter return from a scatterometer is used to retrieve vector windspeed. In contrast, the backscatter from an imaging radar consists of the return from a largesurface area, which is then binned according to either time delay or Doppler shift. Thissubdivides the field-of-view (FOV) into many small areas, which, when combined with theradar motion, produces an image of the area covered by the FOV, where the image consistsof the relative changes in backscatter.

This chapter describes how radars work and the relation of the observed backscatter tothe properties of the ocean surface. The chapter also describes techniques for subdividingthe radar FOV into smaller bins. Specifically, Section 10.2 derives the radar equation anddescribes its application to the ocean surface. Section 10.3 describes four different antennaconfigurations used in remote sensing. Sections 10.4 and 10.5 discuss two techniques usedto subdivide the FOV, called range and Doppler binning. Section 10.6 summarizes aircraftobservations of backscatter from a wind-roughened ocean surface, and its dependence on

308


10.2 Radar equation 309

t0

Transmission

Time

Radar

ΦT

τ

z

x

y

Pulse

Reflection R0

Fig. 10.1. A pulse of energy incident on an isolated target. See the text for definition of variables.

incidence and azimuth angle. In particular, at near-vertical incidence, the backscatter isspecular, decreases with increasing wind speed and is independent of azimuth angle. Incontrast, at oblique incidence angles, the backscatter depends on resonant Bragg scattering,which causes the backscatter to increase with wind speed and vary with azimuth anglerelative to the wind direction. The section also discusses the backscatter dependence onV- and H-polarization.

10.2 Radar equation

The discussion of the radar equation follows Ulaby et al. (1982, Section 7.1) and Elachi(1987, Chapter 6). Specifically, Section 10.2.1 derives the radar equation for a perfectlytransmissive atmosphere and an isolated non-emitting object, then extends this discussionto scattering from an extended surface. Section 10.2.2 discusses radar polarization andSection 10.2.3 describes how an absorbing and emitting atmosphere, an emitting surfaceand the instrument noise respectively affect the radar return.

10.2.1 Radar backscatter from an isolated object and an extended surface

For the scattering of an electromagnetic pulse from an isolated object or target,Figure 10.1 shows the configuration of the antenna and target; the inset shows the transmit-ted pulse and the reflected return. The target is an isolated irregularly shaped object locatedin the radar far field at a range or distance R0 from the radar, the atmosphere throughwhich the pulse travels is perfectly transmissive, and the blackbody radiation emitted bythe target is negligible compared with the magnitude of the backscattered energy. Theantenna boresight points at the target. The antenna has an aperture A, a gain G (θ , φ) and


310 Introduction to radars

a maximum boresight gain G0. At some time t0, the radar transmits a pulse of duration τ ;this pulse interacts with the target to reflect a fraction of the incident energy back to theantenna. Because the magnitude of the scattered energy depends on the target shape, com-position and conductivity, the material properties of the target contribute to the nature ofthe backscatter. In summary, the radar transmit/receive cycle divides into three steps: trans-mission, scattering and reflection at the target, and reception of the reflected pulse, whichare discussed in this order.

The antenna transmits a pulse with a radiant flux T. From Equations (8.8) and(8.13), in the boresight direction, the transmitted power has the following radiant intensityI0:

I0 = G0T/(4π ) (10.1)

The pulse interacts with the target in four possible ways. It can be transmitted throughthe target, absorbed within it, scattered away from it, or backscattered toward the antenna.For the case when no energy is transmitted through the target, the target area AT is thecross-sectional area of the target at right angles to the boresight direction, so that the solidangle subtended by the target at the radar is

= AT/R20 (10.2)

Combining Equations (10.1) and (10.2) and assuming that 1 and that the targetis located in the boresight direction, the power RS incident on the target can be writtenas

RS = TG0AT/(4πR2

0

)(10.3)

As the pulse encounters the target, the incident energy excites eddy currents that are eitherabsorbed within the target or generate a re-radiated power. For a particular orientation of thetarget relative to the antenna, if fA is the fraction of incident power absorbed and dissipatedby the target, then the magnitude of the re-radiated power is TS = RS (1 − fA). Further,if the gain at the target of the re-radiated power in the antenna direction is GTS, and ITS isthe radiant intensity in the antenna direction, then

ITS = TSGTS/(4π ) (10.4)

Because the solid angle subtended by the antenna at the target is A = A/R20 , the power

R received at the antenna is

R = ATSGTS/(4πR2

0

)(10.5)

Combination of the transmission, target interaction and reception of the reflected pulsedescribed in Equations (10.3) through (10.5) shows that the ratio of the received to trans-mitted power can be written as

R/T = [G0/

(4πR2

0

)] [AT (1 − fA) GTS

] [A/

(4πR2

0

)](a) (b) (c) (10.6)


10.2 Radar equation 311

In Equation (10.6) the term (a) is proportional to the transmitted power measured at thetarget; (b) gives the target properties; (c) is proportional to the power received at the antenna.Equation (10.6) shows that terms (a) and (c) are written in terms of the antenna propertiesand the range R0, while term (b) contains all of the target properties including its area,fraction of absorbed energy, and power pattern. Because the target properties are difficultto measure and not by themselves of much interest, they are grouped into one term calledthe radar scattering cross section σ with dimensions of m2, where

σ = AT(1 − fA)GTS (10.7)

Substitution of Equation (10.7) into (10.6) gives the following form of the radar equation:

R/T = σG0A/(4π )2 R40 (10.8)

Equation (10.8) shows that the ratio of received to transmitted power varies inversely asthe fourth power of range, so that the radar must combine a powerful transmitter with asensitive receiver. To eliminate the antenna aperture A from (10.8), Ulaby et al. (1981,Section 3–2.5 and Equation 3.133) show that, for an antenna with no resistive losses, thegain can be written as

G0 = 4πA/λ2 (10.9)

Substitution of (10.9) into (10.8) yields

R/T = [G2

0λ2/(4π )3R4

0

]σ (10.10)

Rearranging terms in Equation (10.10) yields

σ = [R/T] [(4π)3R4

0/(G2

0λ2)]

(10.11)

From Equation (10.11), σ is a function of λ, R0, the ratio of the received to transmittedpower and the known antenna properties.

In contrast to an isolated target, the half-power FOV AFOV of an antenna pointed atthe ocean contains an extended surface of scatterers and reflectors. If the ocean spatialproperties are uniform within the FOV, then, by analogy with Equation (10.7), σ is linearlyproportional to AFOV. Given this dependence of σ on area, a dimensionless cross sectionσ 0 can be defined from

σ = σ0dAS (10.12)

In (10.12), dAS is a differential element of surface area and σ0 is the normalized scatteringcross section or normalized radar cross section (NRCS). From this definition, σ 0 is dimen-sionless and, for constant surface properties, independent of surface area. For an extendedsurface and following Stewart (1985), Equation (10.10) can be rewritten in terms of σ0 as

R

T= λ2

(4π )3

∫AFOV

G2(0, φ) σ0

R40

dAS (10.13)



Consider the special case of a narrow-beam scatterometer pointed at the ocean surface,with an FOV of area AFOV small enough that R0, θ and φ are approximately constantover the FOV. For this case, Chelton et al. (2001b) show that G(θ, φ) can be replaced bythe boresight antenna gain G0 such that Equation (10.13) yields the following algebraicequation for σ0:

σ0 = (R

/T

) [R4

0(4π )3]/[λ2G2

0 AFOV]

(10.14)

If the antenna properties and the magnitudes of the transmitted and received power areknown, then, from (10.14), σ0 can be calculated. With the additional assumptions ofa noise-free instrument, a non-radiating environment and a non-attenuating atmosphere,Equation (10.14) is applicable to narrow-or pencil-beam instruments such as the altimeter.The magnitude of σ0 depends on the ocean scattering properties, as well as on the radarfrequency, polarization, and the azimuth and look angles. Before discussion of the scat-tering properties, the next sections discuss polarization and how the return is affected byatmospheric attenuation and emission, instrument noise and the surface emissivity.

10.2.2 Polarization

The electromagnetic waves generated by radars are generally plane-polarized. For Earthremote sensing, the radars transmit and receive in either the V or the H plane. Antennasthat both broadcast and receive in either V or H are called VV or HH antennas. The other,less common, options are broadcast in H and receive in V (HV), and broadcast in V andreceive in H (VH). Because the return power is much smaller for VH and HV, at this time,the most common satellite radar modes are HH and VV. For a specific incidence angleand frequency, the measurement of all four polarization combinations (HH, HV, VV, VH)completely specifies the surface reflection properties and is equivalent to determining theStokes parameters (Boerner et al., 1998). As Chapter 13 describes for SARs, radars thatoperate in all four modes are called polarimetric.

10.2.3 Contributions of the ocean and atmosphere to the radar return

For a radar viewing the ocean through the atmosphere, the correction for atmosphericattenuation and the contributions from the various emission terms must be included in theσ0 retrieval. For a real atmosphere and a reflecting and emitting ocean surface, the receivedpower R can be written as

R = ′σ + TN (10.15)

where ′σ is the received power that is attenuated by the atmosphere and TN is the thermal

noise (Spencer et al., 2000). The term TN can be written

TN = N + B (10.16)


10.3 Determination of σ 0 within an FOV 313

where N is the instrument noise and B is the sum of the environmental emissions.Specifically, B equals the sum of the surface emitted radiance, the upwelling atmo-spheric radiance and the reflection of the downwelling atmospheric and extraterrestrialradiances.

The instrument noise N sets the lower bound on the radar resolution. The noise issometimes described in terms of a noise floor, which corresponds to the signal level atwhich σ0 equals the noise. This occurs for a signal-to-noise ratio of 1, and is often describedin terms of a noise-equivalent sigma-zero (NEσ0) given in dB. The noise floor gives theoptimum σ0 resolution; the atmosphere, the blackbody radiances from the ocean surfaceand extraterrestrial sources contribute additional terms that must either be estimated andremoved, or be so small relative to the received σ0 that they can be ignored. One of theadvantages of radars over the passive microwave and VIR instruments is that, subject toavailable power, the designer sets the magnitude of the transmitted pulse, so that, by makingthis pulse sufficiently large, the noise is minimized.

The atmospheric attenuation affects the return as follows. If σ is defined as the receivedpower corrected for atmospheric attenuation, then

σ = ′σ /t2 (10.17)

In (10.17), t is the spatially varying and time-dependent atmospheric transmissivity thatis adjusted for incidence angle; the reason why it is squared is that the radar pulse makestwo passes through the atmosphere. Most radars and scatterometers operate at frequenciesless than 14 GHz, where, as Chapter 9 shows, except for heavy rain, the transmissivitiesare close to 1. For the wind scatterometers, Chapter 11 describes the various methods usedfor determination of σ . Because SAR users are more concerned about relative rather thanabsolute changes in backscatter, the attenuation and environmental blackbody terms aregenerally ignored. The nadir-viewing altimeter described in Chapter 12 is a special case,in that its primary purpose is to determine the time difference between the transmittedand received pulses, or the distance between the satellite and the surface. In summary, theabsolute determination of σ0 involves measurement of the following terms: the radar return,the instrument and environmental noise and the atmospheric transmissivity.

10.3 Determination of σ0 within an FOV

There are several ways to retrieve the dependence of σ0 on the surface conditions, polar-ization, and the look and azimuth angle. The first is that, in combination with Equation(10.14), a pencil-beam scatterometer is pointed at different areas of the surface and theσ0 distribution is defined. The second is to use a slant-looking broad-beam radar, thento subdivide the surface footprint into many smaller areas. This subdivision takes placein at least two ways, called range and Doppler binning. In range binning, the return isplaced into bins based on the range or time delay between pulse generation and reception.In Doppler binning, the surface footprint is subdivided according to the Doppler shift of



θ

θ

(d)

(b)

(c)

w

l

45o

y

x

(a)

Fig. 10.2. The configuration of four different antennas used in remote sensing. (a) the nadir-viewingaltimeter parabolic antenna, (b) the side-looking parabolic antenna, (c) the side-looking rectangularantenna, (d) the scatterometer stick antenna, oriented at 45° to the flight path in a plane parallel tothe surface. For each case, the light gray area on the surface is the FOV, while the dark gray swathswithin the FOVs are, in (c), a contour of constant range, and in (d), a contour of constant Dopplershift.

the return. As the following shows, scatterometers and imagers use both techniques. Thissection describes several common satellite radar antennas; the following sections describethe different kinds of binning.

Figure 10.2 shows four antenna configurations used in radar remote sensing and theirFOVs. Relative to the antennas, location within the FOVs is described by an x, y coordinatesystem oriented in the cross-track (x) and along-track (y) directions. In this coordinatesystem, along-track is parallel to the flight direction, cross-track is at right angles to itand the coordinate origin is at the sub-satellite point. From the figures, the antennas have


10.4 Range binning 315

the following characteristics. Figure 10.2(a) shows the altimeter case of a nadir-pointingparabolic antenna and its circular FOV, where, from Equation (8.5), the antenna half-powerbeamwidth θ1/2 is

θ1/2 ∼ λ/D (10.18)

Figure 10.2(b) shows the same parabolic antenna pointed off-nadir, where the FOV is anellipse described by the intersection of θ1/2 with the surface. The SeaWinds scatterometerdescribed in Chapter 11 uses this antenna configuration.

Figure 10.2(c) shows a rectangular side-looking radar with its long axis parallel to theflight direction. The configuration is used with the SAR; a typical antenna has a lengthl = 10 m and width w = 2 m. Equation (10.18) applies to each axis, so that the half-powerbeamwidth generated by l in the along-track direction is θ1/2, and that generated by w inthe cross-track direction is θ1/2, where

φ1/2 ∼ λ/l, θ1/2 ∼ λ/w (10.19)

Thus as Figure 10.2(c) shows, a rectangular antenna generates a wide beam in the cross-track direction and a narrow beam in the along-track direction. Within the surface footprint,the dark gray curve is a contour of constant range or time delay. Finally, Figure 10.2(d)shows the scatterometer case of a high-aspect-ratio stick antenna. This generates a longnarrow FOV, with the long FOV axis at right angles to the length, the short axis at rightangles to the width. Within the FOV, the dark gray curve is a contour of constant Dopplershift.

10.4 Range binning

This section describes how range binning works, and shows that its resolution variesinversely with pulse length. Section 10.4.1 discusses the constraints on the generation ofshort pulses and describes a technique called chirp that synthesizes short pulses from longpulses. Section 10.4.2 describes the constraints on the pulse repetition frequency (PRF).

In range binning, the backscattered energy received at a side-looking radar from withinthe surface footprint is binned according to the time delay between transmission andreception of the pulse. Figure 10.3 shows the interaction of a single pulse with the surface.If d is the length of the surface projection of the pulse, c is the speed of light and τ is thepulse duration, then d is approximately given by

d = cτ cos θ (10.20)

For range binning to work, d must be much smaller than the swathwidth. Figure 10.4 showsa schematic drawing of a transmitted pulse and the binning of its return into equally spacedtime intervals. If the average time delay corresponding to each bin is converted into across-track distance, then for each pulse the average binned power can be plotted versusdistance. If the radar moves at a uniform velocity, generates multiple pulses and is oriented



h

R0

xd Cross-track

cτ

Along-track

y

Radar

θ Δθ1/2

FOVd

Fig. 10.3. The interaction of a single pulse with the surface, where cτ is the pulse length and d is itsprojection on the surface.

Transmitted signal

t1 t2 t3 t4 t5 t6 t7t0. . . .

Pow

er

Time

Reflected return

τ

Fig. 10.4. The binning of the radar return by time delay or range. The horizontal lines within eachbin represent the average received power.

so that it looks in the cross-track direction, this procedure generates a two-dimensionalimage in the along- and cross-track directions.

For this procedure, the cross-track resolution x depends on τ and is calculated asfollows. Figure 10.5 shows the interaction of an incident pulse with two targets separatedby a distance s. When the pulse reaches the first target, some of its energy is reflected.The remainder of the transmitted pulse propagates to the second target, where a secondreflection occurs. For the second reflection to reach the first target, it must travel a distance s,which means that the echoes generated by reflection from the two targets are separated by2s. Therefore, as long as the distance between the two targets is greater than half theprojected pulse length, so that 2s > d, the two targets generate separate and identifiablereturns. This means that the minimum cross-track resolution x is

x = d/2 (10.21)

Thus, for a given pulse length, even if the time bins are very small, the surface resolutioncannot be less than that specified in Equation (10.21). Because the resolution improves as


10.4 Range binning 317

x

d

Cross-track direction

sd

(a)

Targets

x

x

(b)

(c)

2s

1

Pulse

Pulse

Pulse

1

2

Fig. 10.5. A radar pulse of length d incident on two targets and its subsequent reflections. The twotargets are separated by a distance s. (a) The incident pulse, (b) the reflection 1 of the pulse from thefirst target, and (c) the reflection 2 from the second target.

the length of the pulse decreases, the next section describes the chirp technique for thegeneration of short pulses.

10.4.1 Chirp

There are two restrictions on the generation of very short pulses. First, for a center orcarrier frequency f0 and from Fourier transform considerations, a pulse of duration τ hasa frequency bandwidth fB ∼ τ−1. For example, a 10-cm pulse length corresponds toτ = 0.3 ns, so that fB = 3 GHz. Because of EMR leakage into adjacent frequency bandswhere there are a large number of other users, such short pulses cannot be used. Second, eventhough for the standard radar frequencies (C, X-band) a 3-ns pulse with its 1-m length anda 0.3-GHz bandwidth is within its assigned bandwidth, for the return to have a satisfactorysignal-to-noise ratio one requires a large peak power, which for short pulses is expensiveand difficult to generate. Because of these problems, and following Ulaby et al. (1982,Section 7-5.3), many radars replace short pulses with long frequency-modulated pulses,which have the same integrated power and bandwidth as the desired short pulses. Because,within each pulse, the frequency increases linearly with time, this pulse type is called a“chirp”. When the reflection of the chirped pulse is received, the signal is run through a filterthat reconstitutes the short pulse. Consequently, the chirped pulse has the same frequencybandwidth as the short pulse, but is longer, of much lower power and can be reconstitutedinto the desired short pulse. In the following, because the short non-chirped pulses and longchirped pulses have equivalent properties, the chirped pulse is treated as if it were a short,single-frequency pulse.



FOV

h

dp

R1

θ1θ2

R2

Radar

x

Fig. 10.6. Determination of the maximum pulse repetition frequency (PRF) for a side-looking radar.To simplify the figure, the first pulse is allowed to propagate below the surface. See the text for furtherdescription.

10.4.2 Pulse repetition frequency

Radars are often designed such that their pulses repeat at a regular interval τp. The pulserepetition frequency (PRF) is defined as

PRF = 1/τp (10.22)

From Equation (10.22), a repeat rate of 90 pulses per second corresponds to a PRF of 90 Hz.For most satellite instruments, it is desirable to make the PRF as large as possible, since, byobtaining multiple looks of the same region, the signal-to-noise ratio can be increased byaveraging the returns. The swath width in the cross-track direction, however, sets an upperlimit on the PRF. To calculate the maximum PRF, Figure 10.6 shows a characteristic swathgeometry. For a single pulse, the reflection occurs first from the near edge of the swath,then from the far edge. If the PRF is too great, then for successive pulses the echo from thesecond pulse returns from the near edge before the echo from the first pulse returns fromthe far edge. These overlapping echoes generate ambiguity in the return, making the dataworthless and setting an upper limit on the PRF.

Calculation of the maximum PRF proceeds as follows. On Figure 10.6, dp = cτp is thedistance between successive pulses, R1 is the range to the near edge of surface swath; R2

is the range to the far edge. The requirement that the first pulse reflection returns from thefar edge before the second pulse reflection returns from the near edge yields the inequality

dp = cτp > 2 (R2 − R1) (10.23)

In terms of the PRF, (10.23) becomes

PRF <c

2(R2 − R1) (10.24)


10.5 Doppler binning 319

U0λλ0

(a) (b)

Fig. 10.7. The change in wavelength associated with electromagnetic waves generated from (a) astationary source and (b) a moving source, where the source velocity is uniform and non-relativistic.

For a hypothetical satellite at an altitude of 800 km with θ1 = 21° and θ2 = 45°, the pulseseparation must be greater than about 560 km or 1.9 ms, yielding a maximum PRF of530 Hz.

The restriction in Equation (10.24) does not prohibit the interleaving of pulses or burstsof pulses. For example, the TOPEX altimeter generates a burst of pulses, followed by aperiod when it receives their echoes in sequence. Also, the twin-pencil-beam SeaWindsinstrument described in Chapter 11 alternates among the inner beam pulse, outer beamecho, outer beam pulse and inner beam echo. To avoid ambiguity in any of these schemes,the PRF of any sequence of pulse transmission and reception, such as that of the innerbeam, must satisfy (10.24).

10.5 Doppler binning

For a radar or scatterometer pointed in an arbitrary direction relative to the spacecrafttrajectory, the Doppler shift of the return signal can also be used to bin the return. Thereason why this is possible is that the surface velocity and the Doppler shift relativeto the spacecraft depend on the antenna view angle relative to the trajectory. For realaperture radars, Doppler processing involves the generation of a long pulse at a con-stant f0, then binning the return according to its Doppler shift. Instruments such asthe SEASAT and NSCAT scatterometers employed this technique, and, as Chapter 13describes, the SARs obtain their resolution from a combination of range and Dopplerbinning. Given the importance of this concept, in the following, Section 10.5.1 reviewsthe concept of Doppler shifts, and for a flat surface derives the location of the lines ofconstant Doppler shift, called isodops. Section 10.5.2 describes the spatial resolution ofthe Doppler binning and Section 10.5.3 shows how the Earth’s rotation alters the isodoplocations.

10.5.1 Dependence of the Doppler shift on view angle

Figure 10.7 compares the difference between waves radiated from an idealized stationaryand a moving source of electromagnetic waves, where in both cases the source radiates



Spacecraft track

Sub-satellite track

Isodop

γ

Fig. 10.8. The spacecraft and sub-satellite tracks, the surface isodop, the scatterometer FOV and itsview angle γ relative to the spacecraft track.

spherical waves at a constant frequency f0 and wavelength λ0. For the stationary casein Figure 10.7(a), the time between crests is t = 1/f0. Figure 10.7(b) shows the sameradiating source moving at a velocity U0 toward a stationary observer at the right. Duringt , the transmitter moves a distance U0 t , so that the received λ is shortened by anamount

λ = λ0 − U0t = λ0 − U0/f0 (10.25)

or

λ = λ − λ0 = −U0/f0 (10.26)

Because c = λf , if λ changes by λ, f changes by

f/f0 = −λ/λ0 (10.27)

From Equations (10.26) and (10.27), f = U0/λ0. If the transmitter and receiver movetogether at a uniform velocity toward a stationary reflecting surface, the Doppler shift isdoubled, so that

f = 2U0/λ0 (10.28)

Now suppose that the scatterometer views a flat surface at a constant oblique view angle γ

relative to the spacecraft trajectory (Figure 10.8). The component of the spacecraft velocityin the γ-direction is U0 cos γ , so that the Doppler shift received at the spacecraft is

f = 2U0 cos γ/λ0 (10.29)

From (10.29), Figure 10.8 shows a characteristic isodop along which f is constant.



φ

Spacecraft track

Surface plane

γ

θ

y

h R0

FOV

Sub-satellite track

Antenna

RB

φx

Fig. 10.9. The geometry of a Doppler scatterometer above a horizontal plane, where φ is the azimuthangle, θ is the incidence angle and γ is the view angle relative to the spacecraft track. See the textfor further description.

Because the location of a point on the surface relative to the spacecraft trajectory is morecommonly described by the look angle θ and the azimuth angle φ, for a flat surface, thefollowing derives the relation between γ and θ , φ. Figure 10.9 shows the configuration ofthe antenna relative to a flat non-rotating Earth. The satellite is at altitude h, the distancefrom the antenna to the FOV is R0, the along-track distance of the FOV from the antennais y and the projection of R0 into the plane of the spacecraft is RB. For γ , φ and θ , thefollowing relations hold:

cos γ = y/R0, cos φ = y/RB, sin θ = RB/R0 (10.30)

From (10.30), cos γ = cos φ sin θ . Equation (10.29) can then be written as

f = (2U0 cos φ sin θ )/λ0 (10.31)

which gives the dependence of f on U, φ and θ .Consider a scatterometer similar to the NSCAT discussed in Chapter 11 that is traveling

to the right above a plane surface at an altitude of 800 km and a velocity U0 = 6.7 km s−1.From Equation (10.31), Figure 10.10 shows the pattern of isodops and the circles ofconstant range. The figure shows that the combination of range and Doppler binningallows the entire surface to be gridded into unevenly shaped cells. Both Figure 10.10 andEquation (10.31) show that the largest values of f occur in the fore and aft directions atφ = 0 and π where f = ± U0/λ, while, at right angles to the spacecraft trajectory,f = 0. For the NSCAT carrier frequency of φ0 = 14 GHz, the maximum Doppler shift



10–1–2

1

0

–1

–2

2

Along-track distance (103 km2)

Cro

ss-t

rack

dis

tanc

e (1

03 k

m2 )

Increasing Doppler

Decreasing Doppler

flight

direction

2

Fig. 10.10. The solid lines are the isodops contoured at equal intervals of 0.1 fmax on the surfaceplane for a satellite in horizontal motion above the plane; the dashed circles are lines of constant range(derived from Ulaby et al. (1982), Equation 7.46). The origin lies directly beneath the spacecraft; thegray bar shows a typical FOV. See the text for further description.

in the forward direction is fmax = 6.4 × 105 Hz; in the aft direction, the minimum is−6.4 × 105 Hz. The gray bar inclined at 45° shows the idealized FOV of a stick antenna.Examination of this FOV shows that near the origin the isodops are closely spaced; furtherfrom the origin they are further apart. Consequently, for spatial cells defined by isodopsthat are equally spaced in frequency, their dimensions increase with distance from theorigin.

A special case relevant to the SAR concerns the behavior of the isodops at lookangles close to the cross-track direction. Equation (10.31) and Figure 10.10 show that, ifφ = π/2 − δ, where δ is the azimuth angle relative to the cross-track direction and definedso that it is positive in the forward direction, then, for small δ,

f = (2U0 sin δ sin θ )/λ0 (2U0 δ sin θ )/λ0 (10.32)

Equation (10.32) shows that even though f = 0 in the cross-track direction, for azimuthangles close to this direction, f varies linearly with δ. Chapter 13 uses this relation in thederivation of the SAR resolution.



f1 f3 f4 f5 f6f0. . . .

Pow

er

f2Frequency

f7Time

Transmitted signalBinning of the return by Doppler shift

τ

Fig. 10.11. Binning of the return pulse by Doppler shift, where the frequency width of each Dopplerbin is proportional to a uniform displacement in range. The horizontal lines within each bin are theaveraged return.

10.5.2 Doppler surface resolution

Doppler binning is used in two different ways. First, for certain of the wind scatterometers,the surface distribution of σ0 is determined from Doppler binning of relatively long pulses.Second, the SAR processing uses both Doppler and range binning to combine the returnsfrom a sequence of many short pulses in a computationally intensive procedure that yieldsa high resolution both in the along- and in the cross-track directions. This section discussesthe binning of a single long return; Chapter 13 discusses the SAR case.

Section 10.4 shows that, for range binning, the cross-track resolution improves as thepulse length decreases. In contrast, this section shows that the Doppler resolution improvesas the pulse length increases. From Fourier transform considerations and for a pulse oflength τ , the smallest resolution fmin to which the Doppler shift can be resolved is

fmin = 1/τ (10.33)

Equation (10.33) shows that, unlike the short pulse used in the range binning case, forDoppler binning, the longer the pulse, the smaller fmin and the better the Doppler resolu-tion. Because the Doppler resolution or equivalently the surface spatial resolution improveswith increasing pulse length, one advantage of Doppler binning over range binning is thatthe radars can utilize longer, lower-power pulses.

The Doppler determination of the surface properties proceeds by transmission of a longpulse with carrier frequency f0, reception of the return, and removal of the carrier. The mod-ified return is then passed through a series of filters with bandwidths corresponding to thedesired Doppler shifts, where the return is averaged within each filter. Figure 10.11 showsa schematic diagram of the transmitted and received pulse, where the received power isplaced into a series of bins defined by the filter bandwidths. For example, for the NSCATpulse length of τ = 5 ms, fmin = 200 Hz. For this case, Naderi et al. (1991) showthat, to obtain a 25-km resolution in the cross-track direction, the first bin in the nearswath position has a bandwidth of fbin = 15,000 Hz; the last bin has a bandwidth of2000 Hz. Given that fmin = 200 Hz, the accuracy of the spatial resolution decreases from



1% to 10% across the swath. In contrast, if the pulse length is reduced by a factor of 5 toτ = 1 ms, the accuracy across the swath decreases from 7% to 50%.

10.5.3 Rotation of the Earth

Because the Doppler shift responds to surface velocity, the processing must also considerthe relative surface motion induced by the Earth’s rotation. At the equator, the longitudinalvelocity of the Earth is 0.5 kms−1. If a spacecraft moving north crosses the equator atright angles, the cross-track direction is no longer a line of zero Doppler shift. Instead,for a spacecraft velocity of 6.5 km s−1, the isodops are tilted by an angle equal to thetangent of the Earth and spacecraft velocities, or by 4°. Similarly, if the spacecraft crossesthe equator moving south, the angle is reversed so that the total angular shift between thesatellite traveling north and south is 8°. As Chapter 11 shows, for the scatterometers tocompensate for this Doppler shift, either the spacecraft is rotated or the return is adjustednumerically.

10.6 Oceanic backscatter

Ocean backscatter divides into that from the open ocean and that from sea ice and fromobjects such as ships, oil rigs and icebergs. Although the σ0 of the open ocean dependson surface roughness and not directly on wind speed, wind speed is generally used as aproxy for roughness. In the following, Section 10.6.1 describes reflection from objects,Section 10.6.2 describes the difference between oceanic specular and Bragg scatter andSection 10.6.3 discusses aircraft observations of backscatter.

10.6.1 Specular and corner reflectors

Unlike the ocean surface, objects such as ships, icebergs and oil rigs present reflective wallsto the incident radiation. When these surfaces are perpendicular to the incident radiation,the reflection is specular and the return is strong. Figure 10.12 shows that when theseobjects consist of vertical surfaces, the energy reflects off the ice or ocean surface, then offthe vertical surface, so that the combination of the ocean and the vertical surface forms acorner reflector and the antenna again receives a strong return. As the radar images of shipsin Chapter 13 show, such reflectors are bright.

10.6.2 Two kinds of oceanic backscatter

As Sections 5.2 and 9.4.1 discuss, the nature of the reflection or backscatter from the oceansurface depends on the wavelength distribution of the surface waves relative to the radiationwavelength λ. In general, the incident energy is scattered from short waves and reflectedfrom long waves, where the long waves satisfy the radius-of-curvature condition given in


10.6 Oceanic backscatter 325

Corner reflector

Ocean surface

Fig. 10.12. Corner reflection from a floating or bottom-mounted object with reflective vertical walls.

Equation (5.9). For radar backscatter from an ocean surface, Plant (1990) discusses thecomposite surface models that are similar to the two-scale models described in Section9.4.1. The composite surface consists of a large-scale surface that satisfies the radius-of-curvature restriction, and a small-scale surface with an rms amplitude much less than λ.The effect of the large-scale surface is to advect and tilt the wind-generated patches ofsmall-scale roughness. As Plant describes, the wavelength separating the two scales is oforder λ, with a complicated dependence on incidence angle and the rms roughness.

For the case of no winds and a flat surface, specular reflection occurs, with its proper-ties governed by the Fresnel coefficients described in Chapter 5. As the wind speed androughness increase, coherent specular reflection decreases and incoherent scatter increases.Figure 10.13 shows the reflection and scattering of a radiance that is both normally andobliquely incident on specular and wave-covered ocean surfaces. For normal incidenceon a specular surface, Figure 10.13(a) shows that all of the incident radiance is returnedto the antenna. For normal incidence on a rough surface, Figure 10.13(b) shows that thearea of those facets perpendicular to the incident radiation decreases, so that the incidentenergy is in part specularly reflected back to the antenna and in part reflected and incoher-ently scattered away from the antenna. For normal incidence, this means that σ0 decreaseswith increasing U. Because, as Section 2.2.1 describes, the maximum ocean wave sloperarely exceeds 15°, for incidence angles θ < 15°, σ0 continues to decrease as θ and Uincrease.

For θ > 15°, Figure 10.13(c) shows that there is no return for specular reflection, while,for a wave-covered surface, Figure 10.13(d) shows that only incoherent backscatter occursin the antenna direction. In spite of the lack of specular reflectors at large look angles,early radar experimenters observed strong backscatter even for θ as large as 70° (Barrickand Swift, 1980). The source of this large-angle backscatter is called Bragg scatter, whichis named after William Bragg’s investigation of the backscatter generated by radiationincident on a regular crystal structure (Ulaby et al., 1982, p. 842). Bragg found that, forspecific incidence angles and frequencies, or when the crystal lattice spacing equalled half



(a) (b)

(c) (d)

Fig. 10.13. The specular reflection and incoherent scattering of a radiance incident on a surface:(a) normal incidence, specular surface; (b) normal incidence, wave-covered surface; (c) obliqueincidence, specular surface; (d) oblique incidence, wave-covered surface. See the text for furtherdescription.

the projection of the incident wavelength on the lattice, the backscatter exhibited strongresonances. For the ocean, if the surface wave spectrum contains a wavelength componentwith a similar relation to the incident radiation, Bragg resonance also occurs.

Figure 10.14 shows a schematic drawing of the Bragg scatter generated by the interactionbetween an incident radiance and a specific water wavelength. In this example, the incidentradiance is based on the 23° look angle of the ERS-1 5.3-GHz SAR, corresponding toλ = 56 mm. For this geometry, Bragg resonance occurs if there exists a surface wavecomponent with a λW equal to half the surface projection of the radar wavelength λ, or when

λW = λ/(2 sin θ ) (10.34)

If Equation (10.34) is satisfied, then the power reflected back to the antenna from twoadjacent water wave crests is in phase, so that radiances that are incoherently backscatteredfrom the waves add coherently at the antenna, explaining the strong return observed forθ > 15°.

From examination of figure 10.14, a more general form of this relation is

(2λW/λ) sin θ = n, n = 1, 2, 3, 4, . . . (10.35)



θ

λ

λ

θ

λ/2

W

Fig. 10.14. A schematic drawing of Bragg scatter modeled after the ERS-1 SAR. For the numbersgiven in the text, λW = 72 mm. See the text for further description.

so that there are whole families of Bragg-scattering solutions. Given that the wind generatesa continuous spectrum of short ocean waves, resonant waves are generally present. Because,as Section 2.2.4 shows, the mean-square wave slope and surface roughness increase withwind speed, Bragg scatter increases with U. Further, observations and modeling results showthat Bragg scatter also occurs from short waves riding on long ocean swell. In summary, asU increases, for near-nadir incidence angles, σ0 decreases, whereas for oblique angles σ0

increases.

10.6.3 Aircraft observations

Beginning in the 1940s and culminating in the 1970s, a series of aircraft experimentsinvestigated the dependence of σ0 on U, θ , azimuth angle and polarization (Jones andSchroeder, 1978). Using an aircraft-mounted pencil-beam scatterometer set at a varietyof incident and azimuthal angles, Jones and his colleagues carried out three kinds ofexperiments. First, during periods of steady offshore winds, the aircraft flew as much as45 km away from the coast and back while observing the surface at a variety of fixedincidence angles. For this case, where the ocean swell amplitudes and wavelengths increasewith distance from the coast, Figure 10.15 shows that the VV and HH backscatter isapproximately constant and independent of fetch. This and similar observations establishedthat the wind-generated small-scale surface roughness and resultant σ0 are generated locallyand are independent of fetch and swell height.

Second, for several different wind speeds, and with the scatterometer set at fixed inci-dence angles between 0° and 50°, the aircraft flew along flight lines in different directionsrelative to the wind. From observations made with the scatterometer pointed downwind,



–20

0

–400 4 8 12 16 20 22 24 26 28 30 32 34 36 38 40 42

Fetch (km)

–20

–40

0VV

HH

σ0

(dB

) σ

0 (d

B)

Fig. 10.15. The dependence of the VV- and HH-scattering cross section on fetch, for an aircraftscatterometer flown downwind and away from a lee shore. The scatterometer frequency is 13.9 GHz;the look angle is 53°. Ross and Jones (1978) do not specify whether the scatterometer pointed upwindor downwind. On the horizontal axis, the scale change at 20 km occurs on the original figure. Thewind speed varied between 10 and 13 m s−1 during the flight. (Figure 5 from Ross and Jones (1978),C© 1978 Kluwer Academic Publishers, used with permission.)

10

0

–10

–20

–30

–401 10 100

Wind speed (m s–1)

Symbol 0 (deg)01020304050

10

0

–10

–20

–30

–401 10 100


Symbol 0 (deg)01020304050

σ HH

(dB

)

σ VV

(dB

)

Fig. 10.16. The VV- and HH-scattering cross section versus wind speed and θ . The scatterometer ispointed downwind. The reason that σ0 exceeds 0 dB at 0° and 10° is due to the factor of (4π )3 inEquation (10.14). (Figures 7c and 7d from Jones et al. (1977), C© 1977 IEEE, used with permission.)

Figure 10.16 shows the VV and HH dependence of σ0 on θ and U. The results for thescatterometer looking upwind and crosswind are similar (Jones et al., 1977). The figureshows that, for θ less than about 10°, specular reflection is dominant, and that, as Uincreases, σ0 decreases. In contrast, for θ > 15°, where Bragg scatter applies, σ0 increaseswith U. Between these two cases at an incidence angle of 10°–15°, the effects of Bragg



–6

–10

–14

–18

–22

–260 60 120 180 240 300 360

Upwind Crosswind Downwind

15.0

6.5

3.0

Azimuth angle relative to wind direction R (deg)

(m s–1)

(dB

)σ 0

φ

Fig. 10.17. The VV-scattering cross section as a function of azimuth angle for three wind speeds andθ = 30°. The upwind direction is at an azimuth angle of 90°. (Figure 2 from Jones et al. (1978),C© 1978 American Institute of Aeronautics and Astronautics, used by permission of AIAA.)

and specular scatter cancel out, so that σ0 is independent of U. Also, at any constant U, σ0

decreases as θ increases, so in all cases the return power decreases with increasing lookangle. Finally, Figure 10.16 shows that, for θ 20°, the VV return is significantly greaterthan the HH. In summary, as θ increases, the nature of the backscatter changes from aprocess dominated by specular reflection, where the return decreases as U increases, to onedominated by Bragg scatter where the return increases with U.

Third, the aircraft flew in a series of highly banked circles while observing the surface atdifferent fixed values of θ . As in the investigation of the passive microwave emission fromthe sea surface described in Section 9.4.5, this maneuver conically scanned the antenna over360° of azimuth. For three wind speeds and a VV antenna at θ = 30°, Figure 10.17 showsthe dependence of σ0 on U and on the azimuth angle relative to the wind direction φR definedin Equation (9.6). At each wind speed, the curves are symmetric around the wind direction,with their maxima in the upwind and downwind directions and minima in the crosswinddirections, so that σ0 varies approximately as cos(2φR). The source of this variabilityis the azimuthal distribution of wind-generated short waves and roughness described inSection 2.2.4. Figure 10.17 also shows that, as U increases, σ0 increases, and that theupwind maxima are slightly larger than the downwind maxima, where this difference iscalled the upwind/downwind asymmetry. The source of this asymmetry is the preferentialgrowth of parasitic capillary waves on the downwind faces of the longer waves.

In an extension of this discussion to polarimetric observations, Yueh et al. (2002) com-pare a two-scale theoretical model with aircraft scatterometer observations of backscat-ter at VV, HH and HV polarizations. Because, for symmetry reasons, the VH backscat-ter is identical to HV, they omit the VH case. Figure 10.18 shows the results of their



Upwind Downwind

–12

–14

–16

–18

–20

–22

–24

–26–180 –90 0 90 180 –180 –90 0 90 180

–30

–32

–34

–36

–38

σHH

σVV σHV

φR (deg)

Upwind Downwind

φR (deg)

σ 0 (d

B)

σ 0 (d

B)

Fig. 10.18. Theoretical dependence of σ0 on φR for a polarimetric 14-GHz scatterometer at a 45°incidence angle and for a 10 ms−1 wind speed. (Figure 3 from Yueh et al. (2002), C© 2002 IEEE, usedwith permission, figure courtesy of Simon Yueh.)

two-scale scattering model. On the figure, the curves for each of the backscatter combi-nations (VV, HH, HV) appear similar and are symmetric about the wind direction, withmaxima in the upwind and downwind directions, and minima in the crosswind directions.The left-hand panel on Figure 10.18 shows that, σVV has the strongest response, whichis about 7 dB larger than the σHH. In contrast, the right-hand panel shows that the σHV

response is nearly 20 dB smaller than that of σVV. Because the HV and VH responses aresmall compared with VV and HH, they are not at present used in the vector wind retrieval.The next chapter describes the use of the VV and HH response curves in retrieval of thevector wind speed, and Chapter 13 describes how the modulation of the Bragg scatter bywind and waves allows radars to retrieve a wide variety of ocean surface phenomena.


11

Scatterometers

11.1 Introduction

Ocean winds drive the ocean currents, transfer gases, heat, moisture, energy and momen-tum between the atmosphere and ocean, and, through these processes, influence regionaland global climate. In driving the large-scale ocean circulation and small-scale mixing,winds contribute to ocean ecosystems. Hurricanes, typhoons and winter mid-latitude stormspresent a threat to shipping and coastal regions (Atlas et al., 2011).

Surface winds are the largest source of momentum for the generation of surface wavesand basin-scale ocean currents. The oceanic distribution of vector winds determines theheight distribution and propagation direction of ocean swell, and allows prediction of theeffect of this swell on ships, offshore structures and seacoasts. Because, in regions such asthe Southern Hemisphere, surface observations of ocean winds by island weather stations,moored meteorological buoys and ships are sparse, without scatterometers, large areasof ocean would lack wind observations. Scatterometer data are particularly important forimprovement of the forecast accuracy in such regions (Chelton et al., 2006). For numericalweather forecasts, Bi et al. (2011) show that the inclusion of these ocean winds leads toimprovements in days 4 through 7 of the forecasts.

The observations have led to specific fine-scale improvements that are of great regionalimportance. For example, the observation and prediction of rapidly developing oceaniccyclones particularly benefits the shipping industry. High-resolution satellite observationsmake it possible to track developing storms and improve marine safety. For example,between 2000 and 2010, there were on average 94,000 ships at sea, of which 160 werelost per year, with the greatest loss among dry cargo vessels and fishing vessels (Allianz,2012). During the 1980s and 1990s, severe storms sank approximately 200 supertankersand container ships with lengths greater than 200 m (Atlas et al., 2011). In 1985, 0.4%or 300 per year of 76,000 vessels were lost; in 2009, these losses had declined to 0.15%or 150 per year of 103,000 vessels. Improved weather forecasts demonstrably helped toreduce these loss rates.

Liu (2002) summarizes the current state of scatterometry and its applications to atmo-spheric and oceanic studies. Scatterometer observations fill the gaps in the data-sparseSouthern Hemisphere, and provide observations of the surface wind stress and wind-stress

331


332 Scatterometers

curl that drive the numerical models of ocean circulation (Riesen and Chelton, 2008;Liu et al., 2010). Atlas et al. (2011) show that, compared with surface models, the assim-ilation of satellite winds into global models increases the calculated wind speeds and thewind-stress curls. As Section 11.10.4 shows below, scatterometers also monitor icebergpositions and sea ice extent.

For Atlantic hurricanes, scatterometer winds have extended the forecast lead-time foridentification of potential hurricanes. This is especially true for the small atmosphericvortices that form close to Africa, are precursors to hurricanes, lack clouds for visualobservation and are too small to be identified in numerical models (Katsaros et al., 2001;Brennan et al., 2009). Scatterometers have improved the understanding of winds in thePacific Inter-Tropical Convergence Zones (ITCZ) (Liu, 2002) and of the coupling betweenwinds and SST in the ITCZ (Chelton et al., 2001a). They have also led to the discoveryof a long wake downwind of the Hawaiian Islands (Xie et al., 2001) and to an improvedunderstanding of the Asian and African monsoons (Liu, 2002), and of the nature of coastalwind jets and eddies in the Gulf of Tehuantepec off Central America (Bourassa et al.,1999).

Although discussions frequently emphasize strong winds in the form of storms, hurri-canes or typhoons, wind speeds of less than 5 m s−1 account for nearly 40% of the hourlyaveraged winds (Figure 2.1). Because weak winds are concentrated in the tropics andsubtropics where the majority of the ocean-to-atmosphere heat flux occurs, shifts in theirpatterns affect the global heat flux balance. The ability to track these winds contributes toforecasting of El Nino (Shankaranarayanan and Donelan, 2001).

This chapter describes the three kinds of wind scatterometers and compares them withthe passive microwave WindSat instrument described in Section 9.7. It also discusses theiraccuracies and presents examples of retrieved winds. Each scatterometer works by takingmultiple looks at the same sea surface area either from different directions or at differentpolarizations. As Chapter 10 shows, because the wave properties and surface scatteringcross section σ0 are functions of wind speed and the azimuthal difference φR betweenthe wind direction and the scatterometer look angle, such multiple looks can retrieve thewind speed and direction. Two additional requirements must be met in addition to thatfor multiple looks. First, because the wind retrieval requires precise measurement of σ0,the received backscatter must be corrected for noise, atmospheric attenuation and thebackground environmental radiances; second, the wind solutions must be corrected forpossible ambiguities.

As Section 10.2.3 describes, an accurate measurement of σ0 requires that, for eachtransmitted pulse or group of pulses, the scatterometer must measure not only the receivedpower R, but also the atmospheric transmissivity t and the total thermal noise TN,which is the sum of the instrument noise and the background radiances from the surfaceand atmosphere. Rain contributes significantly to the transmissivity because, as Chapter9 shows, heavy rain can mask the surface. These quantities must either be determinedsimultaneously or, for the case of t, be provided from other satellite instruments or fromclimatological lookup tables. As the following sections show, the different instrumentsemploy a variety of methods to measure R, TN and t.


11.2 Background 333

The scatterometer-derived wind products also depend in part on the wind directionsderived from the numerical weather prediction (NWP) models. As Section 11.3.2 shows,depending on the number of scatterometer looks, the scatterometer produces one to fourdifferent wind vector solutions, separated by azimuth angles of ±90° or ±180°. The wayin which the false wind solutions, called ambiguities, are removed is by using the NCEP orECMWF wind directions as a first guess.

In the following, Section 11.2 summarizes the various wind missions and gives theirrequirements for accuracy and coverage. Section 11.3 describes how scatterometers retrievethe vector wind speed. Sections 11.4 and 11.5 describe the NSCAT, AMI and ASCAT scat-terometers. Section 11.6 describes the rotating-beam SeaWinds scatterometer, its internalcalibration and its wind speed and direction retrieval accuracy. Section 11.7 describes therelative advantages and disadvantages of the different instruments. Section 11.8 discussesthe ISS-RapidScat instrument scheduled for deployment in 2014 on the International SpaceStation (ISS); Section 11.9 describes the Cross-Calibrated Multi-Platform (CCMP) project,which provides a variety of CDR archival wind products; Section 11.10 gives examples ofretrieved winds and of the scatterometer observations of the Antarctic pack ice.

11.2 Background

Table 11.1 lists the past, present and some of the proposed future vector wind missions,including for completeness the passive microwave SeaWinds that Section 9.7 describes.The scatterometers divide into three classes. The first consists of the short-lived NASASEASAT-A Satellite Scatterometer (SASS) and the NASA Scatterometer (NSCAT) onthe Japanese Advanced Earth Observing Satellite-1 (ADEOS-1); these instruments usestick-like antennas and Doppler bin the returns. The second consists of the AdvancedMicrowave Instrument (AMI) scatterometer on the European Remote-sensing SatellitesERS-1 and ERS-2 and the European Advanced Scatterometer (ASCAT) on the EuropeanMETeorologie OPerationnelle (METOP-A and METOP-B) satellites; each of these usesthree long rectangular antennas and range bins the returns. The third is the class of rotatingbeam scatterometers represented by the SeaWinds mounted on the dedicated QuikSCATsatellite and on the short-lived ADEOS-2. These use a rotating dish antenna to generatea pair of conically scanned pencil beams at two different incidence angles that transmitpulses, then range bin the returns.

Similar rotating scatterometers are on the Indian Oceansat-2 and the Chinese HY-2A.In future work, in 2014, the pending China–France Oceanography Satellite (CFOSAT) andthe International Space Station are both scheduled to carry SeaWinds-class scatterometers.Also, the Japanese have requested that the United States provide a rotating-dish scatterom-eter for the GCOM-W2 mission that is scheduled for launch in about 2016 (Bourassa et al.,2010b). In 2013, the satellite wind constellation consists of METOP-A and METOP-B inthe same orbit respectively with 2040- and 2130-local ascending equator-crossing times,and Oceansat-2 with a local noon ascending crossing time.

The NASA scatterometers operate at Ku-band (14 GHz); the European scatterometersat C-band (5.3 GHz), where λ = 6 cm at C-band and 2 cm at Ku-band. As Chapter 9 shows,

Trim

:247mm

×174m

mTop:14.762m

mG

utter:23.198mm

CU

UK

2533-11C

UU

K2533/M

artinISB

N:978

1107

019386

Novem

ber26,2013

8:47

Table 11.1. List of satellite vector wind missions in order of their launch dates.

Satellite Agency Instrument Frequency/operation Launch date Status/end date

SEASAT NASA SASS 14.6 GHz, four-antennas, Doppler bin, left,right

June 1978 October 1978

ERS-1 ESA AMI 5.3 GHz, three-antennas, range bin, right side July 1991 June 1996ERS-2 ESA AMI 5.3 GHz, three-antennas, range bin, right side April 1995 January 2001ADEOS-1 NASA/ NASDA NSCAT 14 GHz, six-antennas, Doppler bin, left, right August 1996 June 1997QuikSCAT NASA SeaWinds-1 13.4 GHz, two rotating pencil beams June 1999 November 2009a

ADEOS-2 NASDA/ NASA SeaWinds-2 13.4 GHz, two rotating pencil beams December 2002 October 2003Coriolis US Navy WindSat Multi-frequency, rotating passive microwave

antennaJanuary 2003 –

METOP-Ab ESA ASCAT-A 5.3 GHz, two sets of three antennas, rangebin, left, right

2006 –

Oceansat-2 India OSCAT 13.52 GHz, two rotating pencil beams September 2009 –HY-2A China Scatterometer 13.256 GHz, two rotating pencil beams August 2011 –METOP-Bb ESA ASCAT-B Identical to ASCAT-A September 2012 –CFOSAT China/France Scatterometer 13.256 GHz, two rotating pencil beams 2014 (pending) –International SpaceStation (ISS)

NASA/JPL ISS-RapidScat 13.4 GHz, two rotating pencil beams 2014 (pending) –

METOP-C ESA ASCAT-C Identical to ASCAT-A 2016 (pending) –GCOM-W1 Japan/United States Scatterometer – 2016 (proposed) –

a Antenna ceased to rotate, instrument continues to produce data from a single direction.b In 2013, METOP-A and METOP-B operate in the same orbit, with METOP-B half an orbit out-of-phase (50 min) with respect to METOP-A. Both

satellites produce data. This tandem operation will continue until the METOP-C launch in 2016 (PO.DAAC, private communication, 2013).SASS stands for SEASAT-A Satellite Scatterometer; AMI, Advanced Microwave Instrument; NSCAT, NASA Scatterometer; ASCAT, Advanced

Scatterometer; OSCAT, Oceansat Scatterometer; CFOSAT, China–France Oceanography Satellite.From ASCAT (2013a), CFOSAT (2013), CEOS (2012), ISS-RapidScat (2013b), Oceansat-2 (2013) and Song et al. (2012).


11.2 Background 335

Fig. 11.1. The SeaWinds scatterometer mounted on the QuikSCAT satellite. The QuikSCAT antennahas a diameter of 1 -m. (Courtesy of NASA/JPL/Caltech, used with permission.)

the advantage of C-band is that, at this frequency, the atmospheric transmissivity is almostidentically equal to 1, while at Ku-band it is nearly 1. Because the short capillary-gravitywaves are more responsive to these changes than the longer waves, Ku-band scatterometershave a greater sensitivity to changes in wind speed than do C-band scatterometers. Thedisadvantage of Ku-band is that the shorter radiation wavelength has a greater response toraindrops roughening the sea surface.

As Table 11.1 shows, the first scatterometer mission was the 1978 NASA SASS stickscatterometer (Johnson et al., 1980). This was followed by the European AMI fan-beamscatterometers on ERS-1 and -2; these began operation in 1991 and terminated in 2001.The SASS successor was the NSCAT launched in August 1996 on the Japanese ADEOS-1satellite. Because of the catastrophic failure of a solar panel, the ADEOS-1 mission endedon 30 June 1997, so that NSCAT lasted less than a year (Wentz and Smith, 1999).

Given the gap in satellite wind coverage generated by this loss, in June 1999, the Sea-Winds scatterometer was launched on the dedicated US QuikSCAT satellite (Figure 11.1).


336 Scatterometers

Table 11.2. QuikSCAT scatterometer mission requirements for arealcoverage and wind accuracy.

Quantity Requirements Applicable range

Wind speed ±2 m s−1 (rms) 3–20 m s−1

10% 20–30 m s−1

Wind direction ±20° (rms) for the closest ambiguity 3–30 m s−1

Spatial resolution 25 km σ0 cells25 km Wind cells

Location accuracy 25 km (rms) Absolute10 km (rms) Relative

Coverage 90% ice-free ocean every day –Mission duration 36 months –

Adapted from Perry (2001).

As Table 11.1 shows, during 2001 SeaWinds was the only functioning wind scatterometer.It was joined in December 2002 by an identical scatterometer on ADEOS-2, which failedin October 2003, and in January 2003 by the polarimetric passive microwave WindSatinstrument described in Sections 8.6.5 and 9.7.

Table 11.2 lists the QuikSCAT mission requirements; Naderi et al. (1991) give similarrequirements for NSCAT. For the scatterometer wind measurements to be of global orregional value to the meteorological community, accurate wind measurements must beobtained from the entire ice-free ocean at daily intervals. For wind speeds of 3–20 m s−1,the rms speed accuracy must be better than 2 m s−1; for 20–30 m s−1, the rms accuracy mustbe within 10% of the wind velocity. The directional accuracy of the best wind solution musthave an rms error of no more than 20°. The location of each σ0-measurement cell shouldhave an rms accuracy of 25 km, and the winds should be determined within cells withcharacteristic dimensions of 25–50 km. As the following sections show, these requirementsfor accurate winds and global coverage dictate the scatterometer orbit and swath width.

11.3 How scatterometers derive the wind velocity

Each of the scatterometers listed in Table 11.1 retrieves the vector wind speed by takingmultiple looks at the same surface area at different azimuth angles and polarizations.Because, as Figure 10.18 shows, the retrieved values of the cross-polarized σHV and σVH

are much smaller than σW and σHH, the scatterometers operate at HH or VV. The SEASATSASS made only two such looks, the AMI made three looks and NSCAT made four looksat three different look angles and two polarizations from each side of the satellite. Forthe SeaWinds rotating beams, the number of looks varies from two to four, depending onposition within the swath. For multiple looks, the following describes the technique usedto retrieve wind speed and direction.


11.3 How scatterometers derive the wind velocity 337

Satellite orbital track

Sea surface

Sub-satellite track

h

45o135o

FOV

Fig. 11.2. Example of several looks by a scatterometer at the same FOV.

Figure 11.2 shows the conceptual scatterometer design. For a steady wind, each scat-terometer retrieves the backscatter from the same FOV at two or four different times,azimuth angles and polarizations. For the three beams shown on Figure 11.2, the antennalook angles relative to the satellite trajectory are 45° ahead, at right angles to the trajectoryand 45° behind. For directional wind retrieval to be possible, Bragg scattering must domi-nate, so that the antenna Earth incidence angles must be greater than 15°–20°. Assume thesatellite is at an altitude of 800 km, with a surface velocity of about 7 km s−1. If the surfacetrack of the FOV is at a distance of 500 km from the sub-satellite track, then the mid-beamobserves it about 70 s after the forward beam and the aft beam observes it an additional 70 slater. This procedure gives three measurements of σ0 over a period of about two minutes.From these observations, assuming steady winds and with the addition of surface weatherforecasts, the next section shows that the vector wind speed can be derived through use ofthe dependence ofσ0on azimuth angle shown in Figures 10.17 and 10.18.

11.3.1 Geophysical model functions

Determination of the wind velocity from multiple measurements of σ0 requires knowledgeof the functional relation between σ0 and the near- surface winds, where this relationis called the geophysical model function (GMF). Because the look- and azimuth-angle-dependent backscatter is proportional to sea surface roughness and thus more related to thewind stress than to the 10-m wind speed U, scatterometer measurements of wind velocityare indirect. The wind velocity used in vector wind retrieval is the neutral stability windvelocity measured at a height of 10 -m above sea level, where neutral stability means inthe absence of atmospheric stratification (Bourassa et al., 2010a). Although the followingrefers to the neutral stability wind speed as either the wind speed or 10-m wind speed, thescatterometer and observed winds differ slightly.


338 Scatterometers

The importance of the atmospheric stratification is that it modifies the momentumtransport through the surface boundary layer. When the ocean surface is warmer than theatmosphere, the boundary layer is unstable, so that momentum is more easily transferredfrom the 10-m winds to the surface. For this unstable atmosphere, a specific U produces agreater surface roughness and more backscatter than for a stably stratified atmosphere, sothat unstable stratification makes the scatterometer-inferred neutral winds larger than theobserved, while a stable stratification makes them smaller. Consequently, before comparisonof scatterometer and buoy winds and depending on the observed atmospheric stratification,the buoy winds must be adjusted to be greater or smaller than their observed values. Thisadjustment has typical values of 0.1–0.2 m s−1 (D. Chelton, private communication, 2003).Other factors such as organic or inorganic slicks that increase surface tension and reducethe ocean surface roughness also produce an apparent smaller wind speed.

The most general form of the model function gives σ0 as a function of the polarizationP, where P represents a VV or HH antenna, the incidence angle θ , the wind speed U andthe relative wind direction φR. This relation can be written as

σ0 = F (P,U, φR) 11.1

Based on aircraft and satellite observations similar to those described in Section 10.6.3,and for a constant U and fixed θ and polarization, an empirically derived truncated Fourierseries the σ0 dependence on φR described (Wentz et al., 1984; Wentz and Smith, 1999;Brown, 2000):

σ0P = A0P(1 + A1P cos φR + A2P cos(2φR) + · · · ) 11.2

Although Wentz and Smith (1999) state that the contributions to Equation (11.2) of higher-order terms such as cos(3φR), cos(4φR), . . . do not exceed 4% of the first three terms,more recent GMFs include five harmonics (Ricciardulli and Wentz, 2011). Comparison ofthe scatterometer winds with data sets derived from surface observations and from othersatellites permits the empirical derivation of the coefficients in Equation (11.2). Examplesinclude comparison with NDBC buoy winds (Freilich and Dunbar, 1999), and with SSM/Iwind magnitudes at small wind velocities and ECMWF NWP winds at larger velocities(Wentz and Smith, 1999), and, for U > 20 m s–1, with WindSat speeds and directions(Ricciardulli and Wentz, 2012a).

For QuikSCAT, the initial form of the model function was the Ku-2001, which wasdeveloped at a time when only a limited amount of high-wind-speed data was available.Because only about 0.2% of rain-free winds have velocities greater than 20 m s−1, thismeant that, for greater velocities, the Ku-2001 GMF had to be extrapolated, which waslater shown to overestimate the magnitude of the retrieved winds (Ricciardulli and Wentz,2012b). The current SeaWinds model function is the more accurate Ku-2011, which,as Section 11.6.4 shows, corrects the inaccuracies in the Ku-2001 GMF that occur forU > 20 m s−1 by comparison with the high-wind-speed SeaWinds retrievals (Ricciardulliand Wentz, 2011).



0 100 200 300

σ 0 (dB

)–10

–15

–20

–25

–30

–35

3

5

8

12

20

47o (HH)–10

–15

–20

–25

–30

–350 100 200 300

55o (VV)

3

5

8

12

20

Upwind Crosswind Downwind CrosswindUpwind Crosswind Downwind Crosswind

oR (deg) oR (deg)

Fig. 11.3. The geophysical model function for the QuikSCAT incidence angles and polarizations of47° HH and 55° VV. The curves are lines of constant wind speed; the numbers below each curve givethe wind speed in m s−1. Upwind is at 0°; downwind at 180°. (Courtesy of Michael Freilich, used withpermission.)

Although winds measured at buoys play an important role in this validation, problemsexist with their accuracy at both small and large U (Zeng and Brown, 1998). At small U, thebuoy and scatterometer winds both have poor directional accuracies, and, at these velocities,ocean currents can bias the scatterometer winds relative to the buoy measurements. At largeU, problems occur with buoy tilt, with the effect of spray on the buoy anemometer, and, forheavy swell conditions, with uncertainty about the anemometer height relative to the seasurface. These buoy problems mean that, for U > 20 m s−1, the validation of wind speedbecomes difficult and must be done using a variety of other sources.

As an example of the QuikSCAT GMF, Figure 11.3 shows the dependence of σ0 onU, direction and polarization. As Section 10.6.3 describes, the maxima of these curvesapproximately occur in the upwind/downwind directions; the minima, in the crosswinddirections. Four factors characterize the model curves: a general increase in σ0 with U, anupwind/crosswind difference, an upwind/downwind asymmetry and a decrease in sensitiv-ity with increasing wind speed.

From Figure 11.3, the dependence of σ0 on φR and the other factors described abovepermit the retrieval of the wind direction. The figure shows that the difference in magnitudeof the upwind and crosswind σ0, called the upwind/crosswind ratio, is largest at smallU, then decreases with increasing U. The source of the upwind/downwind asymmetry isthe preferential formation of capillary waves on the downwind faces of the longer waves(Section 2.2.1). Because the scatterometer views these capillary waves when it looksupwind, the magnitude of the upwind value of σ0 is slightly greater than its downwindvalue. Although this asymmetry is small, it makes possible the determination of a uniquewind direction from four looks. In general, the magnitude of this asymmetry increaseswith incidence angle, is larger for HH than for VV and is largest for small U (Freilich,2000). As Freilich shows, the sensitivity of σ0 to changes in U and the magnitudes of


340 Scatterometers


0 302010 40

σ 0 (d

B)

0

–10

–20

–30

–40

–50

Fig. 11.4. The dependence of σ0 on polarization and wind speed; V-pol, dashed line; H-pol, solid linefor Ku-band (13.4 GHz). The figure shows the sensitivity loss at high wind speeds. (Redrawn fromMeissner et al., (2010), page 6.)

the upwind/crosswind ratio and the upwind/downwind asymmetry increase with incidenceangle. Also, Section 10.6.3 shows that, for the same incidence angle, σ0 is about 7 dB largerat VV than HH. This difference explains why the SeaWinds outer beam is VV and the inneris HH, so that the two beams have about the same return power.

Another important feature of the GMF is that σ0 does not increase linearly with U;instead, at large velocities, for fixed incidence and azimuth angles, σ0 increases approx-imately as log U (Freilich, 2000). For the 11.4-GHz V-pol and H-pol bands, Figure11.4 shows that the sensitivity ofσ0 decreases with increasing wind speed, and that thefalloff in sensitivity occurs especially for U > 20 m s−1 (Meissner et al., 2010).

The model functions described by Equation (11.2) are given in lookup tables for A0P,A1P and A2P and higher-order coefficients as functions of wind speed and direction, lookangle and polarization. The fan-beam scatterometers such as the NSCAT, AMI and ASCATrequire that the model function be specified for a range of look angles from approximately15° to 65°. Because these scatterometers have approximately 20 observational cells in thecross-track direction, they require relatively complicated lookup tables. In contrast, becausethe SeaWinds model functions require only two look angles, they are easier to upgrade toa greater resolution in wind speed and direction than the fan-beam functions.

11.3.2 Derivation of the vector wind speed from the model function

Based on NSCAT, Figure 11.5 shows how the σ0 derived from these multiple looks is usedto estimate the vector wind speed (Naderi et al., 1991). On the figure, the curves are not theconstant wind speed contours shown in Figure 11.5, rather they are contours of constant



15

10

50 60 120 180 240 300 360

Azimuthal look angle (degrees from north)

U (m

s–1

) 2 2 2 2

3 3

4

Fig. 11.5. Loci of the possible wind vectors derived from co-located σ0 measurements from differentantennas: —, 45° antenna azimuth angle (VV); – – –, 135° (VV); . . . . . . , 65° (HH); — - —, 65°(VV). The arrows marked by the 2© show the four solutions derived from two looks; the arrowsmarked by the 3© show the two solutions derived from three looks, and the arrow marked by the 4©shows the single solution derived from four looks. (Figure 5 of Naderi et al. (1991), C© 1991 IEEE,used with permission.)

σ0 that give the dependence of U on φR. The curves are discussed in the order listed in thecaption.

First, the solid curve is derived from a single VV observation of σ0 at a 45° azimuthangle relative to the flight direction. For this observation, the curve shows that the windspeed solutions lie between 6 and 15 m s−1 with no directional information.

Second, the dashed curve is the solution for a VV observation of σ0 at right angles to thefirst. The solid and dashed curves representing these two looks intersect at the four pointsmarked by the arrows and the 2©. Each of these intersections represents possible windsolutions called ambiguities. At these points, the wind speeds are about 10 m s−1 with fourchoices of direction separated from one another by approximately 90°. This case of twolooks and four ambiguities corresponds to the outer SeaWinds swath and the entire SASSswath.

Third, the dotted curve shows the solution for an observation at 65° and HH, wherethe first three curves have two common intersections marked by the arrows and the 3©.Because these two wind solutions are identical in magnitude and approximately 180° apartin direction, three looks yield the correct wind magnitude, but do not reveal whether thewind is blowing to or from a specific direction. Finally, the short-dash–long-dash curve isthe solution for an observation at 65° and VV. The four curves intersect at the single pointmarked by the arrow and the 4©, corresponding to a scalar wind velocity of 10 m s−1 and a


342 Scatterometers

wind direction of 40°. Examination of the two intersections marked by 3© and 4© shows thatthere is only a small difference between the correct and the 180° ambiguous solution, wherethe cause of this difference is the upwind/downwind asymmetry. Without this asymmetry,the 180° ambiguity could not be eliminated.

Because this small asymmetry is easily obscured by noise, many scatterometers use onlythree looks and accept the two ambiguities. These are reduced to one direction using twotechniques. The first is the application of a median filter to an array surrounding the cellthat eliminates isolated errors. The second, a technique called “nudging”, uses the winddirection from an external NWP source to select the ambiguity closest to the external field(Freilich and Dunbar, 1999; Bettenhausen et al., 2006).

11.4 NSCAT scatterometer

The 13.995-GHz NSCAT scatterometer was launched on August 17, 1996 on ADEOS-1.The satellite was in a Sun-synchronous orbit at an altitude of 795 km, a period of 101 minutesand a sub-satellite velocity of 6.7 km s−1; the wind retrieval was based on Doppler binning.

Naderi et al. (1991) describe NSCAT in detail. It consisted of six identical dual-polarization stick antennas, measuring about 3 m in length, 6 cm in width, and 10–12 cmin thickness. Each antenna produced a fan beam with incidence angles of 20° < θ < 55°in the along-beam direction, and a 0.4° beam width in the cross-beam direction. Figure11.6 shows the NSCAT illumination pattern, where the left-hand swaths are at angles of 45°,65° and 135° relative to the flight direction, and the right-hand swaths are at angles of 45°,115° and 135°. The lack of Doppler response at right angles to the spacecraft explains thisasymmetric choice of angles. There are three antennas on each side of the spacecraft, and,because the antennas at 65° and 115° operate at both VV and HH, the antennas made fourdifferent measurements. In the cross-track direction, the swath widths are 600 km. Directlybeneath the spacecraft, in a region measuring ±165 km from the nadir track, specularbackscatter dominates the return and directional wind retrieval is impossible. This nadirgap occurs for all fan-beam scatterometers, whether range- or Doppler-binned. Outside ofthis gap, each swath is divided into 24 Doppler cells, measuring 25 km in the cross-trackdirection.

To obtain a 25-km resolution in the along-track direction, each antenna was transmittedand received at intervals of 3.74 s, during which time the spacecraft traveled 25 km. Withinthis period, because the NSCAT had a single transmitter/receiver that rotated among theeight different beams, each beam was sampled within a subperiod of 468 ms. Within thissubperiod, the scatterometer measured R and TN. To do this, the subperiod was dividedinto 29 observational cycles of 16-ms duration that consisted of 25 transmit/receive cyclesand 4 observations of noise. A transmit/receive cycle consisted of a 5-ms transmitted pulse,and 11 ms of receive. For the received pulses, Section 10.5.2 describes the Doppler binningprocedure. The four noise measurements consisted of 5 ms with no transmission followedby 11 ms of receive, which within each footprint provided a measurement of TN. To obtainσ0, R and TN were averaged over their respective observational periods, then TN wassubtracted from R to obtain ′

σ in Equation (10.15). The backscattered power corrected


11.5 AMI and ASCAT scatterometers 343

Beam-6 (VV)

Beam-5(VV, HH)

Beam-4 (VV)

45o

65o

135o

600 km

Left wind swath

Beam-3 (VV)

Beam-2(VV, HH)

Beam-1 (VV)45o

135o

600 km

Right wind swath

Sub-satellite track

Nadir gap

330 km

115o

Fig. 11.6. The configuration and coverage of the NSCAT antennas. The surface swath is shown ingray, the antenna surface footprints are outlined, the nadir gap is white. (Adapted from Figure 7 ofNaderi et al. (1991).)

for attenuation σ was then obtained from Equation (10.17), where the transmissivity wastaken from a climatological lookup table.

As Section 10.5.3 shows, the Doppler shift observed by the scatterometer is also afunction of the Earth’s rotation, so that, in the NSCAT processing, the center frequency andbandwidth of each Doppler cell were adjusted as a function of distance from the equatorso that the size and positions of the surface bins relative to the satellite did not change. Incontrast, SASS had only four stick antennas at 45° and 135° to right and left of the spacecrafttrajectory, and its onboard Doppler filters were fixed (Johnson et al., 1980). This causeddifficulties near the equator, where the Doppler cells observed by the fore and aft antennashad different lengths, which reduced the cell overlap in the two-look intercomparisonof σ0.

11.5 AMI and ASCAT scatterometers

This section describes the wind retrievals by the 5.3-GHz ESA Advanced Microwave Instru-ment (AMI) on the ERS-1 and -2 satellites, and its successor, the Advanced Scatterometer(ASCAT) on METOP-A, METOP-B and the planned METOP-C.


344 Scatterometers

Nadir gap

Flight direction

225 km

475 km

45o

Illuminated area

135o

Swath

Fig. 11.7. The surface swaths of the ERS AMI scatterometer antennas.

11.5.1 The Advanced Microwave Instrument (AMI)

The Advanced Microwave Instrument (AMI) flew on the ERS-1 and ERS-2 satellites; theMETOP series carry its ASCAT successor. The ERS satellites were in a Sun-synchronouscircular orbit at an altitude of 785 km, a nominal period of 100 minutes and a 1030-local equator-crossing time. The AMI was a vertically polarized C-band scatterometerthat combined a high-resolution SAR with a low-resolution wind scatterometer, using acommon transmitter and receiver and two separate antennas (Attema, 1991). The SAR useda large rectangular antenna; the scatterometer used the three large-aspect-ratio rectangularantennas. The system operated in three modes: a high-resolution SAR image mode thatwas only used when the satellite was within range of a ground station so that the data couldbe directly downloaded, a low-resolution SAR mode used for wave observations and thescatterometer mode. The wave and scatterometer mode were recorded onboard for laterdownloading. Because the scatterometer and SAR used the same electronics, wind datawere not always taken near the ground stations.

Figure 11.7 shows the footprints of the AMI scatterometer antennas. The three rectan-gular antennas generated beams to the right of the spacecraft at azimuth angles of 45°, 90°and 135°. The central antenna measured 2.3 m × 0.35 m and the fore and aft antennasmeasured 3.6 m × 0.25 m. The central antenna had a beam width of 24° in elevation and1.4° in azimuth; the fore and aft antenna beam widths were 26° in elevation and 0.9° inazimuth. For the fore and aft antennas, the receiver center frequencies were adjusted to


11.5 AMI and ASCAT scatterometers 345

account for their respective Doppler shifts. To minimize the effect of the Earth’s rotationon the scatterometer, the satellite was actively rotated about its nadir axis in what is calledyaw steering, so that the Doppler shift observed by the mid-antenna beam was alwayszero.

Because of the nadir gap, the swath begins at ±225 km from nadir and has a cross-trackwidth of 475 km. The AMI used range binning to observe σ0 within cells with cross-trackand along-track widths of about 50 km. The instrument pulses consisted of constant-frequency waves with a power of several kilowatts (Gelthorpe et al., 2000). For the centralantenna, the pulse duration was 70 µs; for the fore and aft antennas, the duration was130 μs, where the fore and aft pulse lengths were longer because of the oblique antennaazimuth angles. For the central antenna, the PRF was 115 Hz, and for the fore and aftantennas the PRF was 98 Hz, so that, for each antenna, the time between pulses was about104 µs. This relatively long inter-pulse interval was used in three ways: to receive R, torecord an internal calibration pulse and to make a passive observation of TN. Because thisprocedure was followed for every pulse, calibration of the return and removal of TN wasstraightforward.

For each pulse, σ0 was calculated by applying the calibration, removing the system andenvironmental noise, then correcting for atmospheric transmissivity from a climatologicallookup table. For each antenna, σ0 was resampled onto a 25-km square grid, with 19 datapoints across the swath. The individual σ0 were then resampled to a 50-km resolution toimprove their signal-to-noise ratio, where, across the swath, the noise was nearly constantat about 6% of the signal (Ezraty and Cavanie, 1999). The three looks yield two wind speedestimates where the best wind solution was determined by comparison with NWP solutions.Surface transponders and observations of the Amazon rain forest with its relatively uniformbackscatter provided additional external calibrations and a check on instrument drift anddegradation.

11.5.2 The Advanced Scatterometer (ASCAT) on METOP

The AMI observations terminated in January 2001; its replacement is the European C-bandAdvanced Scatterometer (ASCAT-A and ASCAT-B) on METOP-A and METOP-B. Unlikethe ERS spacecraft, the METOP series does not include a SAR. Figure 11.8 shows theconfiguration of the ASCAT antennas and their surface swaths; the instrument is a C-bandrange-binned scatterometer with six antennas that are mounted in pairs and are similar indesign to AMI, except that they look off to both sides of the spacecraft, doubling the swathwidth while keeping the nadir gap. Its twin swaths are offset to the left and right of thesatellite ground track by about 350 km, for a total separation between swaths of 700 km,where the width of each swath is about 550 km (ASCAT, 2013c). Because the forecastmodels require daily, near-global coverage, the wide swath is especially important for theoperational METOP-A and -B.

In contrast to the scatterometers used on ERS, which relied on the transmission ofcontinuous-wave pulses with durations of around 100 µs and peak powers of several


346 Scatterometers

Nadir gap

350 km

45o

135o

Flight direction

Swath

550 km

Fig. 11.8. The configuration of the antennas and surface swaths of the METOP-A and -B AdvancedScatterometer (ASCAT), respectively launched in 2006 and 2012. (Adapted from Rostan (2000).)

kilowatts, ASCAT transmits chirped pulses with a longer duration of around 10 ms and arelatively low peak power of 120 W. Similar to AMI, the pulse repetition interval for eachantenna of ASCAT includes a transmission, reception of the echo, an internal calibrationpulse and a noise measurement, where this cycle takes about 0.2 s (Gelsthorpe et al., 2000).Soisuvarn et al. (2010) describe the current ASCAT CMOD-5 geophysical model function.

Each beam measures the radar backscatter on either a 25-km or a 12.5-km grid, so thateach swath is divided into 21 or 41 wind vector cells (WVC). These two resolutions bring theeffective swath width to respectively 525 km (21 × 25) or 512.5 km (41 × 12.5). Becauseof the satellite motion, each WVC provides three independent backscatter measurementsthat are separated by a short time delay. Given that the three looks yield two possible windsolutions, the ambiguities are reduced to a single estimate through comparison with theNWP winds. The operational data produced by these satellites are available at a 25- and50-km resolution, where the 25-km data are designed for coastal regions and are availableare the PO.DAAC website (ASCAT, 2013b).

11.6 The rotating beam scatterometers

The class of rotating beam scatterometers is among the most important. These scatterome-ters include QuikSCAT, which operated for a decade, the Indian Oceansat-2 scatterometer,data from which are currently used in numerical forecast models, and the Chinese scat-terometer on the HY-2A satellite. These are wide-swath instruments with no nadir gap.Because of the importance of its decadal time series as the basis of a climate data recordand the similarity of its operation to the other rotating beam instruments, this sectionconcentrates on QuikSCAT.


11.6 The rotating-beam scatterometers 347

SeaWinds Orbit track

250 km

Nadir track

Nadir

Cross track

47o 55o

beam

18 rpm

700 km900 km

h = 800 km beam

Fig. 11.9. The SeaWinds conceptual design and scan coverage for the listed incidence angles. In thedark portion of the swath, the winds are determined from four looks; in the light portion, from twolooks. (Adapted from an unpublished figure of Michael Freilich.)

11.6.1 The SeaWinds scatterometer

The SeaWinds scatterometer was on the QuikSCAT and ADEOS-2 satellites. QuikSCATflew at an altitude of about 800 km; Spencer et al. (1997, 2000) describe its designand operation. QuikSCAT had a 0600 ascending equator-crossing time; ADEOS-2 hada 1030 descending crossing time. As Table 11.1 shows, the Indian Oceansat-2 and theChinese HY-2A satellites carry similar scatterometers; the Oceansat-2 data are publicallyavailable. Oceansat-2 is in a Sun-synchronous orbit at an altitude of 720 km with a localnoon ascending crossing time; HY-2A is at an altitude of 970 km.

With adjustments for their different altitudes, the rotating pencil beam instruments worksimilarly. SeaWinds consists of a 1-m rotating parabolic antenna, with two offset feeds thatgenerate two 13.4-GHz pencil beams at different incidence angles (Figure 11.8). The innerbeam operates at HH, an off-nadir angle of 40° and an incidence angle of 47°; the outerbeam operates at VV, an off-nadir angle of 46° and an incidence angle of 55°. OSCAToperates similarly, with an HH inner beam and a VV outer beam (Fore et al., 2013). TheQuikSCAT antenna rotates at 18 rpm; its surface footprints have diameters of approximately25 km. The return from this footprint can either be binned in its entirety or, as shown below,divided into a number of range-dependent cells. As Figure 11.9 shows, the SeaWinds swathhas an overall width of 1800 km with no nadir gap, or much wider than the ASCAT swath.The swath divides into two parts: in the dark gray areas, the winds are determined fromfour looks; in the light gray areas, from two looks. Part of the two-look region occurs atdistances for which only the outer beam takes data, and part occurs adjacent to nadir.

Figure 11.10 shows the rotating pattern of a single SeaWinds footprint; during onerotation, the satellite advances about 25 km. For the four-look region, Figure 11.11 shows


348 Scatterometers

Fig. 11.10. The surface scanning pattern of a single SeaWinds beam. The diameter of a single FOVis about 25 km. (Figure courtesy of Michael Freilich, used with permission.)

t4t1 t2 t3

Nadir track90

0 km

700

km

FOV

Fig. 11.11. An example of how two looks by the outer beam and two looks by the inner beam generatefour looks at the same FOV. (Redrawn from an undated NASDA publication on ADEOS-2.)

that the FOV is viewed twice by the outer beam looking forward at time t1 and backwardat t4, and twice by the inner beam looking forward at t2 and backward at t3. Spenceret al. (1997) show that the wind retrieval performance of the SeaWinds varies with distancefrom the nadir track, where the best wind retrievals occur when the azimuthal differencesbetween observations are close to 90°, so that, even in the four-look region, the quality ofthe retrieved winds is not uniform.



Table 11.3. SeaWinds parameters.

Parameter Inner beam Outer beam

Rotation rate 18 rpmPolarization HH VVZenith angle 40° 46°Surface incidence angle 46° 54°Slant range 1100 km 1245 km3-dB footprint (along-scan × cross-scan) 24 × 31 km 26 × 36 kmPulse length (unchirped) 1.5 msPulse length (chirped) Programmable, >2.7 µsAlong-track spacing 22 km 22 kmAlong-scan spacing 15 km 19 kmGround swath 1400 1800

Adapted from Spencer et al., (2000, Table 1) and ISS-RapidScat (2013a, Table 1).

25 km

35 km

Antenna look direction

Rotationdirection

Fig. 11.12. The division of the SeaWinds footprint into range slices. See the text for additionaldescription.

Table 11.3 lists some properties of the SeaWinds beams. The transmit/receive cyclealternates between the two beams as follows: inner beam transmit, outer beam receive,outer beam transmit, inner beam receive, so that each echo returns after the followingtransmit pulse. For both beams, the overall PRF is about 192 Hz, corresponding to atransmit/receive cycle of about 5.2 ms, within which the antenna rotates about half a beamwidth.

The footprints are an ellipse measuring approximately 25 km in azimuth and 35 km inrange. Within this footprint, which is sometimes called an egg after its shape, range binningis used to improve the resolution (Perry, 2001; Fore et al., 2013). Figure 11.12 shows the eggfootprint, and the division of the egg into five different range bins, called slices that measure


350 Scatterometers

Signal spectrumNoise filter

Signal + noise filter

Noise spectrum

fc

Ret

urn

pow

er

Frequency

Fig. 11.13. The SeaWinds filters used for detection of signal and noise. The figure shows the signaland noise spectra, and the filters used to discriminate between the two. (Adapted from Figure 6 ofSpencer et al. (1997).)

7 km × 25 km. There are five slices per footprint, and in the analysis σ0 is calculated forboth the full footprint and the slices. This means that the scatterometer measures σ0 at avariety of resolutions, including the full beam footprint, the slice footprints and a variety offootprints made up of combinations of slices. For each of these, ground processing locatesthe geographic center of the egg and its slices, and for wind processing, matches the overlapof the slices from different footprints.

Since the OSCAT on Oceansat-2 has been in orbit, both its beams have drifted incalibration. This was in part remedied through use of simultaneous observations fromQuikSCAT that provided for measurement and mitigation of this drift (Jaruwatanadiloket al., 2012). In 2009, after the QuikSCAT antenna ceased to rotate, the calibration consistedof comparison of the OSCAT measurements with the point measurements of QuikSCAT,and with OSCAT observations of regions such as the Amazon Basin with relatively stableuniform scattering properties. Because ASCAT works at C-band, it is difficult to use as anOSCAT calibration source. As Section 11.8 discusses, in 2014, when the ISS-RapidScat isdeployed, one of its functions will be to serve as a calibration source for OSCAT.

11.6.2 Internal calibration and removal of noise

At every half rotation, SeaWinds generates an internal calibration pulse as a check onthe scatterometer gain. For noise removal and unlike the other scatterometers, SeaWindsmeasures TN and R simultaneously (Spencer et al., 2000). From Figure 11.12, thismeasurement works as follows. The return signal has a center frequency fc that is adjustedfor the azimuth-dependent Doppler shift. Around fc, R has a symmetric peaked spectrumthat lies within an 80-kHz bandwidth; in contrast, TN has a flat, broad spectrum thatoverlaps R. To recover the signal and noise, for each pulse, the return is passed throughtwo filters centered on fc, one with a broad 1-MHz bandwidth, the other with an 80-kHz



bandwidth. The broad filter primarily measures noise; the narrow filter measures signal andnoise. To a good approximation, subtracting one from the other yields the corrected signal.The advantage of this simultaneous measurement of signal and noise is that it can accountfor conditions where the surface or atmospheric properties change rapidly, such as nearan ocean front or at the ice edge. The disadvantage is that, unlike the AMI and NSCAT,the measurements of TN and R are not independent. Spencer et al. (2000) show that,compared with NSCAT, the noise increase associated with this method is small.

11.6.3 Atmospheric transmissivity and rain

As Equation (10.17) shows, the radar backscatter from each wind cell must be correctedfor the atmospheric transmissivity t and masked for rain. Both in the atmosphere and atthe surface, rain affects the backscatter measurements. In the atmosphere and as Section9.2.3 discusses, rain modifies the received radiance in two ways, namely by attenuation ofthe radiance along its path from the surface to the instrument and by enhancement of thereceived radiance from raindrop-induced Rayleigh and Mie scatter. Even though rain affectsonly about 7% of the scatterometer observations, heavy rain occurs during meteorologicalevents such as hurricanes and typhoons and often accompanies periods of sustained highwinds (Weissman et al., 2012). At the surface, raindrops cause roughening, affect thebackscatter and alter the GMF response. Even for rain-free conditions, at high wind speeds,the droplets generated from breaking waves and the spray generated by wind shear atthe wave crests clutter the surface. Because, at the shorter wavelengths, the scatterometeris more sensitive to small-scale surface roughness and the atmospheric attenuation has agreater variability, both problems are more serious at Ku-band than at C-band.

Because rain greatly affects the scatterometer returns, its wind retrievals are restricted toconditions of no or light rain. Even though the scatterometer antenna is a less than optimalradiometer, the attenuation in the signal return caused by rain is used to mask the data.Given that QuikSCAT did not carry a passive microwave radiometer, t was provided froma global monthly mean SSM/I-derived climatology that is interpolated in time and space tothe surface wind cell, then calculated for the scatterometer look angle (Perry, 2001; Lunguand Callahan, 2006). For SeaWinds on the short-lived ADEOS-2, the AMSR radiometerprovided co-located observations of columnar water vapor, liquid water and rain rate.

11.6.4 Accuracy of the wind speed and direction retrieval

For U < 20 m s−1, the SeaWinds GMF was initially generated by comparison with buoyand NWP winds. Ebuchi et al. (2002) compare the early model functions including theKu-2001 GMF with buoy winds. For wind speeds less than 15 m s−1, they find that the rmsdifference between the observed and scatterometer winds is less than 1 m s−1 and the biasis negligible. Above this speed, they observed a growth in positive bias. For wind direction,they found an overall rms difference of 25o, while, for the restricted range of 3 m s−1

< U < 20 m s−1, the rms difference was about 20o. For U > 20 m s−1, aircraft observations


352 Scatterometers

0 2520105 150

10

20

30


Roo

t-m

ean-

squa

re e

rror

(de

g)

Fig. 11.14. For rain-free conditions, the rms error in wind direction as a function of weed speed forwinds derived from WindSat (dashed line) and from the QuikSCAT Ku-2011 GMF (solid line) ascompared with co-located NCEP wind direction. (Redrawn from Figure 4, Ricciardulli et al. (2012.)

showed that, for velocities of 20–30 m s−1, the Ku-2001 GMF overestimated the windspeeds by 20%–25% (Renfrew et al., 2009).

To correct this discrepancy at high wind velocities, Ricciardulli and Wentz (2011) derivedthe new QuikSCAT Ku-2011 model function. Because, at high wind speeds, the buoy andNWP winds are less reliable than at low speeds, they derived this GMF from comparisonof QuikSCAT observations with coincident rain-free WindSat hurricane-derived windsdescribed in Section 9.7.

This comparison is possible because the scatterometers and WindSat measure the windsdifferently. The scatterometer responds to the azimuthal distribution of surface roughness,while the radiometer responds to changes in the surface emissivity, which at low windspeeds is dominated by waves and roughness, and at high wind speeds by the areal extentof foam. Because at low wind speeds (< 6 m s−1), the wind direction signal in the surfaceemissivity is very small, the scatterometer provides a significantly better direction retrievalthan the radiometer. At high wind speeds, the radiometer primarily responds to foam; thescatterometer responds to the surface roughness under the foam. Further, as Figure 11.4shows, for U greater than about 20 m s−1, the scatterometer is less sensitive to changes inwind speeds than the nearly linear radiometer dependence shown in Figure 9.21.

Because the WindSat winds that Section 9.7 describes are considered accurate forspeeds less than 30 m s−1, the Ku-2011 GMF is based on seven years of co-located valuesof QuikSCAT with the WindSat high winds data set (Ricciardulli and Wentz, 2011). In theiranalysis and using the WindSat rain-detection algorithm, they discard all rain-contaminateddata, so that the Ku-2011 GMF is valid for rain-free winds for 0 U 30 m s−1 (Meissneret al., 2011a). As Ricciardulli et al. (2012) state, using a similar methodology, they plan toreprocess the ASCAT GMF with WindSat data.

From comparison of the WindSat and QuikSCAT Ku-2011 winds with co-located NCEPwinds under rain-free conditions, Figure 11.14 shows for the two instruments the rms error



0 2520105 150

10

20

30

GFDex Aircraft wind speed (m s–1)

Qui

kSC

AT

win

d sp

eed

(m s

–1)

30 35

Fig. 11.15. Comparison of the aircraft winds from the Greenland Flow Distortion experiment(GFDex) experiment compared to QuikSCAT Ku-2011 winds. The different symbols are the resultsfrom different flights; the solid line is the line of prefect agreement; the dashed line is the least-squaresfit. For the Ku-2011 wind speeds relative to the GFDex speeds, the bias is 0.62 m s−1, the rms erroris 1.9 m s−1, the correlation coefficient is 0.867, the slope of the least-squares agreement is 1.131,and the rms difference in wind direction is 9.3o. See the text for further description. (Adapted fromFigure 7, Ricciardulli and Wentz (2011); GFDex aircraft data from Renfrew et al. (2009).)

in wind direction as a function of wind speed (Ricciardulli et al., 2012). For QuikSCAT andfor U > 6 m s−1, the directional error is about 10o. For comparison, the error in WindSatdirections strongly diverge at low wind velocities, but in the 10–20 m s−1 range have errorscomparable to QuikSCAT.

Similarly to the WindSat comparison with aircraft data described in Section 9.7, theKu-2011 QuikSCAT data were also compared with the rain-free aircraft wind observationsfrom the Greenland Flow Distortion experiment (GFDex) flights (Renfrew et al., 2009).Their 2-min averages of wind speed and direction were matched in position and time tothe QuikSCAT wind retrievals. Figure 11.15 compares the GFDex and the QuikSCAT Ku-2011 observations. The rms difference in wind speed between the two data sets is less than2 m s−1; the rms difference in wind direction is less than 10 deg. These errors are better thanthe requirements listed in Table 11.2, suggesting that the Ku-2011 algorithm is valid forrain-free conditions and wind speeds less than 30 m s−1. It also shows that the calibrationprocedure for the Ku-2011 using WindSat was successful, and gives better agreement withhigh wind velocity data than the Ku-2001 results.

For different rain rates, Ricciardulli and Wentz (2011) describe a comparison of buoywind speeds with co-located values derived from the WindSat all-weather algorithm and theQuikSCAT Ku-2011 GMF. The WindSat comparison shows that as the rain rate increasesfrom 0 to heavy rain (>8 mm h−1), the absolute value of the bias remains less than


354 Scatterometers

1 m s−1 while the standard deviation increases from 0.9 to 2 m s−1. In contrast and asexpected from its rain-free derivation, for the QuikSCAT retrievals, the bias increases froma value of 0 and standard deviation of 0.9 m s−1 for no rain, to a bias of 7.1 m s−1 and astandard deviation of 4.5 m s−1 for heavy rain.

Comparison of the advantages and disadvantages of the WindSat and QuikScat instru-ments and algorithms shows that, for the case of no rain, the wind speed retrievals arecomparable. For velocities less than 10 m s−1, the QuikSCAT wind directions are superior.For rain, WindSat gives much better results than QuikSCAT.

11.7 Advantages and disadvantages of the different scatterometers

The greatest disadvantage of the fan-beam scatterometers is their nadir gap in the windcoverage. In contrast, QuikSCAT provides a broader swath with no nadir gap, yieldingan improved daily coverage. QuikSCAT had a near global 93% coverage and a 25-kmresolution that with some loss in accuracy can be processed to 12.5 km.

Other advantages of the rotating antenna scatterometers are as follows. First, becausethe 2–3-m-long large-aspect-ratio rectangular or stick antennas required by the fan-beamscatterometers require unobstructed fields-of-view from the spacecraft, they cannot beaccommodated on all vehicles. Also, these antennas must be designed to fold into a compactpackage to fit into the launch vehicle, so their deployment in space is more difficult andsubject to problems. In contrast, the QuikSCAT dish antenna is easier to accommodate anddeploy. Second, the QuikSCAT geophysical model function can be specified at only twodiscrete incidence angles, rather than at the broad range of incidence angles associated withASCAT. Third, because all of the QuikSCAT energy is incident at a specific angle onto asmall surface footprint, the backscatter also avoids the fourth-power decrease with rangethat occurs across the fan-beam swath. Fourth, the fan-beams by necessity have a nadir gap,and, because of the fourth-power decrease, have narrower swaths than the rotating pencilbeams.

The QuikSCAT disadvantages are as follows. First, because the antenna constantlyrotates, there is less integration time available for averaging of adjacent measurements andnoise reduction. In contrast, the entire fan-beam swath is illuminated with each pulse, so thatthe available averaging time is greater. Second, the fan-beam observations of a particularFOV are always made at the same azimuth angles, while the QuikSCAT observations occurat a variety of azimuth angles. Because the wind algorithms work best for azimuth anglesseparated by 90° and have greater errors for azimuth angles separated by 180°, unlike thefan-beam instruments, the QuikSCAT observational accuracy varies across the swath.

Figure 11.16 gives a tabular comparison of the different antenna and swath configu-rations of the five wind scatterometers. The third row shows the surface patterns of thedifferent instrument antennas; the seventh row compares the instrument swaths, wherethe fixed Doppler filters of the SASS generate its variable swath width. The figure showsthat SeaWinds and ASCAT provide the best coverage and that only the rotating beamscatterometers and WindSat lack the nadir gap.


11.8 The ISS-RapidScat 355

Frequency

Instrument

Scan pattern

SASS

14.6 GHz

AMI (ERS-1, -2)

5.3 GHz

NSCAT

13.995 GHz

SeaWinds

13.402 GHz

ASCAT

5.3 GHz

Incidence angle

Beam resolution Mixed Doppler Range binning Variable Doppler Scanning pencil Range binning

Resolution 50 km 50 km 25 km 12.5, 25 km

Swath

22°–55° 20°–50° 20°–50° 47°–55° 20°–50°

25 km

1800 km

Daily coverageOperation dates

Variable 41% 77% 93%2006–13; 2012–1999–09, 2002–031996–971991–2001197880% (estimated)

500 km 500 km 500 km 600 km 600 km 550 km 550 km

Fig. 11.16. Comparison of the properties of the five scatterometers. (Adapted from Figure 3 fromAtlas et al. (2001), C© 2001 American Meteorological Society, used with permission.)

11.8 The ISS-RapidScat

The planned deployment of the Ku-band ISS-RapidScat to the International Space Station isa two-year mission. The ISS-RapidScat has three goals: to mitigate the loss of QuikSCAT, toserve as a calibration standard for the scatterometer constellation, particularly for OSCAT,and to study the diurnal variation of ocean winds (ISS-RapidScat, 2013a).

Regarding the role of ISS-RapidScat in the scatterometer constellation, in 2013, therewere three scatterometers used in operational forecasting, the ASCATs on METOP-A and -Band the OSCAT on Oceansat-2. Given the OSCAT problems with drift, one role of ISS-RapidScat is to serve as an OSCAT calibration source. The ISS-RapidScat instrument isbuilt from QuikSCAT hardware and has similar look angles and polarizations as well as anidentical rotation rate, except because of its lower altitude, the antenna diameter is reducedfrom 1 m to 0.75 m and its data will be sent to the ISS for transfer to Earth. In 2014, aSpaceX Dragon capsule will deliver the instrument to the ISS. The ISS-RapidScat groundprocessing is identical to QuikSCAT (ISS-RapidScat, 2013b).

The ISS is not an ideal scatterometer platform. First, because of atmospheric drag, theISS altitude varies between 435 km and 375 km, or about half the QuikSCAT altitude,where the exact altitude is a function of time that depends on the schedule for boosting theISS back to a higher altitude. Second, during resupply missions, the attitude or orientationof the ISS will vary, requiring adjustments in the day-to-day operations of the instrument.Third, unlike the other wind satellites, the ISS is not in a Sun-synchronous orbit; instead,


356 Scatterometers

it is in a prograde orbit inclined at 51.6o. At time intervals of 0.5–1 h, this orbit intersectsthose of the other scatterometers and provides coincident coverage. As the ISS orbit pre-cesses, these intersections shift in latitude and longitude, which will allow determinationof any geographic bias between ISS-RapidScat and the other wind satellites. The ISS orbitprecession also means that ISS-RapidScat can study the diurnal variability of tropical andsub-tropical winds, which will improve our understanding of the tropical atmosphere.

11.9 Cross-calibrated multi-platform winds (CCMP)

Atlas et al. (2011) describe the Cross-Calibrated Multi-Platform (CCMP) project, whichderives climate data records of merged ocean wind data sets. In CCMP, the satellite datasets are cross-calibrated satellite winds derived from instruments such as SSM/I, SSMI/S,AMSR-E, TMI, QuikSCAT and WindSat that are processed by the company RemoteSensing Systems (REMSS, 2013). The CCMP also uses the ECMWF analyses and surfacedata from buoys and ships.

In the derivation of the CCMP data sets, the satellite and in situ data are combinedusing a variational analysis method (VAM). Within VAM, ECMWF provides a first guessof the gridded wind field. The VAM is used to assimilate all of the surface and satellite datasets and to preserve the small-scale features in the satellite data that are not visible in theECMWF analysis (Atlas et al., 2011). The PO.DAAC website currently includes thirteendifferent CCMP wind data sets that are derived from the different satellite data sets (CCMP,2013). These are gridded at a latitude/longitude resolution of 0.25 deg × 0.25 deg; theirtime scales range from 1 month to daily to six-hourly.

The CCMP product contains three processing levels. The primary data set is the Level-3.0 analysis that contains the 6-h gridded VAM analyses. This analysis, which makes useof all of the available satellite data sets, begins on 1 July 1987 and currently ends on31 December 2011. The second is the Level-3.5 analyses, which consist of the Level-3.0 analyses averaged over 5-day and 1-month periods. The Level-3.5 analyses divideinto 3.5a and 3.5b, where, for Level-3.5a, only those grid points that contain one or moresatellite observations are used in the averages, while in Level-3.5b, all grid points are filled ifnecessary with ECMWF data. The third are the 12-h Level-2.5 analyses that correspond toa particular satellite sensor; these are valid for the instrument lifetime. For Level-2.5 andfor each data point, wind directions from the VAM analyses are interpolated in time andposition, then assigned to the data sets (CCMP, 2009). Each data set is available viaanonymous ftp from CCMP (2013), where the site also contains a number of visualizationtools.

11.10 Applications and examples

This section gives three examples of scatterometer wind retrievals, then discusses aSeaWinds backscatter image of the Antarctic sea ice. The wind examples include a NorthPacific weather front, a large-scale example of daily winds from the Atlantic and Pacific,and a strong wind event off the Pacific coast of Central America.



QuikSCAT surface winds - Sep. 2, 1999 - 15:30Z

s

160oW 150oW

50oN

40oN

20m s–1

Fig. 11.17. A single ascending SeaWinds swath located in the North Pacific, just south of the AlaskaPeninsula and acquired on September 2, 1999 at 1530 UTC. The wind vectors are given at intervalsof 25 km; the vectors are color-coded so that black vectors are rain-free, red vectors are rain-contaminated. The inset arrow shows the wind scale. (Courtesy of Jerome Patoux and Robert Brown,used with permission.) See color plate section.

11.10.1 A weather front in QuikSCAT swath data

Figure 11.17 shows a single swath of QuikSCAT wind vectors across a front in the NorthPacific taken on September 2, 1999 at 1530 UTC. The swath is 1800 km wide and is centeredjust south of the Alaskan Peninsula. The black vectors are rain-free; the red vectors arerain-contaminated. The arrows outside of the figure at the top right and middle left mark thediscontinuity associated with the QuikScat transition from four to two looks. The line ofdiscontinuity in wind direction running from the bottom left to the upper right is a weatherfront; the adjacent red vectors show a frontal rain band. At the lower right, the anomalouslylarge wind vectors may be the result of improper rain-flagging. Figure 11.17 shows that themany wind vectors retrieved within the swath provide a powerful tool for case studies offronts and other wind and storm systems. It would be impossible to obtain a comparablecollection of wind measurements from ship observations.


358 Scatterometers

Pacific

Atlantic

Fig. 11.18. The QuikSCAT ocean wind field for April 19, 2000 for the Pacific and Atlantic Oceans.The lines and arrows show the wind direction; the colors show the wind speed. (The images wereobtained from the NASA/NOAA sponsored data system Seaflux at JPL through the courtesy ofW. Timothy Liu and Wenqing Tang, used with permission.) See color plate section.

11.10.2 Hemispheric winds

For the Atlantic and Pacific Oceans, Figure 11.18 shows the QuikSCAT winds for April19, 2000. On the plate, the lines and arrows show wind direction; the colors show windspeed, where yellow and green represent wind speeds greater than 13.5 m s−1. In the North



20° N

15° N

10° N

5° N110° W

0 0.5 1.0 1.5 2.0 2.5 km

100° W 90° W

Fig. 11.19. A QuikSCAT image of a Tehuano event at Chivela Pass in southern Mexico taken at 00UTC on December 1, 1999. The Atlantic is on the upper right; the Pacific is on the left. The colorbar gives the scale of the land topography; the contoured shades of blue and arrows show the windspeed and direction, where darker shades of blue and longer arrows indicate greater speeds. The windspeed contours are at intervals of 1.5 m s−1. (Courtesy of Mark Bourassa and Josh Grant, used withpermission.) See color plate section.

Atlantic, the strong winds southeast of Greenland are associated with a storm approachingthe British Isles; in the North Pacific, a similar cyclonic storm occurs just south of theAleutian Islands. In the South Pacific, strong winds occur south of Australia and east ofNew Zealand. In the South Atlantic, strong winds also occur between South America andAfrica.

11.10.3 Gulf of Tehuantepec

The Sierra Madre Mountains located along the Pacific coast of Mexico and Central Americaplay an important role in the regional meteorology. For the winter cold fronts that propagatesouth across the Gulf of Mexico from North America, the mountains act as a barrier betweenthe Gulf and the Pacific. Only two gaps in these mountains permit the flow of cold denseair into the Pacific: Chivela Pass in southern Mexico and the low-lying terrain around thecentral Nicaraguan lake district. Within these gaps, the air flow can be strongly accelerated.Bourassa et al. (1999) report observations of wind velocities in Chivela Pass as large as60 m s−1. For December 1, 1999 at 00 UTC, Figure 11.19 shows a QuikSCAT-derivedexample of these winds into the Gulf of Tehuantepec, where such a wind event is called aTehuantepecer or Tehuano wind. On the plate, land topography is shown in color accordingto the scale below; over the ocean, the shades of blue and the white arrows show thewind magnitude and direction, where darker shades of blue indicate stronger winds. In the


360 Scatterometers

B10A

Fig. 11.20. Backscatter properties of the Antarctic continent and the surrounding sea ice derived froma 24-hour average of QuikSCAT σ0 measurements on 19 July 1999. (Figure courtesy of David Long,Brigham Young University (BYU), used with permission.)

Atlantic, the image shows the flow acceleration approaching the pass, and in the Pacific,the concentration of large velocities adjacent to the coast. The image is derived from 25-kmgridded QuikSCAT winds following the scheme described in Pegion et al. (2000). In theGulf of Tehuantepec, these winds generate the cold coastal upwelling that Figure 7.18shows at a small scale.

11.10.4 Polar ice studies

As an example of QuikScat observations of land and sea ice, Figure 11.20 shows, for July19, 1999, a 24-hour average of the QuikScatσ0 measurements of the Antarctic continentand the surrounding sea ice. To remove the wind signal, the open water surrounding thepack ice has been masked. Because of the strong radar returns from continental snow andice, the Antarctic continent has a large range of backscatter with several very bright regions.In contrast, the pack ice surrounding the continent is darker with a smaller dynamic range.Within the pack ice and in Drake Passage, the bright objects are icebergs, where the source



of their brightness is corner reflection from their vertical walls. The bright rectangularobject just outside of the passage at the left of the image is a 21 km × 42 km large icebergcalled B10A. The B10A iceberg broke off the end of the West Antarctic Thwaites ice shelfin about 1992 and since that time has drifted around the continent. As Long and Drinkwater(1999) describe, daily scatterometer images of the pack ice show its extent, circulationpatterns and response to winds, without the concerns about water vapor at the ice edge thatoccur in the passive microwave sea ice algorithms. The imagery is also used by the NationalIce Center to track large icebergs and to post their positions as hazards to navigation.


12

The altimeter

12.1 Introduction

The radar altimeter transmits short pulses of energy vertically downward toward the oceansurface, then receives the reflected signal. The return yields information on the global dis-tribution and variability of sea surface height, ocean swell amplitude and scalar wind speed.Specifically, the time difference between the transmitted and received signals measures thedistance or range between the satellite and the sea surface, the shape of the return yieldsthe significant wave height (SWH) and the magnitude yields the scalar wind speed. If thesatellite orbit is precisely determined and the range is corrected for a variety of ionospheric,atmospheric and ocean surface factors, these observations measure, to an accuracy of2–3 cm, the changes in sea surface height (SSH) associated with tides, geostrophic currentsand other oceanic phenomena.

This chapter describes how the altimeter works, discusses its sources of uncertainty anddescribes some of its oceanographic applications. Wunsch and Stammer (1998) and thecollection of papers edited by Fu and Cazenave (2001) contain more detailed and extendeddiscussions of the TOPEX altimeter results, and Chelton et al. (2001b) describe the physicsof the TOPEX altimeter and its associated error budget. Morrow and Fu (2010) organizedand provide the introduction to a special issue of Marine Geodesy on the JASON-2 mis-sion; see JASON-2 (2010) for a listing of the papers. Fu (2010) describes the current stateof the altimeter measurements and their application to the ocean circulation. At scales of150–200 km, multiple altimeters provide near-global coverage of the temporal and spa-tial scales of ocean variability, the meridional transports of heat and the distribution andproperties of ocean eddies.

Altimeters make two additional contributions. First, because the sea surface respondsto changes in the gravitational attraction generated by topographic features on the oceanfloor, altimeter observations of relatively small sea surface displacements contribute to animproved knowledge of the seafloor topography (Smith and Sandwell, 1997; Smith, 2010).Second, because the altimeter serves as a precision tide gauge, it has also enhanced ourknowledge of deep ocean tides and their dissipation (Wunsch and Stammer, 1998).

One difficulty with altimeter measurements is that SSH must be measured relative to thegeoid, which is the shape that the ocean surface takes while rotating with the Earth in the

362


12.2 Shape of the Earth 363

absence of winds, currents and tides. The combination of data from gravity and altimetermissions with in situ observations has at present determined the geoid to length scales ofabout 20 km (Smith, 2010).

For users, the JPL Physical Oceanography Active Archive Center (PO.DAAC) containsaltimeter data in a variety of browse images and downloadable files that are corrected forthe biases and uncertainties discussed in this chapter (PO.DAAC, 2013). This permits auser to work with the data without understanding, for example, how to correct for theinverse barometer effect. In spite of this data availability, the descriptions of the trade-offbetween orbit period and equatorial spacing, the factors that determine the surface footprintsize and resolution, and the contributions of the ionosphere, atmosphere and ocean surfaceroughness to the error budget should help the reader understand both the potential of thealtimeter and its limitations.

In the following, Section 12.2 describes the satellite orbit and the shape of the Earth anddefines the variables used in the SSH retrieval. Section 12.3 summarizes the historical oceanaltimeter missions; Sections 12.4 and 12.5 describe the TOPEX/POSEIDON altimetermission and its successors, JASON-1 and JASON-2. Sections 12.6 and 12.7 describe howthe altimeter works, discuss the interaction of the altimeter pulse with the sea surface andshow how ocean swell and sea surface roughness alter the reflected pulse. Section 12.8discusses the altimeter error budget; Section 12.9 gives examples.

12.2 Shape of the Earth

Figure 12.1 shows the variables used to describe the shape of the Earth and the sea surface.Along the radial line between the satellite and the Earth’s center of mass, the altimetermeasures the height or range h(χ,ψ, t) of the satellite above the sea surface, where χ islatitude and ψ is longitude. The other radial variable is the height H (χ,ψ, t) of the satelliteabove the ellipsoid, which is known relative to the Earth’s center of mass (JASON-2, 2011).As Section 12.4.4 discusses under the topic of precision orbit determination (POD), threedistinct methods are used to determine H and the satellite orbit. The difference between Hand h is hS(χ, ψ , t), the height of the sea surface above the ellipsoid, where

hS = H − h (12.1)

The goal of the altimeter is to determine hS to within the 2–3-cm accuracy necessaryto resolve geostrophic flows. As Equation (12.1) shows, this determination depends on theaccurate measurement of two quantities, the satellite height H in its orbit above the ellipsoidand its range h from the sea surface. These measurements are equally important and, as thischapter shows, are made in very different ways.

The sea surface height hS is described in terms of three successive approximations;the ellipsoid, the geoid and the variable sea surface height (Wunsch and Stammer, 1998;Chelton et al., 2001b). The first is the reference ellipsoid ER(χ,ψ), which is the shape ofthe time-independent uniform distribution of the Earth’s mass generated by gravitational


364 The altimeter

Satellite

Satellite orbit

Reference ellipsoid

Earth’s center of mass

h( χ, ψ, t)

hS( χ,

χ,

χ,

ψ, t)

H( χ, ψ, t)

ER( χ, ψ)

Local vertical z

Geoidundulation

ζ( ψ, t)

N ( ψ)

Geoid, N + ER

Sea surface height

Fig. 12.1. The altimeter geometry showing the satellite orbit, the reference ellipsoid, geoid undulationand height of the sea surface above the Earth’s center of mass, where χ is latitude and ψ is longitude.See the text for further description. (Adapted from Figure 3, Wunsch and Stammer (1998).)

and centrifugal forces. The short axis of the ellipsoid runs through the poles, the longaxis runs through the equator and it is symmetric about the polar axis. The length of theequatorial axis is such that at the equator the ellipsoid surface corresponds to mean sealevel. The JASON ellipsoid has a polar radius of about 6359 km and an equatorial radiusof 6380 km and accounts for about 90% of the geoid. The sea surface height is composedof the steady-state geoid and the time-varying dynamic topography.

Problems with the ellipsoid occur because of the uneven distribution of the Earth’smass. At a range of horizontal scales of 10 to 1000 km, lateral gravity forces determine thesurface topography, so that a region of excess mass at the sea bottom such as a continentalridge attracts water to produce a topographic rise, while mass deficits generate valleys(Figure 12.2). The sea surface produced by this uneven mass distribution is the equipotentialsurface corresponding to the sea level in the absence of external forces such as winds andtides, but with the presence of the Earth’s rotation. This surface is defined relative to theellipsoid and is called the geoid undulation N (χ,ψ), where the corresponding geoid is thesum N + ER (Wunsch and Stammer, 1998). Following common practice, this book calls Nthe geoid.

The geoid is derived from expansions of spherical harmonics fitted to a combinationof the gravity satellite data described in Chapter 14, the altimetry data described in this



1 km

10 m

Marine geoid

Ocean bottom

4 km

Fig. 12.2. The effect of a rise and depression in the seafloor topography on the marine geoid. Thehorizontal scale is of order 10 to 1000 km. The arrows show the local gravitational accelerations,which are normal to the geoid. (Adapted from Figure 10 of Chelton (1998) and from discussion inSmith (2010).)

chapter and in situ data. The ability of the geoid to resolve spatial features depends onits number of harmonics. Relative to the ellipsoid, N has an amplitude of about ±100 m.Figure 12.3 shows the marine geoid derived from the University of Texas UTGF26 modelwith 26 spherical harmonics and a spatial resolution of about 1500 km (Bindschadler et al.,1987, Figure 6a). The geoid has a topographic low south of India and a high north ofNew Guinea. The current geoid is the Earth Geopotential Model 2008 (EGM2008) with2190 spherical harmonics and a spatial resolution of about 5 arcmin or 10 km (Pavlis et al.,2012). At the scale of Figure 12.3, EGM2008 and UTGF26 are identical.

For an example of the geoid variability at shorter length scales, Figure 12.4 shows theocean surface response to changes in the seafloor topography over distances of 10–1000 km.The upper part of the figure gives the altimeter response in meters; the lower part gives thebottom topography in kilometers. Figure 12.4 shows that the subsurface ridges associatedwith the Line Islands and the Hawaiian Ridge generate a sea surface response of 1–5 m. TheMurray Fracture Zone also generates a topographic depression, while the seamounts do nothave a noticeable effect on the surface, probably because of their small geographic extent.The combination of altimeter measurements of the sea surface response to topographywith depth soundings and gravity measurements from ships are used to construct bottomtopographic charts (Smith and Sandwell, 1997; Smith, 2010).

Relative to the geoid, the third surface is the sea surface height ζ (χ,ψ, t), defined as

ζ (χ,ψ, t) = hS(χ,ψ, t) − N (χ,ψ) (12.2)

The height ζdescribes the sea level variability relative to the geoid induced by a widevariety of atmospheric and oceanographic phenomena. These include geostrophic flows,

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20

0 30 60 90 120 150 180 210 240 270 300 330 360Longitude

80

60

30

0

–30

–60

–80

Latit

ude

20

40

–40

40

0

–60

0 20

–40

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–50

75

65

–100

0

Fig. 12.3. The undulations of the oceanic geoid at contour intervals of 5 m, where the 0-m contour is darkened. The geoid is the University of TexasUTG26 model; the rms accuracy is about 1 m. (Figure 6a from Bindschadler et al. (1987); not subject to US copyright.)



5

0

–52000

3000

4000

5000

6000 0 600

km

Dep

th (

m)

Geo

id h

eigh

t (m

)

Line Islands

Hawaiian Ridge

MusicianSeamounts

MurrayFracture Zone

Southwest Northeast

23o N162.27o W

Fig. 12.4. Geoid height from the GEOS-3 altimeter and the corresponding bottom profile along thesub-satellite track. The long-wavelength regional geoid is subtracted from this profile to emphasizebottom topography. (Figure 3 from Watts (1979), C© 1979 American Geophysical Union, repro-duced/modified by permission of AGU; discussion from Wunsch et al. (1981).)

tides, atmospheric pressure changes, and seasonal heating and cooling. The geoid describesthe ocean at rest; ζdescribes the non-equilibrium surface of a dynamic ocean.

The sea surface height has both steady and variable components. The steady componentsinclude features such as the mean flows of the Gulf Stream and Kuroshio; the variablecomponents include tides, fluctuations associated with the weight of the atmosphere, thesurface response to seasonal oceanic heating and cooling, planetary waves and variablecurrents and eddies. As Table 2.1 shows, the presence of long period planetary waves,eddies and currents means that relative to the geoid, ζhas a variability of about 1 m. Thepurpose of the altimeter is to measure ζand determine the sea surface response to a varietyof geophysical forcing.

For measurements of ζ to be of oceanographic value, both H and h must be determinedto an accuracy of 2–3 cm. As the following sections show, the satellite orbital position His determined to a centimeter accuracy from a combination of three different positioningsystems: laser ranging, radio ranging and Global Positioning System (GPS) measurements.


368 The altimeter

The pulse round-trip travel time determines the range h. In addition to the uncertainty inorbital radial position, many factors contribute to the uncertainty in h. For range, variationsin V produce apparent changes of as much as 30 cm, and the diurnal and annual cycles of theionospheric free electrons produce changes of order 1 m. Rain and variations in the massof atmosphere along the altimeter path also contribute to the range uncertainty. Finally, theocean is not a quiescent specular reflector, but is covered by waves ranging from capillariesto large-amplitude ocean swell, where all of these waves affect the range retrieval and errorbudget.

12.3 Past, present and future altimetric satellites

The past, present and proposed altimeter missions include an experimental altimeter onSkylab in 1973, the single-frequency altimeters launched on GEOS-3 in 1975, SEASAT in1978, Geosat in 1985–1990, and the ERS-1 and ERS-2 altimeters that operated from 1991 to2000. The more accurate dual-frequency altimeters began with TOPEX/POSEIDON in1992 and continued with JASON-1 in 2001 and JASON-2 in 2008. TOPEX, JASON-1 and JASON-2 occupy orbits that are specifically designed for topography and are notSun-synchronous. Because of concerns about atmospheric drag and the need for preciseorbit determination, the ideal altimeter satellite would have the size and shape of a cannonball.

Consequently, the most successful altimeter missions are compact low-drag satellitesthat carry an altimeter with supporting measurements of atmospheric water vapor, liquidwater and ionospheric free electrons. As the next two sections discuss, these conditionsare nearly satisfied by two groups of ocean topography missions. The first consists of theTOPEX/POSEIDON and JASON-1, JASON-2 and forthcoming JASON-3 altimeters; thesecond, the ERS-1, ERS-2, ENVISAT, SARAL and forthcoming Sentinel-3 altimeters.The satellites of the first group are in a 10-day exact repeat orbit between ±66° at a1336-km altitude; those of the second group are in a 35-day exact repeat orbit between±81.5° at an 800-km altitude. The orbit of the second group provides coverage of thehigh-latitude northern European seas. As Section 12.9.4 shows, the complementary orbitsof both groups contribute to studies of oceanic variability. Table 12.1 lists the past, presentand proposed altimeter satellites.

12.4 TOPEX/POSEIDON

As an example of the above instruments, this section describes the TOPEX/POSEIDONaltimeter, its supporting instruments and surface calibration. Specifically, Section12.4.1 describes the satellite and its choice of orbit, and Section 12.4.2 describes theTOPEX Microwave Radiometer. Section 12.4.3 describes the determination of the free-electron concentration, and Section 12.4.4 describes three techniques used for precisionorbit determination. Section 12.4.5 concludes with a description of the surface calibration.

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Table 12.1. List of satellite altimeter missions in order of their launch dates.

Satellite Agency Instrument Frequency/operation Launch date Status/end dateSEASAT NASA ALT 13.5 GHz June 1978 October 1978Geosat US Navy – 13.5 GHz March 1985 January 1990ERS-1 ESA Radar Altimeter (RA) 13.8 GHz July 1991 June 1996Geosat Follow-On (GFO) US Navy – 13.5 GHz 1998 2008ERS-2 ESA RA 13.8 GHz April 1995 January 2001ENVISAT ESA RA-2 3.2, 13.6 GHz June 1999 May 2012TOPEX/ POSEIDON NASA/ France ALT (United States);

SSALT (France)5.3, 13.6 GHz; 13.65 GHz 1992 2006

JASON-1 NASA/France POSEIDON-2 5.3, 13.6 GHz December2001

July 2013

OSTM/JASON-2 NASA/France POSEIDON-3 5.3, 13.6 GHz June 2008 –CryoSat-2a ESA SIRAL-2 13.575 GHz, three different

modesAugust 2011 –

HY-2A China Alt Dual-frequency Ku-, C-band August 2011 –SARAL India/France AltiKa 35.75 GHz, Ka-band altimeter February 2012 –JASON-3 NASA/France Dual frequency 2015 –Sentinel-3A, B, Cb ESA SRAL Dual frequency 2015 –

a Described in Chapter 14.b The Sentinel-3 series will be launched at 18-month intervals.SSALT stands for Solid State altimeter; OSTM, Ocean Surface Topography Mission; SIRAL-2, SAR Interferometric Radar Altimeter-2;SARAL, Satellite with ARgos and AltiKa; AltiKa, Ka-band Altimeter; SRAL, SAR Radar Altimeter. AltiKa is an experimental single-frequency broad-band altimeter; SRAL is the successor to RA-2. Mission and instrument descriptions from Altimetry (2013).


370 The altimeter

MICROWAVERADIOMETER

LASERRETROREFLECTORARRAY

ALTIMETERANTENNA

NADIROMNIANTENNA

DORIS ANTENNA

COMMAND AND DATAHANDLING MODULE

POWERMODULE

PROPULSIONMODULE

ATTITUDE CONTROLMODULE

HIGH-GAINANTENNA

GPSDRANTENNA

ZENITHOMNIANTENNA

SOLARARRAY

+X(ROLL)

+Z (YAW)

X(ROLL)

Y(PITCH)

Z(YAW)

Fig. 12.5. The TOPEX/POSEIDON satellite. For scale, the diameter of the altimeter antenna is1.5 m. (Figure 1 from Fu et al. (1994), C© 1994 American Geophysical Union, reproduced/modifiedby permission of AGU.)

12.4.1 The satellite and its orbit

The TOPEX/POSEIDON satellite was a joint project between NASA and the Frenchspace agency, the Centre National d’ Etudes Spatiales (CNES) (Figure 12.5). TOPEXis an acronym for TOPography EXperiment; POSEIDON is a dual French and Englishacronym: Premier Observatoire Spatial Etude Intensive Dynamique Ocean et Nivosphere,and Positioning Ocean Solid Earth Ice Dynamics Orbiting Navigator. The cumbersomename reflects the difficulties of international collaboration (Wunsch and Stammer, 1998).TOPEX was launched on August 10, 1992 into an exact repeat orbit and took data fromSeptember 1992 through January 2006. The TOPEX altimeter consisted of two redundantsystems, called Side A and Side B. TOPEX Side A operated from launch through to itsfailure in February 1999, when the altimeter switched to Side B that continued to operateuntil 2006.

A number of considerations determined the TOPEX choice of orbit. First, for a singlesatellite mission, the temporal and spatial resolutions compete with one another. Because, atthe time of launch, the geoid was not well enough known to calculate the SSH independently,the repeat orbit allowed averaging and removal of the temporal component, and estimationof the geoid. The temporal resolution is determined by how long it takes for the satellite to


12.4 TOPEX/POSEIDON 371

Fig. 12.6. The orbit tracks of TOPEX/POSEIDON for the 10-day orbit cycle 013. Gaps in thetrajectories indicate missing data. (Courtesy of Robert Benada, used with permission.)

repeat a particular orbit; the spatial resolution by the equatorial spacing between successiveorbits. A short repeat period yields a large spatial separation; a long repeat period yieldsa small separation. Second, TOPEX is not in a Sun-synchronous orbit, rather it is at ahigher altitude. This choice of altitude reduces atmospheric drag; its disadvantage is that,because the ratio of transmitted-to-received power has a fourth-power dependence on range,the altimeter must supply more power to achieve a satisfactory signal-to-noise ratio. Thechoice of a non Sun-synchronous orbit was to avoid aliasing the 24-hour or diurnal tidesthat would otherwise generate a spurious mean displacement (Wunsch and Stammer, 1998).Third, the orbit design meant that, in the subtropics, the ascending and descending pathscross each other at nearly right angles. At the crossover points, this choice of crossing anglepermits accurate retrievals of the two geostrophic velocity components. Fourth, at about10-day intervals, the TOPEX orbit samples the same locations.

The result of these considerations is that TOPEX occupies a circular orbit at an altitudeof 1336 km, a period of 112 minutes and an inclination providing surface coverage between±66° of latitude. The satellite makes approximately 14 orbits per day, for a ground speedof about 6 km s−1. The orbits exactly repeat at a period of 9.916 days, referred to as a10-day repeat cycle. Figure 12.6 gives the TOPEX ground track over a single 10-day cycleand shows that, with the exception of the Atlantic north of Iceland, TOPEX covers mostof the ice-free ocean. For this orbit, the equatorial separation between adjacent tracks is


372 The altimeter

320 km, and, away from the northern and southern extremes, the ascending and descendingtracks cross each other at large angles. The restrictions on temporal sampling imposed bythis orbit mean that the highest frequencies observable in the data have a 20-day period.However, the relatively large separation between the TOPEX successive orbit tracks andthe 10-day separation between exact repeat tracks means that, while a single altimeterprovides information only on mesoscale ocean features, when combined with observationsfrom altimeters in the ENVISAT orbit, the spatial resolution is less than 100 km (Cheltonet al., 2011a).

The advantage of the exact repeat orbit is that, over a sufficiently long averaging periodand at any point along the track, a time average hS(χ,ψ) of the sea surface height relativeto the ellipsoid can be defined as an approximation to the geoid. This average includesboth the geoid and the spatial changes in sea surface height associated with steady currents.Relative to this average, the variability in sea surface height ζ (χ , ψ , t) is defined as

ζ (χ, ψ, t) = hS(χ, ψ, t) − hS(χ, ψ) (12.3)

where hS is the instantaneous height measurement from Equation (12.1). Over many 10-daycycles and at spatial scales greater than the track separation, Equation (12.3) allows thedetermination of the variable flow properties.

TOPEX contained two separate altimeters that share a single 1.5-m-diameter parabolicantenna. These are the NASA dual-frequency altimeter (ALT or TOPEX) operating atC-band (5.3 GHz) and Ku-band (13.6 GHz) with wavelengths of 6 and 2 cm, and the CNESsingle-frequency solid-state altimeter (SSALT or POSEIDON) operating at 13.65 GHz.The advantage of a dual-frequency altimeter is that, at each frequency, the altimeter hasa different response to variations of ionospheric free electrons and rain. Because of theseresponses, these altimeters can measure the columnar electron density and determine itseffect on the electromagnetic phase speed, as well as identify regions of heavy rain. AtC-band, the ALT has a half-power beamwidth of 2.7°, a gain of 35.9 dB and a PRF of1220 Hz; at Ku-band, it has a beamwidth of 1.1°, a gain of 43.9 dB and a PRF of 4200 Hz(Zieger et al., 1991). In both cases, the instrument uses the chirp technique described inSection 10.4.1 to generate a pulse with bandwidth fB = 320 MHz, so that the pulseshave an effective duration of 3.125 ns or a length of 1 m. The TOPEX and POSEIDONaltimeters alternated their observations, such that over eleven cycles TOPEX operates forten cycles, POSEIDON for one. The success of SSALT on TOPEX is the reason why adual-frequency POSEIDON altimeter is the only altimeter on JASON-1.

TOPEX carried four additional instruments, the TOPEX Microwave Radiometer (TMR)used for determination of L, V and U, and three instruments used for POD, where oneof the POD instruments also measured free-electron density. For the TOPEX and JASONseries, the three POD instruments and ground systems were the NASA Laser RetroreflectorArray (LRA) on the satellite and its associated laser ground stations, the CNES Dopplertracking system called Doppler Orbitography and Radiopositioning Integrated by Satellite(DORIS) and GPS receivers provided by NASA. The following sections discuss the TMR,the ionospheric correction, the POD systems and the surface calibration sites.



12.4.2 TOPEX Microwave Radiometer (TMR)

The purpose of the TMR was to measure V, L and to flag regions of heavy rain. As Cheltonet al. (2001b) show, variations in the tropospheric concentrations of V and L alter the realpart of the index of refraction and thus the electromagnetic phase speed. These changes aresometimes grouped under the name refraction; because they reduce the phase speed, theygenerate an apparent additional distance to the sea surface called range delay. The rangedelays induced by these changes are of order 1 m; for example, a change in V from 0 to70 mm of columnar water equivalent yields a range delay of 50 cm (Wunsch et al., 1981).For cloud liquid water, the effect of L on range is 1–2 orders smaller than V and is generallyignored. Because the rain rate RR strongly affects the transmissivity, the phase speed andthe scattering surface, regions of heavy rain are masked.

TMR was a nadir-viewing radiometer that was built almost entirely from SMMR spareparts and operated at the 18-, 21- and 37-GHz SMMR frequencies described in Section8.6.1 (Janssen et al., 1995). Its operation was similar to the radiometers on JASON-1 and JASON-2. Because TMR is nadir viewing, the vertical and horizontal polarizationsare identical, so TMR has only three channels. These are used to solve for V, L andU in a manner similar to the SSM/I algorithm described in Section 9.6.1, where SSTwas provided from a lookup table. The retrieved V and L were used to calculate thetransmissivity, phase speed and range delay along the two-way altimeter path. TOPEX setsa rain flag in two ways. First, if L exceeds a preset threshold, rain is assumed and the pixel ismasked. Second, because for the altimeter the rain-induced attenuation is an order greater atKu than at C-band, a rain flag is also set if the difference in attenuation between the twofrequencies exceeds a threshold (Chelton et al., 2001b). The TMR footprint is also spatiallyconstrained. At 21 GHz, TMR has a 35-km- diameter footprint, but, because of the sidelobeinterference described in Section 8.5, its observations cannot be used within 50 km of land(Ruf and Giampaolo, 1998). As shown below and compared with TMR, the JASON-1 andJASON-2 radiometers have greatly improved performances.

12.4.3 Ionospheric free electrons

As Section 4.2.5 describes, the density of ionospheric free electrons varies with strong diur-nal and interannual cycles, where their density retards the electromagnetic phase velocityat a rate proportional to their columnar concentration (Chelton et al., 2001b, Section 3.1.3).Specifically, if hion is the range delay in cm and ρion is the electron columnar density inTECU, the dependence of hion on f and ρion is

hion ∼ ρion/f2 (12.4)

Equation (12.4) shows that the range delay decreases with increasing f. If the effects ofV and RR are removed from h, then measurements at the two altimeter frequencies yieldtwo equations for hion and ρion, so that hion can be calculated and removed from h.At f = 5.3 GHz, hion = 1.45 cm/TECU; at f = 13.6 GHz, hion = 0.22 cm/TECU.Since ρion varies between 10 and 120 TECU, at 5.3 GHz, hion varies from about 10 to


374 The altimeter

160 cm; at 13.6 GHz, hion varies from 2 to 30 cm (Chelton et al., 2001b). As the nextsection describes, the ionospheric correction can also be determined from the DORISmeasurements.

12.4.4 Precision orbit determination (POD)

As stated above, the satellite height H is the second critical variable in the determination ofSSH. POD is defined as the precise determination of the satellite position at regular timeintervals and in three dimensions relative to the Earth’s center of mass, where the resultanttime series is called the orbit ephemeris (Chelton et al., 2001b). For the SSH retrieval tobe of oceanographic value, H must have an accuracy of 1–2 cm. As Tapley et al. (1994),Chelton et al. (2001b) and Lambin et al. (2010) describe in detail, TOPEX, JASON-1 andJASON-2 each have three POD systems. These are satellite laser tracking, GPS positioning,and DORIS radio tracking. The laser and DORIS measurements determine the spacecraftposition and velocity at irregular intervals; the GPS measurements continuously determinesatellite position. Combination of these measurements with numerical orbit models allowscalculation of a precise orbit.

Following Chelton et al. (2001b), the POD systems work as follows. First, on TOPEX,the NASA-provided Laser Retroreflector Array (LRA) is mounted around the base of thealtimeter antenna and is used in combination with a network of satellite laser ranging (SLR)stations, where the station locations are known to within a centimeter (SLR, 2013). For2012, Figure 12.7 shows the station locations; there are about 50 stations available fortracking a specific satellite. These stations observe the satellite within about a 15° latituderadius. These laser measurements of spacecraft range determine the three components ofspacecraft position. Although the lasers require cloud-free conditions, because their opticalwavelengths are not affected by water vapor or ionospheric refraction, their measurementshave a 1-cm precision.

Second, the DORIS tracking system determines the spacecraft velocity using an onboardreceiver in combination with a global network of about 50 ground beacons, again withina 15° observational radius (DORIS, 2013). The DORIS beacons broadcast continuouslyand omnidirectionally at 0.4 and 2.04 GHz. When the spacecraft receives these signals, itsvelocity is determined from the observed Doppler shifts at a precision of 0.5 mm s−1. Thesemeasurements determine the changes in satellite velocity due to radiation pressure and drag.Measurements at the two DORIS frequencies determine the free-electron concentrationsalong the DORIS slant paths, which permit their removal from the range estimates. Forthe POSEIDON altimeter, the electron measurements are extrapolated to the nadir pathfor removal of the ionospheric phase delay, although with less accuracy than the dual-frequency ALT measurements. JASON-1 and -2, ENVISAT and SIRAL also use DORISfor orbit determination and geolocation. The oblique SLR and DORIS measurements ofposition and velocity are used with a numerical model to produce a precise orbit. Cheltonet al. (2001b) state that DORIS is the primary contributor to the orbit accuracy, while theSLR contribution is to align the orbit center with the Earth’s center of mass.

Trim

:247mm

×174m

mTop:14.762m

mG

utter:23.198mm

CU

UK

2533-12C

UU

K2533/M

artinISB

N:978

1107

019386

Novem

ber26,2013

8:37

Fig. 12.7. The 2012 distribution of the satellite laser ranging (SLR) tracking stations. Their 20° elevation visibility masks have a radius of about15° latitude. (From SLR (2013), courtesy of NASA Goddard Space Flight Center, not subject to US copyright.)


376 The altimeter

Fig. 12.8. The constellation of GPS satellites that are at an altitude of 20,200 km. (Figure from GPS(2013), not subject to US copyright.)

Third, TOPEX carried a GPS Demonstration Receiver (GPSDR) that continuouslytracked the satellite position (Bertiger et al., 1994). The GPS space system consists of24 satellites orbiting at an altitude of 20,200 km with a 12-h period, where the satellitesare distributed into six orbit planes (Figure 12.8). The satellites broadcast at 1.58 and1.23 GHz, where the two frequencies allow for correction of ionospheric delays (GPS,2013). At any time, the GPSDR collected navigation data from between five and nine ofthese satellites. Data from a minimum of four satellites allow TOPEX to determine itsposition with an rms radial accuracy of ±2 cm (Fu et al., 1994). The advantage of GPS isthat it continuously determines satellite position with a potentially better accuracy than SLRand DORIS and without their spatial and temporal gaps. The continuous GPS tracking alsomeans that its orbit solution is less dependent on a numerical model (Chelton et al., 2001b,Section 4.2).

12.4.5 Surface calibration

TOPEX had two surface calibration sites, the US Platform Harvest, which is a Texaco oilplatform located in the Pacific about 10 km west of Point Conception on the central Cali-fornia coast, and the French Lampione Rock site between Sicily and Tunisia (Christensen



Fig. 12.9. Examples of the TOPEX and JASON surface calibration measurements made at PlatformHarvest. (Figure 1 from Christensen et al. (1994), C© 1994 American Geophysical Union, repro-duced/modified by permission of AGU.)

et al., 1994; Haines et al., 2010). Harvest is still in use; Lampione has been superseded byother Mediterranean sites. Harvest lies directly beneath an ascending orbit path; Lampi-one, beneath a descending path. Figure 12.9 illustrates the measurements made at Harvest;similar measurements were made at Lampione. The Harvest platform is in the center ofa radar pulse, but is small enough that it does not affect the return. It has served as acalibration site from 1992 until the present. Harvest has three separate tide gauges, anupward-looking water vapor radiometer, and instruments for measuring ionospheric free-electron density, sea state, and meteorological parameters such as relative humidity andatmospheric pressure.

Harvest also has a GPS receiver so that the Harvest and satellite sea level measurementsshare a common reference frame. When an altimeter satellite passes over Harvest, four


378 The altimeter

SLR stations, GPS and DORIS measure the satellite position. The combination of the sealevel and satellite position measurements means that the satellite range measurement isdetermined independently of the altimeter, providing a check on its accuracy and drift. Oneproblem with Harvest is that its location is so close to the coast that sidelobe contaminationmakes the TMR water vapor measurement unusable; instead, the values of V at Harvest areextrapolated from offshore measurements. As discussed below, a new JASON-2 radiometeralgorithm corrects the TMR land contamination problem at Harvest.

There are currently calibration facilities at Bass Strait, Tasmania, and Gavdos Islandsouth of Crete (Mertikas et al., 2010). The Gavdos site is of particular interest because it issituated under a JASON orbit crossing point and is adjacent to an ENVISAT orbit.

12.5 JASON-1/JASON-2

12.5.1 JASON-1

The successor to TOPEX is the US/French JASON-1 satellite launched on December 7,2001. Although JASON-1 has a similar design to TOPEX, because of advances in electronicminiaturization, its mass was only 500 kg compared with 2400 kg for TOPEX. JASON-1carries only the POSEIDON-2 altimeter, which is a solid-state dual-frequency Ku- andC-band (5.3- and 13.6-GHz) instrument based on SSALT. For POD, JASON-1 uses GPS,DORIS and the satellite laser ranging stations, that determine the satellite position to anaccuracy of 2–3 cm (Haines et al., 2002).

For atmospheric correction, JASON-1 carries the JASON Microwave Radiometer (JMR),which is a three-frequency nadir-looking microwave radiometer similar to TMR. JMRoperates at 18.7, 23.8 and 34.0 GHz, which differ slightly from the TMR frequencies. Thecombination of channels retrieves water vapor, wind-induced roughness and cloud liquidwater, which are used to set a rain flag. The reasons for the frequency changes are asfollows. First, the changes from 21.0 to 23.8 GHz and from 37.0 to 34.0 GHz reduce thepossibility of interference from the higher harmonics of the 5.3-GHz altimeter. Second, thechange from 18.0 to 18.7 GHz means that the frequency matches the WindSat radiometer.Because the algorithms accommodate these frequency changes, the rms accuracy of thewater vapor retrieval is nearly identical to TMR at 1.2 cm.

JASON-1 has the same orbit and ground track as TOPEX, providing continuity of theobservations. Initially, JASON-1 was positioned in the TOPEX orbit behind and within60 s or 500 km of TOPEX. In this common orbit and for a period of about six months afterlaunch, JASON-1 and TOPEX cross-calibrated their instruments by taking near simulta-neous measurements of the same sea surface areas. At the end of this calibration period,TOPEX was moved into a parallel orbit that was positioned midway between two adjacentJASON-1 orbits. Until TOPEX failed, this altimeter pair doubled the surface resolution, atwhich time JASON-1 returned to its original orbit. In this orbit, the JASON-1 surface cali-bration sites are the existing US Harvest site and a French site at a Mediterranean locationcalled Corsica-Capraia.


12.5 JASON-1/JASON-2 379

Fig. 12.10. An artist’s conception of the JASON-2 satellite in orbit. For scale in the figure, the antennadiameter is 1.2 m. On the figure, the AMR with its 1-m antenna is at the top of the satellite, the DORISantenna protrudes from the satellite at the bottom (Figure courtesy of NASA.)

12.5.2 JASON-2

The JASON-2 satellite was launched in June 2008. Figure 12.10 shows an image of thesatellite; Zaouche et al. (2010) describe its operation. The JASON-2 Advanced Micro-wave Radiometer (AMR) uses the same three frequencies as the JMR; its antenna is a1-m-diameter paraboloid focused on the altimeter footprint. For the AMR, Brown (2010)describes a new algorithm that is unbiased for observations at distances greater than 10 kmfrom land. This algorithm will be applied to the historic JMR and TMR data and shouldimprove the retrospective calibration.

JASON-2 also carries the Global Positioning System Payload (GPSP) receiver that tracksnavigation signals from as many as twelve GPS satellites. The DORIS receiver can trackup to seven ground stations simultaneously, compared with only two for JASON-1. TheDORIS electronics are hardened to avoid problems with the South Atlantic Anomaly. ALaser Retroreflector Array (LRA) permits laser tracking. These three orbit trackers are


380 The altimeter

independent of each other and, as shown in Table 12.3 later, yield an improved orbitcompared with TOPEX.

12.5.3 The tandem mission phases

As part of their verification campaigns, both JASON-1 and JASON-2 flew in tandem withtheir respective previous missions, JASON-1 with TOPEX and JASON-2 with JASON-1.The tandem campaigns consisted of the two satellites flying in the same orbit and within55 seconds of each other over periods of about six months, so that the satellites observed thesame ocean areas. For JASON-1 and TOPEX, the tandem mission lasted for 210 days, afterwhich TOPEX was moved to a new orbit midway between the JASON-1 ground tracks.Similarly, for JASON-1 and JASON-2, the tandem mission continued for 180 days, afterwhich JASON-1 moved to the midway orbit. Since the two satellites overfly the same regionwithin a minute of each other, the two satellites observe the same ocean and atmosphericproperties. When the two range measurements from the tandem missions are subtractedfrom one another, the sources of the differences are the instrument and model errors.Examples of problems discovered from this differencing include errors in the TOPEX seastate bias model, difficulties with the TOPEX and JASON radiometers and regional errorsrelated to the reference frames used to compute the orbits (Nerem et al., 2010).

12.6 Altimeter interaction with a specular sea surface

This and the following section discuss the precise measurement of the distance h betweenthe satellite and the sea surface. This section considers the case of pulse reflection from aspecular surface; Section 12.7 describes the complications that arise for reflection from awave-covered surface. Within the present section, Section 12.6.1 shows that, for small off-nadir look angles, the range retrieval is independent of look angle, Section 12.6.2 derivesthe beam footprint and Section 12.6.3 describes the retrieval of the round trip travel time.

12.6.1 Effect of variable pointing angle on range retrieval

The altimeter boresight direction unavoidably varies about nadir. For example, Figure12.11 gives the early time history of the averaged off-nadir look angle of the TOPEXboresight direction and shows that this angle settled to a value of about 0.05°. With thispointing accuracy and from the TOPEX altitude of 1340 km, the projection of the altimeterboresight onto the surface lies within a 1.2-km-radius circle centered on nadir. Simpletrigonometry shows that the range variation along the boresight direction associated withthis uncertainty is 0.5 m, or of the same order as the height variations associated withgeostrophic currents. In spite of this variation, because the altimeter generates sphericalwaves, the following shows that, for small off-nadir look angles, the measured range isindependent of θ .


12.6 Altimeter interaction with a specular sea surface 381

Ang

le (

0.01

deg

rees

)

30

25

20

15

5

10

280 300 420320 340 360 380 400Days past 01/01/1992

0

Fig. 12.11. Time history of the daily averaged off-nadir pointing angle for TOPEX cycles 4–14.(Figure 4 from Fu et al. (1994), C© 1994 American Geophysical Union, reproduced/modified bypermission of AGU.)

For nadir- and slant-looking antennas, Figure 12.12 shows schematic diagrams of theradiating wavefronts for the nadir- (a) and slant-looking cases (b). In both cases the antennasare at a height h above the sea surface, and have a half-power beamwidth of θ1/2. Figure12.12(b) shows that, for a spherical wavefront, as long as θ < θ1/2, the pulse from thetilted antenna has a component propagating in the nadir direction, so that its round-trip traveltime is the same as for the nadir-look case. This independence of the range measurementfor small off-nadir look angles is a major reason for the success of the altimeter.

12.6.2 Pulse-limited footprint

Because the altimeter generates short pulses, the resultant footprint is smaller than thebeamwidth-limited footprint described in Section 8.2.1. This smaller FOV is called thepulse-limited footprint and has an area proportional to the pulse duration τ . The analysisproceeds as follows. For a specular surface and a nadir-looking antenna, the time t0for thepulse leading edge to travel from the antenna to the sea surface is

t0 = h/c (12.5)

Figure 12.13 shows the pulse encounter with the sea surface and the footprint size, whereto simplify the figure the pulse is shown passing through the surface without reflection.


382 The altimeter

τ

Δθ1/2

h

BoresightNadir

Δθ1/2

θ

(a) (b)

Nadir

Fig. 12.12. The propagation of a spherical wavefront for cases of (a) a nadir-looking and (b) aslant-looking antenna, both with a greatly exaggerated beamwidth.

h

r

d

Sea surface

(a) (b)

Δθ1/2

Fig. 12.13. The encounter of the radar pulse with a specular surface, in (a) sideview and (b) top view.The dark solid line at the surface in (a) shows the diameter of the illuminated area corresponding tothe circle in (b).

From the figure, if t ′ = t − t0 and 0 ≤ t ′ ≤ τ , the footprint radius r is written

r2 = (d2 − h2) = (ct)2 − (ct0)2 = c2[(t0 + t ′)2 − t2

0

](12.6)

For t ′ t0, Equation (12.6) becomes

r2 = 2c2t0t′ = 2hct ′ (12.7)


12.6 Altimeter interaction with a specular sea surface 383

h

r1 r2

(a) (b)Δθ1/2

Fig. 12.14. The annular area illuminated by the pulse for t ′ > π , in (a) sideview and (b) top view.

Equation (12.7) shows that, for 0 ≤ t ′ ≤ τ , the footprint is a disk with its area increasinglinearly with t ′. Assume that the altimeter has a narrow-beam nadir-pointing antenna ofconstant gain G0 as described in Equation (10.14), and that the surface conditions within thefootprint are uniform. For this case, the power backscattered to the antenna and σ0increaselinearly with t ′. From Figure 12.13 and Equation (12.6), the maximum radius of theilluminated disk is proportional to τ and is given by

r2 = 2hcτ (12.8)

As the wavefront continues to propagate and for t ′ > τ , Figure 12.14 shows that the surfacefootprint becomes an annulus described by

r22 = 2hc(t − t0), r2

1 = 2hc[t − (t0 + τ )] (12.9)

so that r22 − r2

1 = 2hcτ , and the area of the illuminated footprint remains constant atAmax = 2πhcτ . In summary, for 0 ≤ t ′ ≤ τ , the illuminated area increases linearly withtime; for t ′ > τ , the area remains constant until r2 extends beyond the halfpower beamwidth,at which time the return power falls off to zero.

For a specular surface, the above arguments show that the maximum disk and annulusareas are equal and proportional to τ . For TOPEX, τ = 3.125 ns for a pulse length of 0.9 m,so that r = 1.6 km and Amax = 8 km2. In contrast, the C-band beamwidth-limited footprinthas a diameter of about 60 km; the corresponding Ku-band footprint has a diameter of about26 km, so that, for a specular surface, the pulse-limited footprint is much smaller than thebeamwidth-limited footprint. As Section 10.4.1 discusses, to avoid interference with otherspectrum users, the minimum pulse length is restricted to about 1 m, so that these are theminimum altimeter footprints. Given this interaction with the surface, the calculation of theround-trip travel time is next described.


384 The altimeter

t2t0 2t0 + τ

ΦR

, σ 0

Half-power return

Plateau

2to+ τ/2Noise floor

tRT

+ τ/22t0

Fig. 12.15. The time dependence of the backscattered energy and scattering cross section for thereflection received from a specular surface. The horizontal line shows the height at which the backscat-ter return equals half its plateau value; the vertical line marks the corresponding time. See the text forfurther description.

12.6.3 Determination of the round trip travel time

Figure 12.15 shows the return from an idealized interaction of the pulse with a specularsurface. It divides into four parts. First, before the return pulse arrives, the instrumentobserves only the noise floor. Second, as the leading edge of the return arrives at theantenna, R increases linearly with time, proportionally to the increase in footprint area.Third, when the footprint becomes an annulus, the return power is constant so that R

reaches a plateau. Fourth, at the trailing edge of the return where the annulus becomesgreater than the half-power beamwidth, R drops off in what is called plateau droop. Giventhis interaction, the round-trip time tRT for the midpoint of the pulse is defined as that timewhen the received reflection of the illuminated footprint equals half of its maximum sizeor when

tRT = 2t0 + τ/2 (12.10)

From this discussion, determination of tRT becomes a question of finding the midpoint ofthe region of linear slope. An onboard tracking algorithm that determines when the returnpower equals half the difference between the plateau level and the noise floor provides anestimate of tRT.

Two factors complicate this determination: off-nadir pointing angles and ocean wavesand surface roughness. Off-nadir pointing angles have two effects. First, slightly moreenergy is reflected away from the antenna, reducing the plateau level so that it must beadjusted for look angle. Second, if the angle is large enough, then in addition part of thecircle or annulus falls outside of the beamwidth-limited footprint. This means that, evenwith the plateau level adjusted for look angle, the plateau droop occurs earlier, making itmore difficult to determine the plateau level.


12.7 Effect of surface waves on the altimeter return 385

Increasing U

t2t0 2t0 + τ

ΦR

, σ 0

PlateautRT

+ τ/22t0

Fig. 12.16. The decrease in plateau level with increasing wind speed.

12.7 Effect of surface waves on the altimeter return

When surface waves are present, three factors alter the radar return: small-scale surfaceroughness, the random nature of the sea surface and large-scale ocean swell. First, as thewind speed increases, the increase in roughness and mean-square surface slope reflectsand scatters and reflects more energy away from the antenna, so that the plateau leveldecreases with increasing U. Second, because of the nature of scattering from surfaces withrandomly distributed slopes, the idealized signal shown in Figure 12.15 has a large randomcomponent that must be removed by averaging (Chelton et al., 2001b). Third, an increasein the ocean swell height reduces the slope of the leading edge of the return in Figure 12.15,which yields an algorithm for retrieval of H1/3.

12.7.1 Small-scale roughness and the determination of U

As Figure 10.16 shows for a nadir-oriented radar, the increase in sea surface roughnessand mean-square slope with increasing U causes σ0 to decrease. Ignoring for the momentthe random signal component, Figure 12.16 shows for wind-induced roughness that thedecrease in σ0 with increasing U reduces the plateau level while leaving the rise timeunchanged. Because this response to surface roughness also occurs when ocean swell ispresent, this U-dependence forms the basis for a wind speed algorithm (Chelton et al.,2001b, Section 7). Because off-nadir pointing angles also reduce the plateau level, toretrieve U the return must be adjusted for pointing angle. Because the surface roughnessassociated with rain cells attenuates the return and generates a false wind speed signal,rain must be identified and masked. Further, the dependence of the plateau level on Umeans that the sensitivity and linearity of the altimeter electronics and the range-retrievalaccuracy are also functions of U. As the next section shows, because of the advantages ofoperating within the linear region of the altimeter electronics, an onboard function calledthe Automatic Gain Control (AGC) adjusts the gain of the return so that, when measuredin digital counts, the plateau level is held constant (Lillebridge, 2009).


386 The altimeter

Time

Dig

ital c

ount

s

(c)

(b)

(a)

Fig. 12.17. The effect of averaging a simulated return from a Gaussian distribution of wave heightswith H1/3 = 10 m: (a) single return; (b) average of 25 returns; (c) average of 1000 returns. Thelower axis represents the noise floor. (Figure 1b from Townsend et al. (1981), C© (1981), KluwerAcademic/Plenum, used with permission.)

12.7.2 Automatic Gain Control (AGC) and averaging of the return

For a random wave field, the return from any individual pulse is very noisy. To reducethe noise, the AGC carries out the following sequence of operations. First, it adjusts theindividual returns for off-nadir pointing angles, then averages the returns over a sufficientperiod of time such that the mean signal dominates. Figure 12.17 shows for a simulatedreturn that, as the number of averaged pulses increases, the return approaches the idealizedshape in Figure 12.15. The AGC then adjusts the plateau level of the averaged return so thatin digital counts it is constant. Weaker signals receive more gain; strong signals none at all.This adjusted value is transmitted to the ground for estimation of σ0 and U; the half-powerpoint and tRT are determined by the difference between the plateau level and the noise floor.For the TOPEX altimeter, which transmitted and received 4000 pulses per second, the datawere averaged at the satellite over 50 ms or 200 pulses. For oceanographic purposes andon the ground, the data are further averaged over 1 s (Chelton et al., 2001b, Section 2). For


12.7 Effect of surface waves on the altimeter return 387

MSLH1/3

First encounter of pulse with wave

Last encounter

Fig. 12.18. The encounter of the wavefronts with ocean swell; MSL is mean sea level. The curvatureof the wavefronts is greatly exaggerated.

a specular surface, the averaged surface footprint measures about 9 km in the along-trackdirection and 3 km in the cross-track. As the next section shows, the footprint size alsoincreases with the ocean swell amplitude.

12.7.3 Effect of ocean swell

The long-period ocean swell has two effects: it increases both the footprint size and the risetime of the return power. For the altimeter, the swell amplitude is described in terms of thesignificant wave height H1/3 (Section 2.2.3). From TOPEX observations, a typical value ofH1/3 is 2 m; the largest mean monthly value is about 12 m; the largest instantaneous valueis 15–20 m (Lefevre and Cotton, 2001).

Figure 12.18 illustrates the pulse encounter with ocean swell. The presence of swellmeans that the first pulse reflection instead taking place at t0, now takes place at about

t1 = t0 − H1/3/(2c) (12.11)

Similarly, at nadir the last pulse reflection takes place at

t2 = t0 + H1/3/(2c) + τ (12.12)

Similarly to the specular case and for t1 < t ≤ t2, the footprint is a disk with its areaincreasing linearly with time. For t > t2, the footprint becomes an annulus, so that themaximum illuminated area Amax becomes

Amax = 2πh(cτ + H1/3) (12.13)

Equation (12.13) shows that Amax increases linearly with H1/3. For TOPEX, cτ is about1 m, so that, for H1/3 = 3 m, Amax is four times its specular value. Table 12.2 shows thedependence on H1/3 of Amax, its corresponding diameter and the along-track and cross-track


388 The altimeter

Table 12.2. The dependence on the significant wave heightH1/3 of Amax and its diameter for a single pulse, and the

along-track and cross-track dimensions of the 1-s averagedfootprint from Equation (12.13).

H1/3

(m)Amax

(km2)Diameter(km)

Footprint(km × km)

0 8 3.2 9 × 33 34 6.5 12 × 66 59 8.7 15 × 9

15 134 13 19 × 13

t+ τ/2 + τ+ c

Swell

Specular surface

Dig

ital c

ount

s

tRTPlateau

2t0 2t0H1/3+ c2t0

H1/3

Fig. 12.19. Comparison of the time dependence of the backscattered signal from a specular surfacewith that from ocean swell.

dimensions of the 1-s averaged surface footprint. As H1/3 increases from 0 to 15 m, theAmax diameter increases from 3 to 13 km, which is still less than the 26-km diameter of theKu-band bandwidth-limited footprint. This increase in area with H1/3 is called defocusing.For an H1/3 of 3 m, the footprint measures 12 km × 6 km, while in regions with heavyswell, such as the Antarctic Convergence, the footprint size approaches 20 km × 15 km.This shows that the presence of swell increases the area of the surface footprint and limitsthe altimeter spatial resolution.

Figure 12.19 compares the behavior of the return signal both in the presence and in theabsence of ocean swell and shows that when swell is present the rise time is longer and theslope of the response is reduced. In spite of this change, the half-power point for the AGC-adjusted plateau level occurs at the same time delay as for a specular surface. Consequently,for the wave-covered surface, the round-trip travel time can be retrieved using the specularsurface procedure. The inverse dependence of H1/3 on this slope permits retrieval of theglobal fields of H1/3 and allows description of their seasonal variation (Lefevre and Cotton,2001).


12.8 Errors and biases in retrieval of sea surface height 389

12.8 Errors and biases in retrieval of sea surface height

In the following, Sections 12.8.1–12.8.4 show that the errors and biases in the hS retrievalhave four sources: altimeter noise, atmospheric errors, sea state bias and errors in orbitposition. Section 12.8.5 combines these errors into a total error budget and shows that,for a single altimeter overpass and a 2-m significant wave height, the uncertainty in theretrieved SSH is 4.1 cm for TOPEX, 3.3 cm for JASON-1 and 3.1 cm for JASON-2.These numbers can be reduced by long-period averages. Section 12.8.6 then discusses twophysical phenomena, the inverse barometer effect and ocean tides, both of which causereal changes in sea surface height and generate additional uncertainties in the retrieval ofgeostrophic height.

12.8.1 Altimeter noise

The altimeter noise of TOPEX and the JASON satellites is based on 1-s averages of therange measurements for H1/3 = 2 m, with units of cm (Fu et al., 1994). This noise varieswith SWH and increases until, at H1/3 3 m, it reaches a stable value of 2.0–2.5 cm.

12.8.2 Atmospheric sources of error

The atmospheric corrections and uncertainties divide into three categories: dry troposphere,wet troposphere and ionosphere. Dry troposphere refers to all tropospheric gases exceptwater vapor and liquid water; wet troposphere to water vapor and cloud liquid water;ionosphere to free electrons.

Dry troposphere. The dry tropospheric range delay varies with the amount of atmosphericmass between the sensor and the surface or equivalently with sea level pressure, and equals0.27 cm for a 1-mbar increase in pressure. Corrections for this delay use the surface pressurefields produced by the European Centre for Medium-range Weather Forecasts (ECMWF).Based on the ECMWF rms pressure accuracy of 3 mbar, the associated range error is 0.7 cm(Chelton et al., 2001b).

Wet troposphere. The wet troposphere range delay has contributions from V and RR,where the contributions from L are sufficiently small that they are ignored, while heavyrain is masked. For V, comparison of TMR with ground-based radiometer and radiosondemeasurements shows that the uncertainty in the TMR values of V yields a range error ofabout 1.1 cm (Fu et al., 1994). The JMR retrieval is assumed to have the same accuracy.

Ionospheric free electrons. For TOPEX and JASON-1, the ionospheric range correctionderived from the dual-frequency altimeters has an error of about 0.5 cm. For the single-frequency POSEIDON altimeter on TOPEX, the ionospheric correction is determined frommeasurements made by the slant-range, two-frequency DORIS signals. Given the additionaluncertainties associated with the adjustment of this slant measurement to a vertical path,the DORIS measurement uncertainty is 1.7 cm, or about three times the altimeter value.


390 The altimeter

12.8.3 Sea state bias

Sea state bias is generated by ocean swell and can be divided into two parts. Both generatea wave-height-dependent range bias in the retrieval of sea surface height. The first is theelectromagnetic (EM) bias, which refers to the apparent depression of the mean sea levelcaused by the interaction of the radar pulses with the waves. The second is the trackeror skewness bias, which refers to the additional apparent surface depression generated bytracker determination of the half-power point. The sum of these two is called the total seastate bias. Post-processing can reduce the skewness bias; the EM bias cannot be furtherreduced (Chelton et al., 2001b, Tran et al., 2010). These quantities are currently groupedtogether under sea state bias and set equal to about 1% of the SWH.

Electromagnetic bias. In an ocean swell field, EM bias occurs because the wave troughsare better reflectors than the crests, so that the mean reflecting surface is depressed belowmean sea level. Two factors increase this bias: parasitic capillary formation on the wavecrests and finite amplitude waves. For the first, preferential formation of parasitic capillarieson wave crests scatters energy away from the antenna and adds to the depression of the meanreflecting surface. For the second, as the wave slope akW increases, the waves develop broadtroughs and narrow crests (Section 2.2.1). Because the broad troughs are better reflectorsthan the crests, the mean reflecting surface is further depressed.

From observational studies, the EM bias is negative and approximately linearly propor-tional to H1/3, where the constant of proportionality depends on geographic region and onU (Chelton et al., 2001b). Waves of a given H1/3 can consist either of long-period sinu-soidal waves of small akW, as occurs for waves generated by a distant storm, or of locallystorm-generated trochoidal waves with large akW. Consequently, the wave slope or exactbias cannot be inferred from H1/3, and can only be partially parameterized in terms of Uand H1/3 (Chelton et al., 2001b).

Tracker or skewness bias. As Sections 12.6.3 and 12.7 describe, the function of theonboard tracker is to determine the midpoint of the region of linear rise in the altimeterreturn. In this calculation, the algorithm assumes that the wave amplitude has a Gaussiandistribution. Because the actual waveform is non-Gaussian or skewed, the tracker generatesan additional negative offset. The part of this offset that is proportional to H1/3 is generallyincluded in the EM bias. At H1/3 = 2 m, the error in the TOPEX skewness bias is about1.2 cm (Fu et al., 1994); at H1/3 = 10 m the error reaches a maximum value of about 4 cm(Chelton et al., 2001b). In practice, because it is difficult to separate skewness from EMbias, for TOPEX, JASON-1 and JASON-2, the rms error of the sea state bias approximatelyequals 1% of H1/3.

12.8.4 Errors in orbit determination

At short time scales, uncertainties in the satellite orbital position are the largest source ofrange error. Orbit errors divide into single-pass errors, which are associated with a singlerange estimate, and the error associated with monthly or greater time scale averages over


12.8 Errors and biases in retrieval of sea surface height 391

Table 12.3. The single-pass rms measurement errors for the differentcomponents of the TOPEX, JASON-1 and -2 error budgets for their GDRs.

TOPEX(cm)

JASON-1(cm)

JASON-2(cm)

Range errorsAltimeter noisea 1.7 1.6 1.8Atmospheric correctionsDry troposphere 0.7 0.7 0.7Wet troposphere 1.1 1.2 0.8Ionosphere 0.5 0.5 0.3Sea state bias (H1/3 = 2 m)b 2.3 2 2Altimeter range error (rss) 3.2 3 2.9Orbit radial position (rms) 2.5 1.5 1.0Total sea surface height (rss) 4.1 3.3 3.1Wind/wave accuraciesWind speed (m s−1) 2 1.5 0.9SWH (H1/3) (m) 0.2 10% or

0.4c

5% or0.25d

a Based on 1-s averages of the range estimates for a 2-m SWH (Fu et al., 1994,Chelton et al., 2001b).

b Can be expressed as 1% of SWH, whichever is greater.c Whichever is greater.d Not yet validated, but is the goal of the analysis.

TOPEX data adapted from Chelton et al. (2001b, Table 11); JASON-1 data fromPerbos (2004); JASON-2 data from JASON-2 (2011, Table 2).

spatial scales of a few hundred kilometers. For a single JASON-2 orbit pass, the rms error isabout 1.0 cm, where both random and systematic errors contribute to this estimate (Cheltonet al., 2001b, Table 11; JASON-2, 2011, Table 2).

12.8.5 Summary and error discussion

There are three kinds of data records. The first are the Operational Geophysical DataRecords (OGDRs) that are the non-validated near-real-time products available with a3-hour latency, with onboard orbit estimation and predicted corrections. The second arethe Interim Geophysical Data Records (IGDRs) that are available with a two-day latencyand have intermediate orbit estimates and analyzed corrections. The final product is theGeophysical Data Records (GDRs) that are fully validated products delivered within sixweeks and have the highest precision (Zaouche et al., 2010).

For the GDRs, Table 12.3 gives the error budget for the TOPEX and JASON-1, -2 altimeter measurements. The table shows that there are two kinds of range errors: those


392 The altimeter

generated by altimeter noise, the atmosphere and sea state, and those in the radial positionof the satellite. The combination of these two yields the total measurement error. Table12.3 also lists the accuracies of the wind speed and significant wave height retrievals. Forrange errors alone, the root sum of the squares (rss) of the various contributions yieldsan error of 3.2 cm for TOPEX, 3.0 cm for JASON-1 and 2.9 for JASON-2. The largesterrors are those associated with orbit radial position, sea state bias and altimeter noise. Forlonger time and spatial averages over time scales of one month or greater and over spatialscales of a few hundred kilometers, the total error is reduced to about 2 cm (Chelton et al.,2001b).

12.8.6 Environmental sources of uncertainty

In addition to the height changes generated by geostrophic flows, the sea surface height isalso physically altered by ocean tides and the inverse barometer effect. The relative motionof the Earth, Moon and Sun generates the tides; the inverse barometer effect is the surfaceresponse to spatially variable changes in sea level pressure. Because these are real changesin sea surface height, they are not included in Table 12.3. For determination of geostrophicheight, however, they must be removed from the altimeter signal.

Tides. Ocean tides occur at specific discrete frequencies, with components at semi-diurnal, diurnal, fortnightly, monthly, semi-annual and annual periods. Tides produce ele-vation changes of about 1–3 m, and, except for very large ocean waves, are the largestcontributor to ocean surface variability (Wunsch and Stammer, 1998). Previous to TOPEX,tidal models were primarily based on observations made from a global network of coastaland island tidal stations. Because the altimeter measures tidal height in the interiors ofocean basins, the combination of TOPEX and surface observations with numerical tidalmodels means that the amplitudes of the major tidal components are now known to an errorof 1 cm (Le Provost, 2001). Given these models, most of the tidal signal can be removedfrom the altimeter range retrieval, which greatly improves the accuracy of the retrievedsurface height.

Inverse barometer. The inverse barometer effect describes the hydrostatic response ofthe sea surface to spatially variable changes in sea level pressure at time scales greater thanabout two days. Because a spatially uniform change in sea level pressure does not affect sealevel height, this pressure fluctuation must occur relative to the spatially averaged pressure.For pressure changes satisfying these conditions, a 1-mbar increase in pressure generatesa 1-cm decrease in the surface elevation. The inverse barometer correction works wellover the open ocean, but breaks down in small marginal seas and in the western boundarycurrents. Although the inverse barometer and dry troposphere corrections are both functionsof sea level pressure, they differ fundamentally. The dry troposphere correction yields anelectromagnetic range delay independent of surface displacement; the inverse barometereffect is a physical surface displacement. Similarly to the dry troposphere correction, theinverse barometer effect is removed using ECMWF surface pressure fields. The 3-mb errorin the ECMWF fields corresponds to a surface-displacement error of 3 cm (Chelton et al.,2001b).



Sea surface height (cm)–160 –120 –80 –40 –20 0 20 40 60 80 120 160–60

Maximum vector

30 cm s–1

60oS

60oN

0oN

120oE60oE360oE300oE240oE180oE120oE

Fig. 12.20 The 4-year average of the TOPEX ocean surface elevation relative to the Earth GeopotentialModel 96 (EGM96) geoid. The arrows show the geostrophic velocities. Near-equatorial values areomitted because of the breakdown of the geostrophic relation; small velocities are omitted for clarity.Because they are dominated by geoid error, all flows with length scales less than 500 km are omitted.(Courtesy of Detlef Stammer, Figure 6a from Wunsch and Stammer (1998), with permission, fromAnnual Review of Earth and Planetary Sciences, Volume 26, C© 1998, by Annual Reviews.) See colorplate section.


Altimeter measurements provide information about the mesoscale ocean properties andtheir variability. For flows with length scales greater than about 100 km where the geoid isknown, they yield both the steady and variable geostrophic flow properties (Wunsch andStammer, 1998; Fu, 2010). At shorter scales where the geoid is insufficiently determined, themeasurements yield information on the variability of the flows around an altimeter-definedmean sea level. The sea surface height exhibits two kinds of variability: those associatedwith local changes in the water column density and volume, called steric changes; and thoseassociated with redistribution of mass. Steric changes are caused by seasonal heating andcooling and by precipitation and evaporation; mass redistribution is caused by variabilityin ocean currents and by planetary waves.

12.9.1 Large-scale geostrophic flow

Figures 12.20 and 12.21 illustrate the large-scale properties of the global circulation. Forthese and the following examples, ζ is corrected for tides and the inverse barometer effect.The first shows the sea surface height and the geostrophic flow determined relative to thegeoid; the second shows the flow variability relative to the mean sea surface height. Figure12.20 shows the four-year TOPEX average (October 12, 1992 to October 9, 1996) of seasurface height ζ measured relative to the geoid as defined in Equation (12.2). The image isfiltered to remove features with scales less than about 500 km. On the plate, the colors show


394 The altimeter

Root-mean-square SSH (cm) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30


60oS

60oN

0oN

0

Fig. 12.21 Root-mean-square (rms) elevation anomalies for 4 years of TOPEX data (Courtesy ofDetlef Stammer, Figure 8a from Wunsch and Stammer (1998), with permission, from Annual Reviewof Earth and Planetary Sciences, Volume 26, C© 1998, by Annual Reviews.) See color plate section.

SSH; the arrows show the geostrophic flow. At the equator, the arrows are omitted becauseof the breakdown in geostrophy. Examination of Figure 12.20 shows that the total range inSSH attributable to geostrophic flows is about 3 m. The smallest SSH values occur aroundAntarctica, where the northward increase in SSH corresponds to the Antarctic CircumpolarCurrent. The largest heights occur in the western Pacific and in the Indian Ocean off SouthAfrica. In the Pacific, these are associated with the Kuroshio and with the western boundarycurrent off Australia; in the Indian Ocean, with the Agulhas Current System. In the Atlantic,the gradients in sea surface height associated with the Gulf Stream and the Brazil–MalvinasConfluence are also visible.

As an example of the variability at shorter spatial scales and for the same four-year periodas Figure 12.20, Figure 12.21 shows the rms variability of ζ relative to ζ as defined inEquation (12.3). Because subtraction of ζ removes all of the geoid undulations as well as thesteady geostrophic currents, these anomalies are valid for all length scales. Examination ofFigure 12.17 shows that the largest variability occurs in the regions of the western boundarycurrents, including the Gulf Stream, Kuroshio, the Agulhas Current, as well as in portionsof the Antarctic Circumpolar Current, with an especially large variability south of Africa.Because of the four-year time average, over much of the ocean, the variability approachesthe ±2 cm TOPEX noise floor applicable to long-term averages (Chelton et al., 2001b).

12.9.2 Seasonal variations in sea surface height

The four panels of Figure 12.22 show the seasonal SSH anomalies relative to a nine-yearTOPEX mean. The panels show the Northern Hemisphere autumn (September–November),



180oE 240oE 300oE 360oE 60oE 120oE

Sea surface height (cm)–14 –12 –10 –8 –6 –4 –2 0 2 4 6 8 10 12

60oN

0oN

60oS

Sept - Nov

Dec - Feb

Mar - May60oN

0oN

60oS

Mar - May

Jun - Aug60oN

0oN

60oS

60oN

0oN

60oS

120oE

Fig. 12.22 Seasonal mean anomalies of the TOPEX sea surface heights relative to the 9-year meanfield. Top image is September–November 1992–2000; second is December 1992–2000 throughFebruary 1993–2001, third is March–May 1993–2001; fourth is June–August 1993–2001. Contourinterval is 2 cm. (Courtesy of Detlef Stammer, used with permission.) See color plate section.

winter (December–February), spring (March–May) and summer (June–August). FollowingStammer and Wunsch (1994) and Wunsch and Stammer (1998), these anomalies have twosources: the steric changes caused by seasonal heating and cooling, and the dynamic changesin major current systems due to seasonal wind variations.

Examination of Figure 12.22 shows that the Northern and Southern Hemisphere SSHanomalies are six months out of phase, with a complicated response in some regions dueto seasonal winds. In the North Atlantic and Pacific, the anomalies are greatest in autumn


396 The altimeter

and least in spring. Because of the intense winter heat exchanges, the largest annual changeof about 20 cm occurs in the Gulf Stream and Kuroshio. Away from these current systems,the annual Northern Hemisphere change is about 12 cm. In the Southern Hemisphere, theresponse is reversed, in that the anomalies have a maximum in March–May and a minimumin September–November.

The Southern Hemisphere annual change is about 6 cm, or about half that of the NorthernHemisphere. Because the large Northern Hemisphere winter land areas are much colderthan the oceans, the northern winter offshore winds cool the ocean more than in the SouthernHemisphere, so that the northern ocean experiences a larger annual temperature changethan the southern. In both hemispheres, because cold seawater is relatively insensitive tochanges in temperature, the largest steric changes occur at mid- instead of high latitudes.

Figure 12.22 also shows how the large-scale current and wind systems contribute to theannual variability. The equatorial pattern is complicated because it is averaged over two ElNinos, 1992–93 and 1997–98, and because of the complicated zonal structure of easterlyand westerly flows. North of the equator, the plate shows the banded seasonal characterof the North Equatorial Current and Counter Current. The Counter Current achieves itsmaximum eastward flow in September–November and its minimum flow in March–May,while the North Equatorial Current exhibits the opposite behavior. A similar but weakersystem occurs south of the equator. In the northern Indian Ocean, the large change inseasonal amplitude is driven by the oceanic response to seasonal monsoon winds.

12.9.3 Two decades of sea level rise

For January 1993 through March 2012 and based on the combined sea surface heightrecords of TOPEX, JASON-1 and JASON-2, Figure 12.23 shows the trend of global meansea level (GMSL) (Beckley et al., 2010). Over the past 20 years, GMSL has increased byabout 6.4 cm. The derivation of this curve and particularly the intercalibration of the JASONinstruments and of sides A and B of the TOPEX altimeter was a difficult procedure. In thecalibration, the sea surface height time series was compared with corresponding variationsmeasured by a global network of 64 tide gauges, where the tide gauge stations were correctedfor crustal rise (0.3 mm yr−1). From the comparison and intercalibration, the global risein sea level is estimated at 3.2 ± 0.4 mm yr−1 or 3.2 cm per decade, as corrected for aglacial isostatic adjustment of 0.3 mm yr−1. The curve shows the annual and semi-annualvariability generated by the annual oceanic heating and cooling (Figure 12.22).

In the last century and from tide-gauge measurements, sea level rise was about1.7 mm yr−1, so that in this century, its rate has nearly doubled (Boening et al., 2012).On Figure 12.23, the letter “L” marks the 5-mm decrease that occurred between March2010 and May 2011. As Boening et al. (2012) discuss, this drop is associated with the2010–2011 El Nino/La Nina transition shown in Figure 9.20. They attribute it to changesin precipitation that occurred during the La Nina, which had greater precipitation over landand less over the ocean, with flooding in Australia, Pakistan and China. They conclude that



1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

–20–15

–10

–5

0

5

10

15

20

25

30

35

40

45

50

5560

Sea

Hei

ght V

aria

tion

(mm

)

TOPEX Alt A

TOPEX Alt B

JASON–1

JASON–2

Year

L

Fig. 12.23. The global mean sea level rise from January 1993 through March 2013 based on thecombined TOPEX, JASON-1, and JASON-2 missions, and sea surface height versus time for theTOPEX, JASON-1, JASON-2 missions. The data points from the TOPEX Side A altimeter are ingray; TOPEX Side B are black; JASON-1 are gray; JASON-2 are black. The irregular black curveshows the variation after application of a 60-day Hanning filter; this includes the annual and semi-annual variability; the slanted straight line is a least-squares fit to the data. GMSL stands for globalmean sea level. The point “L” identifies the decrease in sea level associated with the 2010–2011El Nino/La Nina event. See the text for further description. (Figure courtesy of Brian Beckley andNASA Goddard Space Flight Program, not subject to US copyright, the figure is an updated versionof Figure 16 in Beckley et al. (2010).)

the 2010/11 La Nina was the strongest cold event in the past eight decades and generatedthe excess in land water storage that led to the observed decrease in GMSL.

12.9.4 Western propagation of eddies

This section examines the westward propagation of small-scale eddies in two ways. First, forthe Indian Ocean, Figure 12.24 illustrates the propagation of long-period features in the seasurface height fields with scales of order 100 km. Although these were previously thoughtto be Rossby waves, Chelton et al. (2011a, 2011b) show that these features are nonlinearmesoscale coherent structures that they call eddies. These eddies are similar to Rossbywaves in that they are long-wavelength baroclinic waves that propagate to the west withvariations of ocean surface height of only about 10 cm (Cushman-Roisin, 1994). Becauseof their relatively long wavelengths and slow phase speeds, their surface manifestations arevisible in TOPEX data. For TOPEX cycle 60, the left-hand figure shows the geographicdistribution of the SSH anomaly in the Indian Ocean. The arrow marks a long rectangular


398 The altimeter

Fig. 12.24. Eddies in the Indian Ocean. The left-hand figure shows the geographic distribution ofthe anomaly in sea surface height in the Indian Ocean for TOPEX cycle 60 corresponding to the10-day period May 1–11, 1994. The rectangular strip outlined in black at 25° S is also outlined inthe right-hand Hovmoller diagram. On this diagram, the horizontal axis corresponds to the centralportion of the Indian Ocean; the vertical axis is the TOPEX cycle number. In each case, the colorscorrespond to SSH defined in the right-hand scale. The characteristic upper left to lower right tiltwithin the Hovmoller diagram illustrates the westward propagation of these features. (Courtesy ofPaolo Cipollini; Figure 5 from Killworth (2001), C© 2001, with permission from Elsevier Science.)See color plate section.

strip of observations at 25° S. The right-hand figure, which is called a Hovmoller diagram,shows the SSH anomalies within this strip plotted against longitude in the horizontal andTOPEX cycle number in the vertical. The diagram shows the characteristic tilt of the SSHpattern from lower right to upper left, which corresponds to the westward propagation ofthe crests and troughs associated with these eddies.

Second, from an automated investigation of sixteen years of altimeter data from ERS-1,ERS-2 and ENVISAT, and from TOPEX and JASON-1, Chelton et al. (2011b) examinethe properties of 35,891 of these eddies with lifetimes >16 weeks. The eddies had typicalamplitudes of 10 cm and radii of 100 km. They found that the eddies originated nearlyeverywhere in the ocean, and examined their propagation on 45 longitudinal sections.Within these eddy fields, they also identified larger features with scales of about 300 kmthat also propagated to west.

In Figure 12.25, the upper panel compares the latitude dependence of the observedwestward propagation speed of the average of the large-scale propagation features (blackdots), the average of the small-scale nonlinear eddies (gray dots) and the propagation speed



Latitude

Latitude

Wes

twar

d pr

opag

atio

n sp

eed

(cm

s–1

)

Rat

io o

f obs

erve

d to

R

ossb

y-w

ave

mod

el o

f pha

se s

peed

s

Fig. 12.25. The latitudinal variation of westward zonal propagation speeds observed in the altimetrydata. The black dots are the average speeds of the large-scale features in sea surface height alongdifferent zonal sections that emphasize the large-scale features; the gray dots are the average speedsof small-scale nonlinear eddies with lifetimes >16 weeks that lie within ±1.5° of latitude of thecenter latitudes of the same zonal sections. The gray line shows the latitudinal profile of the globalzonal average of the speeds of all small-scale eddies, where, for each latitude band, the gray shadingshows the 25%–75% quartile range of the distribution of the eddy speeds. The black line showsthe theoretical speeds of the Rossby wave phase speeds. The lower panel shows the ratios of thevarious speed estimates to the Rossby wave phase speeds. See the text for further description. (Figurecourtesy of Dudley Chelton, from Figure 22 of Chelton et al. (2011b), copyright Elsevier, used withpermission.)


400 The altimeter

for baroclinic linear Rossby waves (black lines), where the averages are taken within thesame latitude bands with widths of ±1.5°. For the sub-figures, the horizontal axis is thelatitude range between 50° S and 50° N. The gray line is the global zonal average ofthe propagation speeds of all eddies with lifetimes >16 weeks; the gray shading showsthe 25%–75% quartile range of the eddy speed distribution. Figure 12.25 shows that thelarge-scale features propagate about 33% faster than the eddies, that both move faster thanthe linear Rossby waves and that the eddy speeds in the Southern Hemisphere are about20% faster than those in the Northern Hemisphere. The figure shows that the westwardphase speeds increase with decreasing latitude, where no waves were observed in the ±25°equatorial band. The lower panel compares the speed of the observed features with that ofthe Rossby waves, where the dashed line is that of perfect agreement (Chelton and Schlax,1996). Figure 12.25 shows that, with few exceptions, the observed speeds are 1–2 timeslarger than those of the Rossby waves. Even though the figures show that speeds of theeddies and large-scale features approximately follow the Rossby solution, Chelton et al.(2011b) found very little evidence of linear Rossby waves.


13

Imaging radars

13.1 Introduction

Side-looking imaging radars provide a powerful way to retrieve ice and ocean surfacebackscatter properties at a high resolution and under nearly all weather conditions. Giventhat many geophysical processes modulate the Bragg scattering waves, the returns fromthese radars can be formed into images that display a wide variety of surface phenomena.Other advantages are that, depending on the processing, the resolution can be of ordermeters, and, at the frequencies used by these radars, the atmosphere is transparent exceptfor heavy rain.

There are two kinds of satellite imaging radars: synthetic aperture radar (SAR) andthe real-aperture side-looking radar (SLR). The SLR is a range-binned instrument with asurface resolution of about 1 km; the SAR is a more complicated instrument with resolutionsas fine as 3 m. Because the radar pulses illuminate the surface, the instruments provideday and night coverage. SAR is the principal radar imager used in oceanographic research,where SARs have been flown by the United States, Canada, ESA, Germany, Italy, Japanand Russia. Because the SLR operates similarly to SAR in the cross-track direction andwas used by Russia and Ukraine for sea ice monitoring through the year 2000, this chaptercovers both instruments but emphasizes SAR.

SARs provide a variety of information about oceanographic and sea ice processes. Forthe ice-free ocean, SAR is used in the study of internal waves (Hsu and Liu, 2000), surfacewaves (Heimbach and Hasselmann, 2000), and ocean eddies (DiGiacomo and Holt, 2001).Other phenomena visible in SAR include shallow-bottom topography, ocean currents,surface patterns of rain and wind, and the presence of oil and other surface-modifyingsubstances. Specular reflectors such as ships, offshore structures and icebergs are alsovisible (Kim et al., 2011). For the polar pack ice, SARs observe the ice edge position and,because of the general increase in surface roughness with ice thickness, also determine theareal extent of different ice types (Kwok et al., 1992). SAR is used for detection of spilledoil, for near-real-time monitoring of ships and fishing vessels, oceanic border enforcement,and for measurement of wind and waves (Hurley, 2010). Lastly, SAR is used to determinethe flow of the Antarctic and Greenland ice caps, which affect oceanography through theircontribution to sea level rise (Rignot, 2008; Moon et al., 2012).

401


402 Imaging radars

SARs operate in a variety of modes. The Standard mode has a 100-km swath width anda typical resolution of 25 m. The ScanSAR mode has a swath width of 350–500 km anda resolution of 75–150 m. This wide-swath mode is of particular value to ocean and icestudies. In the Arctic, overlays of the RADARSAT-1 ScanSAR swaths are used to constructthe Arctic snapshot, which is a 3- to 6-day image of the entire ice cover. For the period1996–2007, the RADARSAT Geophysical Processing System (RGPS) analyzed these datato derive the velocity, deformation and age of the offshore pack ice (ASF, 2013a). ForAntarctica, RADARSAT-1, RADARSAT-2 and the PALSAR ScanSAR have been used tomap the continental ice sheet (Rignot, 2008). In the open ocean, Norway and Canada usethe RADARSAT-1 and RADARSAT-2 ScanSAR mode for monitoring and managing offishing fleets in national and adjacent international waters and for observation and trackingof oil spills (Olsen and Wahl, 2000, Pichel and Clemente-Colon, 2000; Bannerman et al.,2009, RADARSAT-2, 2013b).

Both SAR and SLR depend on the relative motion of the spacecraft or aircraft togenerate an image, have antennas that are generally much longer in the along-trackthan in the cross-track direction and generate oblique fan beams at right angles to thespacecraft trajectory. In most cases, the fan beams operate at look angles greater thanabout 20°. At these angles, the return avoids specular reflection and strongly dependson Bragg scatter. The SAR operation is complicated and data-intensive; for any pixel ina SAR image, the brightness is derived from the phase and amplitude of the backscat-ter recorded from hundreds of pulses transmitted over a period of about 0.5 s. Becauseof the complications introduced by this procedure, understanding SAR imagery requiresinformation on how SAR works and on the engineering constraints imposed by the solararray, antenna, electronics and associated ground system. Interpretation of the imagery alsorequires knowledge of the dependence of Bragg scatter on incidence angle and surfaceconditions.

In the following, Section 13.2 describes the general design of the SLR and SAR, andSection 13.3 derives the SLR resolution. Section 13.4 derives the SAR resolution anddiscusses the image constraints imposed by the PRF and system noise, then describes theeffect of relative motions such as those associated with ocean currents, ships or surfacewaves on the images. Using the currently operational RADARSAT-2 SAR as an example,Section 13.5 discusses the SAR design, its imaging modes and its operational constraints.Section 13.6 describes other operational SARs; Section 13.7 gives examples of SAR openwater and pack ice imagery.

13.2 Background

This section describes how SLR and SAR work, discusses the concept of resolution andhow it differs from the visible/infrared case, describes SARs that operate at multiplepolarizations, discusses the interferometric SAR and concludes with a summary of thepast, present and future satellite SARs.


13.2 Background 403

Cross-track

Along-track

Satellite track

A

Ground track

Surfacefootprint

XS

w

l

θ

pulse

y

x

Δφ1/2

Δθ1/2Nadir

h

Cross-track beamwidth

Along-track beamwidthYS

R0

Projection of pulse onto surface

Antenna

Fig. 13.1. The viewing geometry for the SAR and SLR antenna: w is the antenna width; l is thelength. For clarity, the along-track width of the surface footprint is greatly exaggerated relative tothe cross-track; typical footprint dimensions are 3 km × 100 km. At the scale of the figure, thealong-track beamwidth would be only slightly larger than the width of the line marked x.

13.2.1 General description

A SAR or SLR satellite antenna has typical dimensions of about 10 m in the along-trackdirection, 2 m in the cross-track, and looks off to the side of the spacecraft at incidence anglesof 20°–50°. The antennas are made up of many distributed transmitter/receiver elements inwhat is called an active phased array (Luscombe et al., 1993; Riendeau and Grenier, 2007).Although the antennas described in this chapter are rectangular, a SAR can also consist of aparabolic antenna with a front feed, as illustrated by the 1990–1994 Magellan SAR Venusmapping mission (A. Freeman, private communication, 1999). Satellite SARs operate withPRFs of 1000–2000 Hz and at frequencies of 1–10 GHz, corresponding to wavelengths of3–25 cm. The reason for this choice of frequencies is that, for f < 1 GHz, the radars areaffected by reflection and absorption in the ionosphere, by terrestrial sources of radiationand by the galactic radiance described in Section 9.3; and, for f >10 GHz, by atmosphericabsorption.

Figure 13.1 shows the viewing geometry and the half-power FOV or surface footprint ofa rectangular side-looking radar antenna of width w and length l that looks off at right anglesto the spacecraft trajectory. For the RADARSAT-1 and -2 SAR antennas, w = 1.5 m andl = 15 m. The size of the surface footprint follows from the definition in Equation (10.19)of the half-power beamwidths θ1/2 and φ1/2 in the along- and cross-track directions.


404 Imaging radars

For an antenna at an altitude h and incidence angle θ , the cross-track swath width XS in thesurface plane approximately equals

XS = θ1/2R0/cos θ = θ1/2h/cos2 θ = λh/(w cos2 θ ) (13.1)

In (13.1), the distance from the radar to the surface is R0 = h/ cos θ . Derivation of (13.1)depends on the assumption that θ1/2 θ , while the additional cos θ term converts thebeamwidth that is normal to the boresight direction into the surface swath width. A typicalvalue of XS is 100 km. Similarly, the along-track swath width YS is approximately equals

YS = φ1/2R0 = φ1/2h/cos θ = λh/(l cos θ ) (13.2)

so that YS is inversely proportional to the antenna length l. For RADARSAT, a characteristicvalue of YS is about 3 km, so that the footprint has a very narrow aspect ratio.

Following Section 10.4 and for both SAR and SLR, the pulse length determines thecross-track resolution. The two imagers differ in their determination of the along-trackor azimuthal resolution. Because the SLR relies only on range binning, its azimuthalresolution corresponds to the YS in Equation (13.2) and thus improves with increasing land decreasing range. If the RADARSAT antenna were operated as an SLR, it would beincapable of distinguishing two objects if their cross-track separation were less than about3 km.

In contrast, the SAR can achieve a theoretical azimuthal resolution equal to l/2 or half theantenna length. The SAR achieves this resolution through the following procedure. Phys-ically, the SAR divides into two parts, the antenna and its associated transmitter/receiver,and its memory or echo store. Consider the point A in Figure 13.1. In the SAR coordinatesystem, the point enters the swath to the left and exits on the right. The point takes about0.5 s to pass through the RADARSAT swath, during which time it is illuminated with about103 pulses. For the SLR, the instrument records only the amplitude time history of the echofrom each pulse.

In contrast, the SAR records the time history of both amplitude and phase of each echo,creating what is called a coherent radar. Within this set of stored data, every spatial pointthat passes through the illuminated footprint has a unique history in terms of time, rangeand Doppler shift. If, during the illumination period, the relative positions of the surfaceelements do not change, then a computationally intensive analysis of the pulse sequenceproduces a high-resolution surface image in both range and azimuth. This computation isapproximately equivalent to the synthesis of an antenna aperture with a length equal tothe swath width, or, for RADARSAT, to about 3 km. In actuality, the SAR works evenbetter than a long antenna, because, as Section 13.4.1 shows, the combination of range andDoppler processing produces an azimuthal resolution that is independent of range.

13.2.2 Resolution and pixel size

There are two definitions of resolution used in remote sensing. The first is used in thevisible/infrared and passive microwave and is the FOV diameter or pixel size in the resultant


13.2 Background 405

(a) (b)Δx Δx Δx(c)

A B A BA B

Fig. 13.2. Example of the two definitions of resolution, where A and B are two objects and x isthe constant resolution distance. (a) Resolution in the VIR, where the resolution is defined as theFOV diameter and equals the pixel size, and the two objects are separated by x. Because theobjects generate dark adjacent pixels, they cannot be separately distinguished in the image. (b) Radarresolution, where x is the minimum separation at which the two objects can be discriminated. Onthe figure, the object separation equals the resolution, the pixel size is half the resolution, and thetwo objects are separately visible in the image. (c) The two objects separated by less than the radarresolution distance, showing that they cannot be discriminated. See the text for further description.

image (Section 1.6.6). The second is used for active radars and is the minimum separationbetween two objects at which they can be distinguished (Raney, 1998, pp. 12–14). For thefirst case, Figure 13.2(a) shows a series of FOVs with two objects represented by verticalbars and separated by the FOV diameter x. Because the image represents these objectsas adjacent dark pixels, they cannot be separately resolved. For the second case of theradar resolution, the pixel size equals half the resolution distance. Figure 13.2(b) showsthat, for this case, two objects separated by the resolution distance are resolvable, whileFigure 13.2(c) shows that objects separated by less than this distance are not. Anotherway to demonstrate the difference between pixel size and resolution comes from theNyquist criterion (Jenkins and Watts, 1968). This states that, to resolve a spatial variationof wavelength λS, the signal must be sampled at a minimum spacing of λS/2, so that thepixel spacing is again half the resolution distance.

13.2.3 Polarization

SAR pulses are polarized, generally in the horizontal (H) or vertical (V) plane. Antennasthat broadcast and receive in both H or V are called HH or VV antennas. Another modeoccurs where the antenna broadcasts in H and receives in HH and HV, or broadcasts in Vand receives in VV and VH, where VH and HV are called the cross-polarization modes. AsSection 10.2.2 describes, SARs that measure all four modes (HH, HV, VV, VH) are calledpolarimetric SARs that operate in a quad-pol mode. In quad-pol, the SAR first transmitsa V-pulse, and measures the V and H returns (VV, VH). It then transmits an H-pulse andmeasures the H and V returns (HH, HV). The reason for alternating between transmissionof H and V pulses instead of transmitting both pulses simultaneously is that ambiguitiesoccur in distinguishing between VV and HV, and HH and VH. The polarimetric SARs havethe advantage that they provide more information about the surface; their disadvantage isthat they are much more data-intensive than SARs that operate at a single polarization.Depending on the SAR, many antennas work in all of the above modes. Each mode has a


406 Imaging radars

h

Antennas

Surface elevation

Flight track

Nadir track

Cross-track

Baseline

A B

Fig. 13.3. The geometry of a cross-track interferometer. The two antennas are at a specific altitude in aparallel track, and are separated by a precisely determined baseline. The antennas make simultaneousobservations of the same surface area from two different locations.

different sensitivity to the feature of interest; for example, the VH mode is much better atship detection than VV (Hurley, 2010; Hannevik, 2010). In other research areas, Bannermanet al. (2009) discuss the applications of polarimetric SAR to the detection of oil slicks;Kim et al. (2011) describe its application to iceberg research.

13.2.4 Interferometric radars

SAR and SLR interferometry consists of taking data from the same area either from twodifferent locations or at two different times, then using the combined data to determinevariations in surface displacement or velocity (Madsen and Zebker, 1998; Rosen et al.,2000; Gens, 2013). From Massonnet and Feigl (1998), interferometry is widely employedin land mapping, in studies of the land deformation associated with earthquakes and instudies of the flow of the Greenland and Antarctic ice caps (Rignot, 2008; Joughin et al.,2010). In oceanography, it has been used for wave measurements (Zhang et al., 2009).The two kinds of interferometric SAR operations are called cross-track and along-trackinterferometry.

Cross-track interferometry consists of two antennas at the same along-track, but differentcross-track, positions taking simultaneous radar images of the same surface area (Figure13.3). The antennas are separated in the cross-track direction by a carefully measured andmaintained baseline distance or separation, typically of order meters. The interferometergeometry is determined by three factors: the antenna size, the baseline separation and theinstrument altitude. There are at least two possible operating configurations. The first isthat one antenna transmits and receives (A in the figure); while the B antenna just receives,


13.2 Background 407

A

B

Baseline

Antennas

Flight Track

h

Surface

Radial velocity

Nadir track

Cross-track

Fig. 13.4. The geometry of an along-track interferometer. The two antennas are at a specific altitudein the same track, and are separated by a known baseline. The specific surface area is first illuminatedby antenna A, then, at a slightly later time, by antenna B.

so that two antennas receive the reflection from the transmitted signal. An alternativeconfiguration is the so-called ping-pong mode, where antenna A transmits with A and Breceiving, followed by B transmitting with A and B receiving, and so forth. For each pulseand each surface pixel, combination of the returns yields the phase difference between thesignals, where this difference in phase is proportional to the difference in path length fromthe antennas to each pixel. Given precise knowledge of the geometry, the surface heightat each pixel can then be calculated. As Chapter 14 describes, the ESA mission CryoSat-2carries a cross-track SAR Interferometric Radar Altimeter (SIRAL) used in investigationsof ice sheet and pack ice properties.

Along-track interferometry consists of the use of two antennas on the same trajectory totake two images of the same surface area from the same orbit position but at different times(Figure 13.4). For this case, the phase differences observed at each pixel can be analyzedto yield radial displacement. Zhang et al. (2009) describe its use in ocean wave studies.

13.2.5 Past, present and proposed satellite SAR missions

Table 13.1 lists some of the past, present and proposed civilian satellite SAR missions. Thetable gives the satellite names, the responsible organization or country, the SAR frequencyand polarizations, the launch year and approximate lifetime. The first civilian SAR wasthe NASA SEASAT SAR launched in 1978. Since that time, US civilian SARs have flownonly on short-duration Space Shuttle missions. SEASAT was followed by the RussianALMAZ (diamond) SAR, and the ERS-1 and ERS-2 SARs. SEASAT and ERS-1 and-2 lacked onboard data storage and could take data only within the receiving masks of theirground stations. During 1995, ERS-1 and ERS-2 were placed in the same orbit and madealong-track interferometric measurements.


408 Imaging radars

Table 13.1. Civilian satellite SAR missions.

SatelliteAgency orcountry

f (GHz),polarization

Launchdate

End ofoperations Constellation

SEASAT NASA 1.3, HH 1978 1978ALMAZ USSR 3, HH 1991 1992ERS-1 ESA 5.3, VV 1991 2000JERS-1 Japan 1.3, HH 1992 1994ERS-2 ESA 5.3, VV 1995 2011RADARSAT-1 Canada 5.3, HH 1995 –ENVISAT (ASAR) ESA 5.3, VV, HH;

VV,VH; HH,HV

2002 2012

ALOS (PALSAR) Japan 1.3, quad-pol 2006 2011RADARSAT-2 Canada 5.405, quad-pol 2007 – Same orbit as

RADARSAT-1TerraSAR-X Germany 9.65, quad-pol 2007 –TanDEM-X Germany 9.65, quad-pol 2010 – Tandem with

TerraSar-XCOSMO-SKYMED Italy 9.6, quad-pol 2007–2010 – Four satellitesSentinel-1A and -1B ESA 5.405, VV, HH;

VV, VH;HH, HV

2013–2014 Two satellites(second launchin 2015–2016)

RADARSATConstellation

CSA 5.3, quad-pol 2018 Three satellites

Pre-1999 data from Raney (1998, Tables 2–4, 2–5 and 2–6); post-2000 data from ASAR (2013a);PALSAR (2013); RADARSAT (2013); TanDEM-X, (2013a); COSMO-SkyMed (2013a; Sentinel-1(2013); Snoeij et al. (2008); and Torres et al. (2012).

The Japanese SARs consist of the L-band SAR on the Japanese Earth Remote Sens-ing satellite (JERS-1) and its successor, the Phased Array L-Band SAR (PALSAR), onthe Advanced Land Observing Satellite (ALOS). The Canadian RADARSAT-1 SAR, thefirst operational wide-swath SAR, has a polarimetric successor on the currently flyingRADARSAT-2, as well as on the proposed three-satellite RADARSAT Constellation. Thesuccessors to the ERS-1 and -2 SARs are the ENVISAT Advanced SAR (ASAR) thatoperated in both VV and HH, and the pending Sentinel-1A and -1B missions. Simi-larly to the ERS and ASAR, the Sentinel SARs will operate two modes: a general SARmode and a specific mode designed for ocean wave studies. Germany operates the satel-lite pair TerraSAR-X and TanDEM-X that fly in the same orbit with a separation ofabout 400 m (TanDEM-X, 2013b). These use along-track interferometry to produce aglobal digital elevation model (DEM) and are primarily a land mission. Italy operates theCOSMO-SKYMED four-satellite constellation, which has military, civil and research appli-cations (COSMO-SkyMed, 2013b).


13.4 How the SAR achieves its resolution 409

13.3 Resolution of side-looking radars (SLRs)

This section derives the resolution of the SLR, where in the cross-track direction, the samederivation applies to the SAR. As Figure 13.1 shows, the SLR looks off to one side of thesatellite track, sends out short pulses of energy, then receives the backscattered energy andbins it by range. Because the spacecraft velocity is much less than the speed of light, as theSLR moves along its flight track the image is built up line by line as the echo from eachpulse is received and binned. An SLR flew on the USSR KOSMOS series of satellites andon the subsequent Ukraine/Russia OKEAN and OKEAN-O (Operational) satellites, wherethese SLR observations ended in the year 2000. Mitnik and Kalmykov (1992) describe theoperational SLR on the KOSMOS satellites and give examples of imagery; in Russia, theSLR data were received on the equivalent of a fax machine. The KOSMOS SLR had aground resolution of 1–3 km and can be thought of as an all-weather AVHRR.

The SLR resolution is a function of range both in the along-track direction and in theazimuthal direction. In the azimuthal direction, if the separation of two targets at the samerange is so small that both targets lie within the YS from Equation (13.2), then energyfrom the same pulse is simultaneously reflected from both targets so that they cannot bedistinguished from one another. Therefore, the optimum SLR along-track resolution ySLR

equals the swath width, so that

ySLR = YS = φ1/2R0 = R0(λ/l) (13.3)

Equation (13.3) shows that the along-track resolution decreases linearly with R0 or withdistance from the satellite.

In the cross-track direction and from Section 10.4, the SLR cross-track resolution xSLR

equals half the projection of the pulse length onto the surface or, in terms of the pulseduration τ ,

xSLR = cτ/(2 sin θ ) (13.4)

Equations (13.3) and (13.4) show that, as θ increases from nadir, xSLR decreases andySLR increases. Two limiting cases occur for θ → 0 and θ → π /2. First, as θ → 0 or nearnadir, the energy is reflected back simultaneously from the surface, so that xSLR → ,ySLR = θ1/2 h, and the SLR is unusable.

Second, as θ → π /2 or, for a horizontal look angle, xSLR → cτ /2 and achieves itsminimum, and ySLR → , so that the SLR is again unusable. Between these two extremes,the resolutions vary with θ , so that the SLR resolution in both dimensions depends on θ . Ashorter pulse length can improve the cross-track resolution, but only a longer antenna anda smaller φ1/2 can improve the along-track resolution.

13.4 How the SAR achieves its resolution

This section describes how the SAR achieves its resolution and discusses some of theconstraints on its operation. Specifically, Section 13.4.1 derives the SAR azimuthal res-olution; Section 13.4.2 discusses the constraints imposed on its resolution by the PRF.


410 Imaging radars

XS

xYS

Flightdirection

FOV

yδ

Fig. 13.5. The SAR surface footprint, the lines of constant range and the orthogonal surface isodops,which lie approximately at right angles to the flight direction. Relative to x, the y-dimension is greatlyexaggerated.

Section 13.4.3 describes the constraints imposed by instrument and environmental noise;Section 13.4.4 describes speckle, which is the noise created by random surface backscatter.Finally, Sections 13.4.5 and 13.4.6 discuss problems that occur with SAR images. Theseare the need for radiometric balancing of the image and the problem of range walk, whichis the image distortion generated by relative motion within the surface footprint.

13.4.1 SAR resolution derived from Doppler beam sharpening

The optimum azimuthal resolution of a SAR antenna equals half the antenna length, or l/2,where this result is independent of cross-track range and frequency. Ulaby et al. (1982)derive this result in several ways; of these, this section presents the one called Dopplerbeam sharpening. This analysis involves the Doppler tracking of an individual target acrossthe surface footprint and yields a derivation of the azimuthal resolution.

For a non-rotating Earth and an antenna looking at right angles to the spacecraft trajectoryand within a surface footprint, Figure 13.5 shows several characteristic isodops and lines ofconstant range. If the surface position relative to the spacecraft is defined by x and y, thenwithin the footprint y is much less than x, where δ = y/x is defined as the azimuth anglerelative to the cross-track direction. With the definition of f0 and λ0 as the center frequencyand wavelength of the incident radiation, Equation (10.32) shows that the dependence ofthe Doppler shift f on incidence angle is

f = 2U0δ sin θ/λ0 (13.5)

Substitution of δ and x = R0 sin θ from Figure 13.1 into (13.5) gives

f = 2U0y/(λ0R0) (13.6)



Enters

t

Exits

T0

Δfmin

Time

+ΔfSAR

−ΔfSAR

0

Δf (

Hz)

Fig. 13.6. Tracking an object in frequency space across the SAR footprint, where the target enters atupper left and exits at lower right.

From Equation (13.2), the y-location of the leading footprint edge ymax = YS/2 becomes

ymax/R0 = f1/2/2 = λ0/(2l) (13.7)

with an equal but opposite relation for the trailing edge. Substitution of Equation (13.7)into (13.6) gives the frequency shift fSAR at the leading and trailing edge of the surfacefootprint as

fSAR = ±U0/l = ±1/τS (13.8)

In Equation (13.8), τS is the time it takes for the satellite to travel one antenna length. ForRADARSAT-1 and -2, l = 15 m and U0 = 6.5 km s−1 so that fSAR = ±430 Hz.

Figure 13.5 shows that, relative to the spacecraft, as a fixed target crosses the footprint itsrange decreases until its location is described by y = 0, after which point it increases, whilefor the same transect the Doppler frequency decreases nearly linearly. Since the target rangevaries across the footprint, the variable-range tracking produces what is called a focusedSAR. For comparison, an unfocused SAR assumes that the target is at a constant range.

For the focused SAR and from Equation (13.5), Figure 13.6 shows the Doppler shift asa function of time. Relative to the spacecraft, the target enters the footprint with a Dopplershift of + fSAR and exits with −fSAR. Suppose the target is tracked using a Dopplerfilter, where the center frequency of the filter decreases with time and where the carrierfrequency f0 is removed from the return. If fmin is the minimum frequency interval towhich f can be determined, then, from reorganization of Equation (13.6), the minimumalong-track resolution ymin becomes

ymin = fminλ0R0/(2U0) (13.9)

Equation (13.9) shows that, given fmin, ymin is easily calculated.


412 Imaging radars

The frequency resolution fmin is determined from the illumination time T0, which isthe time for a point on the surface to traverse the swath, or equivalently the time in whichthe satellite travels a distance equal to the along-track swath width, so that, from (13.7),

T0 = R0λ0/(lU0) (13.10)

From basic time-series constraints (Jenkins and Watts, 1968),

fmin = 1/T0 = lU0/(R0λ0) (13.11)

For RADARSAT-1 and -2, T0 is about 0.5 s, so that fmin = 1.2 Hz. Substitution of fmin

into (13.9) shows that the minimum along-track resolution equals half the antenna length,or that

ymin = lU0λ0R0/(λ0R02U0) = l/2 (13.12)

Paraphrasing Elachi (1987, pp. 204–205), this is an unusual result, in that l/2 is inde-pendent of frequency and range, and the shorter the antenna, the better the resolution. Thereason for the range independence is that, when the surface point in question is furtherfrom the actual antenna, the footprint is wider, so that the synthetic antenna is longer. Thisincrease in synthetic length exactly compensates for the resolution decrease caused by thegreater distance. Second, the resolution increase with decreasing antenna length occursbecause a shorter antenna yields a wider footprint and a longer synthetic aperture, therebyproducing a finer resolution. This does not mean that a very small antenna can be used toobtain a very fine resolution, because, as the next section shows, the constraints imposed bythe PRF mean that the antenna area cannot be smaller than a PRF- and frequency-dependentminimum.

13.4.2 Constraints on the PRF

For Equation (13.12) to be valid, the PRF must satisfy the two constraints, one setting afloor on the PRF, the other a ceiling. The floor depends on the antenna length, the ceilingon the antenna width. The combination of these constraints sets a minimum antenna area.

The PRF floor is determined from the antenna resolution. From the Nyquist criterion,the PRF must equal at least twice the largest Doppler shift that occurs in the sample, so that

PRF ≥ 2fSAR (13.13)

To obtain a SAR resolution of l/2, from (13.8) the PRF must satisfy

PRF ≥ 2U0/l (13.14)

Equation (13.14) shows that for the azimuthal resolution to equal l/2, for each translationof an antenna length, the PRF must equal at least two pulses. Given this constraint andfor the 15-m-long RADARSAT antenna with U0 = 6.5 km s−1, the PRF must be greaterthan about 900 Hz. Equation (13.14) sets a PRF floor, and means that, for a very shortantenna to yield a resolution of l/2, the PRF must be very large. If, however, the PRF is less



R0

θ

Δθ

SAR

hm

Illuminated swath

1/2

Fig. 13.7. The SAR geometry used in discussion of the relation between the cross-track swath widthand PRF for a narrow-swath SAR.

than the 2U0/l lower limit in Equation (13.14), the antenna continues to work, but withymin > l/2 (Anthony Freeman, private communication, 1999).

The maximum or ceiling PRF is set by the constraint that the return from each pulsemust be unambiguously identified without confusion from earlier or later pulses. FromSection 10.4.2, this means that the PRF must satisfy Equation (10.24). To derive themaximum possible PRF for the narrow cross-track SAR shown in Figure 13.7, the cross-track beamwidth θ1/2 is assumed to be much less than θ , where at the mean incidenceangle θm, R0 is the distance to the surface. Dropping the subscript on θm and λ0 and aftersome trigonometry, the distance dp between consecutive pulses must satisfy

dp = cτp > 2 tan θR0λ/w (13.15)

Because, from Equation (10.22), PRF = τ−1p , Equation (13.15) can be written

PRF < cw/(2R0λ tan θ ) (13.16)

For the RADARSAT antenna with θ = 45°, λ = 5.6 cm and R0 = 1100 km, Equation (13.16)shows that the PRF must be less than 3600 Hz. From (13.1) a broad cross-track beamwidthcorresponds to a small w, so that, as (13.16) shows, a narrow antenna requires a small PRF.This decrease in PRF with increasing swath width is the reason why broad-swath SARshave a poor resolution and is also why most high-resolution SARs have a relatively narrowswath width in the cross-track direction.

Combination of the inequalities in (13.14) and (13.16) yields

2U0/l < PRF < cw/(2R0λ tan θ ) (13.17)


414 Imaging radars

Reorganization of (13.17) shows that the antenna area must satisfy the following:

lw > 4U0λR0 tan θ/c (13.18)

From (13.18) and at a look angle of θ = 45°, an X-band (10-GHz) antenna requiresthat lw > 2.8 m2; an L-band (1.3-GHz) antenna, that lw > 21.8 m2. For the RADARSATantenna with its 22.5-m2 area and operating at 5.3 GHz and 45°, the minimum requiredarea is 5.3 m2, so that the antenna is larger than its required minimum. For the specialcase of the SeaWinds parabolic antenna described in Chapter 11, with f = 13.4 GHz andθ = 50°, lw > 2.9 m2. This means for SeaWinds to operate as a SAR would require anantenna diameter of about 2 m, which is twice its actual size.

13.4.3 Signal-to-noise constraints

Section 10.2.3 shows that the received power is the sum of the attenuated backscatter return,the instrument noise and the environmental blackbody radiation. The smallest signal that canbe distinguished from the noise must be greater than the instrument noise floor, describedin terms of the noise-equivalent-σ0 (NEσ0). Because of the additional noise contributionsfrom environmental radiation, the actual noise floor is greater. For the radar, the ability tomake the signal-to-noise ratio as large as possible requires a large power output, whichdepends on the size of the solar panels and the capacity of the batteries. For SEASAT,ERS-1 and -2 and RADARSAT-1, a typical value of NEσ0 is −24 dB (Raney, 1998); forRADARSAT-2, the noise floor is about −28 dB and varies slightly depending on look angleand observing mode (Jeffries, 2012).

13.4.4 Speckle

As Ulaby et al. (1982) and Rees (2001) discuss, in addition to the instrument noise andthe environmental blackbody emissions, the backscatter from a uniform surface generatesan additional noise source. For this case, even though adjacent surface elements have thesame σ0, the interaction within each element of the fine-scale structure with the incidentbeam creates a statistical uncertainty in σ0 from pixel to pixel. This uncertainty generatesvariations in image brightness called speckle. Averaging of adjacent pixels reduces speckle,where the number averaged is called the number of looks. This averaging, presented as thenumber of azimuth-averaged samples times the range-averaged, reduces the image varianceand resolution and enhances the image’s appearance.

13.4.5 Radiometric balancing

The backscatter dependence on θ generates another characteristic of SAR images. For aconstant oceanic wind speed, Figure 10.16 shows that σ0 decreases with increasing θ . Thisbackscatter dependence on θ means that the SAR brightness decreases with distance acrossthe swath, so that the image is brighter on the near side and darker on the far side. In the


13.5 RADARSAT-2 SAR 415

processing this decrease is sometimes reduced by removal of a linear trend in brightnessacross the image, where this correction is called radiometric balancing. Several examplesof unbalanced images are shown below.

13.4.6 Range walk

The SAR ability to produce a realistic image depends on there being no relative motionof the surface features. Because Doppler processing responds to surface motion, the SARimagery is distorted by its response to any moving object, current or ocean wave with across-track velocity component. For example, consider a pulse from 1.3-GHz SEASATSAR incident on the ocean surface at θ = 22°. Assume that, within the antenna footprint,a ship moves in the cross-track direction toward the SAR, with a velocity of 10 knots or5 m s−1. As Equation (10.29) shows with the satellite velocity U0 replaced by 5 ms−1, insteadof observing a zero Doppler shift, in the cross-track direction the SAR observes a Dopplershift f of about 20 Hz. From Equation (13.6), this corresponds to a y of approximately0.3 km, so that, on the image, the ship is displaced in the positive Doppler direction bythis distance from its wake and its actual position. Similarly, a ship traveling away fromthe SAR in the cross-track direction is displaced in the negative Doppler direction. Thisvelocity-induced apparent shift in position is called range walk.

From a SEASAT SAR image of the Caribbean, Figure 13.8 shows two examples ofrange walk. The white circles show the locations of two ships and their wakes; the shipsare bright from specular reflection and the wakes are dark, from either oil discharges orcurrents in the wake suppressing the Bragg scatterers. The dark area in the center of theimage is probably pollutants displaced by winds and currents. The wake locations relativeto the ships show that the ships are moving in opposite directions. The left-hand ship ismoving away from the SAR, so that the ship is displaced to the right, or in the direction ofpositive Doppler shift. The right-hand ship is moving toward the SAR, and is displaced inthe opposite direction. Such Doppler shifts associated with moving objects are the cause ofsuch image problems as a moving locomotive displaced from its tracks or cars displacedfrom a highway. Range walk is also caused by irregular satellite motion, such as spacecraftyaw and tilt, or by orbit-changing maneuvers.

13.5 RADARSAT-2 SAR

To illustrate the SAR imaging modes and operational constraints, this section describes theCanadian RADARSAT-1 and -2 SARs. A NASA spacecraft launched RADARSAT-1 onNovember 4, 1995. In exchange, Canada provided NASA with a portion of the SAR data andwith the two periods of Antarctic RADARSAT coverage described below. RADARSAT-2was launched in December 2007 on a French spacecraft by Russia from Baikonur, Kaza-khstan. RADARSAT-1 is owned by the Canadian Space Agency (CSA) and was built byMacDonald, Dettwiler and Associates Ltd. (MDA); RADARSAT-2 is owned by MDA, butfunded by a data purchase from CSA. Table 13.2 lists some of the properties of the two


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50 km 25

km

NIllumination direction

Fig. 13.8. Two examples of range walk from a SEASAT SAR image. The image was acquired in theCaribbean on October 3, 1978. The white circles show the locations of two ships and their wakes; theships are bright from specular reflection; their wakes are dark. (From Fu and Holt (1982), used withpermission, courtesy of Ben Holt.)

satellites. For RADARSAT-2, Figure 13.9 shows the SAR antenna, the X-band downlinkand the solar array, which has an area of 27 m2 and produces about 2.4 kW (Livingstonet al., 2005).

The instrument has a 7-year design life. RADARSAT-2 is in the same orbit asRADARSAT-1, but at a different relative position. The satellite carries two solid-staterecorders, each with a 150-GByte capacity (Livingston et al., 2005). This 300 GBytesof storage is equivalent to about 100 ScanSAR scenes (300 km × 300 km). For groundcommunications and data transfer, RADARSAT-2 has two high-power X-band antennadownlinks that provide a total transfer rate of 210 MBps. At this data rate, and for thenominal 10-min period that the satellite is in view of the ground station, about 40 ScanSARscenes can be downloaded. The downlink is powerful enough that the ground antennas canreceive data at a 5o elevation with a 3-m dish (RADARSAT-2, 2013e).

The RADARSAT-2 orbital position is determined by a combination of onboard GPSobservations, star trackers and a numerical orbit model. Table 13.2 compares the charac-teristics of RADARSAT-1 and -2. RADARSAT-1 can acquire data only to one side of thesatellite; this meant that, for the two RADARSAT-1 Antarctic mapping campaigns, thesatellite had to be rotated by 180o. In contrast, and as described below, the RADARSAT-2



Table 13.2. RADARSAT-1 and -2 SAR characteristics.

Property RADARSAT-1 RADARSAT-2

Altitude 800 km 800 kmInclination 98.6o 98.6o

Image mode Single-sided Dual-sidedOnboard recording Analog Digital (300 GB)Global Positioning None Onboard GPSYaw-steering None YesAntenna length, width 15 × 1.5 m 15 × 1.5 mFrequency/wavelength 5.3 GHz/5.6 cm (C-band) 5.405 GHz/5.5 cmSwath width 10–500 km 10–500 kmLook angle 20 °–49 ° 20 °–49°Polarization HH HH, HV, VV, VHPRF 1270–1390 Hz 1000–3800 HzPulse lengths (compressed) 33, 57, 86 ns 20, 33, 50, 86 nsNoise floor (NEσ0) −23 dB −28 dBa

Spatial resolution 10–100 m 3–100 mSwitching delay between image modes 14 s 1 s

From Ahmed et al. (1990); Raney (1998); Jeffries (2012); Livingston et al. (2005); andRADARSAT-2 (2013d).a Approximate, varies with distance across swath.

antenna can be mechanically oriented to point either to the right or left of the ground track,so that it can easily acquire images from both sides of nadir. Another change betweenthe two RADARSATs is that the observing frequency has been shifted from 5.3 GHz forRADARSAT-1 to 5.405 GHz for RADARSAT-2 (RADARSAT-2 2011). The reason forthis shift is to avoid radio interference with the increased use of the 5.3-GHz frequency bywireless Local Area Networks (LAN).

The 15-m-long RADARSAT-2 antenna is divided into four equally spaced panels thatfold for launch. Each panel contains four columns, each containing 32 sub-arrays, whereeach sub-array consists of 20 dual-polarization transmit/receive modules (Riendeau andGrenier, 2007). For the entire antenna, this yields a total of 640 transmit/receive modulesthat feed 10,240 radiating elements (RADARSAT-2, 2013c). Its 15-m length, which is about50% longer than the ERS SARs, has a fixed azimuthal beamwidth of about 0.2° (Livingstonet al., 2005, Table 3). In the cross-track direction, the antenna has a flexible beam-shapingcapability. Beam-switching between modes takes less than 1 s, so that blocks of imageryfrom the different beam modes provide nearly unbroken surface coverage.

As Raney et al. (1991) and Raney (1998) describe, RADARSAT-1 and -2 are in a dawn–dusk Sun-synchronous orbit, specifically chosen to maximize the exposure of the solarpanels to sunlight. Except over the South Pole, the Sun fully powers the satellite, whichreduces the need for batteries. Under normal operations, the RADARSAT-1 antenna looks


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Fig. 13.9. The RADARSAT-2 spacecraft; the antenna measures 15 m by 1.5 m. (Image courtesy of theCanadian Space Agency, C© MacDonald, Dettwiler and Associates Ltd. (MDA), all rights reserved.RADARSAT is an official mark of the Canadian Space Agency.)

to the right or to the north of the sub-satellite track, so that there is near-daily coverageabove 70° N and no coverage below 79° S. During periods in 1997 and 2000 and underthe Antarctic Mapping Mission (AMM), RADARSAT-1 was rotated about its nadir axisby 180°, which reversed the hemispheric bias and allowed the SAR to acquire compositeimages of Antarctica.

In contrast, the RADARSAT-2 antenna can be slewed so that it can look either to the rightor left of the spacecraft (Figure 13.10). This slew maneuver takes about 10 minutes, doesnot require fuel, occurs at a rate of about 150 slews per month and can be preprogrammedto provide additional viewing opportunities during successive orbits (Jeffries, 2012). Giventhe RADARSAT-2 slew mode, Antarctic imagery is available at all times.

13.5.1 Image modes

The observing modes supported by RADARSAT-2 include all the RADARSAT-1 beammodes. RADARSAT-2 offers two quad-pol modes (VV, VH, HH, HV), both with a 25-kmswath width, but with differing resolutions. For the wider-swath Standard and ScanSAR



29.8o 29.8o

Nadir

SARSAR

Solarpanel

(a) (b)

Fig. 13.10. The different slew modes of the RADARSAT-2 antenna. (a) Looking right of the orbittrack; (b) looking left. The execution of the slew manoeuver from viewing one side to the other takesabout 10 minutes. (Redrawn from RADARSAT-2 (2013f).)

ScanSAR WideScanSAR

NarrowWide

StandardStandard

Fine Fine

250 km

500 km

quad-pol

quad-pol

FineWide-1

Nadir

20o

Satellite track

49o

Fig. 13.11. Some of the different imaging modes for RADARSAT-2; see the text and Table 13.3for additional information. (Satellite insert courtesy of MacDonald, Dettwiler and Associates Ltd.(MDA), reproduced by permission of MDA; C© MDA, all rights reserved.)

modes, the quad-pol mode is not available, instead the satellite transmits in H or V, andreceives in either H or V.

RADARSAT-2 uses its cross-track electronic beam-shaping capability to generateall of the RADARSAT-1 modes, plus five additional modes at multiple polarizations.As Figure 13.11 and Table 13.3 show in order of increasing resolution, these modes


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Table 13.3. Imaging modes of the RADARSAT-2 SAR.

Beam mode

Nominalswath-width(km)

Incidenceangles to leftor right (deg)

Numberof looks Polarization

Resolution(m × m)

ScanSAR wide 500 20–49 4 × 4 Selectivea 100 × 100ScanSAR narrow 300 20–46 2 × 2 Selectivea 50 × 50Wide 150 20–45 1 × 4 Selectivea 25 × 28Standard 100 20–49 1 × 4 Selectivea 25 × 28Standard quad-pol 25 20–41 1 × 4 Quad-polb 25 × 28Fine-Wide 1d 170 20–45 1 × 1 Selectivea 15 × 8Fine quad-pol 25 20–41 1 × 1 Quad-polb 11 × 9Fine 50 37–49 1 × 1 Selectivea 10 × 9Multi-look fine 50 30–50 2 × 2 Selective singlec 11 × 9Ultra-fine 20 30–40 1 × 1 Selectivec 3 × 3

In the third and fifth columns, the number of looks and the resolution are given as range timesazimuth. From Luscombe et al. (1993); RADARSAT-2 (2011); (2013a, 2013d).

a Selective polarization: transmits in H, receives in H and/or V; or transmits in V, receives in Hand/or V.

b Polarimetric mode: transmits in H or V on alternate pulses, receives in both H and V for eachpulse.

c Selective single polarization: transmits in H or V, receives in H or V.d There are three Fine-Wide modes that range in cross-track width from 120 to 170 km, with an

along-track width of 25 km where the resolution depends on the mode (RADARSAT-2, 2013d).

include ScanSAR wide, ScanSAR narrow, Standard, Wide Swath and Fine Resolution(RADARSAT-2, 2013a, 2013d). For these modes, RADARSAT operates at incidence anglesbetween 20° and 50°, and uses the four different pulse lengths shown in Table 13.2 combinedwith different PRFs to obtain flexibility in surface range resolution. For oceanographic pur-poses, the most commonly used modes are Standard and ScanSAR-Wide. The Standardmode produces a 100 km × 100 km image with a 25-m resolution or a 12.5-m pixel size.The ScanSAR wide mode has a 500-km width with a characteristic resolution of 100 m.

ScanSAR operates differently then the Standard mode. For this case, the antenna beamis electronically switched among a number of parallel sub-swaths at a fast enough rate that asynthetic aperture is formed within each sub-swath, allowing the synthesis of a 300–500-kmwide image. Specifically, the imaged area is divided into a series of sub-swaths and sub-frames, through which the instrument cycles sufficiently rapidly that the sub-frames arecontiguous (Raney et al., 1991). The 300-km-wide ScanSAR narrow mode has two sub-swaths; the 500-km-wide ScanSAR wide mode has four sub-swaths. Figure 13.12 showsthe simplest case of two sub-swaths. In this example, ScanSAR begins with the inner swathand samples frame A, switches to the outer swath and samples frame B, then switches backto the inner swath and samples frame C. For ScanSAR to work, frames A and B and frames



Satellite track

Nadir track

Sub-swath

Sub-swath

A

A

C

C

B

B

Fig. 13.12. The sequence of beam positions used in the generation of a two-beam ScanSAR image.The letters on the flight track show the mean position of the SAR during acquisition of the corre-sponding surface image. The along-track widths of the sub-frames are greatly exaggerated. (Adaptedfrom Figure 8, Raney et al. (1991).)

B and C must overlap within their respective azimuthal beamwidths. Although ScanSARpermits the generation of a wide-swath image, because the PRF condition applies to theentire swath, the increase in swath width yields a decrease in spatial resolution, which iscoarser than the Standard swath.

13.5.2 Data storage and data rates

The early SARs had no onboard data storage, but operated only within the receiving maskof a ground station. RADARSAT-1 carries a tape recorder, RADARSAT-2 and other recentSARs use solid-state storage devices that record data for later downloading at one or moreground stations. There are two constraints on the number of stored images, one imposedby the amount of onboard storage, the other by the necessity of downloading the storeddata. Given that the satellites are over their ground stations only for short periods of timeas well as the bandwidth constraints imposed on the download by other spectrum users,there is a limit as to how much data can be downloaded in a single pass. With the conditionthat RADARSAT-2 be at least 5° above the horizon, the maximum downlink period overthe ground station is about 12 minutes. For RADARSAT-2, this problem is reduced by theexistence of many overlapping ground stations.

In the future, there are plans to deal with the download of the large amounts of data frommultifrequency and multipolarization SARs through use of optical downlinks (Giggen-bach et al., 2009). There is a test communications laser on TerraSAR-X called the Laser


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Communication Terminal of TerraSAR-X (LCTSX) that operates at a center wavelength of1064 nm. The use of these optical downlinks may mean that data from the next generationof SARs will be downloaded via broadband communications lasers to cloud-free sites suchas Mauna Loa on Hawaii (A. Freeman, private communication, 1999).

13.6 Other operational SARs

In addition to RADARSAT-2, other recent and pending ocean SARs include the EuropeanASAR, the Japanese PALSAR and the pending ESA Sentinel-1A and -1B satellites. As thefollowing discussion shows, these SARs offer a variety of modes that will improve studies ofocean and ice properties as well as enhance the ability to monitor oil spills and ship traffic.Because TerraSAR-X and TanDEM-X are focussed on DEMs and COSMO-SKYMEDcurrently lacks a marine focus, these satellites will not be discussed.

13.6.1 Advanced Synthetic Aperture Radar (ASAR)

The European ENVISAT was launched in March 2002, operated until 2012 and carried theASAR. ASAR operated at C-band (5.6 GHz) and was an advanced version of the AMI onERS-1 and ERS-2 (Desnos et al., 2000, ASAR, 2013a). ASAR looks to the right of theflight path; its solid-state recorder has a 7.5-GB capacity. The ASAR antenna is made up of320 transmit/receive modules that are used for beam shaping. In terms of coverage, rangeof incidence angles and polarization, the SAR operated at a number of modes, including a400-km-wide ScanSAR mode. Although ASAR did not have a quad-pol mode, it had analternating polarization mode with an operation similar to ScanSAR. In this mode, insteadof carrying out ScanSAR imaging of two adjacent swaths at the same polarization, the SARviews the same surface swath at two polarizations. These include HH and VV, HH andHV, or VV and VH, where the cross-track width of this mode can be as large as 100 km.The ScanSAR mode, however, is available only in HH or VV (ASAR, 2013a). The imagemodes are similar to those described for RADARSAT-2; Section 13.6.3 describes its oceanwave mode.

13.6.2 ALOS PALSAR

The Japanese Advanced Land Observing Satellite (ALOS) is a Sun-synchronous missionlaunched in January 2006 that carries the L-band (1.270-GHz) PALSAR, a joint projectbetween NASDA and the Japan Resources Observation System Organization (JAROS). Themission operated through 2011. PALSAR offered the 40–70-km-wide Standard and 250–350-km-wide ScanSAR modes, as well as an experimental quad-pol SAR. To utilize thesedata, ALOS had a high-speed solid-state data recorder with 96 GB of storage. PALSAR pro-vides a 30-MBps downlink via the geosynchronous Japanese Data Relay Technology Satel-lite and a 15-MBps direct broadcast downlink to ground stations (Rosenqvist et al., 2007).



Because of its polar coverage, it was heavily used in studies of the Greenland and Antarcticicecaps (Rignot, 2008; Rignot and Mouginot, 2012).

13.6.3 Sentinel-1A and -1B

As Torres et al. (2012) describe, the pending ESA two-satellite Sentinel SAR mission isscheduled to have its first satellite launched 2014; the second in 2015–2016. The Sentinelsare the successors to the ERS and ASAR missions, and, in their marine operation, will focuson ocean waves, sea ice and marine surveillance. The antennas will look to the right side ofthe spacecraft and have four modes. These are Strip Map, which consists of a continuous80-km-wide swath with a 5-m resolution, an interferometric 250-km swath, a 400-km-wideScanSAR swath, and a wave mode similar to ASAR. In the wave mode, the SAR measuresthe oceanic wave spectra within regions measuring 20 km × 20 km; these samples are takenat separations of 100 km along the orbit, and alternate between incidence angles of 23° and36.5°, each with a 5-m resolution (Potin, 2011). These data will be assimilated into globalwave models. The instrument will have 180 GB of storage and an X-band downlink rate of65 MBps via two separate antennas. The data will be downloaded through ground stationsand via the geosynchronous European Data Relay Satellite System (EDRS).


SAR is used in open ocean and polar pack ice studies. For the open ocean, Section 13.7.1shows that SAR can view surface and internal waves, ocean fronts and eddies, and monitorfishing fleets and oil spills (Brekke and Solberg, 2005; Hurley, 2010). For the polar packice, Section 13.7.2 shows that SAR can identify different ice types, track ice floes andicebergs, and provide sequential maps of the Arctic ice cover.

13.7.1 Open ocean

Because SARs generally operate at look angles greater than 20°, Bragg scatter from shortocean waves dominates the open ocean radar return. Exceptions include Bragg scatter fromraindrop splashes and backscatter from bright specular reflectors such as offshore structures,ships and icebergs. The SAR response to Bragg scattering means that the instrument canview any large-scale ocean or atmospheric feature that generates, damps or modulates thesewaves. These features include surface slicks, ocean currents, long-period surface waves andinternal waves; the atmospheric features include rain, wind bursts and weather fronts.

The presence of non-uniform ocean currents and bottom topography also affects theshort waves (Phillips, 1977). An adverse current steepens the wave slopes and givesrise to parasitic capillaries; a current in the wave direction reduces the slopes. Such currentsare generated by local winds, long-period surface waves, internal waves and large-scalesystems such as the Gulf Stream. Long waves that propagate over bottom topographyare also steepened, yielding short-wave growth and making the bottom topography visible


424 Imaging radars

Fig. 13.13. Standard mode RADARSAT SAR image of the San Francisco Bay area acquired onNovember 22, 2001 at 14:24 UTC during a descending orbit. The image measures 100 km by100 km. On the image, PR is Point Reyes, SF is the city of San Francisco, SFO is the airport, FI is theFaralon Islands, and GG is the Golden Gate. The illumination direction is from the right, the image isoriented approximately north–south. (RADARSAT data C© Canadian Space Agency/Agence SpatialeCanadienne 2001, used with permission. Processed and distributed by RADARSAT International,courtesy of Ben Holt.)

in the imagery. Fu and Holt (1982) describe these modulation mechanisms in detail andillustrate them with an extensive collection of SEASAT SAR images; Mouchot and Garello(1998) also describe the application of SAR to oceanography and show many of the imagesin Fu and Holt. The following discusses three general examples: ocean swell, oil slicks andinternal waves.

Ocean swell. As an example of the SAR ability to observe ocean swell, Figure 13.13shows, for November 22, 2001, a Standard beam RADARSAT-1 SAR image of the SanFrancisco Bay region and adjacent Pacific Ocean. For the same scene, Figure 13.14 showsan enlarged view of the area around Point Reyes. Both images have a 25-m resolutionand a 12.5-m pixel size and are illuminated from the right. At the time of the imageacquisition, an NBDC buoy just west of San Francisco Bay recorded that the wind wasfrom the west with speeds of 4–6 m s−1 (NDBC, 2013). Both images are radiometrically



Fig. 13.14. Enlarged view of the Point Reyes peninsula from Figure 13.13; the image measuresapproximately 25 km by 25 km. (RADARSAT data C© Canadian Space Agency/Agence SpatialeCanadienne 2001, used with permission. Processed and distributed by RADARSAT International,courtesy of Ben Holt.)

unbalanced, with enhanced brightness to the right. In the open Pacific, a long-period oceanswell is visible as a linear pattern of bright and dark bands propagating toward the coast;in contrast, San Francisco Bay is characterized by an absence of swell, but with patches ofbrightness associated with wind-generated Bragg scatterers. Also visible on this image isthe long linear San Andreas fault, running just inland of Point Reyes, then south throughSan Francisco.

Swell is visible because the capillary waves associated with Bragg scatter form prefer-entially on and just ahead of the crests, in part because of the curvature and in part becausethe troughs are sheltered from the winds while the crests are exposed. This variation incapillary-wave amplitude creates the observed bright/dark pattern. Because the waves arepropagating, they are slightly distorted by range walk. From the SAR image, the deep-waterwavelength of this swell is 350 m, corresponding to a 15-s wave period, which approxi-mately agrees with the 14-s period observed at the buoy. The NBDC buoy shows that theswell has an H1/3 of 4–6 m. This means that in deep water, the swell has a small wave slope.

Figure 13.14 shows the details of the wave diffraction around Point Reyes, and thedecrease in wavelength that occurs as the waves propagate into shallow water. The wavesincident on the exposed coast at A become shorter and brighter as they approach the coast,


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Fig. 13.15. ASAR VV ScanSAR image of an oil spill from the tanker Prestige, taken on 17 November2002 at 1045 UTC. The P marks the ship location, G marks Galacia province, and W shows the locationof ship wakes passing through the spill. (Image C© European Space Agency (ESA) 2002, used withpermission.)

indicating an amplitude increase as they move into shallow water. At the tip of Point Reyesmarked by B, there is a bright region of wave breaking. As the waves move past Point Reyes,they are diffracted by the topography so that, as the waves move into shallow water, theircrests rotate to become parallel to the coast. There is also a wave shadow in the embaymentat C. The image illustrates wave diffraction around an obstacle and shows the usefulnessof SAR in studies of the interaction of ocean swell with coasts and harbors. In the largerimage, the Faralon Islands provide another example of wave breaking and diffraction.

Slicks. SARs can also observe the location and extent of surface slicks. As Section 2.2.5describes, the surface slicks associated with human-induced oil or chemical spills and withnaturally occurring petroleum or biological slicks damp out waves with lengths less thanabout 0.3 m, which greatly reduces the Bragg scatter. Because ships and offshore structuresare specular reflectors and appear bright in the imagery while slicks damp out the Braggscatterers and appear dark, SAR provides a technique for monitoring off-shore oil wells,shipping and fisheries.

Figure 13.15 shows an ASAR image of an oil spill from the tanker Prestige, on 17November 2002, off the Atlantic coast of the Galacia province of Spain (ASAR, 2013b;2013e). The image is a subset of a wide-swath ScanSAR image measuring 400 km ×400 km; the oil spill extends over 150 km. The tanker is visible as a bright spot with a dark



Fig. 13.16. Two RADARSAT-2 images of the Strait of Gibraltar taken in Fine-Wide 1 mode in VV andVH. Images acquired on March 27, 2011 at 06:35:21 UTC. On the images, the Strait measures about14 km across at its narrowest point; G stands for Gibraltar; A for the town of Algeciras. (Adapted fromHurley (2010), see the text for further discussion. (RADARSAT-2 data and products C© MacDonald,Dettwiler and Associates Ltd., 2011. All rights reserved, used with permission. RADARSAT is anofficial mark of the Canadian Space Agency.)

plume of oil coming from it. The smaller bright spots around the ship are support vessels.The tanker is just outside of a major shipping lane that the slick cuts across; other shipswithin the lane are marked by bright spots. At the time of the image, the Prestige had lost10,000 metric tonnes of oil from its 70,000 metric tonne capacity and had fouled 200 kmof beach.

Figure 13.16 shows a RADARSAT-2 image of the Straits of Gibraltar for two polar-izations, VV and VH. The image shows the town of Algeciras and Gibraltar rock. TheVV-image shows ocean features with only a weak return from the ships. In contrast, theVH-figure clearly shows the ships and their locations across the entire image. Hannevik(2010, Table 2) shows that, for a drilling ship moored off Norway, the VH-polarizationgives a much brighter return from the ship relative to the background than the VV-return.Figure 13.16 illustrates how the properties of the return depend on the polarization and theuse of the VH-return for monitoring ship traffic.

Internal waves. Because, as Gasparovic et al. (1988) describe, internal waves generatesurface regions of convergent and divergent currents, SAR can also observe patterns ofinternal waves (Figure 13.17). Specifically, when the wind velocity is in the same directionas the induced current, the capillary-wave amplitudes are reduced; when the current opposesthe wind, the amplitudes are enhanced. Figure 13.18 shows two examples of internal waves.For the continental slope off New Jersey, Figure 13.18(a) shows the propagation of internalwaves in about 35 m of water, where these waves are generated by the interaction of the semi-diurnal tide with the shelf slope (Li et al., 2000). Along the white line in Figure 13.18(a),two packets of internal waves are visible, with average wavelengths of about 700 m and


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Ocean bottom

Internal waves

Induced surface currents

Propagation direction

Wind

Fig. 13.17. The generation of surface roughness by the surface currents induced by long internalwaves. (Adapted from Figure 2 of Hsu and Liu (2000).)

N

b

Raincells

Coral reefs

Dongsha Island

Internal waves

Fig. 13.18. SAR observations of internal waves. (a) Propagation of internal waves on the continen-tal slope off New Jersey taken from a Standard beam RADARSAT image taken on 2240 UTC on31 July 1996. The wave crests are approximately parallel to the isobaths. The white line and arrowshow the direction of wave propagation. (Figure 2 from Li et al. (2000), reprinted from Johns Hop-kins APL Technical Digest with permission, figure C© 2000 The Johns Hopkins University AppliedPhysics Laboratory, RADARSAT data C© Canadian Space Agency/Agence Spatiale Canadienne1996. Processed and distributed by RADARSAT International, courtesy of Pablo Clemente-Colon.)(b) RADARSAT ScanSAR-Wide image taken on April 26, 1998 of the westward propagation ofinternal waves in the South China Sea and in the vicinity of Dongsha Island and its surroundingcoral reefs. The image measures about 240 km by 240 km. Pixel size in original image is 100 m.See the text for further description. (Adapted from Figure 5 of Hsu and Liu (2000), figure C© 2000Canadian Aeronautics and Space Institute, RADARSAT data C© Canadian Space Agency/AgenceSpatiale Canadienne 1996. Processed and distributed by RADARSAT International, courtesyAntony Liu.)



with about eight wave crests per packet. Li et al. (2000) use such images to estimate thewavelength and phase speed of the observed waves, from which they can infer the watercolumn stratification.

For the South China Sea, Figure 13.18(b) shows internal waves in a portion of a ScanSARimage analyzed by Hsu and Liu (2000). The image shows the westward propagation ofinternal waves and, at the lower left, Dongsha Island and its surrounding coral reefs. Thewaves are generated from the interaction of the Kuroshio with the shallow topography inLuzon Strait, which lies outside the image to the east. The internal waves propagate towardDongsha Island, where at the reefs they divide into two packets that interact with each otherwest of the island. Hsu and Liu (2000) use such observations to verify theoretical modelsof internal wave interactions. In the upper part of the image, the bright highly reflectiveareas that resemble clouds are Bragg scatterers generated by rain cells.

13.7.2 Sea ice

Onstott (1992) describes radar backscatter from different classes of sea ice. As the sea icethickness increases from open water, to thin, young, first-year and multiyear ice, the surfaceroughness and backscatter generally increase, so SAR allows discrimination of some icetypes. Exceptions to this general increase include open water, which, because its brightnessdepends on wind speed, can be either brighter or darker than the adjacent ice. Because thepancake ice shown in Figure 2.9(b) has small diameters, raised rims and a quasiperiodicdistribution of floes, Bragg scatter can make it appear bright (Wadhams and Holt, 1991).A phenomenon called “frost flowers” that forms on the surface of new ice also induces abright transient return from Bragg scatter (Nghiem et al., 1997).

With this as background, this section discusses five examples of sea ice imagery. Thefirst three show the Arctic pack ice at three different scales, basin-wide, 500 km and 10 km.Of these, the basin-wide image is an example of the Arctic snapshot, the medium scaleshows the pack ice within the snapshot, and the small-scale image gives a sequence of packice images analyzed with the RGPS. The last two are a multifrequency ScanSAR imageof the southern ocean ice edge and a combined SAR and AVHRR image of an open waterregion in the Bering Sea pack ice.

First, for November 2–5, 1997, Figure 13.19 shows the entire Arctic 500-km-wideScanSAR swath coverage, or Arctic snapshot, as processed at the Alaska SAR facility. Theswaths are radiometrically uncorrected, as shown in the swath marked ‘Chukchi Sea’. Thecoasts are outlined in white; the Chukchi Sea, Alaska and Russia are labeled. The mostprominent feature is the open water in the Chukchi Sea, which is maintained by the warmwater flux through the Bering Strait. Because the snapshot consists of both descendingand ascending passes made over a 3-day period and under different wind and temperatureconditions, the swath brightnesses differ from one another. These snapshots are repeated at3- to 6-day intervals, and are used in the analysis of the pack ice motion and deformation.

Figure 13.20 shows an image of the Beaufort Sea pack ice measuring about 500 kmsquare and taken from the Arctic snapshot. There are two classes of ice in the image. To


430 Imaging radars

Fig. 13.19. The Arctic snapshot, or the 3-day overlay of RADARSAT ScanSAR imagery of ice andopen water in the Arctic Ocean taken within the Alaska SAR Facility receiving mask. The snapshotincludes swaths from Days 306 to 309 or November 2–5, 1997; the ScanSAR was processed at a300-m resolution. (RADARSAT data C© Canadian Space Agency/Agence Spatiale Canadienne 1997.Processed and distributed by RADARSAT International, figure courtesy of Nettie LaBelle-Hamerand the Alaska SAR Facility, used with permission.)

the left, the dark ice is thin first-year ice that formed adjacent to the coast during the fallfreeze-up. To the right, the figure shows the large multiyear ice floes characteristic of thecentral Arctic pack with their bright backscatter, separated from each other by darker leadscovered with thin ice. The large floes have characteristic scales of 25–75 km. The causeof the bright linear features is either specular scattering from pressure ridges or Braggscattering from leads covered with frost flowers.

The snapshots are processed through the RGPS to derive ice statistics and motion. Asan example of this processing and for the 1996 autumn, Figure 13.21 shows a series of



Banks Island

Fig. 13.20. A 500-km-square close-up image of the pack ice in the Beaufort Sea taken from the Arcticsnapshot in Figure 13.19. See the text for further description. (RADARSAT data C© Canadian SpaceAgency/Agence Spatiale Canadienne 1997. Processed and distributed by RADARSAT International,figure courtesy of Nettie LaBelle-Hamer and the Alaska SAR Facility, used with permission.)

nine pack ice images taken over a 41-day period (Kwok et al., 1999). Because older icegenerally has a greater backscatter than young ice, old ice is white, young ice is black. Foreach day, the geographic area is not fixed, rather the RGPS uses correlation methods totrack common ice features, so that the same ice features appear in each image. In the Day312 image, the white outlined square or cell measures 10 km × 10 km; its distortion in thelater images illustrates the shear and divergence associated with the ice motion. The cellarea remains nearly constant until Day 338, when a lead containing open water and thin iceopens within the cell. The lead continues to open between Days 341 and 345, adding to thearea of new ice and distorting the original cell. At the end of the 41-day period, thin newice occupies more than 50% of the cell. Such imagery is used on a large scale to determinethe ice statistics used in the verification of numerical models.

Although the previous SAR images are presented as single-channel, gray-scale images,SARs with multiple observing frequencies can be presented as false-color images. Forexample, Figure 13.22 shows an image acquired on October 5, 1994 from the Weddell


432 Imaging radars

Fig. 13.21. Time series of RADARSAT-1 observations of sea ice at various intervals in the BeaufortSea during 1996, showing the deformation of an initial 10-km-square box over a 41-day periodfrom Day 312 (November 8) to 353 (December 19). The white outlined square on Day 312 isthe 10-km box; the successive images show its deformation. (Figure 1 in Kwok et al. (1999),C© 1999 American Geophysical Union, reproduced/modified by permission of AGU; RADARSATdata C© Canadian Space Agency/Agence Spatiale Canadienne 1996. Processed and distributed byRADARSAT International, courtesy Ron Kwok.)

Sea ice edge by the three-frequency (X-, C-, L-band) Spaceborne Imaging Radar-C/XSAR on the Space Shuttle Endeavour. The image is oriented approximately east–west; theimage dimensions are 240 km by 350 km. The colors correspond to the following: red isC-band VV; green is L-band HV; and blue is L-band VV. Historically, this was the first



350 km

240

km

A

B

C

Fig. 13.22. SAR image of the Antarctic sea ice taken on October 5, 1994, from the SpaceborneImaging Radar C/X-Band Synthetic Aperture Radar (SIR-C/X SAR) on the Space Shuttle Endeavour.The image is oriented approximately east–west, with a center latitude and longitude of about 56.6°S and 6.5° W; its dimensions are 240 km by 350 km. (Courtesy of NASA/JPL/Caltech, used withpermission.) See color plate section.

ScanSAR image. The image shows the boundary between pack ice and open ocean in theWeddell Sea and also shows two large clockwise or cyclonic eddies in the ice. The openocean to the north is a uniform blue, due to the generation of Bragg scatterers by strongwinds. The dark green ice at the lower right labeled A is first-year pack ice, with typicalthicknesses of 0.5 m. The large black region to the center right labeled B is an area ofgrease ice as discussed in Chapter 2 and shown in Figure 2.9(a). Grease ice is a slurry ofsmall ice crystals, with characteristic crystal scales of about 1 mm, which damps out theBragg scatterers, so that it is dark and non-reflective. Figure 13.22 also shows the white orlight blue ice that is advected by the ocean eddies labeled C; this is probably pancake ice.Although multifrequency SARs have only been flown experimentally on the Space Shuttle,they may be flown operationally in the future (SIR-C/X-SAR, 2013).

Finally, Figure 13.23 shows separate and combined ScanSAR and AVHRR images ofthe open water or polynya region south of St. Lawrence Island in the Bering Sea. Suchlarge persistent openings in the ice cover are regions of strong atmospheric heat flux andlarge ice and brine generation (Martin, 2001). The smaller images show near-simultaneousAVHRR and ScanSAR images, where the AVHRR pixel size is 1 km, and the ScanSARpixel size is 200 m. The images are oriented so that north is toward the upper right-handcorner. The wind velocity is approximately northerly at 20 m s−1; the air temperature overthe polynya is about −15 °C.

Because of the northerly winds, the area south of the island is swept clear of pack ice.Within this region, the combination of wind and waves generates frazil ice in the water,where a Langmuir circulation herds the ice into the long linear streaks that are parallel


434 Imaging radars

25

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0

Bac

ksca

tter

(dB

)

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22

20

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a bS

urfa

ce te

mpe

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re (

o C)

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Fig. 13.23. Images of the frazil ice polynya in the Bering Sea south of St. Lawrence Island acquiredon January 9, 1999. Upper left, AVHRR image processed for ice surface temperature and acquired at0431 UTC; upper right, RADARSAT ScanSAR image acquired at 0504 UTC, so that the two imagesare 33 minutes apart. The long axis of the island measures about 200 km. See the text for furtherdescription. (RADARSAT data C© Canadian Space Agency/Agence Spatiale Canadienne 1999. Usedwith permission. Processed and distributed by RADARSAT International; image processing by RobertDrucker and the author.) See color plate section.



to the wind and visible in the image. The AVHRR image is presented in terms of icesurface temperature, calculated using the split-window algorithm of Key et al. (1997).The temperatures show that the frazil ice region south of the island is relatively warm andthe thick pack ice to the north is cold. The large lower image shows a superposition of theAVHRR and SAR images; the AVHRR temperature provides the color, SAR provides thetexture. The combined image shows that the region of Langmuir streaks is relatively warmwhile the surrounding thicker pack ice is colder. The image illustrates the importance ofpolynyas in the Arctic heat balance, and shows how the combination of different imagetypes adds to their value.


14

Other instruments: the gravity missions, ICESat-1 and-2, CryoSat-2, SMOS and Aquarius/SAC-D

14.1 Introduction

This chapter reviews three sets of missions that do not easily fit into the previous chap-ters. The first set includes three gravity missions, the Challenging Minisatellite Payloadmission (CHAMP) launched in July 2000, the US/German Gravity Recovery and ClimateExperiment (GRACE) mission launched in March 2002 and the European Gravity field andsteady-state Ocean Circulation Explorer (GOCE) launched in March 2009. The second setincludes three altimeter missions used for studies of sea and glacier ice. These are the twoNASA laser altimeter missions, the Ice, Cloud, and land Elevation Satellite-1 (ICESat-1)that operated from 2003 to 2009, the ICESat-2 satellite planned for launch in 2017, and thedual-beam radar altimeter on the ESA CryoSat-2 satellite. The third set includes the ESASoil Moisture and Ocean Salinity (SMOS) and the NASA/Argentinian Aquarius/SAC-Dmissions used to measure sea surface salinity (SSS), respectively launched in November2009 and in June 2011.

14.2 Gravity missions

There are two reasons for the importance of a detailed knowledge of the Earth’s gravityfield. First, in the steady state, altimetric retrieval of sea surface height depends on theshape of the ocean geoid and its accompanying gravity field. Second, understanding thetime variability of the Earth’s gravity field contributes to our knowledge of the global watercycle. This variability includes the loss or gain of mass in the polar ice caps, changes inthe mass distribution associated with the oceanic general circulation, redistribution of masscaused by shifts in bottom currents and the effects of runoff, precipitation and evaporation.Before gravity satellites, many different kinds of measurements contributed to the modelingof the geoid. These included combinations of land- and ship-based gravity measurementsand data from the altimeter satellites. The launch of gravity satellites presented the firstopportunity to derive the geoid from a single set of measurements (GRACE, 2013).

If mass were uniformly distributed within the Earth, or, equivalently, distributed inuniform spherical shells of different densities, then, neglecting non-gravitational forcingterms such as the solar wind and atmospheric drag, the satellite orbit would behave as

436


14.2 Gravity missions 437

if the Earth’s mass were concentrated at its center. Since the Earth’s mass is distributednon-uniformly, the gravity-driven motion of the satellite responds differently. Consideran excess mass below the satellite such as a mountain. As the satellite approaches themountain, the lateral gravitational attraction causes the satellite to speed up, then, after ithas passed over the mountain, to slow down. Over many orbits, this changing velocity timeseries can be used to calculate the Earth’s gravity field. As Smith (2010) shows, the closerthe satellite is to the anomaly, the better the spatial resolution. For a trench or seamount atan ocean depth of 4 km, if its width is less than the depth, the associated gravity signal haslittle expression at the sea surface. Similarly, for satellites such as GRACE and GOCE attheir altitudes of 400 km, geographic features with widths less than 400 km will have littleeffect.

Because their mass is used to measure gravity, the satellites have common features. Tominimize the aerodynamic forces on the satellites, their basic shape is that of a cylinder witha high mass and low frontal area, so that the total aerodynamic force acts on the satellitecenter of mass. To avoid displacement in response to internal motion, they also have fewor no moving parts and are temperature-controlled to maintain their density.

14.2.1 Challenging Minisatellite Payload (CHAMP)

In 2000, the German CHAMP satellite was launched into a non-Sun-synchronous orbitat an initial altitude of 454 km, where it operated until 2010. The choice of a non-Sun-synchronous orbit allows the satellite to observe the diurnal gravity components. Because ofatmospheric drag, the orbit slowly decayed, and, midway through the mission, an orbit boostprovided by an engine on the satellite returned it to its initial altitude. For Precision OrbitDetermination (POD), CHAMP used GPS receivers, laser retroreflectors for the satellitelaser ranging described in Chapter 11 and an accelerometer package for measurement ofthe non-gravitational accelerations caused by atmospheric drag and the solar wind. TheCHAMP mission determined the Earth’s gravity field to a resolution of 1000 km (CHAMP,2013). It also served as a test-bed for the successor GRACE mission.

14.2.2 Gravity Recovery and Climate Experiment (GRACE)

GRACE consists of a pair of twin satellites launched in 2002 with the nickname “Tomand Jerry” (GRACE, 2004). The two satellites are in the same Sun-synchronous orbit witha non-repeat ground track with an along-track separation of about 220 km at a 500-kmaltitude (GRACE, 2013). The satellites measure approximately 3 m × 2 m × 1 m andhave a mass of 480 kg (Figure 14.1). Because of atmospheric drag, the orbit height variesbetween 300 and 500 km, the orbit inclination is 89°, the orbital eccentricity is 0.001,and there are about 16 orbits per day. Their measurements are used to generate maps of theEarth’s gravity field at 30-day intervals. The GRACE successor is scheduled for 2017.

The GRACE measurement system has four components. These are the High Accu-racy Inter-satellite Ranging System (HAIRS), the Superstar accelerometers (ACC) that


438 Other instruments

Surface

Accelerate Decelerate

(a) (b) (c)

200 km

Fig. 14.1. A schematic diagram of a pair of GRACE satellites orbiting over a mountain. The scalesare exaggerated. In the approach, (a) the first satellite accelerates due to the gravitational attraction ofthe mountain, this leads to an increase in the pair separation; (b) as the pair passes over the mountain,the first satellite is decelerating and the second is accelerating, leading to a minimum separation;(c) as the pair moves away from the mountain, the second satellite decelerates, leading to an increasein separation. The distance between the two then reaches a constant as the pair moves away from themountain.

measure the non-gravitational forces on the satellite, the Star Camera Assembly (SCA)that determines the satellite position relative to fixed stars and GPS receivers. To stabi-lize the satellites, they each contain a center-of-mass trim assembly (MTA). The HAIRSdual-frequency microwave ranging system operates at 24 and 32 GHz and measures thedistance between the pair with an accuracy of 1 µm, or 1/100 the diameter of a humanhair (GRACE, 2013). The GPS and star tracking systems determine the satellite positionswithin a centimeter; the microwave link determines their relative positions to within amicron.

Figure 14.2 shows the passage of the satellite pair over the excess mass represented bya mountain. As the pair approaches the mountain, the first satellite accelerates, leading toan increasing separation between the pair. Then as they pass over the mountain, the firstdecelerates and the second accelerates, causing a minimum in their separation. Finally, asboth members of the pair pass over the mountain, the second satellite decelerates while theadditional gravitational attraction no longer acts on the first, so that the separation expands.Thus the distance between the pair expands, reaches a minimum, then expands again. Figure14.2 shows these changes in separation to an exaggerated scale, in actuality, they are of theorder of microns. Thus the GPS and laser tracking determine the large-scale position of thesatellites, while the microwave link between the two determines the fine-scale details.

Now consider the Greenland ice cap, which is losing mass at a rate of about 100–1501012 kg yr−1 (Luthcke et al., 2006; Luthcke, 2008). In this case, the satellites behave


14.2 Gravity missions 439

Fig. 14.2. Artist’s rendition of the pair of GRACE satellites. (Figure courtesy of NASA, not subjectto US copyright.)

similarly, except that, for the year-to-year measurements, because of the mass decrease, theamplitude of the change in distance with position decreases with time, allowing calculationof the mass loss. Similarly, changes in the distribution of mass in the ocean, such as throughthe shift of an ocean current, or from an increase in sea surface height due to precipitationor runoff, produce a signal proportional to the mass change (Hobish and Ward, 2012).

Each month, the GRACE project computes a global gravity field expressed as a series ofspherical harmonics (Tapley et al., 2004). From these harmonics, it is possible to computethe change in the mass variation as the ocean water is redistributed, and express thisredistribution in terms of changes in either ocean bottom pressure or sea level (Johnsonand Chambers, 2013). Because the gravity variations over land are 50 times larger thanthose over the ocean, adjacent to coasts the ocean data must be corrected or masked forland contamination. These effects are largest south of Greenland, north of the AntarcticPeninsula and in the vicinity of Banda Aceh, Indonesia, the epicenter of the 26 December2004 earthquake. The GRACE observations give the gravity variations to a 500-km scale.

As an example of GRACE measurements in the Arctic Basin, for August 2002 throughDecember 2006, Peralta-Ferriz and Morison (2010) compare GRACE and in situ measure-ments of ocean bottom pressure (OBP) (Figure 14.3). The in situ measurements consistof the following. First, from April 2003 to April 2008, two bottom-mounted pressurerecorders located near the North Pole recorded pressure at 15-min intervals. Second, from



2003 2004 2005 2006 2007 2008

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(b) Beaufort Sea

(c) Fram Strait

Amplitude (cm) Phase of max. amplitudeJ

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Fig. 14.3. A comparison of time series of GRACE and bottom pressure observations in the ArcticOcean from 2002 to 2008. The upper figure shows the monthly averages of the in situ anomaly inocean bottom pressure (solid red line) and the respective annual harmonic fits (dashed red line) at threelocations, North Pole (a), Beaufort Sea (b) and Fram Strait (c). At each location the gray line showsthe monthly GRACE bottom pressure anomaly and the dashed gray line shows the annual harmonicfit to the GRACE data. All of the time series have their long-term linear trend removed. The lowerfigure shows the amplitude (left) and phase of the GRACE distribution of bottom pressure. The colorbar showing phase increases vertically from June to July. (Figure courtesy of Cecilia Peralta-Ferrizand Jamie Morison, Figure 1 from Peralta-Ferriz and Morison (2010) copyright AGU, used withpermission.) See color plate section.

August 2003 to August 2007, there were two pressure recorders in the Beaufort Sea. Third,from September 2003 to August 2006, there were additional bottom pressure measurementsin Fram Strait. After removal of the long-term linear trend from the OBP and GRACE timeseries, the annual signal had an amplitude of about 2 cm. Comparison of the curves showsthat the in situ and GRACE bottom pressures agree in amplitude and phase. An annual cycleis visible in the time series of both data sets, where the pressure maximum occurs duringAugust–October with the minimum six months later in February–April. The measure-ments fit a model of the bottom pressure response to runoff and precipitation-evaporation(Peralta-Ferriz and Morison, 2010).


14.3 The ICESat-1, ICESat-2 and CryoSat-2 missions 441

14.2.3 Gravity field and steady-state Ocean Circulation Explorer (GOCE)

The GOCE satellite launched in 2009 operates in a Sun-synchronous orbit at an altitudeof 250 km. To compensate for atmospheric drag at this low altitude, the satellite has acontinuously running ion thruster that maintains the satellite at a constant altitude. GOCEmeasures gravity in two different ways: first, by measurement of the gravitation perturbationof its orbit, using the techniques described above; second, by measurement of the responsesof six masses, arranged in orthogonal pairs that respond to local gravity gradients. Thethree axes of the gradiometer allow the simultaneous measurement of three independentbut complementary components of the gravity field. Using these techniques, the GOCEobservations determine the geoid at a spatial resolution of about 100 km and an accuracyof 1–2 cm (GOCE, 2013). Combined with altimetry data, this improved geoid allowscalculation of the properties of such 100-km-scale current systems as the Gulf Stream andthe Antarctic Circumpolar Current.

14.3 The ICESat-1, ICESat-2 and CryoSat-2 missions

This section describes the Geoscience Laser Altimeter System (GLAS) that operated onICESat-1 from 2003 to 2009, and the Advanced Topographic Laser Altimeter System(ATLAS) planned for ICESat-2 that is scheduled for launch in 2017. It then describesthe SAR Interferometric Radar Altimeter-2 (SIRAL-2) on CryoSat-2 that was launched inApril 2010, after a 2004 launch failure destroyed its CryoSat-1 predecessor. The purpose ofICESat and CryoSat is to investigate the topography of both land and sea ice. Because theICESat lasers have a relatively high resolution but are obscured by clouds while the CryoSatradars have a lower but cloud-independent resolution, the two missions are complementary.Their high-resolution ice sheet measurements complement the GRACE low-resolutionobservations of mass loss.

For land ice, ICESat and CryoSat measure the topography of the Greenland and Antarcticice sheets and of the smaller but equally important mountain glaciers. These smaller glaciersare located on the west coast mountain ranges of North and South America, the north coastof Europe and Asia, and on the Tibetan plateau. As these glaciers and ice sheets melt, theycontribute to sea level rise. For sea ice, the satellites measure the surface topography andfreeboard, yielding thickness distributions of the Arctic pack ice. For the Arctic, Section14.3.2 shows that a thickness decrease accompanies the loss in the Arctic summer arealextent observed by the passive microwave instruments. Since the thinning or disappearanceof this pack ice alters the Arctic heat balance, these observations are critical to oceanographyand climatology.

14.3.1 ICESat-1

The ICESat-1 satellite operated at an altitude of 600 km in a near pole-to-pole, non-Sun-synchronous orbit. Its ground track had a 91-day exact repeat orbit with a 33-day sub-cycle



that provided dense spatial coverage of the polar regions up to ±86°. The satellite carriedthree identical lasers, in hopes that each of these lasers would operate for 18 months,providing a five-year lifetime for the instrument.

Unfortunately, because of manufacturing defects, the first laser failed after just 37 daysof operation (Abdalati et al., 2010). After evaluation of the failure, the second laser wasturned on, with the plan that it would operate for 45 days, then be turned off for six months.Because this laser also experienced rapid decay, in fall 2003, the ICESat operations shiftedfrom continuous operation to campaign mode. In this mode, the laser was turned on forthree 33-day periods per year during the Northern Hemisphere fall, winter and spring. In2007, the measurements were reduced to two campaigns per year (winter and fall), and themission ended in November 2009 with the failure of its last laser. In total, ICESat conducted18 separate 33-day campaigns.

GLAS operated at two wavelengths. The first, located in the NIR at 1.064µm, waschosen to enhance the reflection of the laser from the snow surface. The second, in thegreen at 532 nm, measured atmospheric aerosols. The NIR laser pulses had a length of 5 ns,a 70-m surface footprint diameter and a PRF of 40 Hz, so that the instrument sampled thesurface in discrete footprints separated by 175 m. A 1-m-diameter telescope collected thereflected radiance. A combination of laser retroreflectors and GPS provided the precisionorbit determination; a star camera and gyroscopes determined the laser orientation. Foreach location, the time delay between the pulse transmission and reception combined withthe laser-pointing angle determined the surface height of the illuminated spot. In the laseroperation, the instrument sent a pulse, then recorded the reflected energy in analog formthat was later digitized.

14.3.2 ICESat-2

One problem with the use by ICESat-1 of a single laser beam was that for ice sheets,and especially for measurements on a slope, a slight misalignment of the surface trackled to an incorrect elevation estimate. Another problem was that, for the sea ice thicknessretrieval, the large spot size mean that, as shown below, retrieval of ice thickness was moredifficult than for a smaller spot size. Because of these difficulties and the advances in lasertechnology, ICESat-2, which is scheduled for launch in 2017, will use a different higher-resolution laser technique called photon counting as well as a different laser configuration(Neumann et al., 2012).

Compared with ICESat-1, the ICESat-2 orbit will be at a lower 500-km altitude and willcover ±88° in latitude. ICESat-2 will carry the Advanced Topographic Laser AltimeterSystem (ATLAS). ATLAS is a green laser (532 nm) with a 10-kHz pulse repetition rate,which is much faster than ICESat-1. Each pulse is split into three pairs of beams, one pair atnadir, the other pairs offset by 3 km to the right and left of the nadir track (Figure 14.4). Atthe surface, a 90-m lateral spacing separates the pairs of beams; the purpose of these beampairs is to determine the ice sheet slopes over the ice sheets. Compared with ICESat-1,it will transmit a lower energy pulse and will receive the reflected energy using sensitive



Fig. 14.4. A schematic drawing of the ICESat-2 laser configuration. See the text for further descrip-tion. (Figure courtesy of the NASA ICESat-2 program, not subject to US copyright.)

single-photon detectors. This change in strategy, from a single laser pulse return that isdigitized to determine its waveform, to a multiple set of pulse returns that are detected withphoton counters, will yield an improved resolution.

For ICESat-1 and the two central beams of ICESat-2, Figure 14.5 compares the size andspacing of the surface footprints. ICESat-1 is characterized by large footprints with a 175-malong-track spacing; ICESat-2 will have 10-m-diameter footprints with an overlapping 0.7-m along-track spacing and a 90-m lateral spacing. This improved ICESat-2 design shouldprovide improved retrievals of sea ice and ice sheet properties.

Given the importance of these detailed laser measurements to our understanding of thesea ice and ice sheets, NASA established an aircraft program called IceBridge with thepurpose of filling the time gap between the demise of ICESat-1 and the launch of ICESat-2by providing laser and other observations of the Greenland and Antarctic ice sheets, as wellas the polar sea ice. The data from this program are archived at NSIDC. The combinationof ICESat-1, IceBridge and ICESat-2 should yield a 15-year time series of the change involume of the ice sheets as well as long-term coverage and analysis of sea ice thickness.



75 m

Flight track

175 m

ICESat-1

ICESat-2

90 m

Fig. 14.5. A comparison of the configuration of surface footprints for the ICESat-1 laser and for thetwo central beams of ICESat-2. See the text for further description.

14.3.3 ICESat-1 results

As Abdalati et al. (2010) summarize, the ICESat-1 surveys of Greenland and Antarcticaprovided, at a detailed scale, observations of the large-scale changes observed by GRACE.ICESat-1 data also revealed the behavior of Antarctic sub-glacial lakes. From multiyearICESat-1 surveys along repeat tracks, Fricker et al. (2007) measured the local subsidenceand uplift associated with filling and draining of connected sub-glacial lakes located 2–4 kmbeneath the ice surface. Their observations showed that these surface elevation changes wereas large as 10 m.

The ICESat-1 campaigns also provided measurements of sea ice thickness. Figure 14.6is an aircraft image of Antarctic sea ice, with the white ice floes separated by dark openleads. For such distributions of sea ice and water, ICESat determined the ice thicknessfrom measurement of the sea ice freeboard. Because sea ice is about 10% less dense thanseawater, it floats with about 90% of its thickness submerged (Kwok et al., 2009; Kwok,2010). As Figure 14.7 shows, the freeboard height hfrbd is the sum of the thicknesses of thelayers of sea ice hfi and snow hfs above the waterline, where

hfrbd = hfi + hfs (14.1)

The ice depth below the waterline is hdraft. The laser pulse reflects from the snow surfaceand measures its height relative to the geoid. If there is an adjacent lead, then the laseralso measures the sea surface height, hssh, and the difference between the two heights isthe freeboard hfrbd. Because, for many cases, the lead width is less than the pulse diameter,Kwok et al. (2009) were able to use partial returns from open leads to determine thefreeboard. Because the freeboard consists of layers of ice and snow, the snow depth isestimated from a combination of the climatological snowfall and observations of snowdensity. Given the snow thickness and the densities of snow, sea ice and seawater, thefreeboard measurement can be inverted to provide the ice thickness.

In their estimation of the sea ice thicknesses, Kwok et al. (2009) average the retrievedfreeboards along 25-km segments that contain 140 ICESat-1 observations, where the error



Fig. 14.6. An image of a lead in the Antarctic ice cover. The image was taken on 30 October 2009 at75.626087° S, 51.085481°W from a flight altitude of 500 m, from a digital mapping camera mountedon the NASA DC-8 aircraft. The image measures 600 m × 400 m and has a 0.1-m resolution; thewidth of the lead is between 75 and 100 m. (Image courtesy of John Arvesen, NASA, not subject toUS copyright.)

air

seawater

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snow

sea surface hice

hssh

hfs

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reference ellipsoid

lead width

lase

r pu

lse

lase

r pu

lse

Fig. 14.7. A schematic drawing of the sea ice freeboard, snow load, draft and thickness used in theICESat retrieval of sea ice thickness. See the text for further description. (Adapted from Figure 1,Kwok et al. (2009) and from Abdalati et al. (2010), Figure 4.)



in these averages is about 7 cm. For each 25-km segment, the error in the retrieved icethickness is about 0.5 m. For ten different ICESat campaigns, Figure 14.8 shows the sea icethicknesses in the Arctic Basin. The dashed circle shows the northern extent of the ICESat-1data, filled in by interpolation. The sub-figures show that the thickest ice (about 5 m) occursadjacent to Greenland and the Canadian Islands, followed by a thinning toward the centralArctic and the Siberian coast. The figures also show that the annual cycle produces low arealextents in October–November and large extents in February–March. The ON07 (October–November 2007) figure shows the drastic decline in sea ice area discussed in Section9.8, and the reduction in the amount of thick multiyear ice bordering the Canadian andGreenland coast. For the entire period, the winter sea ice volume was about 14,000 km3.For the same period, Kwok et al. (2009) show that, for winter, the first-year ice volumeremained roughly constant, the multiyear ice volume decreased by about 40%, and theoverall volume decreased slightly. Their work shows for the Arctic that the laser altimeterobservations provide consistent estimates of ice thickness distributions and volume.

14.3.4 CryoSat-2

CryoSat-2 is an ice sheet and sea ice radar altimetry mission launched in April 2010 thatoperates in a nearly circular, pole-to-pole orbit at an altitude of 720 km and an inclinationof 92° (CryoSat-2, 2013a). Its orbit has a repeat period of 369 days with 30-day sub-cyclesand an equatorial track separation of 7.5 km. The CryoSat-2 orbit is determined usingDORIS and a laser retroreflector array (Drinkwater et al., 2004; Phalippou et al., 2001).The CryoSat satellite measures 4.5-m long by 2.3-m wide by 2.2-m high. Unlike manysatellites, CryoSat-2 does not have solar panels mounted on wings; instead, the panels areon top of the satellite in what is called a “shed-roof” configuration (Figure 14.9). CryoSat-2is designed to measure sea ice thickness, to provide measurements of ice sheet elevation inregions of steeply sloping terrain and to fill the gaps in altimeter coverage near the poles(CryoSat-2, 2013a).

The principal instrument on CryoSat-2, SAR Interferometric Radar Altimeter-2 (SIRAL-2), consists of two Cassegrain elliptical antennas mounted side-by-side to form a cross-trackinterferometer. The antennas measure 1.15 m by 1.4 m with their long axes parallel to thesatellite trajectory and are separated by a baseline distance of 1.15 m. The purpose ofthe elliptical design is to accommodate both the launch vehicle fairing and the differentbeamwidth requirements in the along- and cross-track directions. Because the satellitecontains both a primary and a complete second copy of SIRAL-2, if the primary fails, themeasurements will continue with the secondary (CryoSat-2, 2013b).

SIRAL operates in Ku-band at 13.575 GHz and in three modes (Drinkwater et al., 2004;Francis, 2001). The first is the low-resolution mode (LRM) where SIRAL acts as a classicsingle-frequency altimeter, using a single antenna to transmit and receive pulses, and theDORIS system provides the ionospheric correction. This conventional pulse-limited modeis used over the ocean and in the pack ice interior where the roughness is less than at theice edge. For this case, a characteristic FOV diameter is about 15 km.


Fig. 14.8. The spatial pattern of arctic sea ice thickness derived from the ICESat-1 derived freeboardheight. The dashed circle shows the northern limit of the ICESat-1 observations and is filled byinterpolation and smoothed with a 50-km Gaussian kernel. The color scale at the bottom shows theice thickness; ON03 stands for October–November 2003; FM04 stands for February–March 2004;these mark the different 34-day ICESat-1 campaigns (From Kwok et al. (2009), Figure 7, copyrightAGU, used with permission.) See color plate section.



Fig. 14.9. An artist’s conception of the CryoSat-2 satellite. The solar array is mounted in a shed-roofconfiguration on top of the satellite; the two SIRAL-2 elliptical radar antennas are visible beneath thespacecraft. See the text for further description. (Image courtesy of ESA, copyright ESA.)

The second is the SAR mode, where, to obtain better resolution in the along-trackdirection, the instrument uses a single antenna to transmit and receive with a PRF that isroughly ten times the low-resolution mode. For bursts of 64 sequential pulses, the instrumentuses SAR/Doppler processing to divide the footprint in the along-track direction into 64sub-bins. Each bin measures about 250 m in the along-track direction and, depending onsurface roughness, up to 15 km in the cross-track direction. This mode is primarily usedover the rougher ice that occurs at the pack ice edge and to retrieve sea ice thicknesses fromfreeboard measurements (Laxon et al., 2013). Unlike the ICESat-1 laser, the CryoSat radarpulse reflects from the ice surface, instead of from the snow surface. The complementarynature of CryoSat-2 and ICESat-2 measurements suggests that a combination of laser andradar altimetry will provide direct measurements of the snow thickness.

The third is the SAR-interferometric (SARIn) mode with its name chosen to avoid confu-sion with InSAR, that measures the ice sheet elevation over regions of sloping topography.In this mode, the instrument transmits from one antenna and receives from both at a PRFthat is twice that of the SAR mode, corresponding to along-track intervals of about 250 m.The LRM mode produces one range measurement per pulse. In contrast and because of


14.4 SMOS and Aquarius/SAC-D 449

its 1.1-m baseline, the SARIn mode produces range measurements that are a function oflook angle for all of the points in the illuminated swath. Because the presence of a slopingsurface means that the first return can be from a point other than nadir, the purpose ofthis mode is to determine this off-nadir angle and its associated range. Depending on thedetailed topography of the ice sheet slope, the surface location of the minimum-distancemeasurement can wander from side to side of the nadir track.

One problem that the SIRAL-2 experiences over the ice sheets occurs because theupper part of the ice sheet, called the accumulation layer, which consists of snow that oververtical distances of tens of meters, is compressed into ice. The laser reflects from the snowsurface; the radar reflects from some depth that is regionally dependent. The hope is thatthis accumulation layer issue will be resolved from comparison of aircraft and surface fieldexperiments.

14.4 SMOS and Aquarius/SAC-D

The two sea surface salinity (SSS) missions are the ESA Soil Moisture and Ocean Salinity(SMOS) satellite and the Aquarius/SAC-D satellite. NASA and the Argentinian SpaceAgency, the Comision Nacional de Actividades Espaciales (CONAE), collaborate on theAquarius/SAC-D mission, where SAC-D is an abbreviation for Satelite de AplicacionesCientıficas-D, the “D” standing for the fourth spacecraft in the series. CONAE provided thespacecraft and certain of its instruments; NASA provided the Aquarius instrument. SMOSwas launched in November 2009; Aquarius/SAC-D in June 2011.

Both SMOS and Aquarius are in dawn–dusk Sun-synchronous orbits and carry 1.4-GHz(L-band) radiometers. These instruments do not rotate; instead they look at the dark sideof the terminator and, over periods of 10–30 days, generate near-global images of SSS.The goal of both missions is to retrieve SSS with an accuracy of 0.2 psu and at a spatialresolution of 100–200 km (Lagerloef and Font, 2010).

The science objectives of these missions are to monitor the seasonal and interannualvariation of the large-scale features of the ocean surface salinity field. The importance of SSSis because of its role in the global water cycle and in the oceanic thermohaline circulation.In the global water cycle, SSS serves as a proxy for evaporation and precipitation, riverrunoff and sea ice formation and melt, where it decreases with precipitation and increaseswith evaporation (Lagerloef et al., 2010; Lagerloef and Font, 2010). Because about 85% ofthe global evaporation and 80% of the global precipitation occur over the ocean, a detailedknowledge of SSS contributes to understanding the global water cycle (Salinity, 2013).Decadal salinity changes include decreasing salinity in the sub-polar North Atlantic andSouthern Oceans, and increasing salinity in the subtropical oceans. Surface salinity andtemperature also determine the surface seawater density and thereby its buoyancy, wherebuoyancy changes drive the thermohaline circulation.

As Section 9.5 discusses and Figures 9.16 and 9.17 show, the emissivity changes dueto salinity can be measured at 1.413 GHz. The sensitivity to salinity changes is greatestfor warm SSTs and least for the cold SSTs that occur in high latitudes. For the two



satellites, the increased sampling rate at higher latitudes in part compensates for this coldtemperature insensitivity. When one wants to retrieve SSS, various other factors affectthe surface emissivity and the received radiances. These include surface roughness, SST,Faraday rotation in the ionosphere, the reflection into the instrument of extraterrestrialsources such as sun glint and the background brightness temperatures of the galaxy andUniverse, the presence of RFI and the necessity to filter for heavy rain. The largest sourceof unwanted emissivity change is that caused by surface roughness. The two instrumentsuse different approaches to the surface roughness correction; Aquarius directly measuresroughness, while SMOS infers it from the ECMWF winds.

For SMOS, Camps et al. (2004) describe the results of an ESA-funded field studyon surface roughness called the Wind and Salinity Experiment (WISE). At 1.413 GHz,the WISE study determined the dependence of brightness temperature on sea state androughness, or as a function of wind speed, incident angle and polarization. The WISEresults provide empirical formulas for the dependence of roughness on the vector windspeed.

Aquarius is a combination passive radiometer/active scatterometer that uses a real-aperture 2.5-m-diameter reflector antenna. For the same surface footprints, Aquarius mea-sures the surface emissivity and the backscatter coefficients, where the combination of theseprovides both the surface emissivity and roughness. In contrast, SMOS uses a syntheticaperture radiometer to determine the emissivity and the ECMWF winds to determine theroughness from the WISE results.

14.4.1. Soil Moisture and Ocean Salinity (SMOS)

The ESA Soil Moisture and Ocean Salinity (SMOS) satellite was launched in November2009 with the goal of observing salinity at a resolution of 0.1 psu over periods of 10–30days and with a spatial resolution of 200 km × 200 km. SMOS carries the MicrowaveImaging Radiometer with Aperture Synthesis (MIRAS) that operates at 1.4 GHz. MIRAShas 69 antenna/receiver modules distributed along three linear arms. The arms are foldedfor launch; in orbit, they deploy into a three-pointed star with an 8-m diameter. Theseobservations form a two-dimensional synthetic aperture radiometer. The SMOS has aminimum resolution of 40 km. The details of the antenna synthesis and its operation arecomplex; Lagerloef and Font (2010) provide an excellent summary.

14.4.2. Aquarius/SAC-D

The Aquarius/SAC-D satellite is a joint CONAE/NASA mission. It consists of two parts:Aquarius, a radiometer/scatterometer combination that measures SSS, and SAC-D, theCONAE spacecraft platform that includes other instruments. Aquarius is designed toprovide monthly near-global maps of sea surface salinity at a spatial resolution of 150 kmand an accuracy of 0.2 psu (Le Vine et al., 2010).



Fig. 14.10. An artist’s view of the Aquarius/SAC-D satellite. The flight direction is at right angles tothe long axis of the satellite. The reflecting antenna and the microwave feedhorns are on the left; thesolar panels are to the right. For scale, the antenna diameter is 2.5 m; it does not rotate relative to thesatellite. The umbrella-like hood protects the electronics assembly from the Sun. The satellite flieswith its long axis approximately at right angles to the flight track, so that the antenna points towardthe night side of the terminator. (Image courtesy of NASA, not subject to US copyright.)

For this mission, CONAE provided the spacecraft, a dual-polarized microwave radiome-ter that operates at 23.8 and 37 GHz, an infrared sensor, a camera, and mission operationand ground systems. NASA provided the Aquarius instrument and the launch vehicle.Figure 14.10 shows the Aquarius/SAC-D satellite. The solar panels are to the right; thereflector antenna and feedhorns are to the left. The spacecraft flies with its long axis approx-imately at right angles to the flight track; to avoid sun glint, the antenna looks at the surfaceon the night side of the terminator. To maintain the radiometer stability, the goal is tomaintain its temperature fluctuations at <0.1 K over seven days; this is done with activeheating and cooling and through use of the sun shield that is located in the figure to theright of the feedhorns.

Aquarius uses three 1.413-GHz dual-polarized feedhorns and a 2.5-m reflector antenna toform three separate cross-track beams that scan in a pushbroom configuration. The satelliteis in a Sun-synchronous exact repeat orbit at an altitude of 657 km in an ascending orbitwith a 6 pm local equator-crossing time. These form a 390-km-wide swath that providesnear-global coverage every seven days. The antenna looks toward the night side of the orbit.Figure 14.11 shows the configuration of the 3-dB surface footprints that are respectivelygenerated by three beams with incidence angles of 28.7°, 37.8° and 45.6°.

Using the same antenna, the instrument alternates between passive and active obser-vations. The passive observations are at 1.413 GHz; the scatterometer observations are at1.26 GHz. The 1.413-GHz band is a protected radio-astronomy window; the 1.260-GHzscatterometer band is shared with other satellite and surface emitters (Spenser et al., 2011,



0 100 200 300 400 500 600 700

0

200

100

–100

–200

300

–300

94 km x 76 km(Inner)

120 km x 84 km(Middle)

156 km x 96 km(Outer)

Flig

ht p

ath

Alo

ng-t

rack

dis

tanc

e (k

m)

Cross-track distance (km)

390-km swath width

Nig

ht s

ide

Antenna view axis

Fig. 14.11. The distribution and approximate size of the three surface footprints for the Aquariusinstrument. See the text for further description. (Redrawn from Le Vine et al. (2007), Figure 3.)

Figure 1). For the Aquarius radiometer, ground-based air surveillance radars are the primarysource of RFI (Le Vine et al., 2007).

There are three separate radiometers, but only one scatterometer. The three radiometersoperate in parallel, while the scatterometer rotates among the three feedhorns (Le Vineet al. 2007). The radiometer and scatterometer observations are interwoven. For bothinstruments, the basic measurement block is 10 ms, consisting of 1 ms of scatterometertransmission and 9 ms of radiometer observations. As shown below, the duration of this shortmeasurement block was dictated by the RFI analysis. When the scatterometer transmits,the radiometer is turned off. The radiometer cycle has a duration of 120 ms, during whicheach radiometer collects seven V and H observations, followed by five 10-ms calibrationsamples.

For each beam, the 60-ms scatterometer sequence consists of six blocks, consisting oftwo noise measurements at V and H, and four polarization measurements that are madeup of two transmit pulses at H that are respectively received at H and V and two transmitpulses at V received at H and V. This 60-ms sequence moves from beam to beam, and, forall three, takes 180 ms to complete. Every 0.72 s, the two cycles overlap, during whichtime the scatterometer completes four 180-ms measurement cycles and the radiometercompletes six 120-ms cycles. These short interwoven sequences mean that the radiometer



Aquarius salinity (psu)33 33.5 34 34.5 35 35.5 36 3736.5 36.5

Fig. 14.12. The annual average salinity for January–December 2012 as derived from Aquarius. Thesalinity data are displayed on a 1° × 1° gridded field calculated from polynomial fitting. (Imagecourtesy of Gary Lagerloef and Hsun-Ying Kao, Earth and Space Research, all rights reserved, usedwith permission. Data courtesy of NASA.) See color plate section.

and scatterometer sample the same surface footprint. For the radiometer, the use of a 5.46-sintegration time reduces the radiometer NET to 0.1 K (Yueh and Chaubell, 2012).

The scatterometer measures the VV-, VH-, HH- and HV-backscatter coefficients; thetotal power derived from these four measurements is an invariant that is independent ofthe Faraday rotation; it is used to retrieve the surface roughness. Because, at L-band, themagnitude of the Faraday rotation is more than 50 times greater than at 10.7 GHz, for thepassive retrieval of SSS to be successful, this rotation must be removed from the brightnesstemperatures (Meissner and Wentz, 2006a). The Faraday rotation means that a radianceleaving the surface with one polarization has a mixed polarization when it arrives atthe sensor. To correct this, the third Stokes parameter is calculated from the sum anddifference of the two received polarizations (V + H, V − H). Given the third Stokesparameter, the Faraday rotation angle is calculated from it and the second (H-pol) Stokesparameter, then is used to correct the received radiances (Le Vine et al., 2013).

In removal of RFI from the received brightness temperatures, each 9-ms block is checkedfor RFI with a threshold filter (Fischman et al., 2009; Le Vine et al., 2012). The data thatfail this test are discarded then the remaining date are averaged into the 1.44-s or 12-cycleblocks. The use of these short time blocks reduces the loss to RFI. Another problem is that,at L-band, the land is much brighter than the ocean, so that, to avoid sidelobe contamination,



the SSS retrieval is masked within 200 km of land. The surface validation data come fromthe co-located Argo floats and the TAO/TRITON array discussed in Chapter 7, whichconsist of about 300 observations/day.

Meissner et al. (2012) describe the salinity retrieval algorithm. The brightness temper-atures from the three feedhorns are corrected for Faraday rotation, flagged for RFI, then,using the data from the CONAE radiometer, are flagged for rain. The radar backscattermeasurements of σ0 are combined with the NCEP windspeed and direction to calculatethe roughness-induced brightness temperature TB. When this TB is removed from thecorrected radiometer brightness temperatures, the results are the brightness temperaturesfor a flat ocean surface. These are used in combination with the temperature/salinity curvesshown in Figure 9.16 to retrieve the desired salinity, where the SST is taken from a GHRSSTdata set.

For January–December 2012, Figure 14.12 shows the annual average sea surface salinity.As Le Vine et al. (2007) observe, Aquarius takes more SSS observations in two monthsthan have been taken by ships since these observations began 125 years ago. The redsare high salinity values; the blues and purples the low values. Because of cold watertemperatures and high winds, the values from the Southern Ocean are unreliable; the slightstriping in the north–south direction is a residual calibration error. The paucity of data fromthe Mediterranean illustrates the problem with coastal contamination. Figure 14.12 showsseveral well-known oceanic features. These include the high-salinity water generated in theNorth Atlantic by the Mediterranean outflow, the higher average salinity in the Atlantic thanin the Pacific and Indian Oceans, the high salinity in the Atlantic and Pacific subtropicalgyres compared with their surroundings, and the low-salinity water associated with bandsof precipitation near the equator and with precipitation in the North Pacific. All thesefeatures are related to large-scale patterns of rainfall and evaporation, river outflow andocean circulation. Regional features include the high-salinity Arabian Sea west of theIndia, which is dominated by evaporation, and the low-salinity Bay of Bengal to the eastdominated by the Ganges River and monsoon rains (Aquarius, 2013a).

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-APP CUUK2533/Martin ISBN: 978 1 107 01938 6 November 25, 2013 17:56

Appendix

Table A.1. The letter designations used forfrequency bands in the microwave.

Letterdesignation

Frequencyrange (GHz)

Wavelengthrange (cm)

L 1–2 30–15S 2–4 15–7.5C 4–8 7.5–3.8X 8–12 3.8–2.5Ku 12–18 2.5–1.7K 18–27 1.7–1.1Ka 27–40 1.1–0.75

Microwaves101 (2013).

Table A.2. MODIS technical specifications and applications.

Primary use Banda

Bandwidth(nm)

Saturationreflectance

RequiredSNR

250-m resolution 1 620–670 1.6 1282 841–876 1.05 201

500-m resolution 3 459–479 1.07 243Bands 1–7 are used for discrimination of

land, clouds and aerosols4 545–565 1.01 2285 1230–1250 0.84 746 1628–1652 1.03 2757 2105–2155 0.33 110

1-km resolution 8 405–420 0.37 880Ocean color 9 438–448 0.26 838

10 483–493 0.19 80211 526–536 0.16 754

(cont.)

455


456 Appendix

Table A.2 (cont.)

Primary use Banda

Bandwidth(nm)

Saturationreflectance

RequiredSNR

12 546–556 0.12 75013 662–672 0.08 91014 673–683 0.06 108715 743–753 0.07 58616 862–877 0.06 516Water vapor 17 890–920 0.75 167Cirrus 18 931–941 1.14 57

19 915–965 0.85 250High cirrus 26 1360–1390 0.89 150

Primary use BandBandwidth(µm)

Saturationbrightnesstemperature (K)

RequiredNET(K)

SST 20 3.660–3.840 333 0.05Forest fires 21 3.929–3.989 429 2.00SST 22 3.929–3.989 329 0.07SST 23 4.020–4.080 329 0.07Atmospheric 24 4.433–4.498 318 0.25temperature 25 4.482–4.549 314 0.25Cloud properties 27 6.535–6.895 323 0.25

28 7.175–7.475 320 0.2529 8.400–8.700 330 0.05

Ozone 30 9.580–9.880 364 0.25SST 31 10.780–11.280 399 0.05

32 11.770–12.270 391 0.05Cloud top altitude 33 13.185–13.485 335 0.25

34 13.485–13.785 341 0.2535 13.785–14.085 339 0.2536 14.085–14.385 371 0.35

a Bands 1–19 and 26 are in nm; bands 20–25 and 27–36 are in µm.SNR, signal-to-noise ratio.NET, Noise-equivalent delta-temperature.Data courtesy of NASA Goddard MODIS project (MODIS, 2013).


Appendix 457

Table A.3. VIIRS technical specifications and applications.

Primary use Band Wavelength (nm)

Nadirresolution(m)

AVHRRequivalentband NET

Day/night low light DNB 500–900 750Ocean color/aerosol M1 402–422 750Ocean color/aerosol M2 436–454 750Ocean color/aerosol M3 478–498 750Ocean color/aerosol M4 545–565 750Imagery I1 600–680 375 1Ocean color M5 662–682 750 1Atmospheric correction M6 739–754 750Vegetation I2 846–885 375 2Atmospheric correction M7 846–885 750 2

Wavelength (µm)

Cloud particle size M8 1.23–1.25 750High thin cirrus M9 1.37–1.39 750Snow I3 1.58–1.64 375Snow M10 1.58–1.64 750 3AClouds M11 2.22–2.28 750Cloud Imagery I4 3.55–3.93 375 3BSST M12 3.66–3.84 750 3B 0.038SST/fires M13 3.97–4.13 750 0.045Cloud top properties M14 8.40–8.70 750SST M15 10.26–11.26 750 4 0.022Cloud imagery I5 10.50–12.40 375 4, 5SST M16 11.54–12.50 750 5 0.040

From Zhou (2011); NET for thermal bands from VIIRS-ATBD (2012). M stands for moderateresolution; I stands for imaging resolution; DNB is the day/night band.

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-REF CUUK2533/Martin ISBN: 978 1 107 01938 6 November 26, 2013 12:48

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http://directreadout.noaa.gov/miami11/docs/5.12_Zhou_Imagers.pdf

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-IND CUUK2533/Martin ISBN: 978 1 107 01938 6 November 26, 2013 12:2

Index

1.41-GHz radio astronomy window, 26860-GHz oxygen complex, 261

AATSR (Advanced Along-Track ScanningRadiometer), 219–221

absorptance (VIR), 70absorption coefficient, 58absorption in seawater

absorption depth, 58CDOM and particulates, effect of, 141phytoplankton, effect of, 142

absorptivity (microwave), 70ACSPO (Advanced Clear-Sky Processor for Ocean),

223–226cloud-free pixels, percentage of, 225single pixel tests, 224spatial uniformity tests, 225

Advanced Land Observing Satellite (ALOS)PALSAR, 422

AERONET (Aerosol Robotic Network), 166aerosol single scattering, 110aerosols

composition, 83–84, 165field measurements, 166global distribution, 167land-generated, 83marine-generated, 83retrieval of path radiances, 165–168volcanic, 84

AGC (Automatic Gain Control), altimeter, 386altimeter

and ocean swell, 387–388effect of variable pointing angle, 368error budget, 391noise, 389orbit errors, 390past, present and future missions, 368POD (precision orbit determination), 374pulse-limited footprint, 381–383required accuracy, 367round trip travel time, 384surface roughness and wind speed, 385

altimeter environmental uncertainties, 392inverse barometer, 392tides, 392

altimeter examplescomparison of eddies with Rossby waves, 398–400large scale flows, 393–394seasonal variability, 394–396two decades of sea level rise, 396westward eddy propagation, 397–398

altimeter mission groupsERS-1, ERS-2, ENVISAT, SARAL, Sentinel-3, 368TOPEX, JASON-1, JASON-2, 368

altimeter sea state bias, 390electromagnetic, 390skewness, 390

altimeter surface calibration, 376–378altimeter tandem missions, 380altimeter, atmospheric sources of error, 389

dry troposphere, 389free electrons, 389wet troposphere, 389

AMI (Advanced Microwave Instrument)scatterometer, 344–345

AMSR2 (Advanced Microwave ScanningRadiometer-2), 256

differences from AMSR-E, 258on GCOM-W1 in A-Train, 258RFI mitigation, 258

AMSR-E (Advanced Microwave ScanningRadiometer-EOS), 255–256

and RFI, 270images, 293multi-variable retrievals, 293

Angstrom exponent, 167antenna

associated solid angles, 241definition, 237gain, 241half-power field-of-view, 240illumination pattern, 237measurement of surface radiance, 242–244power pattern, 239–241

489


490 Index

antenna (cont.)Reciprocity Theorem, 237temperature, 243

antenna pattern correction (APC), 245–247apparent optical properties (AOP), 127Aquarius/SAC-D, 450–454

antenna and beam configuration, 451Faraday rotation, correction for, 453image of global sea surface salinity, 454passive and active modes, 451RFI mitigation, 454salinity retrieval algorithm, 454surface roughness measurement, 454

Argo floatsand SST validation, 217GHRSST error analysis, use in, 217

ASAR (Advanced Synthetic Aperture Radar),422

ASCAT (Advanced Scatterometer) on METOP,345–346

atmosphereconstituents, 81content of water vapor and liquid water, 82emission and absorption, 89molecular absorption and emission, 86–87vertical structure, 79–81

A-Train (Afternoon Constellation), 29AVHRR (Advanced Very High Resolution

Radiometer), 201–202data formats, 202example, 231history, 194

AVHRR/3, 201azimuthal look angle, 273

blackbodies, 66Bouee pour l’acquisition de Series Optiques a Long

Terme (BOUSSOLE), 169Bragg scatter, 326–327

open ocean and SAR, 423sea ice and SAR, 429

Brewster angle, 119brightness, 64buoy winds, limitations, 339

capillary waves, 37parasitic, 39response to changes in wind speed, 37visible/infrared, effect on, 119–122

carotenoids, 137, 143case 1 and case 2 waters, 140CDOM (Chromophoric Dissolved Organic Material),

140from terrestrial runoff, 140global distribution, 186ocean-derived, 140scattering from, 143–147

CDR (climate data records)examples, 24guidelines for generation, 24

CEOS Committee on Earth Observation Satellites), 29CFOSAT (China-France Oceanography Satellite), 333CHAMP (Challenging Minisatellite Payload)

precision orbit determination, 437resolution, 437

cloud detection in visible/infrared, 221–223high thin cirrus, 223MODIS and VIIRS algorithms, 226–227multiple pixel tests, 223single pixel tests, 222uniform thin fog, 222

cloud non-raining water dropletsdistribution of sizes, 83, 263Rayleigh scatterers, 264

clouds, 83global coverage, 226liquid water, 82

CMOD-5 geophysical model function, 346coccolithophores, 190constellations, satellite, 28

coordination role of CEOS, 29examples, 29wind constellation, 355

Coriolis satellite, 258Cross-Calibrated Multi-Platform (CCMP) winds,

356input data sets, 356PO.DAAC archive, 356processing levels, 356

CRTM (Community Radiative Transfer Model), 224CryoSat-2 mission, 446–449CZCS (Coastal Zone Color Scanner), 147

atmospheric correction, 168observational bands, 148

data archives and processing centers, 23, 25data records, types, 24debris, orbital, 10–11decibel, definition, 89detritus, oceanic, 140diffuse attenuation, 134diffuse transmittance, 110–112DMSP (Defense Meteorological Satellite Program),

14Doppler binning, 319–322

application to SAR, 322contribution of Earth’s rotation, 324dependence of Doppler shift on view angle, 319surface resolution, 323–324

DORIS (Doppler Orbitography and RadiopositioningIntegrated by Satellite), 372, 374

determination of satellite position, 374measurement of free-electron concentrations, 374

dynamic height, 47


Index 491

EDR (environmental data records), 24EFOV (effective field-of-view), 18El Nino and La Nina, 49

1998 example, 2342010–11 example, 293effect on sea level rise, 396

electromagetic spectrum, uses of, 55electromagnetic radiation (EMR), 53–54

dispersion relation, 57–58plane wave solution, 54quanta description, 53

ellipsoid, reference, 363emissivity of sea surface in microwave, 273

azimuthal dependence, 273azimuthal dependence, 278, 323–324cutoff wavelength, 275foam, dependence on, 277–278foam-free surface, 276salinity retrieval at 1.41 GHz, 331–332two-scale approximation, 274

empirical bio-optical algorithms, 175–182accuracy, 176–179examples, 179maximum band-ratio, 175, 206–208MODIS, 179SeaWiFS, 176

EUMETSAT(European Organization for the Exploitation of

Meteorological Satellites), 12European Space Agency (ESA), 12extinction, molecular, 87–89extraterrestrial reflectance, 133

Faraday rotation, 272and third Stokes vector, 296removal from Aquarius data, 453

field-of-view (FOV), 240fluorescence, 147

generation by phytoplankton, 173measurement by satellite, 174

fluorescence line height (FLH), 174flux density, 62foam, 41–43

dependence of areal extent on wind speed, 41in microwave, 277masking of solar reflectance in visible/infrared, 161reflectance in visible/infrared, 135

footprint, definition, 240FOV (field-of-view), 16Fraunhofer absorption lines, 150Fresnel equations, 118–119

polarized, 119unpolarized, 119

galactic radiance, 268Garver-Siegel-Maritorena (GSM) semi-analytic

algorithm, 185–186

error estimates, 185retrieval of CDOM, chlorophyll, particulate

backscatter, 185GCOM (Global Climate Observation Missions), 29GDAS (NCEP Global Data Assimilation System), 285GEO (Group on Earth Observations), 28geoid, 364–365

Earth Geopotential Model 2008 (EGM 2008), 365geoid undulation, 364response to bottom topography, 365

GEOSS (Global Earth Observation System ofSystems) program, 28

coordination of national programs, 28promotion of common data formats, 28

geostrophic flow, 46–48geosynchronous satellites, 12–13

spin-scan imagers, 12step-scan imagers, 12

GES DISC (NASA Goddard Earth Sciences Data andInformation Services Center), 175

GFDex (Greenland Flow Distortion Experiment), 299high wind speed validation of SeaWinds, 299validation of QuikSCAT wind retrievals, 353

GHRSST (GODAE High Resolution Sea SurfaceTemperature), 34, 195

notation for water column temperatures, 198products, 230purpose, 195sources, 195

GHRSST Multi-product Ensemble (GMPE), 230Giovanni (Geospatial Interactive Online Visualization

ANd aNalysis Infrastructure) archive, 175Global Drifter Program, 216GOCE (Gravity field and steady-state Ocean

Circulation Explorer), 441GODAE (Global Ocean Data Assimilation

Experiment), 34GPM (Global Precipitation Measurement) mission, 9,

254constellation, 254Core Observatory, 254

GPS (Global Positioning System)precision orbit determination, 376space system, 376

GRACE (Gravity Recovery and Climate Experiment),437–440

comparison with Arctic basin bottom pressures,439

description of satellite pair, 437HAIRS (High Accuracy Inter-satellite Ranging

System), 437measurement of Greenland mass loss, 438monthly global gravity fields, 439resolution, 439response to changes in ocean mass, 439

gravity missions, background, 436–437gray bodies, 69


492 Index

HRD (Hurricane Research Division), NOAA, 296

IceBridge aircraft program, 443ICESat-1 (Ice, Cloud, and land Elevation Satellite),

441–442GLAS (Geoscience Laser Altimeter System), 442problems with laser failures, 442surface sampling, 442

ICESat-1 resultsAntarctica and Greenland, 444retrieval of sea ice thickness, 444–446

ICESAT-1 results, 444–446ICESat-2 (Ice, Cloud, and land Elevation Satellite),

442–443comparison with ICESat-1, 443laser configuration and photon counting, 442

infrared wavelengthsinteraction with the ocean and atmosphere, 203–206reflected solar radiation, 206–208thermal emission and reflection, 203–206

inherent optical properties (IOP), 127instrument, ideal, visible/infrared, 71–76

slant look, 75vertical look, 73

interface, transmission across, 122–126International Ocean Colour Coordinating Group

(IOCCG), 148ionospheric free electrons, 85

effect on altimeters, 373–374role in generation of Faraday rotation, 272

irradiance, 62plane, 62scalar, 62vector, 62

ISS-RapidScat, 355–356and diurnal variability of tropical winds, 356problems with using space station for platform, 355scatterometer calibration source, 355

JASON-1, 378JASON Microwave Radiometer (JMR), 378POSEIDON-2 altimeter, 378precision orbit determination, 378

JASON-2, 379–380AMR (Advanced Microwave Radiometer), 379Global Positioning System Payload (GPSP), 379

JPSS (Joint Polar Satellite System), 15

Kessler cascade, 10Kirchoff’s law, 70Klein–Swift formulation, 285

Lambert surface, 65foam, 162sea surface in infrared, 204

levels of data processing, 23LOCUS (Laboratory for Ocean Color Users), 175

M-AERI (Marine-Atmosphere Emitted RadianceInterferometer), 217

matchup data sets for SST, 215–218, 227MCSST (Multi-Channel SST), 210Megha-Tropiques rainfall mission, 9MERIS (MEdium Resolution Imaging Spectrometer),

147METOP-A, -B, -C (METeorologie OPerationnelle),

15and AVHRR, 225ASCAT scatterometer, 333orbits, 333

microwave observationsadvantages and disadvantages, 236conical scanners, 244idealized antenna, 237–239look angle dependence of surface radiance, 244multi-variable geophysical retrievals, 272, 288–289Rayleigh-Jeans approximation, 236

microwave, atmospheric transmissivitycloud liquid water, 265neglect of cirrus ice crystals, 266oxygen, 263rain rate, 265water droplets, 263water vapor, 263

Mie scattering, 93, 96, 264MOBY (Marine Optical Buoy), 169MODIS (Moderate Resolution Imaging

Spectroradiometer), 147, 155bands, 455calibration, 156on AQUA, 147on TERRA, 147sensor decay, 157SST algorithms, 214SST image, 233thermal bands, 202

MODTRAN, 96Multi-angle Scattering Optical Tool (MASCOT), 145

National Snow and Ice Data Center (NSIDC)Arctic sea ice conditions, blog, 306sea ice time series archive, 300

NCEP (National Center for EnvironmentalPrediction), 161, 217

NDBC (National Data Buoy Center), 215neper (Np), unit of atmospheric absorption, 261NLSST (Non-Linear SST), 212NOBM (NASA Ocean Biogeochemical Model),

186–192and Giovanni, 190data assimulation, 188retrieval of four different phytoplankton species,

188noise

definition, 77


Index 493

noise-equivalent-delta-radiance, 78noise-equivalent-delta-temperature, 78radar, 313

NOMAD (NASA bio-Optical Marine AlgorithmDataset), 170

normalized radar scattering cross section (NRCS),311

NPOESS (National Polar-orbiting OperationalSatellite System), 14

cost-overuns, 15replacement by JPSS, 15

NSCAT scatterometer, 342–343

ocean surface colorquantitative derivation, 128role of internal scattering, 113

oceanic flows, scales of, 49Oceansat-2 scatterometer (OSCAT), 347

cross-calibration with QuikSCAT, 350proposed cross-calibration with ISS-RapidScat,

350oligotrophic, mesotrophic and eutrophic, 140optical depth, 89optical limit (microwave), 275orbits, 4–5

geosynchronous, 7–8Keplerian elements, 5low-inclination, 9sun-synchronous, 8–9

ozone, 84, 109

PACE (Pre-Aerosol, Clouds and ocean Ecosystem),215

addresses shortcomings of existing missions, 192coastal waters, observations in, 193observational bands in ultraviolet, 192

particulates, 140–141Pathfinder SST algorithm, 213–214photosynthesis, 137photosynthetic pigments, 137phytoplankton, 136–137

contribution to global carbon cycle, 136, 162role in marine food web, 136

PIRATA buoy array, 215Planck’s equation

frequency form, 68long-wavelength Rayleigh-Jeans approximation, 68short-wavelength approximation, 69wavelength form, 66

POES (Polar Operational Environmental Satellite)program, 14

polarizationdefinition, 58in passive microwave, 276radar, 312

primary production, 137–138relation to biomass, 138

Vertically Generalized Production Model (VGPM),138

pulse repetition frequency (PRF), 412–414

QuikSCAT, 333, 336

radar scattering cross section, 311radars, 4

and specular reflectors, 324antenna configurations, 314backscatter, 309–311chirp, 317cross-track resolution, 315definition, 308effect of atmospheric attenuation and ocean

emission, 312–313noise floor, 313noise-equivalent sigma-zero, 313pulse repetition frequency (PRF), 318–319range binning, 315–317

radars and oceanic backscatter, 324–330aircraft studies, 327–330Bragg scatter, 326–327incoherent scatter, 325specular reflection, 325

RADARSAT Constellation, 408RADARSAT-1, 415RADARSAT-2, 415–418

antenna slew, 418image modes, 419orbit, 416shift in observing frequency to mitigate RFI, 417

radiance, 63–64and Lambert surfaces, 76definition, 63examples, 76use with satellite instruments, 63

radiant flux, 62radiant intensity, 62radiative transfer in the atmosphere, 101–110

general solution, 104scattering source term, 102Schwarzchild equation, 106thermal-emission source term, 102

radiative transfer in the microwave, 266–268absorption-emission balance, 267effect of rain droplets, 264

rainand Mei scatter, 264droplet size, 83, 264in microwave, 296

rain rate, 82maximum observed value, 265passive microwave vector wind retrievals, effect on,

290, 298retrieval of, 288, 289scatterometer wind retrievals, effect on, 353


494 Index

Rayleigh criterionfor apertures, 72for surface roughness, 116

Rayleigh path radianceand ocean color retrieval, 162mathematical description, 109

Rayleigh scatter, 92by cloud liquid water, 264mathematical description, 93

reflectance, irradianceas a function of chlorophyll concentration, 171–173for clear seawater, 129–131

reflectance, remote sensing, 133reflection and transmission at a flat ocean interface,

117–119reflection at the ocean/air interface

coherent, 116incoherent, 116internal, 113surface, 113

refractive convergence and divergence, 122,124–126

remote sensing, definition, 3resolution, 21, 404Reynolds SST data sets, 219RFI (radio frequency interference), 270–271

definition, 12effect on satellite observations, 56frequency bands affected, 270geographic distribution, 270mitigation, 271

RGPS (RADARSAT Geophysical ProcessingSystem), 402

SARdata storage and transfer rates, 421–422description and operation, 403–404echo store, 404interferometric, 406–407modes, 401past, present and future missions, 407–408polarization, 405PRF constraints, 412resolution, 410–412ScanSAR mode, 420signal-to-noise constraints, 414

SAR imagesradiometric balance, 414range walk, 415speckle, 414

SAR images, open oceanadvantages of VH-polarization for viewing ships,

427internal waves, 427–429ocean swell, 424–426oil spills, 426radiometrically unbalanced, 424

SAR images, sea iceArctic snapshot, 429Beaufort Sea, 429St. Lawrence polynya, 433Weddell Sea ice edge, 431

satellite laser ranging (SLR) stationslocations, 374precision of ranging, 374

satellite missionsand societal concerns, 2–4history, 26–28through 2015, 34

satellites, large multi-instrument missions, 28criticisms of, 28replacement by constellations, 28

scatterers, oceanic, 140–141scattering, 90–92

in clear water, 128in particulate-laden seawater, 143–147isotropic, 92Mie, 92, 94multiple, 90Rayleigh, 92single, 90

scatterometerbinning, doppler, 333binning, range, 333conceptual design, 337contribution of surface observations, 333definition, 308derivation of vector wind speed, 340–342geophysical model function (GMF), 337–340mission requirements, 336past, present and future missions, 333

Schwarzschild equationabsorption-emission balance, 106in infrared, 208in microwave, 266

sea ice, 50and Bragg scatter, 429difference between Arctic and Antarctic, 50ice types, 50

sea ice algorithmsBootstrap, 300examples, 304–307limitations, 303NASA Team, 300NASA Team-2, 300thickness retrieval, 444

sea ice passive microwave algorithms, 300–303sea surface height (SSH), 48, 365–367sea surface salinity missions, 449–450

Aquarius/SAC-D, 449dawn-dusk orbits, purpose of, 449science objectives, 449SMOS (Soil Moisture and Ocean Salinity),

449


Index 495

SeaBAM (SeaWiFS Bio-optical AlgorithmMini-Workshop), 170

SEASAT, 27seawater, properties of clear, 127–129

attenuation depth, 128clearest natural waters, 131

SeaWiFS (Sea-viewing Wide Field-of-view Sensor),147, 152–154

SeaWiFS Bio-optical Archive and Storage System(SeaBASS), 170

SeaWiFS calibration, 154–155lunar, 154sensor decay, 154solar, 154vicarious. See vicarious calibration

SeaWinds Ku-2001 geophysical model functionderivation, 351limitations, 338range of applicability, 352

SeaWinds Ku-2011 geophysical model functionderivation, 352–353range of applicability, 353validation against GFDex, 353

SeaWinds scatterometer, 347–351calibration and noise removal, 350–351correction for atmospheric transmissivity, 351footprint, 349on ADEOS-2, 347on QuikSCAT, 347restriction to negligible rain conditions, 351retrieval of polar sea ice, 360

SeaWinds scatterometer examples, 356–360semi-analytic algorithms (ocean color), 184Sentinel-1A, -1B SARs, 423

launch dates, 423wave mode, 423

SEVIRI (Spinning Enhanced Visible and InfraredImager), 195

shadow zone, 122Side-Looking Radar (SLR)

aperture, 401resolution, 404, 409

signal-to-noise ratio, 77significant wave height (SWH)

altimeter retrieval, 387definition, 44

single scattering albedo, 107single scattering approximation, 107SIRAL-2 (SAR Interferometric Radar Altimeter-2) on

CryoSat, 446–449low-resolution mode (LRM), 446SAR mode, 448SAR-interferometric (SARIn) mode, 448

sky color, contributions fromphysiological properties of the eye, 94Rayleigh scatter, 94

skylight, 112

SMMR (Scanning Multichannel MicrowaveRadiometer), 249–250

and sea ice retrieval, 301problems with, 250

SMOS (Soil Moisture and Ocean Salinity) satellite,450

Snell’s law, 117Snell’s window, 123solar brightness temperature in microwave, 268–270

masking and mitigation, 269role of synchrotron radiation, 268

solar storms, 11South Atlantic Anomaly (SAA), 11

altimeter, effect on, 379MODIS, effect on, 11

spectral forms of the radiation fluxes, 65spherical geometry and radiation, 61SQUAM (NOAA SST Quality Monitor), 230SSM/I (Special Sensor Microwave/Imager), 250–253

calibration, 250imagery, 290open ocean algorithms, 289–291sea ice algorithms, 301

SSMI/S (Special Sensor Microwave Imager/Sounder),250

SSTand ocean surface processes, 197–200biases and errors, 228contributions from moored and drifting buoys,

196foundation temperature, 197, 198from geosynchronous satellites, 195from polar orbiters, 195importance, 194–195ship observations, 196windspeed threshold for daytime retrieval, 200

SST retrieval in microwave, 293accuracy, 293by AMSR-E, 293, 336

SST retrieval in thermal/infrared, 208–210and Planck function, 209AVHRR operational algorithms, 210daytime algorithms, 209dependence on columnar water vapor, 210importance of in situ match-up temperatures,

210nighttime algorithms, 209

Staubel’s invariant, 126Stefan-Boltzmann law, 68stokes parameters

measurement by WindSat, 258Stokes parameters

azimuthal dependence, 282definition, 60inability to retrieve wind direction at low wind

speeds, 285stratified infrared SST algorithms, 213


496 Index

sun glint, 44, 161dependence on wind speed, 161in microwave, 268masks, microwave, 270

sun-synchronous satellites, 13–15sun-synchronous scanning methods, 15–21

cross-track, 16–18hybrid, 19–21pushbroom, 18

Suomi-NPP (NPOESS Preparatory Project), 15surface slicks

and SAR, 426effects on short wind waves, 45

TAO/TRITON buoy array, 215thermal emissivity, 69TOPEX/POSEIDON, 370

orbit, 370Side A, side B altimeters, 370TOPEX Microwave Radiometer (TMR), 373

transmittance, 88, 89beam, 88diffuse, 88

transmittance, atmospheric, 96–99as a function of latitude, 96contribution from different gases, 96for 0.2–1 μm, 96for 0.2–15 μm, 96for 0.25–0.80 μm, 96

TRMM (Tropical Rainfall Measuring Mission), 9,248

calibration, 253low inclination orbit, 192, 286TRMM Microwave Imager (TMI), 253

troposphere, 81

vicarious calibration, 25, 169–171and MOBY, 169procedure, 170–171removal of systematic bias, 170specifications for field site, 169

VIIRS (Visible/Infrared Imager/Radiometer Suite),20, 147, 157–159

bands, 201, 457operation, 20problems, 158scanning method, 20SST algorithms, 214

volcanic eruptions and SST, 228–229

water vapor, atmosphericcontribution to absorption in the microwave, 261in the infrared SST retrieval, 209variability, 82vertical structure, 82

water-leaving radiance, 113, 131–133atmospheric correction, 159–165band-by-band examples, 182

wave breaking, 40droplet explusion, 41foam formation, 40whitecapping, 41

wave generation by winds, dependence on fetch, time,38

waves, oceanazimuthal distribution of slopes, 44largest observed, 38profile dependence on slope, 38

Wien’s displacement law, 67winds, ocean surface

effect of atmospheric stratification, 338histogram of speeds, 35importance to global weather, 331–332neutral stability, 337

WindSat, 258–259all-weather retrieval, 296as a benchmark data set, 285matchup with Hurricane Research Division (HRD)

winds, 296rain-free retrieval, 296retrieval of vector winds, 259, 295–300

WVSST (Water Vapor SST) algorithm, 212

Trim: 247mm × 174mm Top: 14.762mm Gutter: 23.198mmCUUK2533-PLS CUUK2533/Martin ISBN: 978 1 107 01938 6 November 26, 2013 12:30

Fig. 2.7. Oblique photograph of wave breaking and foam generation on the Japan/East Sea takenthrough the front window of a Twin Otter meteorological flight on February 28, 2000. The ambientair temperature was about −8 °C, the aircraft altitude was about 38 m, the flight direction was 330°and the wind speed was 17 m s−1 from 340°, so that the camera is looking into the wind and towardRussia. (Meteorological and flight data courtesy of Djamal Khelif; photograph courtesy of Jon Stairs,used with permission.)

Fig. 4.2. True-color composite image of the Earth taken by the Moderate-Resolution Imaging Spec-troradiometer (MODIS) on 20 March 2012. The image consists of one day of Sun-synchronous orbitalpasses from the sunlit side of Earth. For several swaths, the arrows mark the direct reflection of thesun from sun glint; the letters a, b and c mark storms that are shown on the cloud liquid water figurein Figure 9.18. See the text for additional description. (Image courtesy of NASA, not subject to UScopyright.)


Fig. 6.1. Diatoms from the coastal Pacific off Washington state. The diatom positioned diagonallyacross the picture center is a member of the chaetoceros species; it consists of a chain of silica-shelledsingle cells with spines protruding from each cell and from both ends of the chain. For this species,the width of each cell is 20–25 µm. Inside each cell, the chloroplast contains the photosyntheticpigments, a mixture of green chlorophyll and the brownish yellow carotenoids. Other diatom speciesare adjacent, including a chain of cells below the chaetoceros. (Courtesy of Rita Horner; used withpermission.)

0.01

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Fig. 6.27. Composite SeaWiFS image of the northeast Pacific adjacent to British Columbia, Canadaand Washington and Oregon, United States on September 1, 1999. (a) A true color image, mixed fromSeaWiFS bands at 410, 555 and 670 nm, with Rayleigh scattering removed. (b) The Chl-a distributionfor the same region in mg m−3. Black corresponds to land and to cloud mask. (OrbView-2 Imageryprovided by ORBIMAGE, the SeaWiFS Project and NASA/Goddard Spaceflight Center; processingcourtesy of Brandon Sackmann and Miles Logsdon.)

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Fig. 6.18. A monthly global composite SeaWiFS image of the aerosol optical thickness τA(865) forApril (a) and October (b) 1998, and the Angstrom exponent α for the same periods, (c) and (d).The color bars show the scales; land is black and regions with no data are gray. See the text forfurther description. (Figure 1 from Wang et al. (2000), C© 2000 American Geophysical Union, repro-duced/modified by permission of AGU, courtesy of Menghua Wang; OrbView-2 Imagery providedby ORBIMAGE, the SeaWiFS Project and NASA/Goddard Spaceflight Center.)


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Fig. 6.29. The global annual average for 2011 of the band-ratio Chl-a, the MSP Chl-a, the GSMCDOM dissolved and detrital organic matter absorption at 443 nm and the normalized fluorescenceline height. See the text for further description. (Images used in this plate were produced with theGiovanni online data system, developed and maintained by the NASA GES DISC, as described inAcker and Leptoukh (2007). We also acknowledge the MODIS mission scientists and associatedNASA personnel for the production of the data used in this research effort.)


Chlorophytes

Coccolithophores

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Fig. 6.32. The June 2007 average of the NOBM monthly average distribution of diatoms, coccol-ithophores, cyanobacteria and chlorophytes. See the text for additional description. (Acknowledge-ments are provided in the caption of Figure 6.27.)


–2 0 5 10 15 20 25 30 35

Temperature (oC)

ab

c

d

gf

e

Fig. 7.18. One-month average for May 2001 of the MODIS-derived SST. Black is land, the colorscorrespond to the temperature scale. The letters identify physical features discussed in the text.(Courtesy of MODIS Ocean Group, NASA GSFC and the University of Miami.)

SST (oC) Chlorophyll-a concentration (mg m–3)<0.01 0.05 502010.1 0.5 2 105+15 +30

AVHRR SeaWiFS

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199

8

Fig. 7.19. Comparison of AVHRR SST with SeaWiFS ocean chlorophyll for El Nino conditionsin January 1998 and La Nina during July 1998. See the text for further description. (Courtesy ofFrancisco Chavez, reprinted with permission from Chavez et al., (1999), Figure 1; C© 1999 AAAS;OrbView-2 Imagery provided by ORBIMAGE, the SeaWiFS Project and NASA/Goddard SpaceflightCenter.)


Cloud liquid water

Wind speed

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–1)

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)

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)25

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h–1

)

10

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0(no rain)

Fig. 9.18. Composite image of the distribution of SSM/I wind magnitude, water vapor, cloud liquidwater and rain rate for March 20, 2012. The swaths are the ascending evening passes at 1800 localtime. The color bars to the right give the scale for the distribution of each variable; gray is land, whiteis sea ice, black is missing data or the masked rain rate. On the scales for cloud liquid water and rainrate, the color purple marks the regions with no liquid water or no rain. The letters on the cloud liquidwater figure mark features common to the same day MODIS visible image in Figure 4.2. (SSM/I dataare produced by Remote Sensing Systems and sponsored by the NASA Earth Science MEaSUREsDISCOVER Project. Data are available at www.remss.com. Used with permission.)


Trim

:247mm

×174m

mTop:14.762m

mG

utter:23.198mm

CU

UK

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ISBN

:9781

10701938

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ovember

26,201312:30

–14

14

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SS

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C)

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id w

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January 2010 El Niño January 2011 La Niña

Fig. 9.20. A composite image of the weekly averaged AMSR-E-retrieved values of SST, U, V and Lfor weeks ending on 2 January 2010 and 1 January 2011, where the 2010 image is from the middleof the 2009–10 El Nino and the 2011 image is from the subsequent La Nina. The winds are from thelow-frequency AMSR retrieval. On the images, the white line marks the equator. Black areas over theocean are regions of heavy rain. See the text for further description. (AMSR-E data are produced byRemote Sensing Systems and sponsored by the NASA Earth Science MEaSUREs DISCOVER Projectand the AMSR-E Science Team. Data are available at www.remss.com. Used with permission.)



100%

1979–2010

80%

60%

40%

20%

<12%

100%

80%

60%

40%

20%

<12%

1979–2010

1979–2010 1979–2010

Fig. 9.25. For the period 1979–2010, the average Arctic sea ice extent for March (maximum) andSeptember (minimum), and the average Antarctic ice extent for February (maximum) and September(minimum) as derived from passive microwave. The color bar gives the ice concentration in percent.Gray is land, light blue is open water. See the text for further description. (Antarctic image, Figure 1from Parkinson and Cavalieri (2012); Arctic image, Figure 1 from Cavalieri and Parkinson (2012);courtesy of Claire Parkinson and Donald Cavalieri, not subject to US copyright.)

Fig. 11.17. A single ascending SeaWinds swath located in the North Pacific, just south of the AlaskaPeninsula and acquired on September 2, 1999 at 1530 UTC. The wind vectors are given at intervalsof 25 km; the vectors are color-coded so that black vectors are rain-free, red vectors are rain-contaminated. The inset arrow shows the wind scale. (Courtesy of Jerome Patoux and Robert Brown,used with permission.)


Pacific

Atlantic

Fig. 11.18. The QuikSCAT ocean wind field for April 19, 2000 for the Pacific and Atlantic Oceans.The lines and arrows show the wind direction; the colors show the wind speed. (The images wereobtained from the NASA/NOAA sponsored data system Seaflux at JPL through the courtesy ofW. Timothy Liu and Wenqing Tang, used with permission.)


20° N

15° N

10° N

5° N110° W

0 0.5 1.0 1.5 2.0 2.5 km

100° W 90° W

Fig. 11.19. A QuikSCAT image of a Tehuano event at Chivela Pass in southern Mexico taken at 00UTC on December 1, 1999. The Atlantic is on the upper right; the Pacific is on the left. The colorbar gives the scale of the land topography; the contoured shades of blue and arrows show the windspeed and direction, where darker shades of blue and longer arrows indicate greater speeds. The windspeed contours are at intervals of 1.5 m s−1. (Courtesy of Mark Bourassa and Josh Grant, used withpermission.)

Sea surface height (cm)–160 –120 –80 –40 –20 0 20 40 60 80 120 160–60

Maximum vector

30 cm s–1

60oS

60oN

0oN


Fig. 12.20 The 4-year average of the TOPEX ocean surface elevation relative to the Earth GeopotentialModel 96 (EGM96) geoid. The arrows show the geostrophic velocities. Near-equatorial values areomitted because of the breakdown of the geostrophic relation; small velocities are omitted for clarity.Because they are dominated by geoid error, all flows with length scales less than 500 km are omitted.(Courtesy of Detlef Stammer, Figure 6a from Wunsch and Stammer (1998), with permission, fromAnnual Review of Earth and Planetary Sciences, Volume 26, C© 1998, by Annual Reviews.)


Root-mean-square SSH (cm) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30


60oS

60oN

0oN

0

Fig. 12.21 Root-mean-square (rms) elevation anomalies for 4 years of TOPEX data (Courtesy ofDetlef Stammer, Figure 8a from Wunsch and Stammer (1998), with permission, from Annual Reviewof Earth and Planetary Sciences, Volume 26, C© 1998, by Annual Reviews.)

Fig. 12.24. Eddies in the Indian Ocean. The left-hand figure shows the geographic distribution ofthe anomaly in sea surface height in the Indian Ocean for TOPEX cycle 60 corresponding to the10-day period May 1–11, 1994. The rectangular strip outlined in black at 25° S is also outlined inthe right-hand Hovmoller diagram. On this diagram, the horizontal axis corresponds to the centralportion of the Indian Ocean; the vertical axis is the TOPEX cycle number. In each case, the colorscorrespond to SSH defined in the right-hand scale. The characteristic upper left to lower right tiltwithin the Hovmoller diagram illustrates the westward propagation of these features. (Courtesy ofPaolo Cipollini; Figure 5 from Killworth (2001), C© 2001, with permission from Elsevier Science.)


180oE 240oE 300oE 360oE 60oE 120oE

Sea surface height (cm)–14 –12 –10 –8 –6 –4 –2 0 2 4 6 8 10 12

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Fig. 12.22 Seasonal mean anomalies of the TOPEX sea surface heights relative to the 9-year meanfield. Top image is September–November 1992–2000; second is December 1992–2000 throughFebruary 1993–2001, third is March–May 1993–2001; fourth is June–August 1993–2001. Contourinterval is 2 cm. (Courtesy of Detlef Stammer, used with permission.)


350 km

240

km

A

B

C

Fig. 13.22. SAR image of the Antarctic sea ice taken on October 5, 1994, from the SpaceborneImaging Radar C/X-Band Synthetic Aperture Radar (SIR-C/X SAR) on the Space Shuttle Endeavour.The image is oriented approximately east–west, with a center latitude and longitude of about 56.6°S and 6.5° W; its dimensions are 240 km by 350 km. (Courtesy of NASA/JPL/Caltech, used withpermission.)

25

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ksca

tter

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)

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(c) 1999 CSA

Fig. 13.23. Images of the frazil ice polynya in the Bering Sea south of St. Lawrence Island acquiredon January 9, 1999. Upper left, AVHRR image processed for ice surface temperature and acquired at0431 UTC; upper right, RADARSAT ScanSAR image acquired at 0504 UTC, so that the two imagesare 33 minutes apart. The long axis of the island measures about 200 km. See the text for furtherdescription. (RADARSAT data C© Canadian Space Agency/Agence Spatiale Canadienne 1999. Usedwith permission. Processed and distributed by RADARSAT International; image processing by RobertDrucker and the author.)


2003 2004 2005 2006 2007 2008

–404

–404

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in situGRACE

(b) Beaufort Sea

(c) Fram Strait

Amplitude (cm) Phase of max. amplitudeJ

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Fig. 14.3. A comparison of time series of GRACE and bottom pressure observations in the ArcticOcean from 2002 to 2008. The upper figure shows the monthly averages of the in situ anomaly inocean bottom pressure (solid red line) and the respective annual harmonic fits (dashed red line) at threelocations, North Pole (a), Beaufort Sea (b) and Fram Strait (c). At each location the gray line showsthe monthly GRACE bottom pressure anomaly and the dashed gray line shows the annual harmonicfit to the GRACE data. All of the time series have their long-term linear trend removed. The lowerfigure shows the amplitude (left) and phase of the GRACE distribution of bottom pressure. The colorbar showing phase increases vertically from June to July. (Figure courtesy of Cecilia Peralta-Ferrizand Jamie Morison, Figure 1 from Peralta-Ferriz and Morison (2010) copyright AGU, used withpermission.)

Aquarius salinity (psu)33 33.5 34 34.5 35 35.5 36 3736.5 36.5

Fig. 14.12. The annual average salinity for January–December 2012 as derived from Aquarius. Thesalinity data are displayed on a 1° × 1° gridded field calculated from polynomial fitting. (Imagecourtesy of Gary Lagerloef and Hsun-Ying Kao, Earth and Space Research, all rights reserved, usedwith permission. Data courtesy of NASA.)


Fig. 14.8. The spatial pattern of arctic sea ice thickness derived from the ICESat-1 derived freeboardheight. The dashed circle shows the northern limit of the ICESat-1 observations and is filled byinterpolation and smoothed with a 50-km Gaussian kernel. The color scale at the bottom shows theice thickness; ON03 stands for October–November 2003; FM04 stands for February–March 2004;these mark the different 34-day ICESat-1 campaigns (From Kwok et al. (2009), Figure 7, copyrightAGU, used with permission.)

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