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  • Atmospheric Correction

    forSatellite Ocean Color Radiometry

    ********

    A Tutorial and Documentation

    of the Algorithms Used by the

    NASA Ocean Biology Processing Group

    Curtis D. Mobley

    Sequoia Scientific, Inc.

    2700 Richards Road, Suite 107

    Bellevue, WA 98005

    Jeremy Werdell, Bryan Franz, Ziauddin Ahmad, and Sean Bailey

    NASA Goddard Space Flight Center

    Ocean Ecology Laboratory

    Greenbelt, MD 20771

    June 24, 2016

  • Abstract

    This tutorial is an introduction to atmospheric correction in general and also documentation of theatmospheric correction algorithms currently implemented by the NASA Ocean Biology ProcessingGroup (OBPG) for processing ocean color data from satellite-borne sensors such as MODIS andVIIRS. The intended audience is graduate students or others who are encountering this topic for thefirst time. The tutorial is in two parts. Part I discusses the generic atmospheric correction problem.The magnitude and nature of the problem are first illustrated with numerical results generated bya coupled ocean-atmosphere radiative transfer model. That code allow the various contributions(Rayleigh and aerosol path radiance, surface reflectance, water-leaving radiance, etc.) to the top-of-the-atmosphere (TOA) radiance to be separated out. Particular attention is then paid to thedefinition, calculation, and interpretation of the so-called exact normalized water-leaving radianceand its equivalent reflectance. Part I ends with chapters on the calculation of direct and diffuseatmospheric transmittances, and on how vicarious calibration is performed. Part II then describesone by one the particular algorithms currently used by the OBPG to effect the various steps ofthe atmospheric correction process, viz. the corrections for absorption and scattering by gases andaerosols, Sun and sky reflectance by the sea surface and whitecaps, and finally corrections for sensorout-of-band response and polarization effects. One goal of the tutorialguided by teaching needsis to distill the results of dozens of papers published over several decades of research in atmosphericcorrection for ocean color remote sensing. Any subsequent modifications to the originally publishedtechniques are noted in the documentation. This content of this tutorial is available online asthe Atmospheric Correction chapter of the Ocean Optics Web Book, beginning at http://www.oceanopticsbook.info/view/atmospheric_correction/chapter_overview. A pdf version ofthe report can be downloaded as Mobley et al. (2016) in the publications section of the OceanOptics Web Book.

    Acknowledgments

    This work was supported by NASA Grant NNX14AQ49G to author C.D.M. titled Documentationof NASA Ocean Color Atmospheric Correction Algorithms in Preparation for the 2015 SummerClass in Optical Oceanography and Ocean Color Remote Sensing. This report constitutes partof the final report on that grant. Howard Gordon made useful comments on the computation ofdiffuse attenuation, and he and David Antoine helped with the formulation and interpretation ofnormalized reflectances.

    http://www.oceanopticsbook.info/view/atmospheric_correction/chapter_overviewhttp://www.oceanopticsbook.info/view/atmospheric_correction/chapter_overview

  • Contents

    List of Figures iv

    List of Tables vi

    I The Atmospheric Correction Problem 1

    1 Problem Formulation 4

    2 Example Radiances 8

    3 Normalized Reflectances 133.1 Normalized Radiances and Reflectances . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 The BRDF Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    4 Atmospheric Transmittances 254.1 Direct Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Diffuse Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    5 Vicarious Calibration 29

    II The NASA OBPG Algorithms 34

    6 Gases 386.1 Nonabsorbing Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    6.1.1 Wind Speed and Surface Reflectance Effects . . . . . . . . . . . . . . . . . . . 386.1.2 Pressure Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

    6.2 Absorbing Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.1 Absorption by Ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.2.2 Absorption by NO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    7 Sun Glint 46

    8 Whitecaps 48

    ii

  • 9 Aerosols 509.1 Aerosol Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509.2 Black-pixel Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539.3 Non-black-pixel Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.4 Strongly Absorbing Aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    10 Spectral Out-of-band Correction 60

    11 Polarization Correction 66

    References 70

    iii

  • List of Figures

    1.1 Processes contributing to the TOA radiance . . . . . . . . . . . . . . . . . . . . . . . 6

    2.1 Geometry for example calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Example radiances contributing to the TOA radiance . . . . . . . . . . . . . . . . . . 102.3 Fractional contributions to the TOA radiance . . . . . . . . . . . . . . . . . . . . . . 112.4 TOA radiances for various environmental and viewing conditions . . . . . . . . . . . 12

    3.1 Comparisons of Lu and Lw for a zenith Sun, with and without an atmosphere . . . . 153.2 Comparison of exact normalized and unnormalized water-leaving reflectances . . . . 223.3 Example reflectances contributing to the TOA reflectance . . . . . . . . . . . . . . . 22

    4.1 Direct and diffuse transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    5.1 Flowchart of the atmospheric correction process . . . . . . . . . . . . . . . . . . . . . 36

    6.1 Rayleigh optical thickness and depolarization ratio . . . . . . . . . . . . . . . . . . . 396.2 Transmittance by O2 and H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.3 Transmittance by O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.4 Transmittance by NO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.5 Band-averaged optical depth and cross sections . . . . . . . . . . . . . . . . . . . . . 43

    8.1 Whitecap reflectance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    9.1 Illustration of aerosol volume, number, and particle size distributions. . . . . . . . . 519.2 Relative humidity effects on an aerosol volume and particle size distributions. . . . . 529.3 Dependence of (, 865) on aerosol model . . . . . . . . . . . . . . . . . . . . . . . . 559.4 Remote-sensing reflectances in the NIR . . . . . . . . . . . . . . . . . . . . . . . . . 569.5 Qualitative behavior of (, 865) for blue-absorbing aerosols . . . . . . . . . . . . . . 569.6 Ocean regions for non-black-pixel corrections . . . . . . . . . . . . . . . . . . . . . . 59

    10.1 MODIS sensor response; linear ordinate . . . . . . . . . . . . . . . . . . . . . . . . . 6110.2 MODIS sensor response; logarithmic ordinate . . . . . . . . . . . . . . . . . . . . . . 6110.3 MODIS 412 nm sensor response vs. an idealized 10 nm FWHM response. . . . . . . 6210.4 Rrs spectra as functions of the chlorophyll concentration . . . . . . . . . . . . . . . . 6310.5 Rrs responses for the SeaWiFS 555 nm band vs. an idealized 11 nm FWHM sensor . 6410.6 Example out-of-band correction factor . . . . . . . . . . . . . . . . . . . . . . . . . . 65

    iv

  • 11.1 Geometry for polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

    v

  • List of Tables

    1.1 Radiance notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    5.1 Processing Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Ancillary data needed for atmospheric correction . . . . . . . . . . . . . . . . . . . . 37

    9.1 NIR bands used for aerosol correction . . . . . . . . . . . . . . . . . . . . . . . . . . 54

    vi

  • Part I

    The Atmospheric Correction Problem

    1

  • In several recent years the NASA Ocean Biology and Biogeochemistry Program supported anintensive summer course, Ocean Optics Summer Class: Calibration and Validation in Support ofOcean Color Remote Sensing, at the University of Maine (http://misclab.umeoce.maine.edu/education.php). Those graduate-level classes covered both theory and instrumentation for opticaloceanography and ocean color remote sensing. During those courses, Jeremy Werdell of the NASAGoddard Space Flight Center, Ocean Biology Processing Group (OBPG) gave lectures on how theOBPG calibrates, validates, and processes ocean color data from sensors such as SeaWiFS, MODIS,and VIIRS (Werdell, 2015). His lectures outlined the many complicated steps used for atmosphericcorrection of measured at-sensor radiances and inspired this tutorial.

    The purpose of this tutorial is to expand upon Werdells lectures and review and summarizein one document the entire process of atmospheric correction as currently implemented by OBPG.The algorithms and equations presented here rest on several decades of research going all the wayback to the Coastal Zone Color Scanner (CZCS), which was launched in 1978. References aregiven to the original literature, which can be consulted for historical perspective and the scientificunderpinning

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