geogg141/ geog3051 principles & practice of remote sensing em radiation ( ii)

UCL DEPARTMENT OF GEOGRAPHYUCL DEPARTMENT OF GEOGRAPHY

GEOGG141/ GEOG3051Principles & Practice of Remote SensingEM Radiation (ii)

Dr. Mathias (Mat) DisneyUCL GeographyOffice: 113, Pearson BuildingTel: 7679 0592Email: [email protected]://www2.geog.ucl.ac.uk/~mdisney/teaching/GEOGG141/GEOGG141.htmlhttp://www2.geog.ucl.ac.uk/~mdisney/teaching/3051/GEOG3051.html

http://www2.geog.ucl.ac.uk/~mdisney/teaching/GEOGG141/GEOGG141.html

http://www2.geog.ucl.ac.uk/~mdisney/teaching/3051/GEOG3051.html

UCL DEPARTMENT OF GEOGRAPHY

EMR arriving at Earth

2

• We now know how EMR spectrum is distributed• Radiant energy arriving at Earth’s surface• NOT blackbody, but close

• “Solar constant”• solar energy irradiating surface perpendicular to solar beam• ~1373Wm-2 at top of atmosphere (TOA)• Mean distance of sun ~1.5x108km so total solar energy emitted = 4r2x1373

= 3.88x1026W

• Incidentally we can now calculate Tsun (radius=6.69x108m) from SB Law

• T4sun = 3.88x1026/4 r2 so T = ~5800K


Departure from blackbody assumption

• Interaction with gases in the atmosphere– attenuation of solar radiation

3


Radiation Geometry: spatial relations

4

• Now cover what happens when radiation interacts with Earth System• Atmosphere

• On the way down AND way up• Surface• Multiple interactions between surface and atmosphere• Absorption/scattering of radiation in the atmosphere


Radiation passing through media

5

• Various interactions, with different results

From http://rst.gsfc.nasa.gov/Intro/Part2_3html.html


Radiation Geometry: spatial relations

6

• Definitions of radiometric quantities• Radiant energy emitted, transmitted of received per unit time is

radiant flux (usually Watts, or Js-1)• Radiant flux density is flux per unit area (Wm-2)

• Irradiance is radiant flux density incident on a surface (Wm-2) e.g. Solar radiation arriving at surface

• Emittance (radiance or radiant exitance) (Wm-2) is radiant flux density emitted by a surface

• For parallel beam, flux density defined in terms of plane perpendicular to beam. What about from a point?


Radiation Geometry: point source

7

d dF dAPoint source

r

• Consider flux dF emitted from point source into solid angle d, where dF and d very small• Intensity I defined as flux per unit solid angle i.e. I = dF/d (Wsr-1) • Solid angle d = dA/r2 (steradians, sr)


Radiation Geometry: plane source

8

dS cos

dF

Plane source dS

• What about when we have a plane source rather than a point?• Element of surface with area dS emits flux dF in direction at angle to normal• Radiant emittance, M = dF / dS (Wm-2)• Radiance L is intensity in a particular direction (dI = dF/) divided by the apparent area of

source in that direction i.e. flux per unit area per solid angle (Wm-2sr-1)• Projected area of dS is direction is dS cos , so…..• Radiance L = (dF/) / dS cos = dI/dS cos (Wm-2sr-1)


Radiation Geometry: radiance

9

• So, radiance equivalent to:• intensity of radiant flux observed in a particular direction

divided by apparent area of source in same direction• Note on solid angle (steradians):

• 3D analog of ordinary angle (radians)• 1 steradian = angle subtended at the centre of a sphere by an

area of surface equal to the square of the radius. The surface of a sphere subtends an angle of 4 steradians at its centre.


Radiation Geometry: solid angle

10

• Cone of solid angle = 1sr from sphere

• = area of surface A / radius2

From http://www.intl-light.com/handbook/ch07.html

• Radiant intensity


Radiation Geometry: terms and units

11


Radiation Geometry: cosine law

12

• Emission and absorption• Radiance linked to law describing spatial distn of radiation emitted by

Bbody with uniform surface temp. T (total emitted flux = T4)• Surface of Bbody then has same T from whatever angle viewed• So intensity of radiation from point on surface, and areal element of

surface MUST be independent of , angle to surface normal• OTOH flux per unit solid angle divided by true area of surface must be

proportional to cos


Radiation Geometry: cosine law

13

• Case 1: radiometer ‘sees’ dA, flux proportional to dA• Case 2: radiometer ‘sees’ dA/cos (larger) BUT T same, so emittance of

surface same and hence radiometer measures same• So flux emitted per unit area at angle to cos so that product of

emittance ( cos ) and area emitting ( 1/ cos ) is same for all • This is basis of Lambert’s Cosine Law

Radiometer

X

Y X

Y

Radiometer

dA

dA/cos

Adapted from Monteith and Unsworth, Principles of Environmental Physics


Radiation Geometry: Lambert’s Cosine Law

14

• When radiation emitted from Bbody at angle to normal, then flux per unit solid angle emitted by surface is cos

• Corollary of this:• if Bbody exposed to beam of radiant energy at an angle to normal, the

flux density of absorbed radiation is cos • In remote sensing we generally need to consider directions of

both incident AND reflected radiation, then reflectivity is described as bi-directional

Adapted from Monteith and Unsworth, Principles of Environmental Physics


Recap: radiance

15

• Radiance, L• power emitted (dF) per unit of solid

angle (d) and per unit of the projected surface (dS cos) of an extended widespread source in a given direction, ( = zenith angle, = azimuth angle)

• L = d2F / (d dS cos ) (in Wm-2sr-1)• If radiance is not dependent on i.e. if

same in all directions, the source is said to be Lambertian. Ordinary surfaces rarely found to be Lambertian.

Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm

d

Projected surface dS cos


Recap: emittance

16

• Emittance, M (exitance)• emittance (M) is the power emitted

(dW) per surface unit of an extended widespread source, throughout an hemisphere. Radiance is therefore integrated over an hemisphere. If radiance independent of i.e. if same in all directions, the source is said to be Lambertian.

• For Lambertian surface • Remember L = d2F / (d dS cos ) =

constant, so M = dF/dS = • M = L



Recap: irradiance

17

• Radiance, L, defined as directional (function of angle)• from source dS along viewing

angle of sensor ( in this 2D case, but more generally (, ) in 3D case)

• Emittance, M, hemispheric • Why??• Solar radiation scattered by

atmosphere• So we have direct AND diffuse

components


Direct

Diffuse


Reflectance

18

• Spectral reflectance, (), defined as ratio of incident flux to reflected flux at same wavelength • () = L()/I()

• Extreme cases:• Perfectly specular: radiation incident at angle reflected away from surface

at angle -• Perfectly diffuse (Lambertian): radiation incident at angle reflected

equally in all angles


Interactions with the atmosphere

19From http://rst.gsfc.nasa.gov/Intro/Part2_4.html


Interactions with the atmosphere

20

• Notice that target reflectance is a function of• Atmospheric irradiance• reflectance outside target scattered into path• diffuse atmospheric irradiance• multiple-scattered surface-atmosphere interactions

From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf

R1

target

R2

target

R3

target

R4

target


Interactions with the atmosphere: refraction

21

• Caused by atmosphere at different T having different density, hence refraction• path of radiation alters moving from medium of one density to

another (different velocity)• index of refraction (n) is ratio of speed of light in a vacuum (c)

to speed cn in another medium (e.g. Air) i.e. n = c/cn

• note that n always >= 1 i.e. cn <= c• Examples

• nair = 1.0002926• nwater = 1.33


Refraction: Snell’s Law

22

• Refraction described by Snell’s Law• For given freq. f, n1 sin 1 = n2 sin 2 • where 1 and 2 are the angles from the

normal of the incident and refracted waves respectively

• (non-turbulent) atmosphere can be considered as layers of gases, each with a different density (hence n)

• Displacement of path - BUT knowing Snell’s Law can be removed

After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.

n1

n3

n2

Optically less dense

Optically more dense

Optically less dense

Incident radiation

2

3

1

Path affected by atmosphere

Path unaffected by atmosphere


Interactions with the atmosphere: scattering

23

• Caused by presence of particles (soot, salt, etc.) and/or large gas molecules present in the atmosphere

• Interact with EMR anc cause to be redirected from original path.

• Scattering amount depends on:• of radiation• abundance of particles or gases• distance the radiation travels through the

atmosphere (path length)

After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html


Atmospheric scattering 1: Rayleigh

24

• Particle size << of radiation• e.g. very fine soot and dust or N2, O2

molecules• Rayleigh scattering dominates shorter

and in upper atmos.• i.e. Longer scattered less (visible red scattered

less than blue )• Hence during day, visible blue tend to dominate

(shorter path length)• Longer path length at sunrise/sunset so

proportionally more visible blue scattered out of path so sky tends to look more red

• Even more so if dust in upper atmosphere• http://www.spc.noaa.gov/publications/corfidi/sunset/• http://www.nws.noaa.gov/om/educ/activit/bluesky.htm



Atmospheric scattering 1: Rayleigh

25From http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html

• So, scattering -4 so scattering of blue light (400nm) > scattering of red light (700nm) by (700/400)4 or ~ 9.4


Atmospheric scattering 2: Mie

26

• Particle size of radiation• e.g. dust, pollen, smoke and water vapour • Affects longer than Rayleigh, BUT weak dependence on • Mostly in the lower portions of the atmosphere

• larger particles are more abundant• dominates when cloud conditions are overcast

• i.e. large amount of water vapour (mist, cloud, fog) results in almost totally diffuse illumination



Atmospheric scattering 3: Non-selective

27

• Particle size >> of radiation• e.g. Water droplets and larger dust

particles, • All affected about equally (hence

name!)• Hence results in fog, mist, clouds

etc. appearing white• white = equal scattering of red,

green and blue s



Atmospheric absorption

28

• Other major interaction with signal• Gaseous molecules in atmosphere can

absorb photons at various • depends on vibrational modes of molecules• Very dependent on

• Main components are:• CO2, water vapour and ozone (O3)• Also CH4 ....• O3 absorbs shorter i.e. protects us from UV

radiation


Atmospheric absorption

29

• CO2 as a “greenhouse” gas• strong absorber in longer (thermal) part of EM

spectrum• i.e. 10-12m where Earth radiates• Remember peak of Planck function for T = 300K• So shortwave solar energy (UV, vis, SW and NIR)

is absorbed at surface and re-radiates in thermal• CO2 absorbs re-radiated energy and keeps warm• $64M question!

• Does increasing CO2 increasing T??• Anthropogenic global warming??• Aside....


Atmospheric CO2 trends

30

• Keeling et al.• Annual variation + trend• Smoking gun for anthropogenic

change, or natural variation??

• Antarctic ice core records


Atmospheric “windows”

31

• As a result of strong dependence of absorption• Some totally unsuitable for remote sensing as most

radiation absorbed

Atmospheric windows



• If you want to look at surface– Look in atmospheric windows where transmissions high

• If you want to look at atmosphere however....pick gaps• Very important when selecting instrument channels

– Note atmosphere nearly transparent in wave i.e. can see through clouds!– V. Important consideration....

32



• Vivisble + NIR part of the spectrum– windows, roughly: 400-750, 800-1000, 1150-1300, 1500-1600, 2100-2250nm

33


Summary• Measured signal is a function of target reflectance

– plus atmospheric component (scattering, absorption)– Need to choose appropriate regions (atmospheric windows)

• μ-wave region largely transparent i.e. can see through clouds in this region• one of THE major advantages of μ-wave remote sensing

• Top-of-atmosphere (TOA) signal is NOT target signal • To isolate target signal need to...

– Remove/correct for effects of atmosphere– A major part component of RS pre-processing chain

• Atmospheric models, ground observations, multiple views of surface through different path lengths and/or combinations of above

34


Summary• Generally, solar radiation reaching the surface composed of

– <= 75% direct and >=25 % diffuse• attentuation even in clearest possible conditions

– minimum loss of 25% due to molecular scattering and absorption about equally

– Normally, aerosols responsible for significant increase in attenuation over 25%

– HENCE ratio of diffuse to total also changes– AND spectral composition changes

35


Reflectance

36

• When EMR hits target (surface)• Range of surface reflectance behaviour

• perfect specular (mirror-like) - incidence angle = exitance angle• perfectly diffuse (Lambertian) - same reflectance in all directions

independent of illumination angle)

From http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_5_e.html

Natural surfaces somewhere in

between


Surface energy budget

37

• Total amount of radiant flux per wavelength incident on surface, () Wm-1 is summation of:• reflected r, transmitted t, and absorbed, a

• i.e. () = r + t + a

• So need to know about surface reflectance, transmittance and absorptance

• Measured RS signal is combination of all 3 components



Reflectance: angular distribution

38

• Real surfaces usually display some degree of reflectance ANISOTROPY• Lambertian surface is

isotropic by definition• Most surfaces have some

level of anisotropy


Figure 2.1 Four examples of surface reflectance: (a) Lambertian reflectance (b) non-Lambertian (directional) reflectance (c) specular (mirror-like) reflectance (d)

retro-reflection peak (hotspot).

(a) (b)

(c) (d)


Directional reflectance: BRDF

39

• Reflectance of most real surfaces is a function of not only λ, but viewing and illumination angles

• Described by the Bi-Directional Reflectance Distribution Function (BRDF)

• BRDF of area A defined as: ratio of incremental radiance, dLe, leaving surface through an infinitesimal solid angle in direction (v, v), to incremental irradiance, dEi, from illumination direction ’(i, i) i.e.


1

)(),()',( sr

dEdLBRDF

i

e

Ω'Ω'ΩΩΩ

• is viewing vector (v, v) are view zenith and azimuth angles; ’ is illum. vector (i, i) are illum. zenith and azimuth angles

• So in sun-sensor example, is position of sensor and ’ is position of sun



40

• Note that BRDF defined over infinitesimally small solid angles , ’ and interval, so cannot measure directly• In practice measure over some finite angle and and assume valid


surface area Asurface tangent vector

i2-v

vi

incident solid angle

incident diffuse

radiation

direct irradiance (Ei) vector

exitant solid angle

viewer

Configuration of viewing and illumination vectors in the viewing hemisphere, with respect to an element of surface area, A.



41

• Spectral behaviour depends on illuminated/viewed amounts of material• Change view/illum. angles, change these proportions so change reflectance

• Information contained in angular signal related to size, shape and distribution of objects on surface (structure of surface)

• Typically CANNOT assume surfaces are Lambertian (isotropic)


Modelled barley reflectance, v from –50o to 0o (left to right, top to bottom).


Directional Information

42


Directional Information

43


Features of BRDF• Bowl shape

– increased scattering due to increased path length through canopy

44


Features of BRDF• Bowl shape

– increased scattering due to increased path length through canopy

45


46


Features of BRDF• Hot Spot

– mainly shadowing minimum

– so reflectance higher

47


The “hotspot”

48See http://www.ncaveo.ac.uk/test_sites/harwood_forest/


49



50

• Good explanation of BRDF:• http://geography.bu.edu/brdf/brdfexpl.html


51

• Hotspot effect from MODIS image over Brazil


Measuring BRDF via RS

52

• Need multi-angle observations. Can do three ways:• multiple cameras on same platform (e.g. MISR, POLDER,

POLDER 2). BUT quite complex technically.• Broad swath with large overlap so multiple orbits build up

multiple view angles e.g. MODIS, SPOT-VGT, AVHRR. BUT surface can change from day to day.

• Pointing capability e.g. CHRIS-PROBA, SPOT-HRV. BUT again technically difficult


Albedo

53

• Total irradiant energy (both direct and diffuse) reflected in all directions from the surface i.e. ratio of total outgoing to total incoming• Defines lower boundary condition of surface energy budget hence v. imp. for

climate studies - determines how much incident solar radiation is absorbed

• Albedo is BRDF integrated over whole viewing/illumination hemisphere• Define directional hemispherical refl (DHR) - reflectance integrated over whole

viewing hemisphere resulting from directional illumination• and bi-hemispherical reflectance (BHR) - integral of DHR with respect to

hemispherical (diffuse) illumination

2,1 ΩΩΩ ;Ω dBRDF2DHR =

222

,12;2 ΩΩΩΩΩΩ ddBRDFdBHR =


Albedo

54

SW

dp

• Actual albedo lies somewhere between DHR and BHR• Broadband albedo, , can be approximated as

• where p() is proportion of solar irradiance at ; and () is spectral albedo• so p() is function of direct and diffuse components of solar radiation and so is

dependent on atmospheric state• Hence albedo NOT intrinsic surface property (although BRDF is)


55

Typical albedo values


Surface spectral information

56

• Causes of spectral variation in reflectance?• (bio)chemical & structural properties • e.g. In vegetation, phytoplankton: chlorophyll concentration • soil - minerals/ water/ organic matter

• Can consider spectral properties as continuous • e.g. mapping leaf area index or canopy cover

• or discrete variable • e.g. spectrum representative of cover type (classification)


Surface spectral information: vegetation

57vegetation


Surface spectral information: vegetation

58vegetation


Surface spectral information: soil

59soil


60

Surface spectral information: canopy


Summary

61

• Last week• Introduction to EM radiation, the EM spectrum, properties of wave /

particle model of EMR• Blackbody radiation, Stefan-Boltmann Law, Wien’s Law and Planck

function• This week

• radiation geometry • interaction of EMR with atmosphere

• atmospheric windows

• interaction of EMR with surface (BRDF, albedo)• angular and spectral reflectance properties

geogg141/ geog3051 principles & practice of remote sensing em radiation ( ii)

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