CEGE046/GEOG3051Principles & Practice of Remote Sensing (PPRS) 3: Radiation (ii)

Dr. Mathias (Mat) Disney

UCL Geography

Office: 113, Pearson Building

Tel: 7679 0592

Email: mdisney@ucl.geog.ac.uk

www.geog.ucl.ac.uk/~mdisney

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EMR arriving at Earth

•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

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Departure from blackbody assumption

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

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Radiation Geometry: spatial relations

•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

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Radiation passing through media

•Various interactions, with different results

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

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Radiation Geometry: spatial relations

•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?

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Radiation Geometry: point source

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)

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Radiation Geometry: plane source

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)

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Radiation Geometry: radiance

•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.

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Radiation Geometry: solid angle

•Cone of solid angle = 1sr from sphere

= area of surface A / radius2

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

•Radiant intensity

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Radiation Geometry: terms and units

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Radiation Geometry: cosine law

•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

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Radiation Geometry: cosine law

•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

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Radiation Geometry: Lambert’s Cosine Law

•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

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Recap: radiance•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

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Recap: emittance

•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

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

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Recap: irradiance•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

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

Direct

Diffuse

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Reflectance•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

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Interactions with the atmosphere

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

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Interactions with the atmosphere

•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

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Interactions with the atmosphere: refraction

•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

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Refraction: Snell’s Law

•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

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Interactions with the atmosphere: scattering

•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

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Atmospheric scattering 1: Rayleigh

•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

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

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Atmospheric scattering 1: Rayleigh

From 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

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Atmospheric scattering 2: Mie

•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

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

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Atmospheric scattering 3: Non-selective

•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

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

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Atmospheric absorption

•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

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Atmospheric absorption

•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....

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Atmospheric CO2 trends

•Keeling et al.•Annual variation + trend•Smoking gun for anthropogenic change, or natural variation??

•Antarctic ice core records

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Atmospheric “windows”

•As a result of strong dependence of absorption

•Some totally unsuitable for remote sensing as most radiation absorbed

Atmospheric windows

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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....

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Atmospheric “windows”

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

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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

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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

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Reflectance

•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

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Surface energy budget•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

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

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Reflectance: angular distribution

•Real surfaces usually display some degree of reflectance ANISOTROPY

•Lambertian surface is isotropic by definition

•Most surfaces have some level of anisotropy

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

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)

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Directional reflectance: BRDF•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.

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

1

)(

),()',( sr

dE

dLBRDF

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

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Directional reflectance: BRDF

•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

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

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.

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Directional reflectance: BRDF

•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)

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

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

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Directional Information

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Directional Information

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Features of BRDF• Bowl shape

– increased scattering due to increased path length through canopy

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Features of BRDF• Bowl shape

– increased scattering due to increased path length through canopy

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Features of BRDF• Hot Spot

– mainly shadowing minimum

– so reflectance higher

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The “hotspot”

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

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Directional reflectance: BRDF•Good explanation of BRDF:

•http://geography.bu.edu/brdf/brdfexpl.html

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•Hotspot effect from MODIS image over Brazil

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Measuring BRDF via RS

•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

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Albedo•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,

1ΩΩΩ ;Ω dBRDF2DHR =

222

,1

2;2 ΩΩΩΩΩΩ ddBRDFdBHR =

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Albedo

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)

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Typical albedo values

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Surface spectral information

•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)

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Surface spectral information: vegetation

vegetation

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Surface spectral information: vegetation

vegetation

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Surface spectral information: soil

soil

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Surface spectral information: canopy

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Summary

•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