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UCL DEPARTMENT DEPARTMENT OF GEOGRAPHYOF GEOGRAPHY

GEOGG141/ GEOG3051 Principles & Practice of EM Radiation (ii)

Dr. Mathias (Mat) Disney UCL Geography Office: 113, Pearson Building Tel: 7679 0592 Email: [email protected] 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 • We now know how EMR spectrum is distributed • arriving at Earth’s surface • NOT blackbody, but close • “” • solar energy irradiating surface perpendicular to solar beam • ~1373Wm-2 at top of atmosphere (TOA) • Mean distance of ~1.5x108km so total solar energy emitted = 4πr2x1373 = 3.88x1026W

8 • Incidentally we can now calculate Tsun (radius=6.69x10 m) from SB Law 4 26 2 •σ T sun = 3.88x10 /4π r so T = ~5800K

2 UCL DEPARTMENT OF GEOGRAPHY Departure from blackbody assumption

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

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• 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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• Various interactions, with different results

From http://rst.gsfc.nasa.gov/Intro/Part2_3html.html 5 UCL DEPARTMENT OF GEOGRAPHY

• Definitions of radiometric quantities • Radiant energy emitted, transmitted of received per unit time is radiant (usually , or Js-1) • density is flux per unit area (Wm-2) • is radiant flux density incident on a surface (Wm-2) e.g. Solar radiation arriving at surface • Emittance ( or ) (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?

6 UCL DEPARTMENT OF GEOGRAPHY

Point source dω dF dA

r

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

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dF ψ ω

Plane source dS dS cos ψ

• 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 ψ to normal • Radiant emittance, M = dF / dS (Wm-2) • Radiance L is intensity in a particular direction (dI = dF/ω) 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 ψ is dS cos ψ, so….. • Radiance L = (dF/ω) / dS cos ψ = dI/dS cos ψ (Wm-2sr-1) 8 UCL DEPARTMENT OF GEOGRAPHY

• 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 = 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 4π steradians at its centre.

9 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: solid angle

• Cone of solid angle Ω = 1sr • from sphere •Ω = area of surface A / radius2

From http://www.intl-light.com/handbook/ch07.html 10 UCL DEPARTMENT OF GEOGRAPHY

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• Emission and absorption • Radiance linked to law describing spatial distn of radiation emitted by Bbody with uniform surface temp. T (total emitted flux = σT4) • 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 ψ, angle to surface normal • OTOH flux per unit solid angle divided by true area of surface must be proportional to cos ψ

12 UCL DEPARTMENT OF GEOGRAPHY

Y X Radiometer ψ Y dA/cos ψ • Case 1: radiometer ‘sees’ dA, flux proportional to dA • Case 2: radiometer ‘sees’ dA/cos ψ (larger) BUT T same, so emittance of surface same and hence radiometer measures same • So flux emitted per unit area at angle ψ ∝ to cos ψ so that product of emittance (∝ cos ψ ) and area emitting (∝ 1/ cos ψ) is same for all ψ • This is basis of ’s Cosine Law

Adapted from Monteith and Unsworth, Principles of Environmental 13 UCL DEPARTMENT OF GEOGRAPHY

• When radiation emitted from Bbody at angle ψ to normal, then flux per unit solid angle emitted by surface is ∝ cos ψ • Corollary of this: • if Bbody exposed to beam of radiant energy at an angle ψ to normal, the flux density of absorbed radiation is ∝ cos ψ • 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 14 UCL DEPARTMENT OF GEOGRAPHY

Recap: radiance • Radiance, L dω • emitted (dF) per unit of solid angle (d ) and per unit of the projected ω ψ surface (dS cosψ) of an extended widespread source in a given direction, ψ (ψ = zenith angle, ϕ= azimuth angle) Projected surface dS cos ψ • L = d2F / (dω dS cos ψ) (in Wm-2sr-1) • If radiance is not dependent on ψ 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 15 UCL DEPARTMENT OF GEOGRAPHY

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 ψ i.e. if same in all directions, the source is said to be Lambertian. • For Lambertian surface • Remember L = d2F / (dω dS cos ψ) = constant, so M = dF/dS = • M = L π 2 π 2 π Lcosψdω = 2πL cosψ sinψdψ = πL ∫0 ∫0

16 Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm € UCL DEPARTMENT OF GEOGRAPHY

• from source dS along viewing Direct angle of sensor (θ in this 2D case, but more generally (θ, ϕ) in 3D case) • Emittance, M, hemispheric • Why?? Diffuse • 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 17 UCL DEPARTMENT OF GEOGRAPHY

Reflectance • Spectral , ρ(λ), defined as ratio of incident flux to reflected flux at same •ρ (λ) = L(λ)/I(λ) • Extreme cases: • Perfectly specular: radiation incident at angle ψ reflected away from surface at angle -ψ • Perfectly diffuse (Lambertian): radiation incident at angle ψ reflected equally in all angles

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Interactions with the atmosphere

From http://rst.gsfc.nasa.gov/Intro/Part2_4.html 19 UCL DEPARTMENT OF GEOGRAPHY Interactions with the atmosphere

R4

R1 R2 R3

target target target target

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

20 From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf UCL DEPARTMENT OF GEOGRAPHY

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 in a

(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

21 UCL DEPARTMENT OF GEOGRAPHY Refraction: Snell’s Law

Incident • Refraction described by Snell’s Law radiation • For given freq. f, n1 sin θ1 = n2 sin θ2 n1 •where and are the angles from the θ 1 θ1 θ2 Optically normal of the incident and refracted waves less dense respectively Optically more • (non-turbulent) atmosphere can be θ 2 n2 dense considered as layers of gases, each with a Path Optically θ 3 unaffected different density (hence n) less dense by n • Displacement of path - BUT knowing 3 atmosphere Path affected by Snell’s Law can be removed atmosphere

22 After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective. UCL DEPARTMENT OF GEOGRAPHY

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: •λ of radiation • abundance of particles or gases • distance the radiation travels through the atmosphere (path length)

23 After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html UCL DEPARTMENT OF GEOGRAPHY Atmospheric scattering 1: Rayleigh

• Particle size << λ of radiation • e.g. very fine soot and dust or N2, O2 molecules • Rayleigh scattering dominates shorter λ and in upper atmos. • i.e. Longer λ scattered less (visible red λ scattered less than blue λ) • Hence during day, visible blue λ tend to dominate (shorter path length) • Longer path length at sunrise/sunset so proportionally more visible blue λ 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

24 After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html UCL DEPARTMENT OF GEOGRAPHY

Atmospheric scattering 1: Rayleigh

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

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

Atmospheric scattering 2: Mie

• Particle size ≈ λ of radiation • e.g. dust, pollen, smoke and water vapour • Affects longer λ than Rayleigh, BUT weak dependence on λ • 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

26 After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html UCL DEPARTMENT OF GEOGRAPHY

Atmospheric scattering 3: Non-selective

• Particle size >> λ of radiation • e.g. Water droplets and larger dust particles, • All λ affected about equally (hence name!) • Hence results in fog, mist, clouds etc. appearing white • white = equal scattering of red, green and blue λ s

After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html 27 UCL DEPARTMENT OF GEOGRAPHY

Atmospheric absorption • Other major interaction with signal • Gaseous molecules in atmosphere can absorb at various λ • depends on vibrational modes of molecules • Very dependent on λ • Main components are:

• CO2, water vapour and ozone (O3) • Also CH4 ....

• O3 absorbs shorter λ 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. 10-12µm 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

• Antarctic ice core records • Keeling et al. • Annual variation + trend • Smoking gun for anthropogenic change, or natural variation?? 30 UCL DEPARTMENT OF GEOGRAPHY Atmospheric “windows”

Atmospheric windows

• As a result of strong λ dependence of absorption • Some λ totally unsuitable for remote sensing as most radiation absorbed 31 UCL DEPARTMENT OF GEOGRAPHY 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 µwave i.e. can see through clouds! – V. Important consideration....

32 UCL DEPARTMENT OF GEOGRAPHY Atmospheric “windows”

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

33 UCL DEPARTMENT OF GEOGRAPHY 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 UCL DEPARTMENT OF GEOGRAPHY 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 (-like) - incidence angle = exitance angle • perfectly diffuse (Lambertian) - same reflectance in all directions independent of illumination angle)

Natural surfaces somewhere in between

36 From http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_5_e.html UCL DEPARTMENT OF GEOGRAPHY

Surface energy budget • Total amount of radiant flux per wavelength incident on surface, Φ(λ) Wµm-1 is summation of:

• reflected rλ, transmitted tλ, and absorbed, aλ

• i.e. Φ(λ) = rλ + tλ + aλ • So need to know about surface reflectance, and • Measured RS signal is combination of all 3 components

After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective. 37 UCL DEPARTMENT OF GEOGRAPHY

Reflectance: angular distribution

• Real surfaces usually display some degree of reflectance • Lambertian surface is isotropic by definition (a) (b) • Most surfaces have some level of anisotropy

(c) (d)

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

38 From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf UCL DEPARTMENT OF GEOGRAPHY 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 δA defined as: ratio of incremental radiance, dLe, leaving surface through an infinitesimal solid angle in direction Ω(θv, φv), to incremental irradiance, dEi, from illumination direction Ω’(θi, φi) i.e.

dL (Ω,Ω' ) BRDF(Ω,Ω') = e [sr −1 ] dEi (Ω' )

•Ω is viewing vector (θv, φv) are view zenith and azimuth angles; Ω’ is illum. vector (θi, φi) are illum. zenith and azimuth angles • So in sun-sensor example, Ω is position of sensor and Ω’ is position of sun

39 After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective. UCL DEPARTMENT OF GEOGRAPHY

Directional reflectance: BRDF

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

viewer incident direct irradiance diffuse (δE ) vector Ωʹ exitant solid i incident solid radiation angle δΩ angle δΩʹ

θv

θi

2π-φv φi

surface tangent vector surface area δA

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

40 From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf UCL DEPARTMENT OF GEOGRAPHY

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)

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

41 From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf UCL DEPARTMENT OF GEOGRAPHY

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/ 48 UCL DEPARTMENT OF GEOGRAPHY

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

50 UCL DEPARTMENT OF GEOGRAPHY • 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

52 UCL DEPARTMENT OF GEOGRAPHY • 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

1 2π DHR = ρ(Ωʹ; 2π )= BRDF (Ω,Ωʹ)dΩ π ∫

2π 1 2π 2π BHR = ρ(2π ;2π )= ρ(Ωʹ)dΩʹ = BRDF(Ω,Ωʹ)dΩdΩʹ ∫ π ∫ ∫

53 UCL DEPARTMENT OF GEOGRAPHY Albedo • Actual albedo lies somewhere between DHR and BHR • Broadband albedo, α, can be approximated as α = ∫ p(λ)α(λ)dλ SW • where p(λ) is proportion of at λ; and α(λ) is spectral albedo • so p(λ) 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)

54 UCL DEPARTMENT OF GEOGRAPHY 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

57 vegetation UCL DEPARTMENT OF GEOGRAPHY

Surface spectral information: vegetation

vegetation58 UCL DEPARTMENT OF GEOGRAPHY

Surface spectral information: soil

59soil UCL DEPARTMENT OF GEOGRAPHY 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 61