CEGE046/GEOG3051 Principles & Practice of Remote Sensing (PPRS) 3: Radiation (ii)

1. 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

2. 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 = 4r2x1373 = 3.88x1026W • Incidentally we can now calculate Tsun (radius=6.69x108m) from SB Law • T4sun = 3.88x1026/4r2 so T = ~5800K

3. Departure from blackbody assumption • Interaction with gases in the atmosphere • attenuation of solar radiation

4. 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

5. Radiation passing through media • Various interactions, with different results From http://rst.gsfc.nasa.gov/Intro/Part2_3html.html

6. 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?

7. dF dA Point source d r Radiation Geometry: point source • 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)

8. Radiation Geometry: plane source  dF  Plane source dS dS cos  • 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)

9. 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.

10. Cone of solid angle = 1sr from sphere •  = area of surface A / radius2 • Radiant intensity Radiation Geometry: solid angle From http://www.intl-light.com/handbook/ch07.html

11. Radiation Geometry: terms and units

12. 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 

13. Radiation Geometry: cosine law X Radiometer dA Y X Radiometer  Y dA/cos  • 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 Adapted from Monteith and Unsworth, Principles of Environmental Physics

14. 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

15. d  Projected surface dS cos  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

16. 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

17. Direct Diffuse 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

18. 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

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

20. R R 2 1 target target R 4 R 3 target target 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

21. 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

22. Incident radiation n1 1 Optically less dense Optically more dense  2 n2 Path unaffected by atmosphere Optically less dense  3 n3 Path affected by atmosphere 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.

23. 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

24. 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

25. Atmospheric scattering 1: Rayleigh • So, scattering -4 so scattering of blue light (400nm) > scattering of red light (700nm) by (700/400)4 or ~ 9.4 From http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html

26. 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

27. 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

28. 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

29. Atmospheric absorption • CO2 as a “greenhouse” gas • strong absorber in longer (thermal) part of EM spectrum • i.e. 10-12m 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....

30. Antarctic ice core records • Keeling et al. • Annual variation + trend • Smoking gun for anthropogenic change, or natural variation?? Atmospheric CO2 trends

31. Atmospheric windows Atmospheric “windows” • As a result of strong dependence of absorption • Some  totally unsuitable for remote sensing as most radiation absorbed

32. 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....

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

34. 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

35. 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

36. Natural surfaces somewhere in between 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

37. Surface energy budget • Total amount of radiant flux per wavelength incident on surface, () Wm-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.

38. (a) (b) (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-reflection peak (hotspot). 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

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

40. viewer incident diffuse radiation direct irradiance (Ei) vector  exitant solid angle  incident solid angle  v i 2-v i surface area A surface tangent vector Configuration of viewing and illumination vectors in the viewing hemisphere, with respect to an element of surface area, A. 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

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

42. Directional Information

43. Directional Information

44. Features of BRDF • Bowl shape • increased scattering due to increased path length through canopy

45. Features of BRDF • Bowl shape • increased scattering due to increased path length through canopy

47. Features of BRDF • Hot Spot • mainly shadowing minimum • so reflectance higher

48. The “hotspot” See http://www.ncaveo.ac.uk/test_sites/harwood_forest/

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