1. GEOGG141/ GEOG3051 Principles & Practice of Remote Sensing EM Radiation (ii)
Dr. Mathias (Mat) Disney
UCL Geography
Office: 113, Pearson Building
Tel:

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

6. Radiation Geometry: spatial relations
Definitions of radiometric quantities
For parallel beam, flux density defined in terms of plane perpendicular to beam. What about from a point?
Schaepman-Strub et al. (2006)
see

7. Radiation Geometry: point sourcedA
Point source r
Consider flux dϕ 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 = dϕ/d (Wsr-1)
Solid angle d = dA/r2 (steradians, sr)

8. Radiation Geometry: plane source dϕ 
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 dϕ in direction at angle  to normal
Radiant exitance, M = dϕ / dS (Wm-2)
Radiance L is intensity in a particular direction (dI = dϕ/) 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 = (dϕ/) / 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. Radiation Geometry: solid angle
Cone of solid angle  = 1sr from sphere
 = area of surface A / radius2
Radiant intensity
From

11. 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 

12. Radiation Geometry: cosine lawX
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

13. Radiation Geometry: Lambert’s cosine law
Observed intensity (W/cm2·sr)) for a normal and off-normal observer; dA0 is the area of the observing aperture and dΩ is the solid angle subtended by the aperture from the viewpoint of the emitting area element.
Emission rate (photons/s) in a normal and off-normal direction. The number of photons/sec directed into any wedge is proportional to the area of the wedge.
Radiant intensity observed from a ideal diffusely reflecting surface (Lambertian surface) surface directly proportional to cosine of angle between view angle and surface normal

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. Recap: radiance Radiance, L L = d2ϕ / (d dS cos ) (in Wm-2sr-1)
Projected surface dS cos  
Radiance, L
power emitted (dϕ) 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 = d2ϕ / (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

16. Recap: emittance Emittance, M (exitance) For Lambertian surface
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 = d2ϕ / (d dS cos ) = constant, so M = dϕ/dS =
M = L
Ad. From

17. 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
Direct
Diffuse
Ad. From

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

20. Interactions with the atmosphere1
target R 4
target R 2
target R 3
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
From:

21. Interactions with the atmosphere: refraction
Caused by atmosphere at different T having different density, hence refraction
path of radiation alters (different velocity)
Towards normal moving from lower to higher density
Away from normal moving from higher to lower density
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 =
nwater = 1.33

22. Refraction: Snell’s Law
Optically less dense
Optically more dense
Incident radiation
 2
 3
 1
Path affected by atmosphere
Path unaffected by atmosphere
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:

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
After:

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

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:

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:

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

31. 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: , , , , nm

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)
Natural surfaces somewhere in between
From

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. Reflectance: angular distribution
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)
Real surfaces usually display some degree of reflectance ANISOTROPY
Lambertian surface is isotropic by definition
Most surfaces have some level of anisotropy
From:

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. 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
surface area A
surface tangent vector i
2-v v i
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.
From:

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

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

50. Directional reflectance: BRDF
Good explanation of BRDF:

51. Hotspot effect from MODIS image over Brazil

52. 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

53. 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
DHR =
BHR =

54. Albedo 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

56. 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)

57. Surface spectral information: vegetation

58. Surface spectral information: vegetation

59. Surface spectral information: soil

60. Surface spectral information: canopy

61. 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