1. Atmospheric effect in the solar spectrum
Vermote et al.
University of Maryland/ Dept of Geography
and
NASA/GSFC Code 614.5

2. Solar Energy Paths

3. atmospheric contribution
direct + direct
diffuse + direct
direct + diffuse
multiple scattering

4. Solar (reflective) spectral domain

5. Observation Geometry Solar zenith angle View zenith angle
Relative azimuth
angle

6. Solution of the Radiative Transfer in the reflective domain for non absorbing atmosphere and lambertian ground
Ground reflectance
(= albedo for lambertian)
Atmospheric reflectance
Atmospheric
Transmissions
Apparent reflectance at satellite level
Atmosphere
spherical albedo

7. Perfect Lambertian Reflector
Radiance of the Perfect Lambertian Reflector Es
Isotropic
radiation

8. Simple Radiative Transfer Equation

9. SRTE (cont.)
Absorbing ground

10. SRTE (cont.) Ei Et

11. SRTE (cont.)

12. SRTE (cont.)  v E0 Er 40

13. SRTE 1 interaction (cont.)

14. SRTE 2 interactions

15. SRTE Multiple Interactions
groundSatm < 1 so when n->∞ then (groundSatm)n ->0
Therefore

16. STRE for non absorbing atmosphere and lambertian ground
Ground reflectance
(= albedo for lambertian)
Atmospheric reflectance
Atmospheric
Transmissions
Apparent reflectance at satellite level
Atmosphere
spherical albedo

17. The composition of the atmosphere

18. Gaseous Absorption (H2O)

19. Modified SRTE to account for absorption
In case of a pure molecular atmosphere (no aerosol) we can write:
m is the air mass = 1/cos(s)+1/ cos(v)
Ugaz is the gaz concentration 10

20. Final SRTE approximation

21. Water vapor effect for different sensors in the near infrared

22. Scattering angle ,
The scattering angle,  is the relative angle between the incident and the scattered radiation
Incident Radiation
Particle 
scattered radiation

23. Phase function
The phase function, P() describe the distribution of scattered radiation for one or an set of particles. It is normalized such as:
since
we have

24. Rayleigh/molecular scattering 1/4
Rayleigh or molecular scattering refers to scattering by atmospheric gases, in that case:

25. Rayleigh/molecular scattering 2/4
The concentration in scatterer is better described by the efficiency they scatter at a certain wavelength or the proportion of direct transmission which is related to the spectral optical thickness 
E0(
Et()/ E0()=e- 
Et(
For Rayleigh is proportional to -4 and for standart pressure is ~ at 0.45 m

26. Rayleigh/molecular scattering 3/4
The rayleigh reflectance, R, could be crudely approximated by:

27. Rayleigh/molecular scattering 4/4
Compute the reflectance of the sky (assumed clear no aerosol) at solar noon at 45degree latitude at vernal equinox looking straight up at 0.45m, 0.55m, 0.65m

28. Aerosol scattering 1/5
aerosol scattering refers to scattering by particles in suspension in the atmosphere (not molecules). The MIE scattering theory could be applied to compute the aerosol phase function and spectral optical depth, based on size distribution, real and imaginary index.

29. Aerosol scattering 2/5
Continental aerosol phase function

30. Aerosol scattering 3/5 single scattering albedo
( ) to account for absorbing
particles

31. Aerosol scattering 4/5
Continental aerosol optical thickness spectral variation 60

32. Aerosol scattering 5/5
Continental aerosol single scattering albedo spectral variation

33. Atmospheric effect: Vegetation 1/3

34. Atmospheric effect: Vegetation 2/3
No absorption, Continental aerosol

35. Atmospheric effect: Vegetation 3/3
Absorption tropical atmosphere, Continental aerosol

36. Atmospheric effect: Ocean 1/2

37. Atmospheric effect: Ocean 2/2

38. Perfect Lambertian Reflector
Isotropic
radiation

39. Different Types of Reflectors
diffuse reflector (lambertian)
Specular reflector (mirror)
Nearly Specular reflector (water)
nearly diffuse reflector
Hot spot reflection

40. Sun glint as seen by MODIS
Gray level temperature image

41. MODIS data illustrating the hot-spot over dense vegetation

42. BRDF atmosphere coupling correction
Lambertian infinite target approximation
BDRF atmosphere coupling approximation

43. Adjacency effect correction
Lambertian infinite target approximation
adjacency effect approximation

44. Adjacency effect correction (practical implementation)

45. Adjacency effect correction (testing)

46. Adjacency effect correction (testing)
Reflectance’s observed over a horizontal transect on the checkerboard. The red bars are the “true” surface reflectance, the blue bars correspond to the top of the atmosphere signal including adjacency effect. The green bars correspond to the corrected data using the infinite target assumption. The open square correspond to the data corrected for the adjacency effect using the operational method developed.

47. Adjacency effect correction (validation)

48. Conclusions
Review of atmospheric effect including the BRDF-coupling and the adjacency effect
Current version of MOD09 (Collection 4) does not include the BRDF-coupling or adjacency effect correction
Collection 5 (start scheduled in Jan06), will include adjacency correction for 250m bands. BRDF-coupling correction is still being evaluated.