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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
3. CASE STUDIES COMPARING DIFFERENT 
REFLECTANCE QUANTITIES 
The following case studies highlight differences of the 
above described reflectance quantities using model 
simulations for a vegetation canopy, and a snow surface, as 
well as MISR data products for several scenes. The 
differences of hemispherical versus directional reflectance 
quantities (i.e., BHR (Case 9) versus DHR (Case 3) and HDRF 
(Case 7) versus BRF (Casel)) are computed for different 
wavelengths regions and various ratios of direct to diffuse 
illumination. 
We concentrate on reflectance and reflectance factor 
quantities. Deriving the bidirectional reflectance 
distribution function from HDRF measurements without 
correcting for the diffuse illumination, leads to severe 
distortions of the resulting function (Lyapustin, 1999). 
3.1 Vegetation canopy reflectance simulations using the 
RPV model 
3.1.1 Methods and data: Using the PARABOLA 
instrument, black spruce forest HDRF data were acquired at 
eight solar zenith angles (35.17, 40.29, 45.2°, 50.2°, 33.0°, 
59.5?. 65.0*, 70.0?) (Deering, 1995). After applying a simple 
HDRF to BRF atmospheric correction scheme, data of the red 
band (650 to 670nm) were fitted to the parametric Rahman- 
Pinty-Verstraete (RPV) model (Engelsen, 1996). Resulting 
fit parameters and the RPV are used to simulate different 
reflectance quantities of a black spruce canopy under 
various illumination conditions. The model was run for a 
solar zenith angle of 30? and increments of direct (d) and 
diffuse irradiance of d =1.0, d = 0.8, d = 0.6, d = 0.4, d = 0.2, 
and d = 0.0. These irradiance scenarios corresponded to BRF 
(d = 1.0) and HDRF for the rest, including the special case of 
white-sky HDRF, i.e. purely diffuse irradiance (d = 0.0). 
3.1.2 Results: Figure 1 (top) reports the HDRF of black 
spruce for indicated direct-diffuse ratios in the solar 
principal plane, assuming the incident diffuse radiation to 
be isotropic. The wavelength range is 650 to 670 nm. As is 
expected for a vegetation canopy, there is a large amount of 
backscattering, and a hot spot at view zenith 30° due to the 
lack of shadowing. For d approaching 0, the anisotropy is 
smoothed and the hot spot becomes invisible. 
Fig. 1 (centre) reports the DHR of black spruce as a function 
of the illumination zenith angle. As previously described for 
vegetation, the DHR increases with increasing illumination 
zenith (Kimes, 1983). For comparison, the white-sky BHR 
(although not a function of any angle) is plotted. The actual 
albedo can be expressed as a combination of DHR and white- 
sky BHR if the diffuse incident radiation is assumed to be 
isotropic. The actual albedo for a given illumination zenith 
angle then lies on a vertical line between the DHR and white- 
sky BHR as shown in the graph for an example of 20° solar 
zenith. 
Finally, Figure 1 (bottom) reports the BRF at nadir view as a 
function of the illumination zenith angle, along with the 
white-sky HDRF at nadir view (although not a function of 
any illumination angle). 
   
  
  
  
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0 10 320 30 4$ SO 60 70 
x 
illumination zenith 
Figure 1. Simulated BRF data for a black spruce canopy in 
the solar principle plane, and corresponding 
HDRF for varying direct to diffuse irradiance 
conditions (top), DHR, and BHR for pure diffuse 
illumination as a reference (centre), BRF at nadir, 
and HDRF at nadir for pure diffuse illumination 
(bottom). 
3.2 Snow reflectance simulations 
3.2.1 Methods and data: This case study presents model 
results from a snow directional reflectance model. The model 
is the coupling of single-scattering parameters and a 
discrete-ordinates multiple scattering model. Single- 
scattering parameters were determined with a ray-tracing 
model for spheroidal particles (Macke, 1996) and the 
multiple scattering calculations were performed with the 
DISORT model (Stamnes, 1988). a 
The single-scattering parameters used in the model were the 
single-scattering albedo, extinction efficiency, and the 
single-scattering phase function. Model results shown here 
are for a spheroid of minimum and maximum radii of 208 um 
and 520 pum, respectively. This spheroid has the same surface 
area to volume ratio as a sphere of radius 250 um. We then 
determined 20 Legendre moments of the single-scattering 
phase function for input to the multiple scattering model. 
The multiple scattering model was run for a solar zenith of 
30°, illumination scenarios as mentioned for the black 
spruce canopy, and the wavelength range from 0.4 to 2.5 um.