International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
3.2.2 Results: In Figure 2, we show resulting BRF and 
HDREF data in the solar principle plane. 
  
0,55 um 
1.10 
5 RM as 
s i 
e DE 
— Uam OS 
dom 06 
d= 04 
3.80 
eon d = 02 
Diffuse 
0.70 Dockworg Forward 
SC 40 20 2 20 40 60 
view zenith angle in principol plüne 
1.03 um 
0.60 
"d 
~~ 
0.50 of 
uU 
T mm ine. n 
(Y A f P Eu ER 
e 0407 BRE 
T de OA 
ui d = 0.6 
0.30 d = 04 
d 0.2 
Diffuse 
0.20 buc hwurd Sure 
O,2Q 
&0 40 20 3 20 4D 62 
view zenith oncle in principal plone 
S f paie 
Figure 2. Simulated snow HDRF data for the range of 
indicated irradiance scenarios, and BRF data in 
the solar principal plane at 0.55 um (top) and 
1.03 um (bottom). 
The models for d = 1.0 through d = 0.2 irradiance exhibit a 
forward reflectance distribution that decreases in magnitude 
with increasing diffuse component. For the totally diffuse 
irradiance scenario, the distribution has a shallow bowl 
shape. This minimum at nadir results from the angular 
intersection of the strong forward scattering phase function 
with the surface. Off-zenith irradiance has a greater chance 
than zenith irradiance of surviving multiple scatterings due 
to the orders of magnitude greater single scattering in the 
forward direction. In other words, zenith irradiance requires 
far more scattering events to produce reflected radiance than 
off-zenith. Therefore, the distribution will have greater 
reflectance at the larger view zenith angles. 
The bowl-shaped distribution for diffuse irradiance becomes 
relatively deeper at longer wavelengths (Figure 2 (bottom)). 
We show the 1.03 um model because this is the wavelength 
range in which snow reflectance is most sensitive to grain 
size (Nolin, 2000; Green, 2002). The enhancement of the 
bowl shape at greater diffuse irradiance is explained as 
above coupled with a decrease in the single-scattering 
albedo at the longer wavelengths. This in turn is due to the 
increase in the imaginary part k of the complex refractive 
index at these wavelengths (Warren, 1982). Only for the BRF 
and d = 0.8 irradiance cases is the distribution properly 
forward reflecting. 
Figure 3 shows DHR of snow relative to the illumination 
zenith angle with the associated white-sky BHR included for 
reference. For both wavelengths, the DHR increases with 
increasing zenith angle but the increase is far greater in 
absolute and relative reflectance for the 1.03 um case. The 
increase in both cases is due to the change in the angle of the 
intersection of the single scattering phase function with the 
surface. The single scattering phase function of ice particles 
364 
in the forward angles is several orders of magnitude greater 
than in the rest of the scattering domain. Therefore, as the 
illumination zenith angle increases, the forward scattered 
photons have a higher probability of escaping the 
snowpack. This in turn increases the albedo of snow. 
Because the single scattering albedo of ice particles (in this 
case a spheroid of radii 208 uum and 520 um) is 0.9999817 at 
0.55 um versus 0.9930210 at 1.03 um, multiply scattered 
photons are more likely to be absorbed at 1.03 um. The 
greater increase in albedo at 1.03 um results then from the 
increase in the contribution of singly scattered photons to 
albedo due to the increase in illumination zenith angle. At 
both wavelengths, the effective illumination zenith angle for 
white-sky BHR is 49-50°, as discussed above. 
0.55 um 
1.00 
= OHR 
8 0.98 ws BHR 
9 rc 
© 
S am. : 0 
C 20 40 60 80 
lllumination Zenith Angle 
1.03 nm 
0.70 
DHR 
S 0.60 ws BHR 
9 
o 
© 
0.50 
Q.40 
0 20 40 60 80 
lilumination Zenith Angie 
Figure 3. DHR versus illumination zenith angle for snow at 
0.55 um (top) and 1.03 um (bottom). The BHR for 
diffuse illumination (white-sky BHR) is included 
for comparison. 
3.3 Analysis of MISR surface reflectance data products 
3.3.1 Methodsand selected datasets: Various land 
surface reflectance products are available from the MISR 
sensor, launched in 1999. MISR has nine cameras with centre 
view directions of 26.1, 45.6, 60.0, and 70.5 degrees in 
forward and afterward direction, as well as one looking in 
nadir direction. All cameras cover four spectral bands with a 
centre wavelength at 446, 558, 672, and 867 nm. The 
crosstrack IFOV and sample spacing of each pixel is 275 m 
for all of the off-nadir cameras, and 250 m for the nadir 
camera. Downtrack IFOV's depend on view angle, ranging 
from 214 m in the nadir to 707 m at the most oblique angle. 
However, sample spacing in the downtrack direction is 
275 m in all cameras (Diner, 1999). 
We briefly describe the retrieval of the land surface products 
HDRF, BHR, BRF, and DHR. For the mathematical 
formulation refer to Martonchik (1998). The top-of- 
atmosphere MISR radiances are atmospherically corrected to 
produce the HDRF and BHR, surface reflectance properties as 
would be measured at ground level but at the MISR spatial 
resolution. The MISR surface retrievals do not explicitly 
incorporate tilt or slope effects (Diner, 1999). The HDRF and 
BHR then are further atmospherically corrected to remove all 
     
   
  
  
     
  
  
  
  
   
     
     
    
   
      
    
  
  
   
   
  
  
  
  
   
  
  
  
  
   
   
    
  
  
  
   
    
    
   
    
    
    
  
  
   
    
   
   
  
  
   
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