The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B6b. Beijing 2008 
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Where L d = radiance reflected from direct solar irradiance of 
sloping pixel 
E d ' = direct solar irradiance of sloping pixel 
However, tree growth is oriented with the gravitational field 
and always vertical to the horizontal plane, not vertical to the 
slope. As a result, the solar incidence angle is constant and the 
direct solar irradiance received by individual crown is 
independent with the slope and aspect of the surface, which 
means the radiance reflected is not affected by topography as 
well. So equation (6) will be not applicable. But for the case of 
a cluster of tree crowns, there is another type of topography 
effect (Gu, 1998). Firstly, because of the mutual shading of tree 
crowns, the pixel of tree crowns can be partitioned to sunlit part 
and shadow part. The sunlit part can receive both direct and 
diffuse irradiance, and the shadow part can only receive diffuse 
irradiance. Secondly, the mutual shading effect is controlled by 
terrain since the relative position of trees is affected by 
topography. As a result, on Sun-facing slopes, the proportion of 
sunlit tree crowns which exposed to the direct illumination is 
larger than that on the slopes facing away from the Sun, which 
eventually lead to the difference of reflected up radiance. So for 
the case of tree crowns, the rate of reflected radiance from 
direct irradiance between sloping pixel and level pixel equals 
the rate of total area of sunlit part of the pixel. By Gu, the rate is: 
L d _ A' cos i (7) 
L. A cos 0 cos a 
a s 
Where A ’ = the total sunlit area of sloping pixel 
A = the total sunlit area of level pixel 
According to the analysis above, for tree crowns, equation (2) 
can be modified as (The situation of circumsolar diffuse 
irradiance is the same as direct irradiance): 
r , COSÌ r . COSi T . T ,, . r 
L — b L d +b KL f + (1 — K)VL f + L t 
cos 6 S cos a cos 0 S cos a 
(8) 
From equation (8), the model can be modified as: 
kL 
(9) 
cos 6. cos a 
- E,+b- 
cos 6, cos a 
KE f + (l-K)VE +E, 
This is the modified model for forest areas where tree crowns 
cover, which is the combination of Sandmeier’s model and SCS 
correction. 
2.3 Parameter Calculation 
The radiative transfer parameters E d , Ef, K can be calculated by 
6S or MODTRAN 4 model etc. The total radiance reflected by 
level pixel (L) can be calculated by: 
L ( E d +E f)Pa (10) 
7t 
Where p a = atmospheric corrected reflectance by 6S or 
MODTRAN 4 etc. 
The slope angle and aspect angle can be calculated from DEM; 
the accurate calculation of E, and V was discussed respectively 
by Proy (1989) and Dozier (1990); Sandmeier’s model provides 
the simplified calculation of them (Sandmeier, 1997). 
3. MODEL VALIDATION 
3.1 Validation Data and Implementation 
The modified model in this paper is specifically for forested 
areas, so it is necessary to use satellite data in forested area to 
validate the effectiveness of the model. In the experiment, the 
30m multi-spectral ETM image of Landsat 7 acquired on May 
14th, 2000 as validation data. Lipin County, Guizhou province, 
China was chosen to be the study area. The study area is typical 
forest and mainly covered by Chinese fir. DEM with an original 
spatial resolution of 25m were used here (see Figure 2). The 
terrain in the area is quite rugged, where the average slope 
angle is 22 degree and the maximal slope angle is 55 degree. 
In this experiment, the radiative transfer parameters in the 
model were calculated by 6S model. The dark objective method 
(Kaufman, 1988; Tian Qingjiu, 1998) was used to estimate the 
aerosol optical thickness, which is a very important input 
parameter of 6S model. The programming tool of the 
experiment is IDL. 
0 m 300 m 600 m 
Figure 2. DEM in the study area 
3.2 Result and Discussion 
In order to evaluate the efficiency of the model, the atmospheric 
corrected image by 6S model was taken as the comparative 
image without topographic correction. In addition, Sandmeier’s 
model is also applied to the same data to make comparison with 
the modified model.