## 3 Results
### ALS-Based Sunlit and Shaded Forest Components
#### 3.2.2 Plot Scale  
For forest plots WPA-P1 (Figure 7a), WPA-P2 (Figure 7e), WPA-P3 (Figure 7i), and PC-P1 (Figure 7m) we obtained the four forest components' distribution maps using the VFSS method demonstrated in Figure 7b,f,j,n, with the view zenith and azimuthal angles of 60\({}^{\circ}\) and 180\({}^{\circ}\), 60\({}^{\circ}\) and 160\({}^{\circ}\), 60\({}^{\circ}\) and 100\({}^{\circ}\), 60\({}^{\circ}\) and 225\({}^{\circ}\), respectively. The zenith and azimuthal angles of solar position were 15\({}^{\circ}\) and 180\({}^{\circ}\), 15\({}^{\circ}\) and 160\({}^{\circ}\), 5\({}^{\circ}\) and 100\({}^{\circ}\), 10\({}^{\circ}\) and 45\({}^{\circ}\), respectively. We modeled the forest background (shown in Figure 7c,g,k,o) and overstory (shown in Figure 7d,h,l,p) distribution maps in the 3 DSMax environment for the corresponding virtual plots for validation purposes. Moreover, we plotted the variation curves of the four forest component proportions with various observation directions at fixed sun positions in both solar principal and perpendicular planes to better characterize their spatial variations in these four plots, as shown in Figure 8.  
Comparing the four forest component results obtained from ALS- and 3 DSMax-based methods, we found that ALS-based shaded components tended to underestimate the ones obtained using the 3 DSMax-based method. This discrepancy was attributed to the incomplete sampling of a forest canopy due to the occlusion effects of tree crowns with the fixed ALS scanning direction, shown in the Figure 8. As shown in Table 3, it was found that the total RMSEs of the four forest component proportions between the ALS- and 3 DSMax-based methods were 6.9%, 5.9%, 8.2%, and 6.4% for plots WPA-P1,  
Figure 7: The original ALS data (insets **a,e,i,m**) and their four forest component estimation results (insets **b,f,j,n**) for four forest plots (i.e., WPA-P1, WPA-P2, WPA-P3, and PC- P1) and the simulated sunlit and shaded forest background (insets **c,g,k,o**) and overstory (**d,h,l,p**) in both WPA and PC sites, respectively. SZA, SAA, VZA, and VAA represent solar zenith angle, solar azimuth angle, view zenith angle, and view azimuth angle, respectively. WPA-P2, WPA-P3, and PC-P1, respectively. Moreover, the estimation accuracy (RMSE = 5.8%, 5.2%, 6.5%, and 5.8%) of the ALS-based four forest components in solar principal plane was better than the ones (RMSE = 8.1%, 6.5%, 9.9%, and 7.0%) from solar perpendicular plane in plots WPA-P1, WPA-P2, WPA-P3, and PC-P1. In addition, it was found that the proportions of sunlit forest background and overstory reached the maximum point in the hotspot position for four plots shown in Figure 8a-d. Moreover, the proportions of visible overstory and forest background held minimum and maximum values at nadir  
Figure 8: Comparisons between the four forest component results obtained from ALS- and 3 DSMax-based results in both solar principal and perpendicular planes for forest plot WPA-P1 (insets **a,e**), WPA-P2 (insets **b,f**), WPA-P3 (insets **c,g**) and PC-P1 (insets **d,h**). The solar zenith and azimuth angles were 15\({}^{\circ}\) and 180\({}^{\circ}\), 15\({}^{\circ}\) and 160\({}^{\circ}\), 5\({}^{\circ}\) and 100\({}^{\circ}\), 10\({}^{\circ}\) and 45\({}^{\circ}\) for forest plots WPA-P1, WPA-P2, WPA-P3, and PC-P1, respectively. Negative view angles correspond to the forward-scattering directions and the positive angles to the backscattering directions. point, respectively. In the solar perpendicular plane, sunlit forest background and overstory (shown in Figure 8e-h) held the maximum values in the nadir direction. It should be noted that as the forest density increased, more obvious abrupt peak values were observed in the sunlit forest background component in the WPA site, shown in Figure 8e-2,f-2,g-2. The apparent changes of forest structure in high-density plots explained these changes as the observation directions deviated from nadir direction.