## 2 Materials and Methods
### Voxel-Based Forest Sunlit and Shaded (VFSS) Components' Estimation  
To investigate the spatial variations of the four forest component proportions, we developed a voxel-based forest sunlit and shaded (VFSS) component estimation algorithm based on the stratified ALS data. There are two steps involved in the VFSS algorithm:  
(1) Sunlit and shaded identification: To identify the sunlit and shaded points for a given sun position, we assumed that the parallel solar radiation beams all came from nadir direction. First, we rotated the stratified forest ALS data (included overstory and background) according to the specific rotation axis and rotation angle, so the parallel solar beam illuminated the forest ALS data from the nadir direction. Then, the voxel-based model [PERSON] et al. (2012); [PERSON] et al. (2012) for forest plot was produced from a revolving ALS data with appropriate voxel size. In this experiment, the optimum voxel size was determined based on  
Figure 2: The histograms of ALS-based individual tree height frequency in both WPA **(a)** and PC **(b)** sites. The fitted probability density function curves (solid black lines) of individual tree height frequency and their corresponding first-order derivation solid curves (red solid lines) used to determine the height threshold (red dots) of forest vertical stratification. the sensitivity analysis described in Section 2.7. Furthermore, we classified all voxels into 'empty' and 'non-empty' based on the presence and absence of points within a voxel. Finally, we extracted the \"line quadrats\" [53] to simulate the transmission paths for all parallel solar beams and identified sunlit or shaded voxel for each 'line quadrats.' In each line quadrat, the first non-empty voxel was considered the sunlit component, and the remaining non-voxels were considered as shaded components. Thus, the forest ALS points were labeled as sunlit overstory, shaded overstory, sunlit background, or shaded background according to the stratification result. Additional attribution information was added to each point as:  
\[(X,Y,Z,L_{ov}/L_{bk},L_{sh}/L_{su}) \tag{2}\]  
where \(L_{sh},L_{su}\) are the labels for the shaded and sunlit components. (2) Visibility determination: To determine the visibility of identified sunlit or shaded points in the step 1(i.e., sunlit and shaded identification process) at a specific observation direction, we assumed the observation direction was always from nadir direction. For the identified sunlit and shaded ALS points, we rotated the ALS points to make the observation direction coincide with the nadir direction and keep the relative location between the observation direction and forest stand. Then, we conducted similar voxelization and line quadrat analysis like the ones in the step 1, and the additional labels were added to each point as:  
\[(X,Y,Z,L_{ov}/L_{bk},L_{sh}/L_{su},L_{vi}/L_{uv}) \tag{3}\]  
where \(L_{vi},L_{uv}\) are the labels for the visible and non-visible components. Finally, we obtained the spatial distributions of the four forest components at a fixed observation geometry. Furthermore, we obtained the proportions of the four forest components based on the number of identified points over the total points of a forest stand. The surrounding trees might present apparent effects on the proportion of the four forest components depending on if the given forest plots were bounded or unbounded forest stands. In this study, the bounded forest stand was defined as an independent forest stand without any surrounding trees, and the unbounded forest stand was defined as a partial forest stand coming from a continuously forested area with the surrounding vegetation. The VFSS algorithm could not be applied directly in the unbounded forest stand without considering the shadowing and occlusion effects of the surrounding vegetation.