## 5 Conclusions  
In this study, we developed a new VFSS algorithm to estimate the proportions of the four forest components using the ALS discrete lidar data in a forested area with topographic variations. This method could estimate the spatial variations of the four forest components with any observation geometry at both landscape and plot levels. Based on the analysis of our results and investigation of various factors affecting the estimation accuracy of the four forest components, we concluded that: (1) The implicitly contained 3D structural information within ALS data makes it possible to stratify the overstory and forest background components vertically, (2) the voxel-based VFSS algorithm is an effective way to simulate the spatial variations of the four forest components, (3) ALS configuration, data characteristics, and voxel size setting affected the estimation accuracy of the four forest components, and (4) the forest structural parameters, topographic variation, and surrounding forest stands had a significant impact on the four forest component proportions. The quantified forest sunlit and shaded proportions can be useful for improving the estimation accuracy of canopy LUE and forest biophysical and biochemical properties. Additionally, it is also beneficial to the studies of forest canopy BRDF using GO models.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Plane**} & **View** & **View** & \multicolumn{3}{c}{**Four Forest Component** & **Proportions** & **Difference (\%)**} \\ \cline{3-8}  & **Azimuth** & **Zenith** & **Shaded** & **Sunlit** & **Shaded** & **Sunlit** & **Background** & **and** \\  & **Angle (\({}^{\circ}\))** & **Angle (\({}^{\circ}\))** & **Background** & **Snowlit** & **Overstory** & **Overstory** & **Overstory** \\ \hline \multirow{6}{*}{Principal plane} & 160 & 0 & 2.6 & 2.2 & 7.9 & 3.1 & 3.9 \\ \cline{2-8}  & 160 & 15* & 0.0 & 3.2 & 0.0 & 3.2 & 3.2 \\ \cline{2-8}  & 160 & 20 & 0.1 & 2.7 & 11.8 & 8.9 &  
**Author Contributions:** [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON] analyzed the data; [PERSON] contributed data; [PERSON] wrote the paper; [PERSON] and [PERSON] contributed analysis tools; [PERSON] modified the paper; [PERSON] gave valuable comments. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Key Research and Development Programs for Global Change and Adaptation (Grant NO. 2019 YFA0606601), National Science Foundation of China (NSFC) (NSFC award #41771374, #41701393), Scientific Research Satellite Engineering of Civil Space Infrastructure Project (Forestry products and its practical techniques research on Terrestrial Ecosystem Carbon Inventory Satellite), and the National Key Research and Program of China (Grant NO. 2017 YFD0600903).  
**Acknowledgments:** This research was conducted at the International Institute for Earth System Science, Nanjing University. The lidar and hyperspectral data were provided by the Precision Forestry Cooperative at the University of Washington. We appreciate the anonymous reviewers for their valuable suggestions and comments to significantly improve this manuscript.  
**Conflicts of Interest:** The authors declare no conflicts of interest.