## 3 Results
### Forest Vertical Stratification
#### 3.1.2 Separation of Overstory and Forest Background  
We obtained the stratified overstory and forest background ALS data in both landscape and plot levels using the forest stratification algorithm (Figure 4). The determined height threshold values in the two study sites (i.e., WPA and PC-1 km) were 7.8 m and 5.0 m. For the forest plots WPA-P1, WPA-P2, WPA-P3, and PC-P1, the height thresholds were 6.0 m, 6.9 m, 5.4 m, and 3.5 m, respectively. Moreover, we validated the forest vertical stratification result using the method described in Section 2.5. As shown in Table 3, the percentages of correctly identified gaps increased from 65% to 87% as forest densities decreased by comparing the total gap size of original ALS data with the ones from stratified overstory data at six transects (Figure 5a). Taking the transect L5 of plot WPA-P1 as an example, we identified gap-A as 33 m and gap-B as 10 m from the original ALS data. Correspondingly, the detected gap sizes based on the stratified overstory data were 30 m and 9 m, respectively (Figure 5b). The percentages of the correctly identified gap size were 90.6% at transect L5.  
Figure 3: Comparisons between the visual- and field-based tree heights (a) and crown diameters (b) in the WPA site. The verified visual-based tree heights and crown diameters were used to validate the ones obtained from the ALS-based method in both WPA (WPA-P1, WPA-P2, WPA-P3) (insets **c–h**) and PC (PC-P1) (insets **i** and **j**) sites.  
Figure 4: Graphs showing four different phases (i.e., original ALS data, tree segmentation, and stratified overstory and forest background) of vertical forest stratification in both landscape and plot. levels (WPA-P1, WPA-P2, WPA-P3, and PC-P1) in both WPA and PC sites.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Plot\#** & **WPA-P1** & **WPA-P2** & **WPA-P3** & **PC-P1** \\ \hline \multirow{6}{*}{Vertical stratification} & Height threshold (m) & 6.0 & 6.9 & 5.4 & 3.5 \\ \cline{2-6}  & Original gap size (m) & 6.0 – 33.0 & 2.0 – 24.0 & 3.0 – 18.0 & 3.0 – 17.0 \\ \cline{2-6}  & Overstorygap size (m) & 5.0 – 30.0 & 2.0– 22.0 & 1.0 – 13.0 & 3.0 – 15.0 \\ \cline{2-6}  & Original gap size (m) & 137.0 & 179.0 & 114.0 & 144.0 \\ \cline{2-6}  & Overstory gap size (m) & 116.0 & 143.0 & 64.0 & 125.0 \\ \cline{2-6}  & Identification percentage (\%) & 85.0 & 79.0 & 65.0 & 87.0 \\ \cline{2-6}  & Gap size RMSE (m) & 2.3 & 2.7 & 4.3 & 1.8 \\ \hline \multirow{6}{*}{Root mean square error (\%)} & Shaded background & 2.6 & 3.8 & 3.3 & 5.6 \\ \cline{2-6}  & Sumlit background & 12.1 & 7.0 & 2.7 & 9.8 \\ \cline{2-6}  & Shaded overstory & 8.9 & 6.9 & 10.1 & _7.7_ \\ \cline{2-6}  & Sumlit overstory & 4.1 & 5.6 & 16.8 & 2.5 \\ \cline{2-6}  & Forest background & 7.3 & 5.4 & 2.9 & _7.6_ \\ \cline{2-6}  & Forest overstory & 6.5 & 6.3 & 13.5 & 5.1 \\ \cline{2-6}  & Background and overstory & 6.9 & 5.8 & 8.2 & 6.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons between the gap sizes obtained from stratified overstory and original ALS data and the root mean square errors of four forest component proportions between ALS and 3 DSmax based in four forest plots (WPA-P1, WPA-P2, WPA-P3, and PC-P1).