## 4 Results  
### ALS Based Tree Density Estimation  
An example result of the LM-based tree detection is shown in Figure 3. The detection rate was calculated to validate ITD and relates the proportion of detected trees to the number of trees measured in the field (Table 2). The validation shows a detection rate of 36%, whereby the detection rates ranged from 43% to 85% considering the different DBH categories (cf. Section 2.2). Figure 3: Result of individual tree detection (ITD) based on ALS data in combination with the local maxima approach. The black crosses mark the individual trees. A canopy height model (CHM) is used as background. Figure 2: Flowchart of the methodology implemented for estimating tree density and mapping forest productivity. [Airborne Prism Experiment (APEX), digital terrain model (DTM), gross primary production (GPP), normalized differenced vegetation index (NDVI), canopy height model (CHM)]. The results of the ITD were used to calculate the TD per plot, expressed in trees/ha. Considering all trees and DBH classes, TD estimation shows a low accuracy with R\({}^{2}\) = 0.39 (\(p\) < 0.0001), and RMSE = 389 [N/ha]. The accuracy increases by excluding small trees (i.e., DBH > 30 cm) to R\({}^{2}\) = 0.35 (\(p\) = 0.0002) and RMSE = 87 [N/ha] (Table 3). If reference plots are stratified in north- and south-facing plots, the accuracy of TD estimates for all trees increases for north-facing plots (R\({}^{2}\) = 0.68 (\(p\) = 0.006), RMSE = 176 [N/ha]) and remains at a low to moderate level for south-facing plots (R\({}^{2}\) = 0.52 (\(p\) < 0.0001), RMSE = 447 [N/ha]). The relationship between measured and estimated TD considering all plots and trees is shown in Figure 4a. We observe a general underestimation of TD estimates in particular with increasing amount of trees/ha that is associated with an increasing number of small trees. Even if only large trees are considered (i.e., DBH > 30 cm), there is a tendency for an underestimation of TD in dense canopies (Figure 4b). The effect of species composition on TD estimates was assessed by stratifying field plots into four classes according to their dominant species. Plots showing individual proportions of less than 60% across all species were considered as mixed [85]. As a result, 18 mixed plots, 10 Larch plots, six Swiss stone pine plots, and one Norway spruce plot were classified. We observe a strong relationship between the amount of trees per ha and the TD estimation error (i.e., the difference between measured trees in the field and estimated trees from ALS data) across species composition (i.e., R\({}^{2}\) = 0.68 for mixed plots, R\({}^{2}\) = 0.97 for larch, and R\({}^{2}\) = 0.90 for Swiss stone pine plots) (Figure 5a). If only large trees are considered (DBH > 30 cm), the TD error tends to be less dependent on TD, but seems to be \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Plots**} & \multicolumn{3}{c}{**All Trees**} & \multicolumn{3}{c}{**DBH \textgreater{} 12**} & \multicolumn{3}{c}{**DBH \textgreater{} 20**} & \multicolumn{3}{c}{**DBH \textgreater{} 30**} \\ \cline{2-13}  & **R\({}^{2}\)** & **RMSE** & **RMSE\%** & **R\({}^{2}\)** & **RMSE** & **RMSE\%** & **R\({}^{2}\)** & **RMSE** & **RMSE\%** & **R\({}^{2}\)** & **RMSE** & **RMSE\%** \\ \hline
**All** & 0.39 & 389 & 77 & 0.40 & 294 & 68 & 0.42 & 201 & 57 & 0.35 & 87 & 40 \\
**North** & 0.68 & 176 & 56 & 0.68 & 124 & 44 & 0.74 & 101 & 39 & 0.80 & 68 & 33 \\
**South** & 0.52 & 447 & 77 & 0.58 & 339 & 69 & 0.53 & 229 & 59 & 0.27 & 93 & 42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Agreement of measured and ALS-based tree density estimation. Statistical assessment is based on the root mean square error (RMSE) in trees ha\({}^{-1}\) and the coefficient of determination (R\({}^{2}\)). Figure 4: Relationship of ALS derived TD and measured tree density for (**a**) all trees; and (**b**) trees with a DBH > 30 cm. The dashed line indicates the 1:1 line.