## 5 Discussion  
### Reliability of Tree Density Retrieval  
We assessed an LM-based approach in combination with ALS data to estimate TD in a heterogeneous alpine forest. Considering all trees with a DBH threshold \(>\)5 cm, a moderate accuracy (i.e., R\({}^{2}\) of 0.39) with a substantial underestimation (RMSE of 389 trees per ha, rRMSE of 70%) was achieved in the heterogeneous alpine environment. This result is in agreement with [PERSON] & [PERSON] [5], who found a relationship between estimated and reference TD of R\({}^{2}\) = 0.40 in a coniferous forest in Norway. Yet, other studies evaluating the TD estimation accuracy report R\({}^{2}\) values ranging from 0.40 to 0.85 [5; 25; 30; 41; 75; 86]. [PERSON] et al. [87] indicate TD estimation accuracies ranging between 40-70% considering several studies carried out in Scandinavian and European forests. The consideration of trees with larger DBHs decreases uncertainties in estimated TD (i.e., R\({}^{2}\) increases up to 0.80, RMSE decreases to 68 trees per ha, rRMSE of 40%). This finding corresponds to results documented by [PERSON] et al. [30], who found a strong relationship for ALS-based TD estimates considering a DBH \(>\) 100 cm (R\({}^{2}\) = 0.85). [PERSON] et al. [88] report a TD estimation accuracy of 87% for trees with a DBH \(>\) 30 cm. The dependency of the TD estimation accuracy on DBH indicates a sensitivity issue of the applied ALS-LM approach, while mainly small trees cannot be differentiated and reliably identified. In fact, we observe better TD estimates using a CHM with higher resolution, which is in agreement with [PERSON] et al. [3]. Our results suggest that forest structure and species composition affect the TD retrieval accuracy. Indeed, crown shape and canopy density determine the success of the LM approach, which basically exploits the morphology of ALS-derived CHMs [41; 76]. If tree crowns are flat or show multiple main branches, the LM approach is likely to fail. Several studies have demonstrated that forest structure strongly affects the capability of ALS data to characterize forest properties [40; 41; 89; 90]. In particular,  
Figure 11: Relationship between TD and forest productivity for north- and south-facing plots. (**a**) In situ measured TD; (**b**) ALS estimated TD. Figure 12: Relationship between TD and forest productivity along four slope-line parallel transects. the occurrence of multi-stemmed trees, as caused by a complex mix of environmental factors, disturbances and historical management [91], impacts the detection of individual trees [92; 26; 93; 90]. Further, in the presence of steep slopes, a spatial misplacement between crown top and stem position on ground is likely and additionally affects the accuracy of ITDs [94; 95]. Structural effects obviously cause ITD and eventually TD estimates to be dependent on actual species. Physiological considerations add another complication and cause TD estimates to be dependent on species composition, in particular in multi-layered heterogeneous forests. European larch, for example, is largely abundant in our study site and a shade intolerant and fast growing species. Therefore, larch trees form and dominate the upper forest canopy layer [53], covering other more shade-tolerant and slow-growing species underneath, e.g., Swiss stone pine and Norway spruce. The multi-layering hides trees and thus impacts the TD estimation accuracy. We observed a dependency of TD estimates on surface orientation, i.e., north- and south-facing. TD estimates were less accurate for south-facing slopes compared to those on north-facing slopes. Since south-facing areas are characterized by a higher TD and the occurrence of multiple-stemmed trees, the lower TD estimation accuracy can be attributed to structural aspects. Optimized ALS data acquisition allows overcoming certain issues discussed above, eventually yielding improved ITD and TD estimates. One option would be the use of multi-temporal ALS data (i.e., leaf-on and leaf-off) [96].