## 4 Results and Discussion
### Limitations  
The analysis of the effect of the time-lag between the field survey and the ALS flight campaign indicates that the proposed co-registration method will be challenged if there is major changes between both dates of observation. This is particularly the case if the trees might have grown, toppled, or been harvested within the time lag between field survey and ALS data collection.  
Since we needed to model synthetic training data based on various assumptions, the transfer of the probability estimations to the original datasets should be done with caution. The procedure of simulating ALS point clouds using crown shape functions is justified by the observation that the most ambiguous cases for co-registration occur in dense forest stands, where individual trees are hard to detect because of overlapping crowns. Nonetheless, non representative point clouds might affect the tree detection characteristics. Although the suitability of the simulated datasets has been tested, it cannot be ensured that the datasets are representative. This is particularly the case because the synthetic survey plots were characterized by increased NNDs compared to the original BWI data. However, the usage of simulated forest stands leads to more objective validation results compared to reference locations derived by visual interpretation.  
Since the number of potential tree pairs and positional inaccuracies complicates the identification of matching tree pairs, the rudimentary tree detection method used in this study might have a negative effect on the algorithm performance. The ANOVA of the co-registration probability grouped by the number of detections per hectare (Figure 11) indicates a significant trend (\(p\) = 0.00). Since the probability  
Figure 10: **(a)** Correlation between the applied probability threshold for a correct co-registration and the resulting number plots classified as correctly co-registered. **(b)** Effect of the year of survey on the co-registration probability. Both figures are based on the original BWI plots. The numbers in brackets correspond to the number of plots. GNSS: Global Navigation Satellite System.  
for a correct co-registration decreases with an increasing number of detections per hectare, commission errors of the detection method should be avoided. Since the angle count sampling technique prefers the selection of dominant trees, and a correct co-registration is possible with just a few trees assigned (Figure 8a), the reliable identification of the dominant trees is more important than the identification of all trees (which might cause increased commission errors).  
Another limitation of the method is that no perfect one-to-one correlation between the predicted and observed probabilities could be achieved. Thus, the predicted matching probabilities provided by the algorithm are a higher order reliability estimation but do not necessarily correspond to actual probabilities. However, since the predicted co-registration probabilities rarely differ from the one-to-one correlation, they seem to represent actual probabilities.  
The parametrization of the \(e\)-norm (defined to assign the tree pairs) should be optimized based on the forest stand characteristics. Since it is only used for the co-registration, it can be adapted for each plot individually after training of the classifier. Using such an optimization might lead to better results compared to the fixed parameters chosen in this study.