## 3 Results  
### Point Cloud Classification  
The classification was performed at point level and by means of a decision tree. Development of the rule-based algorithm was based on combining previous knowledge from fieldwork and visual inspections of AOIs point clouds. By means of statistical parameters for every point cloud, several classes were categorised in every point cloud (Figure 5). Dense and Sparse Aquatic Reed beds were classified in consideration of the statistical parameters of height and density. With the obtained classes, quantification of extents, as well as the expansion of frontline and shoreline was possible. The classification procedures were executed after quality control. The absolute registration accuracy was 8 cm and strip differences averaged 0.022 m, SD 0.039 m, and RMSE 0.045 m. Registration accuracy and low strip differences were accepted as suitable for the study objectives and no further calibration was performed. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **Area (m2)** & **Area (ha)** & **Number of Samples** \\ \hline Sparse Aquatic Reed & 4843 & 0.4843 & 50 \\ Dense Aquatic Reed & 9037 & 0.9037 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sample distribution according to extent of classes. \begin{table}
\begin{tabular}{c c c} \hline \hline Mean Error & \(\mu=\frac{1}{n}\sum\limits_{i=1}^{n}\Delta\text{h}_{i}\) & [42] \\ \hline Standard Deviation & \(\sigma=\sqrt{\frac{1}{(n-1)}\sum\limits_{i=1}^{n}\left(\Delta\text{h}_{i}-\mu \right)^{2}}\) & [42] \\ Root Mean Square Error & \(\text{RMSE}=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\Delta\text{h}_{i}^{2}}\) & [42; 43] \\ \hline \hline \end{tabular} n is the number of tested points in the sample (sample size) and \(\Delta\text{h}_{i}\) represents the difference between RP and Digital Service Models (DSMs) for a point i. The assessment of vertical accuracy was performed considering the Air–Water Interface (AWI) as the zero point. The relative stem height (RSH) was obtained by subtracting the absolute height (length from flower to sediment) minus the water depth. The same absolute height of the water surface used for modelling AWI was used for obtaining the RSH.  
\end{table} 
Table 2: Accuracy measures for Digital Evidence Management system (DEms) presenting normal distribution of residuals. The structural characteristics obtained from cross-sections extracted in one-metre intervals through all point clouds were equally important. Spatial distribution of points and their height in relation to the AWI were key factors for density classification. The height of sparse aquatic need beds for all AOIs varied between 1.80 and 2.40 m. A height of 2 m was found to be the most suitable value for an accurate automatic classification of all point clouds (Figure 6). The density of points was the second parameter considered for classification. Dense aquatic need beds are characterised by tall needs with a height greater than 2 m (520 m.a.s.l. ), a large number of leaves in the upper canopy level, and bare thick stems in the lower canopy level. Regarding the LiDAR data, points were equally distributed in sparse stocks and accumulated in the upper canopy for dense stocks. This break in the spatial distribution was easily identifiable in the points between the AWI and the 1.5 m relative height (519.5 m.a.s.l.). Once the density was calculated for all values under this height, the maximum frequent value in every AOI was always selected for classification thresholds. For clouds with 2-3 strips, this threshold value was 80 points/m\({}^{2}\). According to this definition, Sparse Aquatic Reed beds were classified and the remaining points without classification were assigned to Dense Aquatic Reed beds. Figure 5: Classification scheme used in OPALS for density classification of aquatic need beds. Dashed line boxes are intermediate classes and coloured boxes represent final classes. Point statistics and attributes used for classification thresholds are described between classes.