# Rockfall Modelling in Forested Areas: The Role of Digital Terrain Model Grid Cell Size
## 2 Materials and Methods
### Used Datasets
#### 2.3.3 Simulation with Forest  
The modelling was done also with considering the scenario with the effect of forest. Simulation with forest was done by using tree locations, \(DBH\), and percentage of coniferous trees. Tree locations and additional attributes were using the tool FINT [55]. The tool calculates the positions of dominant and co-dominant trees based on high-resolution digital surface models (DSM); namely, it evaluates for each grid cell in a normalized surface model (NSM), which has a value larger than the defined minimum tree height, whether it is a local maximum by initially using a 3 \(\times\) 3 window. FINT assesses the dominance of the analyzed cell over its surrounding cells [55]. The recommended grid cell size are 0.5, 1, and 2 m, while with the increasing grid cell size, the spatial precision of the calculated tree positions decreases. The tool uses a standard function for calculating the \(DBH\) for each identified tree on the basis of its height:  
\[DBH=\ h^{1.25}, \tag{2}\]  
where \(DBH\) (in cm) presents diameter at breast height and \(h\) the height of the tree (in m). However, the user can use a custom \(DBH\) function based on the relationship between the \(DBH\), tree height, and tree altitude. The location of the trees in provided in a _.txt_ format, and it contains X and Y coordinates for each tree along with the \(DBH\). In the case of this study, we used DTM and a digital surface model (DSM) with a grid cell size of 1 m. The function for calculating \(DBH\) (in cm), based on the height, was adjusted based on the \(DBH\) and height measurements of trees present at both study sites. Fifty trees were measured at each site, 50% coniferous (_Picea abes_ Karst. and _Larix decidua_ Mill at both sites, additionally _Pinus sylvestris_ L. at the first rockfall site), and 50% deciduous tree species (_Fagus sylostatica_ L. at both sites) of various \(DBH\) ranges. \(DBH\) functions were extracted separately for each rockfall site (R\({}^{2}\) = 0.59 for RS1, R\({}^{2}\) = 0.79 for RS2):  
\[DBH\ (\text{RS1})=10.70\ \times\ e^{(0.0529\ \times\ \text{h})}, \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**ROCKFALL SITE 1**} \\ \hline  & \multicolumn{3}{c}{**Intervals Used for Creation of 30 Random**} & \multicolumn{3}{c}{**Optimal rg Values Obtained in Calibration Run 17**} \\  & \multicolumn{3}{c}{**Calibration Runs**} & \multicolumn{3}{c}{**Optimal rg Values Obtained in Calibration Run 17**} \\ \hline _sub area_ & _rg70_ & _rg20_ & _rg10_ & _rg70_ & _rg20_ & _rg10_ \\ area 1 & 0.31 & 0.6 & 0.7 & 0.14 & 0.36 & 0.65 \\  & (0–0.71) & (0.20–0.80) & (0.3–1) & & & \\ area 2 & 0.31 & 0.31 & 0.4 & 0.44 & 0.37 & 0.54 \\  & (0–0.71) & (0–0.71) & 0–0.80 & & & \\ area 3 & 0.31 & 0.35 & 0.4 & & & \\  & (0–0.71) & (0–0.75) & (0–0.80) & & & \\ \hline  & \multicolumn{6}{c}{**ROCKFALL SITE 2**} \\ \hline  & \multicolumn{3}{c}{**Intervals Used for Creation of 30 Random**} & \multicolumn{3}{c}{**Optimal rg Values Obtained in Calibration Run 4**} \\  & \multicolumn{3}{c}{**Calibration Runs**} & \multicolumn{3}{c}{**Optimal rg Values Obtained in Calibration Run 4**} \\ \hline _sub area_ & _rg70_ & _rg20_ & _rg10_ & _rg70_ & _rg20_ & _rg10_ \\ area 1 & 0.21 & 0.4 & 0.5 & 0.26 & 0.21 & 0.31 \\  & (0–0.51) & (0.10–0.70) & (0.20–0.80) & & & \\ area 2 & 0.35 & 0.4 & 0.45 & & & \\ area 2 & (0.05–0.65) & (0.10–0.70) & (0.15–0.75) & & & \\ area 3 & 0 & 0 & 0 & 0 & 0 & 0 \\ area 4 &\[DBH\left(\text{RS2}\right)=7.87\times\text{e}^{\left(0.0529\times\text{h}\right)}. \tag{4}\]  
In addition to the location of the trees, the model also needs information about the ratio between broadleaved and coniferous trees; namely, when modelling with forest, one must provide a raster file where cell values represent the mean percentage of coniferous trees (%) within each raster cell.