# Rockfall Modelling in Forested Areas: The Role of Digital Terrain Model Grid Cell Size
## 3 Results
### Validation of the Modelled Rockfall Runout Zones with and without Forest  
The results of validation of models with different DTM grid cell size and scenarios (with/without the forest), evaluated with GOF indices, are shown in Table 4. The best model performance is in all cases achieved by the forest scenario. DTM1 achieves the best model performance with forest with both rockfalls, which is followed closely by DTM2. At RS1, DTM10 gets better results when forest is not considered in modelling. It is even, according to the GOF indices, performing the best of all models, which can be explained by the overestimation of the model due to the size of the DTM grid cell. At RS2, the differences between the effect of forest and without the effect of forest are small between all grid cell sizes. Figure 4: Models performance results in 30 calibration runs for (**a**) rockfall site 1 (RS1), and (**b**) rockfall site 2 (RS2) according to the rg70, rg20, and rg10. The values of rg70, rg20, and rg10 are for the demonstration purposes adjusted according to the values of rg within the individual subareas altogether, meaning that the values on the x, y, and z axis are actually showing average rg values that were calculated by considering an average rg value of each calibration run considering the subarea size. The real rg values were in the range shown in Table 1. Goodness-of-fit (GOF) indices that were used for the evaluation of calibration runs were average index (AI), success index (SI), distance to the perfect classification (D2 PC), and true skill statistics (TSS), and on this plot, they are merged into a joint result, and the size of the sphere is reflecting the rank performance of each calibration run. The larger the sphere on the graph, the lower the rank, indicating a more successful model performance (rank 4 is the most successful model, rank 120 is the least successful). In the case of RS1, calibration run number 17 has the lowest rank of 8, and in the case of RS2, calibration run number 4 has the lowest rank of 4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**ROCKFALL SITE 1**} & \multicolumn{3}{c}{**ROCKFALL SITE 2**} & \\ \hline _Calibration Run_ & _AI_ & _SI_ & _D2 PC_ & _TSS_ & _Calibration Run_ & _AI_ & _SI_ & _D2 PC_ & TSS \\ \hline
17 & 0.855 & 0.837 & 0.285 & 0.673 & 4 & 0.892 & 0.892 & 0.153 & 0.785 \\
27 & 0.820 & 0.824 & 0.250 & 0.647 & 25 & 0.886 & 0.886 & 0.162 & 0.772 \\
23 & 0.820 & 0.822 & 0.253 & 0.644 & 3 & 0.885 & 0.886 & 0.167 & 0.771 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of GOF indices for the three most successful model runs in the calibration step. The rockfall propagation and runout area decreases with smaller DTM grid cell size in both modelling scenarios at RS1, while it increases at RS2 (Figure 5). All models overestimate the actual rockfall extent at all grid cell sizes but at different locations. The largest overestimation of the propagation area at RS1 is at DTM1 and DTM2 (both scenarios) in the northern part of the rockfall propagation area, while in the southern part, it exhibits the greatest match between the modelled results and actual rockfall outline. On the other hand, overestimation of the model is not present as much at DTM5 and DTM10 (as in DTM1 and DTM2); however, both DTMs underestimate the maximum runout length. The underestimation of the propagation area is the lowest in the southwestern part with all DTMs except with DTM1, where it almost achieves a perfect fit in the forest modelling scenario. There is a difference in the modelled runout area between the northern part and southwestern part of the propagation area, which can be explained by the fact that in the northern part of the runout area, the surface slope is steeper, providing more kinetic energy to the rocks that can move further and cannot be stopped quicker due to the effect of forest. In the southwestern part, the runout distance is larger and changes in slope values are smaller; therefore, the difference in the DTM models' results will be smaller.