## 5 Results
### Gully Erosion Susceptibility Map  
A gully erosion susceptibility map of the Mesima stream catchment was produced (Figure 4a) after assessing the prediction performance of the MaxEnt method. The susceptibility map was obtained by averaging 10 probability estimates using a 10-fold cross-validation analysis. The map indicates the probability of gully erosion occurrence at each point of the study area. The susceptibility values range between 0.01 and 1, with a mean value of 0.257 and a standard deviation of 0.01. The pixels with susceptibility values closer to 1 indicate a high probability of gully occurrence, whereas a low probability happens with values closer to 0. In the map in Figure 4a, we have classified the gully erosion susceptibility values into five classes based on the equal interval method as follows: very low, low, moderate, high, and very high. The areal distribution of the recognised classes is shown in Figure 5. Most of the areas in the catchment fell in the low and very low susceptibility classes (about 78% of the total area); instead, the areas affected by very high and high susceptibility were generally fewer (13.1%). The comparison between the susceptibility map and gully erosion inventory allowed the gullies' spatial distribution in the five susceptibility classes to be verified (Figure 5). The achieved result showed that the susceptibility map displayed a remarkable agreement with the gully inventory. Indeed, about 92.5% of gullies were correctly classified, falling in the areas mapped as having high and very high susceptibility (probability values between 0.6 and 1). Furthermore, less than 1.2% of the recognised gullies fall in the low and very low susceptibility classes (Figure 5). Hence, the susceptibility map highlights a high reliability for detecting gully-prone areas. In addition, the validity of the gully erosion susceptibility map was confirmed also by the computation of the R-index (Figure 5). In particular, the R-index values increase from very low to very high susceptibility classes, remarking that the susceptibility map is in agreement with the spatial occurrence of gullies. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fold Numbers**} & \multicolumn{3}{c}{**Calibration**} & \multicolumn{3}{c}{**Validation**} \\ \cline{2-7}  & \multirow{2}{*}{**Accuracy**} & **Kappa Coeff.** & \multirow{2}{*}{**AUC**} & **Accuracy** & **Kappa Coeff.** & \multirow{2}{*}{**AUC**} \\ \hline
1 & 0.923 & 0.846 & 0.946 & 0.902 & 0.804 & 0.924 \\
2 & 0.932 & 0.864 & 0.954 & 0.912 & 0.824 & 0.948 \\
3 & 0.935 & 0.870 & 0.956 & 0.911 & 0.822 & 0.949 \\
4 & 0.936 & 0.872 & 0.964 & 0.920 & 0.841 & 0.952 \\
5 & 0.946 & 0.893 & 0.969 & 0.916 & 0.832 & 0.952 \\
6 & 0.955 & 0.910 & 0.975 & 0.921 & 0.843 & 0.963 \\
7 & 0.954 & 0.908 & 0.977 & 0.953 & 0.907 & 0.975 \\
8 & 0.938 & 0.876 & 0.969 & 0.916 & 0.833 & 0.954 \\
9 & 0.944 & 0.888 & 0.972 & 0.941 & 0.882 & 0.967 \\
10 & 0.921 & 0.843 & 0.953 & 0.921 & 0.843 & 0.937 \\ \hline Min & 0.921 & 0.843 & 0.946 & 0.902 & 0.804 & 0.924 \\ Max & 0.955 & 0.910 & 0.977 & 0.953 & 0.907 & 0.975 \\ Mean & 0.938 & 0.877 & 0.964 & 0.921 & 0.843 & 0.952 \\ St.dev. & 0.012 & 0.023 & 0.011 & 0.015 & 0.030 & 0.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Predictive performance of calibration and validation phases based on 10-fold cross-validation of the gully erosion susceptibility model. The spatial pattern of the uncertainty associated with the obtained susceptibility map was produced by computing the standard deviation of the 10 estimates of probability gully occurrence (Figure 4b). The uncertainty (standard deviation) values range from 0 to 0.13 (mean value equal to 0.003), which reveal small variation among the 10 estimates of probability and, consequently, they show a high robustness of the prediction model.