## 3 Results
### Evaluation of Gully Erosion Susceptibility Models  
We created four landslide susceptibility models (REPTree, AB-REPTree, Bag-REPTree, and RS-REPTree) using the training dataset. The 10-fold cross-validation method was used to prevent over-fitting and to decrease variability. Heuristic tests were used to find the best values for the parameters of the four models; these are shown in Table 4.  
We validated gully erosion susceptibility models using error and machine learning comparison metrics (Tables 5 and 6). The highest values of the Kappa metric were obtained for the RS-REPTree model (0.61), followed by the Bag-REPTree (0.55), AB-REPTree (0.53), and REPTree (0.53) models. The RS-REPTree model has the highest value (0.33) for the MAE metric, followed by the Bag-REPTree (0.28), AB-REPTree (0.24), and REPTree (0.24) models. The RMSE, RAE, and RRSE metrics indicate that the Bag-REPTree model (RMSE = 0.37, RAE = 56.62, and RRSE = 77.75) has the lowest error. It is followed by the RS-REPTree model (RMSE = 0.38, RAE = 67.68, and RRSE = 77.57) and the AB-REPTree model (RMSE = 0.43, RAE = 49.76, and RRSE = 86.49). The REPTree model has the highest error (RMSE = 0.43, RAE = 79.76, and RRSE = 86.50).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Algorithms** & **Parameters** \\ \hline Base classifier & Reduced-error pruning tree & Seed, 1; The minimum total weight of the instances in a leaf, 2; Number of folds, 10 \\ Ensembles & Bagging & Seed, 1; The number of iterations, 10 \\  & AdaBoost & Seed, 1; The number of iterations, 10 \\  & Random subspace & Seed, 1; The number of iterations, 10 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of algorithms utilized in this study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rank** & **Conditioning Factor** & **Average Merit** & **Standard Deviation** \\ \hline
1 & Rainfall & 0.225 & \(\pm\) 0.012 \\ \hline
2 & Altitude & 0.186 & \(\pm\) 0.009 \\ \hline
3 & River density & 0.106 & \(\pm\) 0.011 \\ \hline
4 & River distance & 0.093 & \(\pm\) 0.015 \\ \hline
5 & Land use & 0.086 & \(\pm\) 0.007 \\ \hline
6 & Lithology & 0.083 & \(\pm\) 0.01 \\ \hline
7 & Profile curvature & 0.031 & \(\pm\) 0.017 \\ \hline
8 & Road & 0.038 & \(\pm\) 0.014 \\ \hline
9 & Aspect & 0.028 & \(\pm\) 0.021 \\ \hline
10 & NDVI & 0.023 & \(\pm\) 0.018 \\ \hline
11 & Slope & 0.02 & \(\pm\) 0.016 \\ \hline
12 & Plan curvature & 0.016 & \(\pm\) 0.018 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The most effective factors for gully erosion occurrence.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Kappa** & **MAE** & **RMSE** & **RAE** & **PRSE** \\ \hline REPTree & 0.53 & 0.24 & 0.43 & 79.76 & 86.50 \\ \hline AB-REPTree & 0.53 & 0.24 & 0.43 & 49.76 & 86.49 \\ \hline Bag-REPTree & 0.55 & 0.28 & 0.37 & 56.62 & 75.30 \\ \hline RS-REPTree & 0.61 & 0.33 & 0.38 & 67.68 & 77.57 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Evaluation of gully erosion susceptibility models using error metrics.  
The machine learning comparison metrics shown in Table 6 indicate that the RS-REPTree model performed best based on TP, FP, precision, recall, F-measure, MCC, AUC, and PRSE values. It is followed by the Bag-REPTree, REPTree, and AB-REPTree models in terms of TP, FP, precision, recall, F-measure, and MCC metrics. The AB-REPTree model performed better than the REPTree model in term of the AUC and PRSE metrics.