## 3 Results
### Spatial Relationship Using WoE Model  
The outcomes of WoE model are shown in Table 3. In elevation, the results of WoE indicate that there is a direct correlation between classes of elevation and GE, and with an increase in elevation, GE also increases. Therefore, the class of \(>\)1600 m with WoE 47.95 had the greatest impact on gully occurrence. The result of slope degree indicate that classes 5\(\sim\)\(<\)10 with WoE 34.96 had a strong relation with GEIM. For slope aspect, NE-facing slopes with a value of 19.46 show high probability of gully occurrence. In the case of plan curvature, among the three classes of concave, flat, and convex, the concave class had the highest value (78.04), and thus a positive correlation with GE. This result is in line with [11; 50]. In TWI, the class of \(>\)11 has the strongest relationship with GE with the highest value (78.04). In the case of the convergence index, the class of 0-10 with values of 13.18 has a positive relation with gully occurrence. With respect to distance from river, class of \(>\)650 with value of 25.86 and regarding distance from road the class of \(>\)3000 m with values of 16.25 had the greatest effect on gully occurrence. For the drainage density factor, the class of \(<\)1.4 km/km\({}^{2}\) showed the highest value (14.23) and thus high correlation with gully occurrence. According to the lithology factor, Gypsiferous marl with greatest value (51.23) is more prone to GE than other lithology units. Concerning LU/LC, most gullies are located in the range land use type and this class with the highest value (21.02) has the strongest relationship with gully occurrence. In NDVI, results indicated that all gullies are located in the class of \(<\)0.11, showing that very low vegetation density renders slopes susceptible to GE.  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Conditioning Factors**} & \multicolumn{2}{c}{**Collinearity Statistics**} \\ \cline{2-3}  & **Tolerance** & **VIF** \\ \hline Constant Coefficient & - & - \\ Slope degree & 0.998 & 1.002 \\ Distance from road & 0.672 & 1.489 \\ Distance from river & 0.323 & 3.094 \\ Plan curvature & 0.674 & 1.483 \\ Lithology & 0.945 & 1.058 \\ LU & 0.864 & 1.158 \\ Drainage density & 0.826 & 1.211 \\ Elevation & 0.920 & 1.087 \\ Convergence index & 0.666 & 1.503 \\ Aspect & 0.299 & 3.343 \\ TWI & 0.942 & 1.062 \\ NDVI & 0.941 & 1.063 \\ \hline \end{tabular}
\end{table}
Table 2: Multi-collinearity of effective factors using tolerance (TOL) and variance inflation factor (VIF).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Class**} & \multirow{2}{*}{**Number of Pixels**} & \multirow{2}{*}{**Pixels of Gullies**} & \multicolumn{5}{c}{**Weights-of-Evidence (WoE)**} \\ \cline{5-10}  & & & & **C** & **S2 (w\({}^{*}\))** & **S2 (w\({}^{-}\))** & **S** & **W** \\ \hline \multirow{8}{*}{1} & \(<\)1200 & 144,200 & 21 & \(-\)3.16 & 0.05 & 0.00 & 0.22 & \(-\)14.41 \\  & 1200\(-\)\(\lambda\)1350 & 348,463 & 89 & \(-\)2.87 & 0.01 & 0.00 & 0.11 & \(-\)26.60 \\  & 1350\(-\)\(\lambda\)1450 & 230,735 & 502 & \(-\)0.37 & 0.00 & 0.00 & 0.05 & \(-\)7.52 \\  & 1450\(-\)1600 & 133,305 & 1057 & 0.33 & 0.00 & 0.00 & 0.00 & 0.00 \\  & \(>\)1600 & 85,376 & 1074 & 1.88 & 0.00 & 0.00 & 0.04 & 47.95 \\ \hline \multirow{8}{*}{2} & \(<\)5 & 705,163 & 896 & \(-\)1.83 & 0.00 & 0.00 & 0.04 & \(-\)44.90 \\  & 5\(\sim\)\(<\)10 & 171,923 & 1259 & 1.34 & 0.00 & 0.00 & 0.04 & 34.96 \\ \cline{1-1}  & 10\(-\)\(\lambda\)15 & 38,854 & 397 & 1.38 & 0.00 & 0.00 & 0.05 & 25.36 \\ \cline{1-1}  & 15\(-\)\(\)\(\lambda\)20 & 13,936 & 121 & 1.13 & 0.01 & 0.00 & 0.09 & 12.13 \\ \cline{1-1}  & 20\(-\)\(\lambda\)25 & 6223 & 50 & 1.03 & 0.02 & 0.00 & 0.14 & 7.22 \\ \cline{1-1}  & 25\(-\)\(\lambda\)30 & 3396 & 15 & 0.42 & 0.07 & 0.00 & 0.26 & 1.62 \\ \cline{1-1}  & \(>\)30 & 2584 & 5 & \(-\)0.41 & 0.20 & 0.00 & 0.45 & \(-\)0.92 \\ \hline \end{tabular}
\end{table}
Table 3: Relationship between conditioning factors and gully erosion using weights-of-evidence (WoE) model.