## Materials and Methods
### Data and Method  
Figure 2 shows the methodological approach applied to map GE susceptibility in the Shahroud watershed using BRT, MARS, and RF models. For preparing an accurate and reliable gully inventory map, extensive field surveys with a DGPS device were performed in the study area to determine the location of the Gullies [27; 28]. Then, among 172 detected gully locations, randomly (70/30 ratio), 121 gully locations (70%) and 51 gully locations (30%) in the polygon format were used for training the  
Figure 1: (**a**) Location of the Semnan provinces in Iran, (**b**) location of study area, and (**c**) gully erosion locations with the digital elevation model map of the Shahroud watershed. testing models [28]. The locations of training and testing gullies are shown in Figure 1. Interventionary studies involving animals or humans, and other studies require ethical approval must list the authority that provided approval and the corresponding ethical approval code. The tools used in present study are ArcGIS10.5, ENVI 4.8, SAGA-GIS 2.1.1, and a DGPS. The basic maps used were geological maps [33], at a scale of 1:100,000, topographic maps, at a scale of 1:50,000, satellite images acquired by Landsat8, and ASTER GDEM with spatial resolution of 30 m [34]. In this study, based on literature review [24; 26; 31] and local conditions of the study area, twelve factors were selected. Elevation map was divided into six classes: \(<\)1200 m, 1200\(\sim\)1350 m, 1350\(\sim\)1450 m, 1450-1600 m, and \(>\)1600 m (Figure 3a). Slope degree affects surface runoff [35], soil erosion, and pattern of drainage density. Slope degree map was classified into six classes [24; 26]: \(<\)5\({}^{\circ}\), 5\(\sim\)10\({}^{\circ}\), 10\(\sim\)15\({}^{\circ}\), 15\(\sim\)20\({}^{\circ}\), 20\(\sim\)25\({}^{\circ}\), 25-30\({}^{\circ}\), and \(>\)30\({}^{\circ}\) (Figure 3b). The aspect map was classified into nine classes (Figure 3c). Positive and negative values of plan curvatures define convexity and concavity of slope curvature, whereas zero is flat surface. The plan curvature map was divided into 3 categories: Concave, Flat, and Convex. The TWI indicator is important for identifying prone areas to GE [36]. TWI is calculated by Equation (1):  
\[\text{TWI}=\text{ln}\bigg{(}\frac{\text{S}}{\text{tan}\propto}\bigg{)} \tag{1}\]  
TWI map of study area is divided into four classes [24; 26; 37] including \(<\)5, 5\(\sim\)\(<\)7.5, 7.5-11, and \(>\)11 (Figure 3e). The convergence index (CI) gives a measure of how flow in a cell diverges (convergence  
Figure 2: Flowchart of research methodology. index in negative and positive values) [38]. The CI map was prepared in SAGA-GIS 2.1.1 and divided into 3 classes: <0, 0-10, and >10 (Figure 3f). In this research, for the computation of the effect of drainage network and infrastructures on GE, the distance from rivers and roads was considered [14] and divided into four classes: <170 m, 170-<370 m, 370-650 m, and >650 m for rivers (Figure 3g) and <500 m, 500-<1500 m, 1500-3000 m, and >3000 m for roads (Figure 3h). The line density tool in ArcGIS 10.5 was used for calculating drainage density and then its map was divided into four categories: <1.4, 1.4-<2.4, 2.4-3.7, and >3.7 km/km2 (Figure 3i). A geological map at a 1:100,000 scale was used to prepare the lithological unit layer. The lithological units were classified into ten categories based on their sensitivity to gully occurrence using expert knowledge method (Figure 3j and Table 1). The advantage of this method is it is easy to use, however this method has certain disadvantages, such as the possibility of a mistake by the expert. The LU/LC map was obtained using Landsat 8 images [39; 40; 41]. The main LU/LC types identified in the study area were range, irrigation farming, and bare lands (Figure 3k). The NDVI map was also produced using Landsat 8 images and classified into 3 categories: <0.11, 0.11-0.25, and >0.25 (Figure 3l). For multi-collinearity checking, the tolerance (TOL) and variance inflation factor (VIF) were used.