## 2 Materials and Methods
### Methodology
#### 2.2.2 Gully Conditioning Factors  
Gully erosion is a complex process that results from the interplay of numerous factors [106; 107]. After reviewing gully erosion literature and considering local conditions and available data, we selected 12 topographic, hydrological, geological, and anthropogenic factors for inclusion in the modeling process.  
The topographic factors chosen for this study are elevation, aspect, slope gradient, plan curvature, and profile curvature. The hydrological parameters are distance to rivers and drainage density. We extracted topographic and hydrological factors from a digital elevation model (DEM) obtained from ALOS PALSAR (Phased Array Type L-band Synthetic Aperture Radar) data, with a cell size \(12.5\times 12.5\) m ([[http://www.eorc.jaxa.jp/ALOS/en/aw3d30](http://www.eorc.jaxa.jp/ALOS/en/aw3d30)]([http://www.eorc.jaxa.jp/ALOS/en/aw3d30](http://www.eorc.jaxa.jp/ALOS/en/aw3d30))) and prepared in ArcGIS 10.3 [93].  
The elevation map has four classes (1800-2000, 2000-2200, 2200-2400, and \(>\)2400 m a.s.l) (Figure 4a). The highest gully frequency ratio (FR) is associated with the 1800-2000 m class (FR ratio = 1.16). The gully aspect map (Figure 4b) has nine classes, and the highest FR values are in the east, northeast, and southeast aspect classes, with values of, respectively, 1.30, 1.17, and 1.13. The slope gradient map has five classes: 0-5%, 5-10%, 10-20%, 20-30%, and \(>\)30% (Figure 4c). The 5-10% class has the highest FR value (1.23). Plan curvature was categorized as convex, flat, and concave forms (Figure 4d). Most gully erosion in the study area occurs in areas mapped as flat (FR = 1.09). There are three classes of profile curvature (\(<-0.35\), \(-0.35\)-0.25, and \(>\)0.25) (Figure 4e). The \(<\)\(-0.35\) class has the highest FR value (1.18).  
Figure 4: \(Cont.\)  
Changing land use, for example deforestation and grazing, is an important cause of soil erosion [76]. For the current study, land use was inferred from Landsat 8 (OLI) satellite imagery and analyzed and processed with the ENVI 5.4 software. The land-use map includes three classes--agriculture, bare land, and rangeland (Figure 4i). Most gullies in the study area are found in the bare land class (FR = 1.21), and lowest number are in the rangeland class (FR = 0.62).  
The incidence of gully erosion is greatest in areas with limited vegetation cover. A normalized difference vegetation index (NDVI) map of the study area was generated in ArcGIS 10.3 from Landsat 8 imagery acquired on 15 June 2017. This map is based on the formula (NIR-Red)/(NIR+Red), where NIR (near-infrared) is band 5 and Red is band 4 of the Landsat 8 imagery. The map includes three NDVI classes: -0.12-0.07, 0.07-0.12, and 0.12-0.37 (Figure 4j). The 0.12-0.37 map class has the largest number of gullies.  
Roads also affect gully erosion, as they intercept and concentrate overland flow [109; 110]. This factor is represented by distances of gully and non-gully sites from roads, which were determined by vectorizing topographic maps and then transforming the data to a raster map using the Euclidean Distance tool in Arc GIS 10.3. Five classes were defined: 0-100, 100-200, 200-500, 500-1000, and \(>\)1000 m (Figure 4i). The largest and smallest number of gullies in the study area are, respectively, in the 200-500 m (FR = 1.10) and 0-100 m (FR = 0.73) classes.