## 3 Methods
Each factor's ratio value was calculated using Equation (2):  
\[VR_{jk}=\frac{V_{jk}^{*}}{V_{jk}}/\frac{T^{*}}{T} \tag{2}\]  
\(VR_{jk}=\) volume ratio of each factor; \(V_{jk}\)* = volume of observed landslide of class \"\(k\)\" of factor \"\(j\)\"; \(V_{jk}=\) volume of class \"\(k\)\" of factor \"\(j\)\"; \(T=\) typical value of the map, such as the total area of the map, the average distance to roads or rivers in each class, the average elevation of each class, and the average rainfall of each class. \(T\)* = typical value of the observed landslide of the map, such as the total area of each class, the average distance of the landslide to roads or rivers, the average elevation of the landslide, and the average rainfall of the landslide. A value of 1 is the neutral value, and the values higher than 1 show a high positive correlation with a certain factor of the landslide [26]. A higher VR value shows that a higher probability of the landslide volume occurs. The RIRA is a method of sensitivity analysis used by calculating the relationship between dependent variables and independent variables. RIRA can assess the relative contribution of each variable by placing greater emphasis on known variables contributing to landslides, and which are sorted by contribution [22]. In addition, each variable has a specific value in the method, which ensures the objectivity of the data calculation. To eliminate the dimensional impact between the independent variables, all data of the factors were standardized using the z-scores method before calculation. The dependent variables (such as the amount of landslide) and the independent variables (such as profile curvature, slope, altitude, NDVI, land-use, geology, distance to rivers, distance to roads, and rainfall) were listed separately. The variables were sorted in order from small to large, and the sensitivity coefficients of each influencing factor were calculated. In order to quantify the impact of landslide-related factors on the landslide, the calculation steps of RIRA were as follows: first, the landslide increase rate (%) was calculated using Equation (3):  
\[RP_{i}=\frac{2(P_{i}-P_{i-1})}{P_{i}+P_{i-1}} \tag{3}\]  
where \(P_{i}\) is the amount of the \(i\)-th landslide (104 m\({}^{3}\)). Then, the increase rate (%) of each impact factor on the landslide was calculated as follows:  
\[R_{i}=\frac{2(t_{i}-t_{i-1})}{t_{i}+t_{i-1}} \tag{4}\]where \(t_{i}\) and \(t_{i-1}\) are the values of the explanatory variable that are sequentially connected. \(Rt_{i}\) is the increase rate calculated for two successively independent variables ordered by the values. Therefore, the Absolute Sensitivity Parameter (s), towards an independent variable, \(t\), was calculated by its mean growth rate:  
\[s_{aj}=\left|\overline{(RP_{i,j}/Rt_{i,j})}_{i=1,N}\right| \tag{5}\]  
Being \(j\) the \(j\)-th independent variable, \(N\) the total number of landslide data, namely slope, aspect, altitude, NDVI, land use, geology, distance to rivers and distance to roads. A factor with a larger absolute value of the s represents the higher sensitivity of the amount of the landslide to the related factor. In the study, the revised increase-rate-analysis (RIRA) method is used to assess the relationship between the factors and landslide. At last, the landslide susceptibility of each subclass was calculated by Equation (6):  
\[S_{ak}=s_{aj}\times VR_{jk} \tag{6}\]  
\(S_{ak}\) is the susceptibility of each \(k\)-\(th\) class. Then, each class susceptibility map can be obtained using the \(S_{ak}\) value in the ArcGIS software. At last, all thematic layers were combined using the \(S_{ak}\) value to derive the landslide susceptibility map of the Yangou watershed. Calculated susceptibility values were classified into areas of very low, low, medium, high, and very high susceptibility using the natural break method available within the ArcGIS software.