## 2 Material and Methods
### Methods
#### 2.3.9 Geographical Detector  
The geographical detector is a technique for detecting the regionally stratified heterogeneity of processes, which reveals the driving factors behind them [44]. Four units make up the geographical detector: factor detector, risk detector, interaction detector, and ecological detector. The geographical detector measures the degree of spatial stratified heterogeneity, which is a phenomenon where the sum of the intra-layer variance is less than the sum of the inter-layer variance; it measures value \(q\).  
The \(q\) value increases as the effect of various environmental factors on the spatial variation of soil erosion increases [45]. \(q\) is used to measure the extent of such influence. Its expression is as follows:  
\[q=1-\frac{\sum_{k=1}^{L}{N_{h}{\sigma_{h}}^{2}}}{N{\sigma^{2}}}=1-\frac{SSW}{ SST} \tag{15}\]  
\[SSW=\sum_{h}^{L}{N_{h}{\sigma_{h}}^{2}} \tag{16}\]  
\[SST=N{\sigma^{2}} \tag{17}\]  
where \(h=\)1, 2... is the classification or partition of the independent variable. \(N_{h}\) and \(N\) are the number of cells in layer \(h\) and the whole zone, respectively. \(\sigma_{h}\) and \(\sigma\) are the variances of the Y-values of layer \(h\) and the whole region, respectively. \(SSW\) is the sum of the within-stratum variance. \(SST\) is the total variance of the region. \(q\) is the explanatory power of the independent variable on the dependent variable, with a value range of [0, 1].  
The geodetector also has the function of interaction detection, which may examine how multiple factors interact, i.e., to determine if factors X1 and X2 combined strengthen or weaken the ability of variable Y to explain itself and also to calculate whether these factors are apart from one another. The calculation technique determines the explanatory power q1 and q2 of the two factors, respectively, and then calculates the g value of the new polygon created by the tangent of the two variable polygons superimposed. Table 1 depicts the connection between the two factors in comparison to the single factor's explanatory power [13]. The basis of interaction is shown in Table 1. To assess if there is a substantial variation in the average value of the characteristics between the factor regions, the risk detector is often utilized. By doing this, high-risk sites for soil erosion may be found.  
NDVI, rainfall, slope, and terrain elevation were used as land use type drivers to identify the dominant land use type drivers in the Loess Plateau forest management sub-region. When soil erosion is used as the dependent variable, LUCC is added as the influencing factor to complete the exploration of the main driving factors of soil erosion in the research area. According to the requirements of the geographical detector, combining the data discretization approach suggested by [PERSON] et al. [44] resulted in the discretization of continuous-type data. Among them, land use data were classified according to categories, and data on vegetation cover were separated into eight groups (<0.3, 0.3-0.4, 0.4-0.5, 0.5-0.6, 0.6-0.7, 0.7-0.8, 0.8-0.9, 0.9-1); according to the equal spacing approach, average annual precipitation data were split into nine categories, while slope data were sorted into eight categories (<5\({}^{\circ}\), 5\({}^{\circ}\)-10\({}^{\circ}\), 10\({}^{\circ}\)-15\({}^{\circ}\), 15\({}^{\circ}\)-20\({}^{\circ}\), 20\({}^{\circ}\)-25\({}^{\circ}\), 25\({}^{\circ}\)-30\({}^{\circ}\), 30\({}^{\circ}\)-35\({}^{\circ}\), >35\({}^{\circ}\)). The above-mentioned attribute values are provided as the operational data of the geographical detector. Elevation data were sorted into eight groups using the equal natural break point approach.