## 2 Materials and Methods
### Methods
#### 2.2.2 The USLE Calculation
Given the necessity of these determining factors, we can conclude that the LS is a sensitive aspect of soil loss prediction by the USLE model [66]. The LS factor is usually limited to a maximum slope angle by 26.6 degrees [67]. Many researchers have proposed a variety of algorithms to overcome this limitation [68; 69]. For example, a recent research [61] has suggested that the formula to calculate L (Equation (3)) which was proposed by [PERSON] and [PERSON] [70] is appropriate for landscape-scale soil erosion modeling and can capture complex topography. \[\mathrm{L}=\frac{\left(\mathrm{A_{ij}+D^{2}}\right)^{m+1}+\mathrm{A_{ij}^{m+1}} }{\mathrm{D^{m+2}\times X_{ij}^{m}\times 22.13^{m}}} \tag{3}\]  
where \(\mathrm{A_{ij}}\) is the contributing area at the inlet of the grid cell (i,j) measured in \(\mathrm{m^{2}}\); \(\mathrm{D}\) is the grid cell size in meters; \(\mathrm{X_{ij}^{m}}\) is equal to \(\sin\ \mathrm{a_{ij}+\cos\ \mathrm{a_{ij}}}\) whereas \(\mathrm{a_{ij}}\) is the aspect direction of the grid cell (i,j); \(\mathrm{m}\) is related to the ratio \(\beta\) of the rill to interill erosion. It is calculated by Equations (4) and (5). \[\mathrm{m}=\frac{\beta}{\beta+1} \tag{4}\]  
\[\beta=\frac{\frac{\sin\ \theta}{0.0896}}{\left[0.56+3\times\left(\sin\ \theta \right)^{0.8}\right]} \tag{5}\]  
In accounting for S factor, the research method of [PERSON] [68] suggests a continuous logistic function (Equation (6)) to estimate the S in the upland area. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Soil Type** & **K Value**[57] & **Area (Hectares)** \\ \hline Arenic Acrisols & 0.28 & 6768 \\ Ferralic Arcrisols & 0.32 & 944 \\ Dystric Fluvisols & 0.44 & 158 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: K factor and soil type in research site. \[S=-1.5+\frac{17}{(1+e^{2.3-6.1\times\sin\ \theta})} \tag{6}\]  
where \(\theta\) is slope angle in degrees. Cropping Management Factor (C)  
This factor depends on the type of crop and the duration of growth, however growing conditions tend to change locally, and the harvesting time is unpredictable [71; 72], therefore it is a difficult factor to measure. Considering this, to determine the C factor it is helpful to reference studies that have reported values for similar land cover [49]. Also, remote sensing data are able to provide information on environmental covariates to predict the C. This helps to avoid the time and cost for investigation in the field [73]. In addition, NDVI which is gathered from satellite imagery, is a common indicator of the C factor calculation [74; 75]. For the tropical regions, [PERSON] et al. [76] developed an equation for obtaining the C-factor by using NDVI. It was applied in this research as Equations (7) and (8). \[C=\frac{(1-\text{NDVI})}{2} \tag{7}\]  
where  
\[\text{NDVI}=\frac{\text{NIR}-\text{RED}}{\text{NIR}+\text{RED}} \tag{8}\]  
In the case, NIR is the surface spectral reflectance in the near-infrared band and RED is the surface spectral reflectance in the red band. NIR and RED were extracted from Landsat 8-Operational Land Imager (OLI) images which were downloaded from the website of the US Geological Survey ([[https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov)]([https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov))). The information of images data are described in Table 2.  
Practice Support Factor (P)  
In the USLE equation, the P factor is used to assess the effectiveness of farming methods, which reflects the effect of practices to protect and limit soil erosion. The values for the P factor are the least reliable in comparison to other factors of the USLE equation [59; 77]. As a result, some researchers often skip this factor and assigned it a value of 1 [11; 78]. However, a number of studies have reported that P factors can be determined based on remote sensing data or previous studies [49; 61]. Some studies used slope classification as a source to calculate \(p\)-value [79], while others used the land use type [80] as an identified indicator for \(p\)-value.