## 2 Materials and Methods
### RUSLE Model
#### Cover Management (C) Factor
The _NDVI_ is a commonly used spectral index that calculates the spectral reflectance difference between red and near-infrared bands of a satellite image according to the following equation:  
\[NDVI=\frac{(NIR-RED)}{(NIR+RED)} \tag{15}\]  
where _NIR_ is the near-infrared band and _RED_ is the red band of the satellite image. The _NDVI_ index ranges from \(-1\) to \(+1\), with the highest values attributed to areas with greater vegetation cover [40]. Many empirical equations have been set up to correlate _NDVI_ values to C-factor values. The C-factor can be derived using the equation proposed by [PERSON] et al. [36], C(vk), which was based on the positive correlation between the _NDVI_ and C-factor in Europe:  
\[C(\text{vk})=e^{[-\alpha(\frac{NDVI}{p-NDVI})]} \tag{16}\] \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{3}{c}{**Corine**} \\ \hline
**Code** & **Label** & **C-Factor** \\ \hline
212 & Permanently irrigated land & 0.1307 \\ \hline
223 & Olive groves & 0.2094 \\ \hline
231 & Pasture & 0.1132 \\ \hline
242 & Complex cultivation patterns & 0.1476 \\ \hline
243 & Land principally occupied by agriculture with & 0.1307 \\  & significant areas of natural vegetation & \\ \hline
311 & Broadleaf forest & 0.0014 \\ \hline
313 & Mixed forest & 0.0014 \\ \hline
321 & Natural grassland & 0.0014 \\ \hline
323 & Sclerophyllous vegetation & 0.0014 \\ \hline
324 & Transitional woodland–shrubs & 0.026 \\ \hline
333 & Sparsely vegetated areas & 0.3062 \\ \hline \end{tabular}
\end{table} 
Table 4: Assigned C-factor values from literature [22]. where \(\alpha\) and \(\beta\) are parameters related to the shape of the curve that associates \(NDVI\) with the C-factor. Furthermore, [PERSON] et al. (2018) assumed that for European climate conditions, an \(\alpha\)-value of 2 and a \(\beta\)-value of 1 seem to be best representative of the equation parameters. [PERSON] et al. (2018) suggested another equation based on \(NDVI\) rescaling, named the denominated rescaled C-factor (C(r)). They found that this equation was more suitable for deriving C-factor values under tropical climate conditions. \[\mathrm{C(r)}=\frac{-NDVI+1}{2} \tag{17}\]  
Furthermore, an improved vegetation-index-based method is available for evaluating the fractional vegetation cover. It efficiently distinguishes between areas of dense vegetation cover and sparsely vegetated areas. \[FVC(\%)=\frac{NDVI-NDVI_{\mathrm{soil}}}{NDVI_{\mathrm{veg}}-NDVI_{\mathrm{soil }}}\times 100 \tag{18}\]  
where \(NDVI\) is the vegetation index of each pixel, \(NDVI_{\mathrm{soil}}\) corresponds to the vegetation index of a \"pure\" soil pixel, and \(NDVI_{\mathrm{veg}}\) corresponds to the vegetation index of a \"pure\" vegetation pixel. It is necessary to determine the \(NDVI\) values for \"pure\" soil and vegetation pixels, respectively. [PERSON] et al. (2018) mentioned that the \(NDVI_{\mathrm{soil}}\) value is around zero for a bare surface; however, this can vary depending on soil conditions (such as soil moisture, roughness, type, and color); thus, this value can be extracted based on the image data. Regarding the \(NDVI_{\mathrm{veg}}\) value, this corresponds to the maximum value for all vegetation pixels. Similar to \(NDVI_{\mathrm{soil}}\), the \(NDVI_{\mathrm{veg}}\) value can change depending on the vegetation type, the seasonal change of the canopy, and other conditions. In order to estimate these values, [PERSON] et al. (2018) proposed an approach based on the derived histogram of the \(NDVI\) data of the image. In fact, the \(NDVI\) value that accounted for 1% of pixels of the histogram was set as \(NDVI_{\mathrm{soil}}\), while the \(NDVI\) value that accounted for 99% of the pixels was set as \(NDVI_{\mathrm{veg}}\). The \(NDVI\) histogram is plotted in the following figure. In this study, \(NDVI_{\mathrm{soil}}\) was estimated as 0.102 and \(NDVI_{\mathrm{veg}}\) was estimated as 0.875. Once the FVC map is derived, [PERSON] et al.