## 2 Materials and Methods
### RUSLE Model
#### 2.3.2 Implementation of RUSLE Model Rainfall Erosivity (R) Factor
In order to evaluate the downscaling method quantitatively, three different statistical methods were calculated, namely the root mean square error (\(RMSE\)), the bias, and the coefficient of determination (R\({}^{2}\)):  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}{(P_{i}-O_{i})}^{2}}{n}} \tag{6}\]  
\[Bias=\frac{\sum_{i=1}^{n}{P_{i}}}{\sum_{i=1}^{n}{O_{i}}}-1 \tag{7}\]  
\[R^{2}=\frac{\sum_{i=1}^{n}{\left[{(P_{i}-\overline{P})\left({O_{i}-\overline{ O}}\right)}\right]}}{\sqrt{\sum_{i=1}^{n}{(P_{i}-\overline{P})}^{2}}}\sqrt{\sum_{i=1} ^{n}{(O_{i}-\overline{O})}^{2}} \tag{8}\]  
where \(P_{i}\) is the downscaled precipitation and \(\overline{P}\) is the mean precipitation, \(O_{i}\) is the ground-observed precipitation and \(\overline{O}\) is the mean ground-observed precipitation, and \(n\) is the number of observations. The daily temporal-resolution precipitation measurements were also used to derive the R-factor by applying Equation (2). In this study, the R-factor was estimated at the point level (precipitation stations). The predicted R-values were then extrapolated to the catchment level using ordinary kriging-based interpolation in the ArcGIS environment. Soil Erodibility (K) Factor  
The most commonly used equation to estimate the K-factor (t ha h ha\({}^{-1}\) MJ\({}^{-1}\) mm\({}^{-1}\)) was proposed by [PERSON] and [PERSON] [24] and reported in the study by [PERSON] et al. [15]:  
\[K=\left[{\left({2.1M^{1.14}\ (12-OM)\ 10^{-4}+3.25\ (s-2)+2.5\ (p-3)}\right)/100} \right]\times 0.1317 \tag{9}\]  
where \(M\) is the textural factor, with \(M=\left({m_{silt}+m_{vfs}}\right)\times\left({100-m_{c}}\right)\); \(m_{c}\) (%) is the clay fraction content (<0.002 mm), \(m_{silt}\) (%) is the silt fraction content (0.002-0.063 mm), \(m_{vfs}\) (%) is the very fine sand fraction content (0.063-0.1 mm), \(OM\) (%) is the organic matter content, \(s\) is the soil structure class, and \(p\) is the permeability class. The suggested erodibility equation can only be recommended if the organic matter content is known and the silt content is below 70%. [PERSON] et al. [15] mentioned that if both criteria are met, this equation is more precise than other equations. Additionally, in the literature, the sand fraction is classified into five classes: very fine, fine, medium, coarse, and very coarse. The very fine sand structure (0.05-0.1 mm) as a sub-factor (\(m_{vfs}\)) in Equation (9) is estimated as 20% of the sand fraction (0.063-2.0 mm);this information is available in the LUCAS topsoil database. In the European Soil Database, soil structure is categorized as humic, poor, normal, or good, as shown in Table 2.  
This dataset was used to determine the structure class values needed for K-factor calculation. In this study, and according to the ESDB, the soil structure was good, corresponding to a very fine granular soil structure; thus, the structure class was 1. In order to determine the permeability class values, the percentage of the soil content (sand, silt, and clay) were plotted in the textural triangle diagram to define the soil texture. According to this classification, the corresponding permeability class was assigned (Table 3). In this study, the soil texture was silty clay loam corresponding to permeability class 5. Once the K-values were calculated for every LUCAS point, they were interpolated to a map using the inverse distance weighting (IDW) method. The IDW is based on the assumption that the soil erodibility at an unsampled point is a distance weighting average of soil erodibility values of the nearby sampling points. Slope Length-Steepness (LS) Factor  
To extract the LS-factor, many algorithms are already built into GIS software programs, such as the System for Automated Geoscientific Analyses SAGA GIS [31]. In fact, SAGA provides numerous combinations of algorithms to derive the topographic data and preprocessing algorithms to fill sinks or for sink removal.