## 3 Materials and Methods
### Methodology
#### 3.2.2 Revised Universal Soil Loss Equation (RUSLE)  
The Revised Universal Soil Loss Equation (RUSLE) model provides a widely known and useful tool for soil erosion assessment [2; 22; 47; 48]. Developed in the late 1970s [23], it was formulated so as to conclude a better estimation of the initial parameters defined by the Universal Soil Loss Equation (USLE) [49]. The derived methodology represents the influence of topography, soil properties, meteorological parameters, and land cover on surface and fill erosion [2; 47; 48]. The average soil loss assessment is enabled by the RUSLE according to the specific study area characteristics [2] and it is based on an empirical equation (Equation (4)), constituting of five factors [24], which can be easily implemented through a GIS framework:  
\[A=R\times K\times LS\times C\times P \tag{4}\]  
where \(A\) is the estimated mean seasonal soil loss (ton h\({}^{-1}\) Season\({}^{-1}\)), \(R\) represents the rainfall erosivity factor (MJ mm ha\({}^{-1}\) h\({}^{-1}\) Season\({}^{-1}\)), \(K\) is the soil erodibility factor (ton h MJ\({}^{-1}\) mm\({}^{-1}\)), \(LS\) is the slope length and steepness factor (dimensionless), \(C\) is the cover management factor (dimensionless), and \(P\) represents the conservation practice factor (dimensionless). These factors are of vital meaning in soil erosion assessment, and they should be very carefully estimated in order to lead to highly accurate results (source). \(R\) factor plays a crucial role in RUSLE modeling since it defines the possibility of erosion risk [49] and it is estimated based on meteorological data from meteorological stations surrounding the study areas as previously mentioned [50]. Using the empirical \begin{table}
\begin{tabular}{c c} \hline \hline
**dNBR Value*** & **Burn Severity** \\ \hline
0.100–0.269 & Low severity \\ \hline
0.270–0.439 & Moderate-low severity \\ \hline
0.440–0.659 & Moderate-high severity \\ \hline
0.660–1.300 & High severity \\ \hline \hline \end{tabular}  
* Values \(\leq\) 0.099 represent unburned areas.  
\end{table} 
Table 3: Burn severity classification according to dNBR values [16; 46]. formulation (Equation (5)) developed by [PERSON] and [PERSON] [50], monthly rainfall data concerning seasonal time periods of 2021, were used to calculate the \(R\) factor:  
\[R=\frac{\sum_{i=1}^{12}(7.05\times r_{10}-88.92\times d_{10})}{N} \tag{5}\]  
where \(R\) represents the rainfall exposivity factor (MJ mm ha\({}^{-1}\) h\({}^{-1}\) season\({}^{-1}\)), \(N\) is the total months calculated annually, \(r_{10}\) is the monthly rainfall exceeding 10 mm, and \(d_{10}\) is the number of days when daily rainfall exceeded 10 mm per month. Specifically, rainfall data acquired from each weather station were implemented using a spatial interpolation technique, inverse distance weighting (IDW), so as to define unknown meteorological values within the study areas. \(K\) factor refers to the rainfall impact on soil properties resulting in soil erosion due to sediment penetration, detachment, and transport [23; 24; 27]. The soil erodibility factor is affected by soil properties such as structure, organic matter, permeability, and soil texture [48]. In this study, the estimation of the \(K\) factor was based on Equation (6) developed by [PERSON] and [PERSON] [51]:  
\[ \begin{split}=0.2+0.3\exp\Bigl{(}0.0256\times Sa\times\left(1- \frac{Si}{100}\right)\Bigr{)}\times\left(\frac{Si}{Cl+Si}\right)^{0.3}\times \left(1.0-\frac{0.25\times C}{C+\exp(3.72-2.95C)}\right)\\ \times(1-\frac{0.2\times SN}{SN+\exp(-5.51+22.95N)})\end{split}  \tag{6}\]  
where \(K\) is the soil erodibility factor (ton h MJ\({}^{-1}\) mm\({}^{-1}\)), \(Sa\) represents the percentage of salt, \(Si\) is the percentage of silt, \(Cl\) is the percentage of clay, \(C\) is the percentage of organic carbon, and \(SN\) stands for SN = 1 \(-\) (Sa/100). Soil data acquisition was based on datasets provided by the ESDAC database [37].