## 2 Materials and Methods
### RUSLE Model
#### 2.3.2 Implementation of RUSLE Model Rainfall Erosivity (R) Factor  
The R-factor for any given period is obtained by summing for each rainstorm the product of total storm energy (\(E\)) and the maximum 30 min intensity (\(I_{30}\)) according to the standard equations used by [PERSON] and [PERSON] [26]. Since detailed rainstorm data are rarely available at standard meteorological stations, daily, monthly, and annual rainfall amounts are often used to estimate the R-factor for the RUSLE. Furthermore, [PERSON] and [PERSON] [27] developed a simple threshold-type regression model that uses daily rainfall data to estimate monthly rainfall erosivity. Their equation was then calibrated and validated for Crete by [PERSON] et al. [28]. The equation considers the monthly rainfall for days with rain greater than 10 mm, as well as the number of the days of month with rainfall greater than 10 mm, as follows:  
\[R=\frac{1}{n}\sum_{j=1}^{n}\sum_{k=1}^{mj}(7.5\times R_{10}-150\times D_{10})_ {k,j} \tag{2}\]  
where \(R_{10}\) is the total rainfall within a month (mm), only for the days with rainfall \(>\)10.0 mm (otherwise, set to zero); \(D_{10}\) is the number of days with rainfall \(>\) 10.0 mm; \(n\) is the number of days covered by the rainfall data; \(k\) is the individual erosive events for each month \(j\); and \(mj\) is the total number of erosive events for each month. The spatial resolution of the downloaded GPM_3 IMERGDL v06 (D: Daily, L: Late run) products is 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\). Consequently, these datasets were downscaled to 10 \(\times\) 10 m. In their studies, [PERSON] and [PERSON] [29] and [PERSON] et al. [30] downscaled the TRMM and GPM datasets, respectively, assuming that the precipitation and other environmental factors (vegetation, topography, albedo, and drought) are strongly related. The downscaling process can be expressed by:  
\[P=f(X_{i})+\varepsilon \tag{3}\]  
where \(P\) is downscaled precipitation, \(X_{i}\) represents environmental variables, and \(\varepsilon\) is the residual. The general approach is to establish a correlation function (\(f\)) between precipitation and environmental variables at coarse resolution and then to use the fine-resolution environmental variable as inputs of (\(f\)) to predict precipitation at fine resolution. Consequently, the downscaled precipitation data are estimated through the equation below:  
\[P_{\text{downscaled}}=P_{\text{estimated}}+P_{\text{residual}} \tag{4}\]  
where \(P_{\text{downscale}}\) is the downscaled precipitation, \(P_{\text{estimated}}\) is the high spatial resolution precipitation estimated from various environmental factors, and \(P_{\text{residual}}\) is the residual between estimated precipitation and GPM. For the west part of Crete, [PERSON] and [PERSON] [29] concluded that the multiple linear regression (MLR) approach performed slightly better than artificial neural network analysis; hence, in this study, the MLR methodology was used for downscaling purposes. With this aim, DEM and NDVI were tested as explanatory variables in the MLR-based downscaling algorithms to downscale GPM monthly precipitation from 10 km \(\times\) 10 km to 10 m \(\times\) 10 m over the study area. The downscaling process was performed following certain analysis steps described previously by [PERSON] and [PERSON] [29]. In order to achieve the MLR analysis, the least squares method was applied to determine the coefficients using the XLSTAT add-in for Microsoft Excel. This is a standard approach in regression analysis based on minimizing the sum of the squares of the residuals between the observed response and the fitted response. The typical form of the model is:  
\[P=ax+b \tag{5}\]  
where \(P\) is the daily precipitation, \(x\) is the DEM, \(a\) is the DEM slope, and \(b\) is the intercept. The daily ground precipitation data for 2020 extracted from 5 stations in Chania prefecture were used to validate the downscaled products.