# Spatial-Temporal Variability of Future Rainfall Erosivity and Its Impact on Soil Loss Risk in Kenya
## 2 Materials and Methods
### Methodological Framework
#### 2.4.2 Rainfall Erosivity (R) Factor  
Rainfall erosivity is the most significant factor in the RUSLE model ([23; 67]); it influences approximately 80% of the total soil loss. The rainfall erosivity factor is the product of raindrop kinetic energy (\(E\)) and the maximum 30 min rainfall intensity (\(I_{30}\)) [64]. Acquiring complete pluviographic data (with a minimum of 20 years in order to capture cyclical rainfall dynamics) is a huge setback in African countries due to insufficient gauged meteorological stations [49]. Different approaches have been used to derive the \(R\) factor within Kenya. [PERSON] et al. [9] and [PERSON] et al. [44] utilized the Fourier index (Equations (2)-(4)) and Modified Fourier Index (Equations (5) and (6)), respectively, while [PERSON] [49] applied the model suggested by reference [64] (Equation (7)) to compute rainfall erosivity for the entire coast of Kenya. With access to some rainfall intensity data, [PERSON] [48] and [PERSON] [68] used (Equations (8)-(10)) to determine estimates for the western and central regions, respectively. Various regression realizations have also been exploited, including [PERSON] and [PERSON] (Equations (11) and (12)) [44], [PERSON] (Equations (13) and (14)) [44] and [PERSON] et al. (Equation (15)) [47]. \[FI\,=\frac{P^{2}i}{P} \tag{2}\]  
\[r_{i}=\frac{125.92\times F\Omega^{0.603}+111.173\times F\Omega^{0.691}+68.73 \times F\Omega^{0.841}}{3} \tag{3}\]  
\[R=\sum_{i=1}^{12}r_{i} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Variables** & **Resolution** & **Sources** \\ \hline \multirow{4}{*}{Elevation} & DEM & 30 m & Shuttle Radar Topography Mission (SRTM) [65] \\  & Slope & 30 m & Shuttle Radar Topography Mission (SRTM) \\  & Flow Accumulation & 30 m & Shuttle Radar Topography Mission (SRTM) \\  & Aspect & 30 m & Shuttle Radar Topography Mission (SRTM) \\ \hline \multirow{4}{*}{Climate} & Baseline Precipitation & 1 km & WorldClim \\  & Observed Precipitation & & Kenya Meteorological Department (KMD) \\  & Predicted Precipitation & & CCAFS \\ \hline Land & Land use land cover & 20 m & CCI-LULC [57] \\ \hline \multirow{4}{*}{Soil} & Sand & 250 m & AfSIS ([[http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m)]([http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m))) [66] \\  & Silt & 250 m & AfSIS ([[http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m)]([http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m))) \\ \cline{1-1}  & Clay & 250 m & AfSIS ([[http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m)]([http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m))) \\ \cline{1-1}  & Organic carbon & 250 m & AfSIS ([[http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m)]([http://www.isric.org/data/afsoilgrids250m](http://www.isric.org/data/afsoilgrids250m))) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data sources for the different datasets applied in this study. where \(P_{i}\) is the average monthly rainfall (mm) for month \(i\), \(P\) is the mean annual precipitation (mm) and \(r_{i}\) is the average monthly erosivity (MJ mm ha\({}^{-1}\) h\({}^{-1}\) month\({}^{-1}\)). \[R_{a}\ =\alpha MFI+\beta \tag{5}\]  
\[MFI=\frac{1}{P}\sum_{i=1}^{12}{P_{i}}^{2} \tag{6}\]  
where \(\alpha\) and \(\beta\) are regression coefficients (taken as 50.7 and \(-1405\), respectively, for the African continent [69]), \(Pi\) is the average monthly rainfall (mm) for month \(i\) and \(P\) is the mean annual precipitation (mm). \[R\ =\sum_{i=1}^{12}{1.735\times 10^{(1.5\ \log 10(\frac{P^{2}}{P})-0.08188)}} \tag{7}\]  
where \(Pi\) is the average monthly rainfall (mm) for month \(i\), \(P\) is the mean annual precipitation (mm) and \(R\) is the rainfall erosivity (MJ mm ha\({}^{-1}\) h\({}^{-1}\) y\({}^{-1}\)).