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Rainfall is one the main drivers of soil erosion. The erosive force of rainfall is expressed as rainfall erosivity. Rainfall erosivity considers the rainfall amount and intensity, and is most commonly expressed as the R-factor in the USLE model and its revised version, RUSLE. At national and continental levels, the scarce availability of data obliges soil erosion modellers to estimate this factor based on rainfall data with only low temporal resolution (daily, monthly, annual averages). The purpose of this study is to assess rainfall erosivity in Europe in the form of the RUSLE R-factor, based on the best available datasets. Data have been collected from 1541 precipitation stations in all European Union (EU) Member States and Switzerland, with temporal resolutions of 5 to 60 min. The R-factor values calculated from precipitation data of different temporal resolutions were normalised to R-factor values with temporal resolutions of 30 min using linear regression functions. Precipitation time series ranged from a minimum of 5 years to a maximum of 40 years. The average time series per precipitation station is around 17.1 years, the most datasets including the first decade of the 21st century. Gaussian Process Regression (GPR) has been used to interpolate the R-factor station values to a European rainfall erosivity map at 1 km resolution. The covariates used for the R-factor interpolation were climatic data (total precipitation, seasonal precipitation, precipitation of driest/wettest months, average temperature), elevation and latitude/longitude. The mean R-factor for the EU plus Switzerland is 722 MJ mm ha(-1) h(-1) yr(-1), with the highest values (>1000 MJ mm ha(-1) h(-1) yr(-1)) in the Mediterranean and alpine regions and the lowest (<500 MJ mm ha(-1) h(-1) yr(-1)) in the Nordic countries. The erosivity density (erosivity normalised to annual precipitation amounts) was also the highest in Mediterranean regions which implies high risk for erosive events and floods.

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Rainfall erosivity as a dynamic factor of soil loss by water erosion is modelled intra-annually for the first time at European scale. The development of Rainfall Erosivity Database at European Scale (REDES) and its 2015 update with the extension to monthly component allowed to develop monthly and seasonal R-factor maps and assess rainfall erosivity both spatially and temporally. During winter months, significant rainfall erosivity is present only in part of the Mediterranean countries. A sudden increase of erosivity occurs in major part of European Union (except Mediterranean basin, western part of Britain and Ireland) in May and the highest values are registered during summer months. Starting from September, R-factor has a decreasing trend. The mean rainfall erosivity in summer is almost 4 times higher (315 MJ mm ha− 1 h− 1) compared to winter (87 MJ mm ha− 1 h− 1).The Cubist model has been selected among various statistical models to perform the spatial interpolation due to its excellent performance, ability to model non-linearity and interpretability. The monthly prediction is an order more difficult than the annual one as it is limited by the number of covariates and, for consistency, the sum of all months has to be close to annual erosivity. The performance of the Cubist models proved to be generally high, resulting in R2 values between 0.40 and 0.64 in cross-validation. The obtained months show an increasing trend of erosivity occurring from winter to summer starting from western to Eastern Europe. The maps also show a clear delineation of areas with different erosivity seasonal patterns, whose spatial outline was evidenced by cluster analysis. The monthly erosivity maps can be used to develop composite indicators that map both intra-annual variability and concentration of erosive events. Consequently, spatio-temporal mapping of rainfall erosivity permits to identify the months and the areas with highest risk of soil loss where conservation measures should be applied in different seasons of the year.

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