## 2 Materials and Methods
### Modelling
#### 2.2.1 \(R\) Factor  
CZ: The \(R\) factor is calculated following the original USLE approach [16]. In this procedure rainfall events are subdivided if there is at least a rain gap (with less than 1.27 mm rainfall) of 6 h, and erosive events are defined as events with at least 12.7 mm of rainfall or a minimum 15 min intensity of at least 25.4 mm h\({}^{-1}\). To derive the rainfall erosivity map, high resolution rainfall (1 min) of recent 10 years of official Czech Hydro-meteorological Institute digital gauge stations is used. The rainfall erosivity maps in different areas of applications in the Czech Republic differ [23]. For the official USLE soil loss tolerance map used in the context of cross compliance, the calculated mean \(R\) factor of the 10 year period is reduced by 40%, based on the comparison of \(R\) factors of original pluviometer data and digital rain gauges in an overlapping training period (decision of Ministry of Agriculture/Ministry of Environment of Czech Republic). \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Test Catchments**} \\ \hline  & **Unit** & **CZ** & **BY** & **AT** \\ \hline _Calclment properties_ & & & & \\ \hline Latitude & \({}^{\circ}\) & 49.77 & 48.41 & 48.16 \\ Longitude & \({}^{\circ}\) & 14.83 & 12.72 & 15.14 \\ Elevation a.s.l. & m & 433 & 420 & 255 \\ Size & km\({}^{2}\) & 7.75 & 10.1 & 7.32 \\ Main slope & \({}^{\circ}\) & 6.3 \(\pm\) 3.9 & 6.7 \(\pm\) 3.8 & 4.6 \(\pm\) 3.9 \\ Mean precipitation & mm a\({}^{-1}\) & 739 & 844 & 764 \\ Mean temperature & \({}^{\circ}\)C & 7.7 & 8.2 & 9.0 \\ \hline _Arable land properties within catchment_ & & & & \\ \hline Mean slope & \({}^{\circ}\) & 5.8 \(\pm\) 2.3 & 6.1 \(\pm\) 2.9 & 4.1 \(\pm\) 2.5 \\ Mean field size & ha & 11.6 \(\pm\) 15.4 & 3.08 \(\pm\) 3.43 & 2.19 \(\pm\) 2.52 \\ Dominant soil type & - & Cambisol & Cambisol & Cambisol \\ Dominant soil texture & - & sandy loam & loam & loam \\ Proportion of arable land & \% & 65.9 & 59.2 & 47.5 \\ Small grain (proportion under soil conservation) & \% (\%) & 83.8 (16.1) & 53.1 (0) & 46.5 (0) \\ Row crops (proportion under soil conservation) & \% (\%) & 13.0 (0) & 45.2 (18.0) & 45.6 (0) \\ Perennial crops & \% & 3.1 & 1.1 & 7.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test catchment characteristics including land management. To apply the CZ approach in BY and AT, high resolution rainfall data from a meteorological station in the surrounding of the BY test catchment (about 5 km apart) and within the AT test catchment were used. BY: To derive the \(R\) factor following Bavarian regulations, a regression between annual precipitation (\(P_{A}\)) and rainfall erosivity is used that is documented in the German Industry Standard 19708 [13]. The regression equation (\(R\) factor = 0.0833 \(\times\)\(P_{A}\) + 1.73; \(R\)\({}^{2}\) = 0.94) was derived from annual precipitation and calculated \(R\) factors from 18 stations in Bavaria using 10 years of precipitation data with a temporal resolution of 1 min rainfall (period: 1967 and 1976) [24]. The \(R\) factor calculations follow [PERSON] et al. [12], which are based on the original USLE approach [16]. However, the definition of erosive events was slightly adapted to German conditions. Erosive events are defined as events with at least 10 mm of rainfall or a minimum 30 min intensity of at least 10 mm h\({}^{-1}\)[13; 12]. The mean annual rainfall, needed to derive mean annual rainfall erosivity for the catchment in Bavaria, is taken from a product of the German Weather Service (DWD) providing yearly data for the time span 1981-2010 in a 1 x 1 km\({}^{2}\) grid, which was interpolated from station data of the DWD and from neighboring counties stations taking elevation into account [25]. The resulting 1 x 1 km\({}^{2}\) erosivity map is aggregated to give a mean erosivity for each municipality. To apply the BY approach in CZ and AT, the mean long-term annual precipitation (2000-2013 and 1986-2016, respectively) from both sites was utilized.