Return periods of erosive rain in Germany

Abstract. Return periods (RPs) of erosive rainfall events are required for erosion risk assessment and for implementing the German Soil Protection Law, which defines farmers' responsibility for erosion damage expected at least once within 10 years. However, no established method exists to quantify the RP of individual erosive rainfall events. Here, we develop and evaluate a framework for estimating the conditional distribution of rainfall erosivities, called erosion indices (EI), to quantify RPs of erosive rainfall events in Germany.

The analysis combines 26,566 erosive events from 115 rain gauge (RG) stations and 1,007,437 from weather radar (RR) measurements covering Germany between 2001 and 2017. Generalised Extreme Value distributions were fitted to compare measurement methods, while empirical cumulative distribution functions were used to calculate RPs directly because RP estimates were highly sensitive to small deviations in exceedance probabilities.

The number of erosive events increased systematically with the long-term mean annual erosivity factor R. Radar-based event frequencies followed a third-order polynomial relationship with R, whereas RG data showed an approximately linear relationship within the smaller range of observed R factors covering only the lower half of the RR data. Differences between RG and RR event frequencies mainly affected small erosive events (EI < 10 N h^‑1), whereas larger events relevant to RP estimation were captured similarly by both methods after applying published scaling corrections.

Across Germany, the return level EI for a given RP could be described by a unified equation relating EI_RP to both RP and the local R factor. For a 10-year RP, the resulting relationship was EI_10yr = 3.46 × R^0.59. The EI_10yr increased from 40 N h^‑1 to 100 N h^‑1 when the R factor increased from 40 N h^‑1 a^‑1 to 500 N h^‑1 a^‑1. Validation against RG-derived estimates yielded a root mean squared error of 8.3 N h^‑1 despite the datasets' contrasting spatial and temporal resolutions and measurement methods.

The results demonstrate that RPs for erosive rainfall events can be quantified consistently using radar-derived erosivity data, adjusted for local climatic conditions via the R factor. The R factor also captured the large interannual variability and thus can likely predict climate change effects on event erosivities. The derived equations provide a practical basis for erosion risk assessment, near-real-time erosion forecasting, and evaluation of legal responsibility for erosion damage under changing climatic conditions. The study further shows that conventional rainfall depth–duration–frequency relationships cannot substitute for erosivity-based RPs because rainfall erosivity exhibits a fundamentally different dependence on event duration and rainfall intensity.