Space–time trends and dependence of precipitation extremes in North‐Western Germany

The assessment of long‐term trends in environmental extremes is a challenging and important subject in the current discussion on global climate change. We propose a new approach for evaluating temporal trends and spatial homogeneity in extremes accounting also for spatial dependence. Based on exceedances over a space–time threshold, we provide estimators for a so‐called scedasis function and the extreme value parameters. Two novel test statistics based on the scedasis function provide a way to assess space–time inhomogeneities. Finally, we propose a procedure to achieve stationarity in space and time and evaluate residual extremal dependence over space through a variogram analysis that includes anisotropy. The methods are applied to daily accumulated precipitation data observed at 64 weather stations in North‐Western Germany. The time period from 1931 to 2014 is considered, separately for northern hemispheric winter (November – March) and summer (May – September). The results reveal a clear seasonal differentiation on extremal behavior with the highest precipitation records and generally heavier tails during summer. Spatial inhomogeneities in the frequency of precipitation extremes are related to topography and are particularly significant during winter. During this season, we further observe significant deviations from time‐stationarity at a few stations, related to a period of a high frequency of extremes around 1992. Spatial anisotropy in the extremal dependence structure is stronger during winter than during summer and reveals an increased dependence in the east–west direction.