Statistical extreme value analysis of precipitation data as enriching information for warnings against severe weather – first steps of the approach for Germany

Extreme precipitation events present significant threats to society, infrastructure, and the economy. To mitigate the potential impacts of such events, it is essential to design appropriate infrastructure, water management systems, and warnings. Guidelines for the hydrological and hydraulic resilience of infrastructure are typically based on statistically derived estimates of return periods and return levels of extreme hydrological events. Therefore, a reliable information on the estimated return periods and return levels is crucial. Furthermore, combining this statistical information with weather forecasts may allow to anticipate the extremity of predicted events and, consequently, to estimate the impact an expected event may have.

Extreme value theory offers a theoretical foundation for the statistical modelling of exceptional phenomena. A common approach for identifying extremes is the block maxima method. After dividing a time series into blocks (e.g., years), the maxima of these blocks are selected, and a distribution is fitted. Based on the extremal types theorem, when the maxima are appropriately renormalized, they can only follow one of three distributions: Fréchet, Gumbel, or Weibull. These are the only possible cases of the generalized extreme value (GEV) distribution. When analysing rainfall, the duration of events is of particular importance: the more rain falls per unit of time, the higher is the resulting runoff. In agreement with the currently used methodology at Deutscher Wetterdienst (DWD), we distinguish 22 duration levels ranging from 5 minutes to 7 days. After identifying annual maxima for each duration level a GEV distribution was fitted to each series of maxima, with the constraint that we fixed the shape parameter at 0.1 (Fréchet distribution). To account for the temporal interdependence of rainfall events across different durations, the framework developed by Koutsoyiannis et al. (1998) was implemented, allowing for the integration of multiple duration levels into a single statistic.

This methodology has been applied to various datasets, including interpolated rain-gauge station data (HYRAS), spatially and temporally homogenized climatological precipitation data derived from weather radars (RADKLIM), and reanalysis data (COSMO REA6 and R6G2). In this preliminary study, the results are compared and assessed with respect to agreements, discrepancies, and inconsistencies, considering the characteristics of each data source.  Comparing the statistical estimates across various data sources is a first step toward developing a methodology to determine the extremity of weather forecasts — an essential part of an impact-oriented warning system for extreme precipitation.

Koutsoyiannis et al., 1998, A mathematical framework for studying rainfall intensity-duration-frequency relationships. J. Hydrol. (206), 118-135, https://doi.org/10.1016/S0022-1694(98)00097-3.