Evaluating Extremes in Climatology with Average Value-at-Risk Measure: Example of Precipitation Data from Upper Vistula Region in Poland

Abstract The ability to predict changes in the right tail of daily precipitation distributions over short time periods, as well as the probability of clustering extreme values, is critical for current risk management. In the present study, we apply the well-established metric average value-at-risk (AVaR) for the first time within the field of climatology. We also investigate the evolution of the return level (RL) and the extremal index (EI), which we refer to as risk measures. In the case of precipitation processes, a rise in the first two and a reduction in the third may result in increased hazards. These methods were applied to the new data on the daily sum of precipitation from the region of Upper Vistula in Poland from 1951 to 2020 to analyze the dynamics of changes across time. We found that AVaR and RL have the smallest values for the middle of the analyzed period (years 1971–2010), while EI has a maximal value around 1963–92. Both the beginning and the end of the investigated period are characterized by more extreme and clustered precipitation events. Furthermore, this paper includes some recommendations for the tools used to compute the measures.