Paul Voit, Maik Heistermann

• Quantifying the extremeness of heavy precipitation allows for the comparison of events. Conventional quantitative indices, however, typically neglect the spatial extent or the duration, while both are important to understand potential impacts. In 2014, the weather extremity index (WEI) was suggested to quantify the extremeness of an event and to identify the spatial and temporal scale at which the event was most extreme. However, the WEI does not account for the fact that one event can be extreme at various spatial and temporal scales. To better understand and detect the compound nature of precipitation events, we suggest complementing the original WEI with a “cross-scale weather extremity index” (xWEI), which integrates extremeness over relevant scales instead of determining its maximum. Based on a set of 101 extreme precipitation events in Germany, we outline and demonstrate the computation of both WEI and xWEI. We find that the choice of the index can lead to considerable differences in the assessment of past events but that theQuantifying the extremeness of heavy precipitation allows for the comparison of events. Conventional quantitative indices, however, typically neglect the spatial extent or the duration, while both are important to understand potential impacts. In 2014, the weather extremity index (WEI) was suggested to quantify the extremeness of an event and to identify the spatial and temporal scale at which the event was most extreme. However, the WEI does not account for the fact that one event can be extreme at various spatial and temporal scales. To better understand and detect the compound nature of precipitation events, we suggest complementing the original WEI with a “cross-scale weather extremity index” (xWEI), which integrates extremeness over relevant scales instead of determining its maximum. Based on a set of 101 extreme precipitation events in Germany, we outline and demonstrate the computation of both WEI and xWEI. We find that the choice of the index can lead to considerable differences in the assessment of past events but that the most extreme events are ranked consistently, independently of the index. Even then, the xWEI can reveal cross-scale properties which would otherwise remain hidden. This also applies to the disastrous event from July 2021, which clearly outranks all other analyzed events with regard to both WEI and xWEI. While demonstrating the added value of xWEI, we also identify various methodological challenges along the required computational workflow: these include the parameter estimation for the extreme value distributions, the definition of maximum spatial extent and temporal duration, and the weighting of extremeness at different scales. These challenges, however, also represent opportunities to adjust the retrieval of WEI and xWEI to specific user requirements and application scenarios.…