Quantifying the extremeness of precipitation across scales

Abstract. Quantifying the extremeness of a heavy precipitation event is important to compare different events, to analyze trends in frequency and amplitude, and to understand related impacts on the ground. While such impacts depend on the event’s spatial extent and duration, many indices neglect at least one of these aspects. In 2014, however, Müller and Kaspar suggested, in this journal, the weather extremity index (WEI) which quantifies not only the extremeness of an event, but identifies the spatial and temporal scale at which the event was most extreme. While the WEI is informative, it does not account for the fact that an event can be extreme at various spatial and temporal scales. Such an event could trigger – simultaneously or subsequently – different kinds of processes and related impacts, such as flash floods and large-scale fluvial floods, which can overlay and amplify each other, so that they essentially become compound events. To better understand and detect the compound nature of precipitation events, we suggest to complement the original WEI, and refer to this complement as the "cross-scale weather extremity index" (xWEI). Unlike the original WEI index, xWEI does not aim to detect the spatio-temporal scale of maximum extremeness, but to integrate extremeness over relevant scales. Based on a set of 101 extreme precipitation events in Germany, we outline and demonstrate the computation of both indices, WEI and xWEI, and analyse how the choice of an index affects the rating and ranking of these events. To that end, we use hourly radar-based precipitation estimates for all of Germany at a spatial resolution of 1 x 1 km, available since 2001. 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 for these cases, though, the xWEI index can reveal cross-scale properties which would otherwise remain hidden. Among the analysed events was also the disastrous precipitation event from July 2021 which devastated large parts of western Germany. This event outranks all other analysed events by far – both with regard to WEI and xWEI. While demonstrating the added value of the cross-scale index, 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, as well as 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. We conclude that the proposed cross-scale extremity index can provide substantial complementary information to existing indices, and could hence be a valuable instrument in both disaster risk management and research.