Use of time lags for sampling combined flood and heavy rainfall events

Research on compound events is crucial due to their increasing frequency and severity in a changing climate. These events, such as simultaneous heatwaves and droughts or concurrent storm surges and heavy rainfall, can lead to cascading impacts that far exceed the damage caused by individual extremes. Understanding the interactions and dependencies between multiple extreme factors is essential to accurately assess risks, improve predictive models and enhance resilience strategies.

In this context, particular attention must be paid to small headwater catchments, where there is a causal relationship between heavy rainfall and river flooding. In the following analyses, this relationship is examined using precipitation data from the Deutscher Wetterdienst (DWD)-RADKLIM and ERA5-Land reanalysis, as well as corresponding discharge gauges in Germany. The influence of different catchment characteristics, such as topography, on the relationship between precipitation and runoff is analysed. Sampling is a critical component for further analysis, particularly for determining joint probabilities of occurrence. This study utilises simultaneous time series of precipitation and runoff to achieve this objective. The maximum discharge within a specified period following an extreme precipitation event is determined, with the time lag between the determination of the maximum value playing a pivotal role. The present analyses provide a comprehensive illustration of the variations between different time intervals. The objective of this study is to demonstrate the influence of this parameter on the relationship between heavy rainfall and runoff in a catchment area, and to discuss the effects this has on the determination of the joint probability of occurrence. The joint probability of occurrence is determined using the correlation coefficient and corresponding copula functions.