Nonstationary Seasonal Design Flood Estimation: Exploring Mixed Copulas for the Nonmonotonic Dependence between Peak Discharge and Timing

The seasonal design flood (SDF) plays an important role in guiding water resources management and floodwater utilization. To estimate the SDF, studies have established the joint distribution of flood peak (i.e., annual maximum daily discharge) and timing (i.e., occurrence date) and assumed a monotonic dependence structure (MDS) between these two flood elements within the bivariate framework. However, the MDS assumption cannot fully represent the flood seasonality dynamics, which might affect the reliable assessments of the bivariate flood risks. To solve this issue, this study proposes a mixed-copula function to model a nonmonotonic dependence structure (NMDS) between flood peak and timing, and then derives the SDFs under nonstationary conditions by using the equivalent reliability method. As the NMDS can characterize the turnaround relationship between peak discharge and timing, the NMDS performs better at modeling observed (1951–2019) flood peaks than the traditional MDS, as reported by a case study in the Wujiang River Basin, China. The results suggest that, within the flood season from May to October, the NMDS-based estimation framework produces higher SDFs in June and July but smaller SDFs in the remaining months than the annual design flood. This allows for reducing the flood control storage capacity to improve floodwater utilization downstream without increasing flood risk. After further investigating the potential effects of a changing environment on peak discharges in the future (2020–2099), it is expected that reservoir regulation might play a more important role in flattening the seasonal fluctuations in floods. These results provide rich information as references for flood risk management and floodwater resources utilization under a changing environment.