Nonstationary seasonal design flood estimation: incorporating the nonmonotonic dependence between annual maximum flood peak discharge and occurrence date by mixed-copula

Abstract

Numerous hydrologic designs require seasonal design flood (SDF) estimates. In SDF estimation, to obtain more reliable SDFs for different time segments within flood season, some studies have established the bivariate distribution of the annual maximum flood (AMF) discharges and timings (dates of occurrence) with single copulas, which implicitly assumes these two flood characteristics to have a monotonic dependence structure (MDS). However, the rationality of this MDS assumption between the AMF discharges and timings has not been investigated. In this study, within the framework of SDF estimation, a mixed-copula function modelling the nonmonotonic dependence structure (NMDS) between the AMF discharges and timings is proposed to characterize the seasonal variation of discharges from increasing to decreasing, and then SDFs under nonstationary conditions are derived using the equivalent reliability method. Compared to the MDS assumption, the NMDS offers a better performance in modelling observed AMDFs (1951~2019) in the Wujiang River Basin. The results suggest that within the whole flood season from May to October, the NMDS-based SDFs in June-July exceed the annual design flood while those in other months are lower than the annual design flood, which allows reducing the flood control storage capacity to improve floodwater utilization in downstream flood management without increasing flood risk. With influences of changing environments on AMF discharges further explored, the seasonal fluctuation in design floods, initially driven by the temporal unevenness of rainfall, is significantly flattened by regulation of reservoirs. These results would be helpful for downstream flood risk management and floodwater resources utilization.