Distribution characteristics of the joint return period of extreme drought events in the upper Yellow River Basin

In this study, we calculated the 1-month standardized precipitation index based on the precipitation data from 43 meteorological stations in the upper Yellow River Basin for the period 1961–2020. We extracted the drought events using the run theory and established optimal distribution models for the characteristic variables of drought events (drought duration and severity) in the study area following the Copula function approach. The models’ goodness of fit was tested with 1,000 iterations of bootstrap sampling. Thereafter, the joint return period of extreme drought events was analyzed. Furthermore, we investigated the relative variation of the joint return period of extreme drought events before and after an abrupt temperature change and the contribution of three factors (probability distributions of drought duration and severity and the dependence structure between the two variables) to the relative variation. The results show that the low-value regions of the joint return period of extreme drought events are mainly distributed over the Huangshui and Taohe River Basins and the Hequ area, indicating that extreme drought events frequently occur in these areas. The high-value regions are mainly in the central and southern Ningxia Plain and the Jingtai, Jingyuan, Huining, and Dingxi areas of the Longzhong Loess Plateau. After the abrupt temperature change in 1996, the kernel density estimator of the joint return period was apparently right-shifted. This shift implied that the return period generally increased after the abrupt temperature change, that is, the risk of extreme drought events has declined. Additionally, the spatial heterogeneity of the return period has increased, with substantial relative variation on the northeastern slope of the Qinghai–Tibet Plateau and its downstream Yellow River section. The relative variation generated by the probability distributions of drought severity and duration exhibited similar spatial distribution characteristics, with basically negative values in the Hequ area and positive values in the western part of the Loess Plateau. The largest relative variation occurred in the Longzhong Loess Plateau and the Ningxia Plain. The spatial distribution pattern of the relative variation caused by the dependence structure was the opposite.