Probability Analysis and Control of River Runoff–sediment Characteristics based on Pair-Copula Functions: The Case of the Weihe River and Jinghe River

Analyzing the encounter frequency of high–low runoff and sediment yield is important for the appropriate dispatching of runoff–sediment resources, as well as river regulation. However, there have been no reports on the utilization of the pair-copula function in analyzing the runoff–sediment characteristics from a probabilistic perspective and conducting probability control on the runoff–sediment yields of different hydrologic stations. This paper builds marginal distribution functions on the basis of kernel distribution theory. In addition, this paper builds the joint distribution functions through pair-copula functions in order to analyze the encounter probability and the compensation characteristics of high–low runoff and sediment at different stations on the Weihe River in China, as well as the origins of runoff–sediment, to conduct probability control of river runoff–sediment resource allocation. The results show that, in different periods, the synchronous probability of high–low runoff of the Weihe River’s Xianyang and Huaxian Stations, and the Jinghe River’s Zhangjiashan Station differ, while that of high–low sediment at the three stations changes little—remaining at around 54%. Therefore, the sediment and runoff of the Weihe River apparently have different origins. In years of high and low runoff, if the runoffs of the Xianyang and Zhangjiashan Stations can be kept within a certain range, then the runoff of the Huaxian Station will be in a particular range, at a certain probability. Sediment at the Huaxian Station can be controlled, in a similar way. These results are of great significance for the water and sediment management department of the Weihe river, in order to reasonably allocate water and sediment resources.