Variation in the dependence structure between runoff and sediment discharge using an improved copula

Abstract

Multivariate hydrological series become nonstationary under the changing environment. In this paper, a new method is proposed to study the change in the dependence structure between runoff and sediment sequences. First, a moving cut transfer entropy is proposed to detect the sudden change point in the dependence structure between runoff and sediment. Then, the Gumbel copula with a new parameter estimation method (MEE) is employed to construct the dependence structure of runoff and sediment before or after the change point for situation with small samples. The new method is applied to the annual runoff and sediment discharge series in Xiliugou River, China. It is found that the dependence structure between runoff and sediment changed abruptly in 2000. The joint probabilistic characteristics of the annual runoff and sediment discharge during the period of 1960–1999 are built based on the values of RMSEs and AICs. The joint distribution of the annual runoff and sediment discharge during the period of 2000–2016 is constructed by the Gumbel copula with MEE. Moreover, the synchronous encounter probability of runoff and sediment decreases from 0.76 to 0.63, and the asynchronous encounter probability rises from 0.24 to 0.37, after the runoff and sediment discharge series presents a significant change in the dependence structure.