Joint probability analysis of streamflow and sediment load based on hybrid copula.

Statistical analysis of streamflow and sediment is very important for integrated watershed management and the design of water infrastructure, especially in silt-rich rivers. Here, we propose a bivariate joint distribution framework based on nonparametric kernel density estimation (KDE) and a hybrid copula function to describe the complex streamflow-sediment dependent structure. In this framework, the non-parametric KDE is used to fit the marginal distribution function of streamflow and sediment variables, and then the hybrid copula function is constructed by using the linear combination of Clayton, Frank, and Gumbel copulas, and compared with five commonly used single copulas (Clayton, Frank, Gumbel, Gaussian, and t). We use the Jinsha River Basin (JRB) in the Yangtze River's (JR) upper reaches to verify the proposed method. The results show the following: (1) Compared with the gamma distribution (Gamma) and generalized extreme value (GEV) distribution of parameters, the marginal distribution function of streamflow and sediment variables can be effectively obtained based on nonparametric KDE. (2) Compared with the single copula, the hybrid copula function more fully reflects the complex dependent structure of streamflow and sediment variables. (3) Compared with the best single copula, the precision of return period based on hybrid copula can be increased by 7.41%. In addition, the synchronous probability of streamflow and sediment in JRB is 0.553, and the asynchronous probability of streamflow and sediment is 0.447. This study can not only improve the accuracy of streamflow and sediment statistical analysis in JRB, but also provide a useful framework for other bivariate joint probability analysis.