Characteristic Analysis and Uncertainty Assessment of the Joint Distribution of Runoff and Sediment: A Case Study of the Huangfuchuan River Basin, China

Exploring the relationship between runoff and sediment elements in a river basin is a prerequisite for realizing the scientific management scheme of runoff and sediment. In this study, six commonly applied probability distributions are utilized to fit the marginal distribution, and three Archimedes copulas are used to fit the joint distribution to build a joint probability distribution model of river runoff and sediment in sandy areas. The synchronous and asynchronous encounter probabilities of runoff and sediment are calculated. The uncertainties of marginal distribution, parameter estimation, and copula function in the process of constructing the joint distribution model framework are analyzed. The results indicate that: (1) The runoff and sediment series from 1954 to 2015 of the Huangfuchuan River basin are divided into three stages by using the cumulative anomaly method and the double mass curve method, and the runoff and sediment in the three stages have strong correlations. In the T-a (1954-1978) and T-b (1979-1996) stages, the optimal joint distribution functions of runoff and sediment are Gumbel, and in the T-c (1997-2015) stage the optimal joint distribution function is Clayton; (2) The synchronous probabilities of runoff and sediment series in the three stages are 69.84%, 84.82%, and 70.72%, respectively, which are much greater than the asynchronous frequencies of abundance and depletion, and this showed that the conditions of runoff and sediment in the river basin are consistent; (3) The joint distribution function is sensitive to the choice of marginal distributions, parameters, and copula functions, and the optimal marginal distribution function, optimal copula function, and the parameters selected by the maximum likelihood estimation method can better fit the runoff-sediment relationship in the river basin and reduce the process uncertainty.