Maximum Entropy–Mixed Copula Method for the Simulation of Monthly Streamflow

Abstract

A new single-site monthly streamflow simulation method that combines the maximum entropy and mixed copula methods is proposed. In this method, the marginal distribution of monthly streamflow is estimated using the maximum entropy theory; this is achieved by the conjugate gradient method of superlinear convergence and low computational expense. Then, a mixed copula is used for the construction of joint distributions of the adjacent monthly streamflow. The developed method is applied to four stations of the Weihe River, China; the results show that the important statistical characteristics of monthly streamflow can be maintained by the entropy-based marginal distribution and that the complex linear and nonlinear dependence between adjacent monthly streamflow can be reproduced by the mixed copula method. Compared with the traditional marginal distribution and the individual copula joint distribution, the entropy-mixed copula method has obvious advantages in goodness-of-fit statistical tests on the marginal and joint distributions. Accurately understanding the monthly runoff distribution is beneficial for flood control during the flood season and solving water shortage problems during the dry season. First, the marginal probability distribution function of each month is established through the principle of maximum entropy. Then, a mixed copula model is used to construct a joint distribution of adjacent monthly runoff. Finally, Gibbs sampling is used to obtain the randomly simulated runoff for each month. The advantage of this method is that it does not require assuming the probability distribution of the runoff series but rather uses important statistical features of the historical series as constraints for deriving the marginal distribution. Accurately describing the complex relationship between water flow sequences, maintaining the statistical characteristics of observation sequences, and improving simulation accuracy are of great significance for water resource planning and management.