Measure of Correlation between River Flows Using the Copula-Entropy Method

Analysis of the dependence between the main stream and its upper tributaries is important for hydraulic design, flood prevention, and risk control. The concept of total correlation, computed by the copula-entropy method, was applied to measure the dependence. This method only needs to calculate the copula entropy instead of the marginal or joint entropy, which estimates the total correlation more directly and avoids the accumulation of systematic bias. To that end, bivariate and multivariate Archimedean and metaelliptical copulas were employed, and multiple-integration and Monte Carlo methods were used to calculate the copula entropy. The methodology was applied to the upper Yangtze River reach in China, which has five major tributaries: Jinsha, Min, Tuo, Jialing, and Wu. Results showed that the selected copulas fitted the empirical probability distributions satisfactorily. There was a significant difference in total correlation values, when different copula functions were used. The copula entropy, calculated using the multiple-integration and Monte Carlo methods, led to similar results. The total correlation among the rivers was not high, and the one between Min and Tuo Rivers was the largest. There was some dependence among Jinsha, Min, and Tuo rivers, which constitutes a threat to flood control by the Three Gorges Dam (TGD). The flows of the Jinsha, Jialing, Min, and Tuo rivers significantly influence the flood occurrence in the Yangtze River.