Correlations Among Rivers Using Copula Entropy

Abstract

Analysis of the dependence between the mainstream 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, is applied to measuring 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 meta-elliptical copulas are employed, and multiple integration and Monte Carlo methods are used to calculate the copula entropy. The methodology is applied to the upper Yangtze River Reach, which has five major tributaries. Results show that the selected copulas fit the empirical probability distributions satisfactorily. There is a significant difference in total correlation values when different copula functions are used. The total correlations among the rivers are not high, and the largest one is between the Min River and the Tuo River. There is some dependence among the Jinsha River, the Min River and the Tuo River, which constitutes a threat to the flood control managed by the Three Gorges Dam (TGD). The flows of the Jinsha River, the Jialing River, the Min River and the Tuo River significantly influence the flood occurrence of the Yangtze River Basin.