基于Copula熵方法的河流之间的相关性研究

Analysis of Correlation between River Flows Using Copula-Entropy Method

摘要: 研究长江干流及其支流之间的总相关性对于长江上游的水力设计、防洪和风险控制非常重要。针对现有的相关性计算方法的不足与缺陷，本文引入Copula熵方法，用来计算多变量之间的相关结构，并推导出Copula熵与互信息的关系与计算方法，采用多重积分法和蒙特卡罗法估计多变量之间的相关性特征。以长江上游的五条主要干支流：金沙江、岷江、沱江、嘉陵江和乌江为研究对象。计算结果表明，当使用不同的Copula函数时，总相关值存在显著差异。长江上游干支流河流之间的总相关性不大，其中岷江和沱江之间的相关性最大，金沙江，岷江和沱江之间也存在一定的相关性，因此，这几条河流有洪水遭遇的可能，对三峡大坝的防洪构成了威胁。

Abstract: Analysis of the dependence between the main stream and its upper tributaries is important for hydraulic design, flood prevention and risk control. In order to solve the disadvantages of the current hydrologic correlation analysis method, the method of copula entropy was introduced to estimate the dependence between Hydrological variables. The relationship between copula entropy and mutual information was discussed and the calculation procedures of copula entropy were deduced, and multiple integration and Monte Carlo methods were used to calculate the copula entropy. The upper Yangtze River was selected for case study. Results show that there is a significant difference in total correlation values, when different copula functions were used. The total correlation among the rivers is not high, and the one between Min and Tuo Rivers is the largest. There are some dependence among Jinsha, Min and Tuo Rivers, which constitutes a threat to flood control by the Three Gorges Dam (TGD). The flows of Jinsha, Jialing, Min and Tuo Rivers significantly influence the flood occurrence in the Yangtze River.