Copula熵方法及其在三变量洪水频率计算中的应用

为解决传统Copula方法在进行联合概率分布拟合过程中要先进行函数类型选择的问题,将Copula函数和最大熵原理进行耦合,通过求解具有最大熵的Copula方程,求得二维联合分布函数,即Copula熵方法。用求得的Copula函数对洪水事件的3个相关变量(洪峰流量、洪水总量和洪水历时)进行两两配对的二维联合分布拟合,并利用Gibbs采样方法和Copula函数实现三变量洪水事件的随机模拟。以淮河鲁台子水文站的实测洪水资料为研究对象,进行实例分析,并通过拟合优度的计算,证明Copula熵方法对多维相关变量概率拟合的有效性以及Gibbs采样方法在三变量洪水事件模拟过程中的有效性。

Copula entropy method and its application to trivariate flood frequency calculation

In order to avoid selection of the type of functions when using traditional copula methods to fit the joint probability distribution, the copula function and the maximum entropy principle were jointly used(in a method also called the copula entropy method), and the two-dimensional joint distribution functions of flood variates were obtained by solving the copula function with the maximum entropy. With the solved copula function, the two-dimensional joint distribution functions of flood variates(peak discharge, flood volume, and flood duration)were mutually constructed. The Gibbs sampling method and copula functions were used to stochastically simulate trivariate flood events. A case study was conducted using the observed flood data from the Lutaizi Hydrological Station on the Huaihe River. A goodness-of-fit analysis shows that the copula entropy method is effective in fitting multivariate probability distributions and the Gibbs sampling method is effective in simulating trivariate flood events.