基于Copula函数的入库洪水与坝址洪水关系研究

采用频率分析法计算入库设计洪水时,需要通过相关分析将坝址洪水系列插补得到对应的入库洪水系列。常用的线性回归法假设两者满足线性关系且入库洪水系列服从正态分布,可能与实际情况并不相符。引入Copula函数构建坝址洪水与入库洪水的联合概率分布和条件概率分布,计算给定坝址洪水时入库洪水的条件最可能值和置信区间,提出了一种基于Copula函数的入库洪水插补新方法。三峡水库的应用实例表明:线性回归法得到的入库洪水值在坝址洪水量级较大时明显偏小,甚至稀遇洪水时不在90%置信区间内。所提方法能较好地反映坝址洪水与入库洪水的内在关系,不仅可以计算入库洪水的各种点估计值,而且能够定量评价估计的不确定性。

Study on Relationship between Reservoir Inflow Flood and Dam-site Flood Based on Copula Function

The transformation of dam-site flood series to corresponding reservoir inflow flood series by correlation analysis is needed when frequency analysis method is used to estimate reservoir inflow design floods. The commonly used linear regression method assumes that these two variables have linear relationship and reservoir inflow flood series follow normal distribution, which may not be conformed to the actual situation. This paper proposed a new interpolation method for reservoir inflow flood based on Copula function, which was adopted to construct the joint probability distribution and conditional probability distribution of dam-site flood and reservoir inflow flood. The conditional most likely values and confidence intervals of reservoir inflow flood are obtained given the value of dam-site flood. The application in the Three Gorges Reservoir indicates that the reservoir inflow flood values estimated by linear regression method are obviously smaller than those by the Copula method when the flood magnitude is large, even are not within the 90% confidence interval when dam-site flood with rare frequency occurs. The proposed method can reflect the inherent relationship between dam-site flood and reservoir inflow flood and give both point and interval estimates of reservoir inflow flood and evaluate the uncertainty of estimation quantitatively.