基于Copula函数的区域洪水频率分析

Regional flood frequency analysis based on copula function

【目的】洪水频率分析为水利工程的规划、设计和运行提供了理论依据。传统的单变量频率分析方法已被广泛的研究和应用,但区域水文站点之间往往相互关联,单站点的独立洪水频率分析并不能满足实际工作的需求。因此,有必要考虑区域洪水变量间的相关关系,建立联合分布,采用多变量联合概率分析方法以提高洪水频率分析的可靠性。同时,由于区域洪水特性差异显著,需要探究Copula函数在不同区域洪水频率分析中的适用性。【方法】基于盘龙江区域的小河(中和)站、松华坝站、昆明站三个水文站以及长江上游区域的寸滩站、清溪场站、宜昌站三个水文站的洪水资料,建立站点年最大洪峰流量的边缘分布函数,用Kolmogorov-Smirnov法检验其拟合优度,分析站点洪水变量间的相关程度,进而利用嵌套Copula法和Copula函数表达式法构建区域三站点年最大洪峰流量的联合分布,采用分位数图法、均方根误差法和AIC信息准则法在选用的T-Copula、GH Copula、Frank Copula、以及Clayton Copula四类函数模型中进行拟合优度评价,通过优选的函数模型分析计算条件概率。【结果】结果显示:盘龙江和长江上游区域站点的年最大洪峰流量序列均可用P-Ⅲ型分布作为其边缘分布,且站点变量间的相关性良好,可运用Copula函数描述其相关关系,以此建立联合分布。其中,在盘龙江区域站点变量间,T-Copula函数拟合效果最优;在长江上游区域站点变量间,Frank Copula函数拟合效果最优。由优选的Copula函数模型预测下游站点的洪水遭遇量级,预测值与实测值的接近程度均达到85%以上。【结论】在区域站点洪水样本序列可求解其边缘分布,且变量间相关性显著的情况下,Copula函数能够较好描述变量间的相关关系。对于洪水特性差异较大的盘龙江和长江上游两个区域可优选出不同类型的Copula函数建立联合分布进行洪水频率分析,且计算结果能够准确的预测区域站点的洪水遭遇量级。研究成果可为区域联合防洪提供科学参考。

[Objective]Flood frequency analysis provides a theoretical basis for the planning, design and operation of water conservancy project. The traditional univariate frequency analysis method has been widely studied and applied, but the regional hydrological stations are often interrelated, and the independent flood frequency analysis of a single station can′t meet the needs of the actual work. Therefore, it is necessary to consider the correlation between regional flood variables, establish joint distribution, and adopt multivariate joint probability analysis method to improve the reliability of flood frequency analysis. At the same time, due to the significant differences in regional flood characteristics, it is necessary to explore the applicability of Copula function in different regional flood frequency analysis.[Methods]Based on the flood data of Xiaohe(Zhonghe) station, Songhuaba Station and Kunming Station in Panlong River region, and Cuntan station, Qingxichang Station and Yichang station in the upper reaches of Yangtze River region, the edge distribution function of the annual maximum flood peak discharge of the stations was established, and its good fit was tested by Kolmogorov-Smirnov method. The correlation degree of flood variables at three stations was analyzed, and then the joint distribution of annual maximum flood peak discharge at three stations in the region was constructed by using the nested Copula method and the Copula function expression method. Quantile graph method, root mean square error method and Akaike information criterial method were used to evaluate the goodness of fit in the selected function models of T-Copula, GH Copula, Frank Copula and Clayton Copula, and the conditional probability was analyzed by the preferred function model.[Results]The result show that the annual maximum flood peak discharge sequence of Panlong River and the upper reaches of the Yangtze River can be used as the marginal distribution of P-Ⅲ distribution, and the correlation between the variables of the stations is good. The Copula function can be used to describe the correlation, and establish the joint distribution. Among the station variables in Panlongjiang region, T-Copula function has the best fitting effect. Among the station variables in the upper reaches of the Yangtze River, Frank Copula function has the best fitting effect. The optimal Copula function model is used to predict the magnitude of flood encounter at downstream stations, and the predicted value is more than 85% close to the measured value.[Conclusion]When the flood sample sequence of regional stations can solve the marginal distribution and the correlation between variables is significant, the Copula function can better describe the correlation between variables. For the two regions of the Panlong River and the upper reaches of the Yangtze River with significant differences in flood characteristics, different types of Copula functions can be selected to establish joint distribution for flood frequency analysis, and the calculation result can accurately predict the magnitude of flood encounters at regional stations. The research result can provide scientific reference for regional joint flood control.