基于Copula函数淮河流域水沙联合分布研究

Study on joint distribution of water and sediment in Huaihe River basin based on Copula function

淮河流域是我国人口密集的地区之一,拥有巨大的社会和经济发展潜力。基于淮河中游吴家渡水文站1950-2015年的径流量和输沙量资料,通过对径流量、输沙量的边缘分布函数和Copula函数的比选,确定最优函数形式并建立淮河流域水沙联合分布模型,运用模型对流域内水沙丰枯遭遇频率进行了计算,进而对比分析了径流量和输沙量单变量和联合变量的设计值并绘制了等值线图。研究结果表明:Gamma型分布对淮河流域的径流量过程和输沙量过程吻合较好。由于Gumbel型联合分布函数的赤则信息准则AIC值(akaike information criterion)最小,故选用Gumbel型Copula函数构建淮河流域水沙分布模型。淮河流域水沙同步的概率为67.2%,水沙异步的概率为32.8%,其中平水平沙出现的概率为27.54%,枯水枯沙出现的概率为25.86%,淮河流域枯水平水年份较多。径流量和输沙量联合变量设计值较单变量设计值要大,计算结果在考虑两者之间联系的基础上,将更具有代表性,且安全性更好。

The Huai River basin is one of the densely populated areas in China and has great potential for social and economic development. Based on the data of runoff and sediment discharge of Wujiadu Hydrological Station in the middle reaches of the Huaihe River in 1950-2015, the optimal function type is determined by comparing the edge distribution function and Copula function of runoff and sediment discharge and the joint distribution model of water and sediment in the Huaihe River basin is established. The encounter frequencies of runoff and sediment in the flood and dry stages are calculated by using the model, and then the design values of single and combined variables of runoff and sediment discharge are compared, and the isoline maps are drawn. The results show that the Gamma distribution is in good agreement with the runoff process and sediment transport process in the Huaihe River basin. Because the Gumbel joint distribution function akaike information criterion(AIC)value is the smallest, the Gumbel Copula function is used to construct the water and sand distribution model of Huaihe River basin. The probability of water-sand synchronization in The Huaihe River basin is 67.2%, and the probability of water-sand asynchronous is 32.8%. The probability of occurrence of flat-water and flat-sand is27.54%, and the probability of occurrence of dry-water and dry-sand is 25.86%. There are many years of drywater and flat-water in the Huaihe River Basin. The design value of the combined variable of runoff and sediment transport is larger than that of the single variable, and the calculated results will be more representative and safer on the basis of considering the relation between water and sediment.