设计洪水峰量最可能组合法的计算通式

针对传统的多变量分析方法在联合重现期水平下选取设计值存在较大的任意性和不确定性，本文利用Copula函数建立洪峰与不同时段洪量的多变量联合分布，采用联合概率密度函数值作为洪水发生相对可能性的度量指标；以满足防洪标准为约束条件，构建了峰量最可能组合的通用模型，并提出采用拉格朗日乘数法进行求解。采用该方法计算汉江流域丹江口水库的最可能设计洪水，并与单变量同频率、多变量同频率估计值对比，结果表明：单变量同频率估计值达不到防洪标准；最可能组合法与多变量同频率法相比，洪峰偏小、长历时洪量偏大，其估计值更符合丹江口水库的应用要求，说明所提方法具有较强的统计基础，更加符合水文现象的内在规律，可用于水库设计洪水计算。

General Formula of the Most Likely Composition Method for Flood Peaks and Volumes Estimation

For conventional multivariate frequency analysis methods,there are an infinite number of combinations of flood peaks and volumes satisfying the flood prevention standard under the given joint return period(JRP);however,different joint design values would lead to differences of flood hydrograph and maximal water level which occurs in reservoir routing.Hence,how to select reasonable design values under given JRP is very important. In this paper,the Copula functions were used to construct the multivariate joint distributions of flood peaks and volumes,and the OR JRP was adopted as flood prevention standard.The normalized joint probability density function value was adopted to measure the relative occurrence likelihood of flood events,and the general model of Most Likely Composition (MLC) of flood peaks and volumes were established subject to the flood prevention standard.The Lagrange multiplier method was adopted to solve the model.The trivariate and four-dimension MLC design floods of Danjiangkou reservoir in Hanjiang basin were estimated using the proposed method,and the quantiles estimated by univariate identical frequency (UIF) and multivariate identical frequency (MIF) methods were compared with those calculated by MLC.The results indicated that the UIF estimations could not satisfy the flood prevention standard;the UIF method assumed that the flood peak is fully dependent upon the flood volume and all the variables are characterized based on univariate distributions.The UIF method cannot take the correlations of hydrologic variables into consideration,and it does not satisfy the inherent rule of flood events. It is also indicated that the MLC method had a smaller flood peak and larger long-duration volume than those by the MIF method.The Danjiangkou reservoir has the capacity of multi-year regulation and the flood volumes are mainly responsible for flood prevention safety,and thus the MLC estimation values are safer.The joint design values of MLC method are more rational according to the application requirements in Danjiangkou reservoir, and consequently the proposed method had a strong statistical basis and could reflect the inherent rules of hydrological events,and it could be used to estimate the design floods of reservoir.