多维联合分布计算方法及其在水文中的应用

Computation methods of multivariate joint probability distribution and their applications in hydrology

本文针对多维对数正态分布,采用统计试验方法,比较研究了基于正态化变换的Moran方法、传统经验频率方法(empirical frequency method简称EFM法)和将多维转化为一维的费永法(FEI)方法共3种多维联合分布计算方法的统计性能。在此基础上,应用南水北调东线工程沿线不同水文区主要站点年径流资料,分析了长江、淮河及黄河流域年径流的丰枯遭遇组合概率。统计试验结果表明,在研究的3个多维联合分布频率计算方法中,Moran方法具有最优的统计无偏性和有效性。对南水北调东线工程沿线区域主要河流径流丰枯组成的分析也表明,Moran方法可以为径流丰枯组合的频率分析提供合理的计算结果,是解决多变量水文统计计算问题的有效方法。

Three computation methods for multivariate analysis, namely the Moran, EFM and FEI method, were compared by means of Monte-Carlo technique. Among them, the Moran method is normalized-based, EFM is an empirical frequency analysis method while FEI is a multi-to-one dimension method. Annual runoff data at controlling stations within the region of the East Route is South-to-North Water Transfer Project were used to analyze runoff encountering probability among Changjiang River, Huai River and Yellow River. Statistical experiment shows that the Moran method is the best approach if evaluated by either statistical unbiaseness or effectiveness. The analysis of the output of the Plentiful or Scanty runoff encountering also shows that the Moran method is effective in solving the problem of multivariate hydrological statistics.