中文摘要：

不同水文区的丰枯遭遇概率分析属于多变量概率分布问题,涉及的水文区越多,变量的维数就越高,问题就越复杂.为找到一种简单通用的多变量（n≥3）水文概率问题的求解方法,以不同水文区丰枯遭遇概率分析为例,引入三维copula函数构建多变量联合概率模型,将其用于分析长江、淮河及黄河流域的径流量的联合概率和条件概率问题。研究结果表明,当变量维数n≥3时,由copula函数可以很容易地构建多变量概率分布模型;对一组水文数据系列,有多个不同copula函数可以选择,可采用拟合优度检验方法择优;copula函数构建的多变量概率模型,可以计算各种条件下的联合概率分布,可以分析各种不同量级水文变量的遭遇概率和条件概率;通过与多维转换为一维方法的比较,三维Frank copula函数具有更优良的拟合优度、无偏性及有效性,且计算更简便。

英文摘要：

Analyzing the probability of synchronous asynchronous encounter of multiple hydrologic regions can be reduced to the problem of estimating multivariate probability distribution functions.However,the problem can become more complicated when more hydrologic regions and variables are involved.This study presents a simple and effective method for solving high-dimensional（n≥3） copula-based multivariate probability distribution functions.The latter is used to analyze the joint probability and the conditional probability of annual runoff in the Yangtze River,Huaihe River,and Yellow River.The result shows a high-dimensional（n≥3） copula-based multivariate probability distribution function can be easily constructed for the three rivers using the methodology.For a given set of hydrological variables,it is possible that several candidate copulas fit the variable reasonably well.The goodness-of-fit test can be applied to identify the best copula.The probability of synchronous asynchronous encounter of multiple hydrologic regions can thus be analyzed based on the best copula.Comparing to the method for converting a multi-dimensional space into a one-dimensional one,the three-dimensional Frank copula is simple,excellent goodness of fit,unbiased,and effective.