两变量水文频率分布模型研究述评

A review of bivariate hydrological frequency distribution

水文变量多特征属性的频率分析,以及各种水文事件的遭遇及联合概率分布问题需要采用多变量概率分布模型解决。总结了当前应用最广泛的几种两变量概率分布模型,对各种模型的适用性和局限性做了详细分析,并介绍了一种新的两变量概率模型——Copula函数。现有模型大都基于变量之间的线性相关关系而建立,对于非线性、非对称的随机变量难以很好地描述;大部分模型假定各变量服从相同的边际分布或对变量间的相关性有严格的限定,从而限制了其应用。Copula函数所构造的两变量概率分布模型克服了现有模型的不足,它具有任意的边际分布,可以描述变量间非线性、非对称的相关关系。作为一种用于构造灵活的多变量联合分布的工具,Copula函数在水科学领域具有广阔的应用前景。

Univariate frequency analysis cannot provide a complete description of hydrologic variables with multicharacteristics, and many hydrological frequency problems should be solved by the bivariate probability distribution model concerning the encounters and joint distributions of different hydrologic events. This article presents a review of various bivariate probability distribution models, and Copulas as a new bivariate probability distribution method are introduced. Advantages and limitations of each of these models are pointed out. Most of the present models are constructed based on the linear correlation of variables, and some of the models usually assume that the variables should have the same marginal distributions or have a strict restriction of correlation between variables. In reality, however, many hydrological events do not have the same type of marginal distributions, and various nonlinear dependence exists among variables. The copula method relaxes the restrictions of traditional bivariate probability models, and no assumption is needed for the variables to be independent or normal or have the same type of marginal distributions. The complex asymmetric and nonlinear correlation among variables can be described using copulas. As a flexible method to construct joint multivariate distribution, the Copula methodology is promising concerning hydrological frequency analysis.