A review of bivariate hydrological frequency distribution

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.