Application of Copula functions in hydrology and water resources: a state-of-the-art review

Copula functions, which are flexible tools for the derivation of joint probability distributions, have been widely and effectively used to deal with multivariable analysis problems in the field of hydrology and water resources. Particularly in recent decades, this method has received great attention from researchers and engineers because of its advantages in multivariate analysis where the marginals of the data are not normally distributed. This paper provides a state-of-the-art review of the last decade of copula functions in multivariate hydrological frequency analysis, coincidence and combination analysis of hydrological events, hydrological stochastic simulation, and hydrological modeling and forecasting, etc. More specifically, application issues such as parameter estimation, variable asymmetry, fitting optimization, tail characteristics, multivariable return period selection, and sampling error are described. Finally, the key points and development direction of Copula functions in the field of hydrology and water resources are considered, which provides guidance for the application of this method in the future.