Index flood–based multivariate regional frequency analysis

Abstract

Because of their multivariate nature, several hydrological phenomena can be described by more than one correlated characteristic. These characteristics are generally not independent and should be jointly considered. Consequently, univariate regional frequency analysis (FA) cannot provide complete assessment of true probabilities of occurrence. The objective of the present paper is to propose a procedure for regional flood FA in a multivariate framework. In the present paper, the focus is on the estimation step of regional FA. The proposed procedure represents a multivariate version of the index flood model and is based on copulas and a multivariate quantile version with a focus on the bivariate case. The model offers increased flexibility to designers by leading to several scenarios associated with the same risk. The univariate quantiles represent special cases corresponding to the extreme scenarios. A simulation study is carried out to evaluate the performance of the model in a bivariate framework. Simulation results show that bivariate FA provides the univariate quantiles with equivalent accuracy. Similarity is observed between results of the bivariate model and those of the univariate one in terms of the behavior of the corresponding performance criteria. The procedure performs better when the regional homogeneity is high. Furthermore, the impacts of small variations in the record length at gauged sites and the region size on the performance of the proposed procedure are not significant.