Multivariate quantiles in hydrological frequency analysis

2 Several hydrological phenomena are described by two or more correlated characteristics. 3 These dependent characteristics should be considered jointly to be more representative of the 4 multivariate nature of the phenomenon. Consequently, probabilities of occurrence cannot be 5 estimated on the basis of univariate frequency analysis (FA). The quantile, representing the value 6 of the variable(s) corresponding to a given risk, is one of the most important notions in FA. The 7 estimation of multivariate quantiles has not been specifically treated in the hydrological FA 8 literature. In the present paper, we present a new and general framework for local FA based on a 9 multivariate quantile version. The multivariate quantile offers several combinations of the 10 variable values that lead to the same risk. A simulation study is carried out to evaluate the 11 performance of the proposed estimation procedure and a case study is conducted. Results show 12 that the bivariate estimation procedure has an analogous behaviour to the univariate one with 13 respect to the risk and the sample size. However, the dependence structure between variables is 14 ignored in the univariate case. The univariate estimates are obtained as special combinations by 15 the multivariate procedure and with equivalent accuracy. 16 17