Multivariate quantiles in hydrological frequency analysis

Abstract

Abstract2 Several hydrological phenomena are described by two or more correlated characteristics. 3These 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 18 3

A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation

“…However, univariate frequency analyses do not procure a full evaluation of the probability of occurrence of the hydrological event (Chebana and Ouarda, 2011). Moreover, the full hydrograph is of interest in the case of dam design, as the inflow peak is transformed into a different outflow peak during the routing process in the reservoir.…”

Estimating covariate functions associated to multivariate risks: a level set approach

“…Consequently, probabilities of occurrence of risks cannot be estimated on the basis of univariate analysis. The multivariate hydrological risks literature mainly treated one or more of the following three elements: (1) showing the importance and explaining the usefulness of the multivariate framework, (2) fitting the appropriate multivariate distribution in order to model risks and (3) defining and studying multivariate return periods (see Chebana and Ouarda [7]), (i.e., multivariate quantile based measures of risks).…”

Design event selection in bivariate hydrological frequency analysis

“…The probability levels α 1 and α 2 can be arbitrarily chosen, taking account of the specific problem under investigation. This subset corresponds to what is referred to by Chebana and Ouarda (2011) as the proper part of the level curve: the probability levels α 1 and α 2 allow one to quantify the desired distances of the extremities of the proper part from the asymptotes.…”

“…Recently, Chebana and Ouarda (2011) proposed the decomposition of the level curve into a naive part (tail) and a proper part (central); they assumed that the naive part is composed of two segments starting at the end of each extremity of the proper part. The authors highlight the importance, in practical application, of specifying the points that define the extremities of the proper part; to this aim they suggest selecting these points according to those of the corresponding empirical version or as close as needed to the asymptotes (the naive part).…”