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

[1] Several types of hydrological events are described with multivariate characteristics (droughts, floods, rain storms, etc.). When carrying out a multivariate regional frequency analysis for these events it is important to jointly consider all these characteristics. The aim of this paper is to extend the statistical homogeneity test of Hosking and Wallis (1993) to the multivariate case. As a tool, multivariate L-moments are used to define the statistics and general copula models to describe the statistical behavior of dependent variables. The usefulness of the methodology is illustrated on flood events. Monte-Carlo simulations are also performed for a bivariate Gumbel logistic model with Gumbel marginal distributions. Results illustrate the power of the proposed multivariate L-moment homogeneity test to detect heterogeneity on the whole structure of the model and on the marginal distributions. In a bivariate flood setting, a comparison is carried out with the classical homogeneity test of Hosking and Wallis based on several types of regions.

.[1] The prevention of flood risks and the effective planning and management of water resources require river flows to be continuously measured and analyzed at a number of stations. For a given station, a hydrograph can be obtained as a graphical representation of the temporal variation of flow over a period of time. The information provided by the hydrograph is essential to determine the severity of extreme events and their frequencies. A flood hydrograph is commonly characterized by its peak, volume, and duration. Traditional hydrological frequency analysis (FA) approaches focused separately on each of these features in a univariate context. Recent multivariate approaches considered these features jointly in order to take into account their dependence structure. However, all these approaches are based on the analysis of a number of characteristics and do not make use of the full information content of the hydrograph. The objective of the present work is to propose a new framework for FA using the hydrographs as curves: functional data. In this context, the whole hydrograph is considered as one infinite-dimensional observation. This context allows us to provide more effective and efficient estimates of the risk associated with extreme events. The proposed approach contributes to addressing the problem of lack of data commonly encountered in hydrology by fully employing all the information contained in the hydrographs. A number of functional data analysis tools are introduced and adapted to flood FA with a focus on exploratory analysis as a first stage toward a complete functional flood FA. These methods, including data visualization, location and scale measures, principal component analysis, and outlier detection, are illustrated in a real-world flood analysis case study from the province of Quebec, Canada.