Multivariate return period calculation via survival functions

Key Points New consistent and well‐founded definition of Multivariate Return Period Easy‐to‐use formulas for performing Multivariate design and risk assessment The new approach is so general that all hydrological sciences may benefit of it The concept of return period is fundamental for the design and the assessment of many engineering works. In a multivariate framework, several approaches are available to its definition, each one yielding different solutions. In this paper, we outline a theoretical framework for the calculation of return periods in a multidimensional environment, based on survival copulas and the corresponding survival Kendall's measures. The present approach solves the problems raised in previous publications concerning the coherent foundation of the notion of return period in a multivariate setting. As an illustration, a practical hydrological application is presented.