Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation

摘要

Most of the hydrological and hydraulic studies refer to the notion of areturn period to quantify design variables. When dealing with multiple designvariables, the well-known univariate statistical analysis is no longersatisfactory, and several issues challenge the practitioner. How should oneincorporate the dependence between variables? How should a multivariatereturn period be defined and applied in order to yield a proper design event?In this study an overview of the state of the art for estimatingmultivariate design events is given and the different approaches arecompared. The construction of multivariate distribution functions is donethrough the use of copulas, given their practicality in multivariatefrequency analyses and their ability to model numerous types of dependencestructures in a flexible way. A synthetic case study is used to generate alarge data set of simulated discharges that is used for illustrating theeffect of different modelling choices on the design events. Based ondifferent uni- and multivariate approaches, the design hydrographcharacteristics of a 3-D phenomenon composed of annual maximumpeak discharge, its volume, and duration are derived. These approaches arebased on regression analysis, bivariate conditional distributions, bivariatejoint distributions and Kendall distribution functions, highlightingtheoretical and practical issues of multivariate frequency analysis. Also anensemble-based approach is presented. For a given design return period, theapproach chosen clearly affects the calculated design event, and muchattention should be given to the choice of the approach used as this dependson the real-world problem at hand.