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

B Gräler,S Grimaldi,B De Baets,M J Van Den Berg,S Vandenberghe,N E C Verhoest,A Petroselli

doi:10.5194/hess-17-1281-2013

Abstract

Abstract. Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return 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 estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand.

Highlights

A very important objective of hydrological studies is to provide design variables for diverse engineering projects
Several applications including sewer systems, dams and flood risk mapping require the selection of storm or hydrograph attributes with a predefined return period
The design values for the synthetic design hydrograph (SDH) with a design return period of 10 yr are calculated based on the 2-D and 3-D approaches presented in Sect

Summary

Introduction

A very important objective of hydrological studies is to provide design variables for diverse engineering projects. There has been an increasing interest in, and need for, simultaneously considering multiple design variables, which are likely to be associated with each other. Standard hydrological design approaches are mostly based on well-established univariate frequency analysis methods. Approaches to describe hydrological phenomena involving multiple variables have recently been proposed, aiding the practitioners in estimating multivariate. B. Graler et al.: Multivariate return periods return periods. As will be described later on, several approaches have evolved over the years. It is not clear how these compare to each other and which one is appropriate for a given application

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Results

Conclusion