Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation
B. Gräler1,M. J. van den Berg2,S. Vandenberghe2,A. Petroselli3,S. Grimaldi6,5,4,B. De Baets7,and N. E. C. Verhoest2B. Gräler et al. B. Gräler1,M. J. van den Berg2,S. Vandenberghe2,A. Petroselli3,S. Grimaldi6,5,4,B. De Baets7,and N. E. C. Verhoest2
1Institute for Geoinformatics, University of Münster, Weseler Str. 253, 48151 Münster, Germany
2Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
3Dipartimento di scienze e tecnologie per l'agricoltura, le foreste, la natura e l'energia (DAFNE Department), University of Tuscia, Via San Camillo De Lellis, 01100 Viterbo, Italy
4Dipartimento per la innovazione nei sistemi biologici agroalimentari e forestali (DIBAF Department), University of Tuscia, Via San Camillo De Lellis, 01100 Viterbo, Italy
5Honors Center of Italian Universities (H2CU), Sapienza University of Rome, Via Eudossiana 18, 00184 Roma, Italy
6Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Six MetroTech Center Brooklyn, New York, 11201, USA
7Department of Mathematical Modelling, Statistics and Bioinformatics, Coupure links 653, 9000 Ghent, Belgium
1Institute for Geoinformatics, University of Münster, Weseler Str. 253, 48151 Münster, Germany
2Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
3Dipartimento di scienze e tecnologie per l'agricoltura, le foreste, la natura e l'energia (DAFNE Department), University of Tuscia, Via San Camillo De Lellis, 01100 Viterbo, Italy
4Dipartimento per la innovazione nei sistemi biologici agroalimentari e forestali (DIBAF Department), University of Tuscia, Via San Camillo De Lellis, 01100 Viterbo, Italy
5Honors Center of Italian Universities (H2CU), Sapienza University of Rome, Via Eudossiana 18, 00184 Roma, Italy
6Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Six MetroTech Center Brooklyn, New York, 11201, USA
7Department of Mathematical Modelling, Statistics and Bioinformatics, Coupure links 653, 9000 Ghent, Belgium
Received: 10 May 2012 – Discussion started: 31 May 2012 – Revised: 27 Feb 2013 – Accepted: 09 Mar 2013 – Published: 02 Apr 2013
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.
