Articles | Volume 17, issue 4
Hydrol. Earth Syst. Sci., 17, 1281–1296, 2013
Hydrol. Earth Syst. Sci., 17, 1281–1296, 2013
Research article
02 Apr 2013
Research article | 02 Apr 2013

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. Verhoest2 B. Gräler et al.
  • 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

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.