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Hydrol. Earth Syst. Sci. Discuss., 9, 6781-6828, 2012
www.hydrol-earth-syst-sci-discuss.net/9/6781/2012/ doi:10.5194/hessd-9-6781-2012 © Author(s) 2012. This work is distributed under the Creative Commons Attribution 3.0 License. |
Joint return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation
1Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, 9000 Ghent, Belgium
2Institute for Geoinformatics, University of Münster, Weseler Str. 253, 48151 Münster, Germany
3Dipartimento per la innovazione nei sistemi biologici agroalimentari e forestali (DIBAF Department), University of Tuscia, Via San Camillo De Lellis, 01100 Viterbo, Italy
4Department of Mathematical Modelling, Statistics and Bioinformatics, Coupure links 653, 9000 Ghent, Belgium
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, 11201 New York, USA
7Dipartimento 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
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 the joint return period be defined and applied? In this study, an overview of the state-of-the-art for defining joint return periods is given. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analysis and their ability to model numerous types of dependence structures in a flexible way. A case study focusing on the selection of design hydrograph characteristics is presented and the design values of a three-dimensional phenomenon composed of peak discharge, volume and duration are derived. Joint return period methods based on regression analysis, bivariate conditional distributions, bivariate joint distributions, and Kendal distribution functions are investigated and compared highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based method is introduced. For a given design return period, the method chosen clearly affects the calculated design event. Eventually, light is shed on the practical implications of a chosen method.
Citation: Vandenberghe, S., van den Berg, M. J., Gräler, B., Petroselli, A., Grimaldi, S., De Baets, B., and Verhoest, N. E. C.: Joint return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation, Hydrol. Earth Syst. Sci. Discuss., 9, 6781-6828, doi:10.5194/hessd-9-6781-2012, 2012.