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

被引:238
作者
Graeler, B. [1 ]
van den Berg, M. J. [2 ]
Vandenberghe, S. [2 ]
Petroselli, A. [3 ]
Grimaldi, S. [4 ,5 ,6 ]
De Baets, B. [7 ]
Verhoest, N. E. C. [2 ]
机构
[1] Univ Munster, Inst Geoinformat, D-48151 Munster, Germany
[2] Univ Ghent, Lab Hydrol & Water Management, B-9000 Ghent, Belgium
[3] Univ Tuscia, DAFNE Dept, Dipartimento Sci & Tecnol Agr Foreste Nat & Energ, I-01100 Viterbo, Italy
[4] Univ Tuscia, DIBAF Dept, Dipartimento Innovaz Sistemi Biol Agroalimentari, I-01100 Viterbo, Italy
[5] Univ Roma La Sapienza, Honors Ctr Italian Univ H2CU, I-00184 Rome, Italy
[6] NYU, Polytech Inst, MetroTech Ctr 6, Dept Mech & Aerosp Engn, Brooklyn, NY 11201 USA
[7] Dept Math Modelling Stat & Bioinformat, B-9000 Ghent, Belgium
关键词
COPULA; CONSTRUCTION; 3-COPULA; MODEL;
D O I
10.5194/hess-17-1281-2013
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
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.
引用
收藏
页码:1281 / 1296
页数:16
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