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

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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.
Keywords
COPULA, MODEL, FREQUENCY-ANALYSIS, DEPENDENT RANDOM-VARIABLES, CONSTRUCTION, 3-COPULA, STORMS, VINES

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Chicago
Gräler, Benedikt, Martinus van den Berg, Sander Vandenberghe, Andrea Petroselli, Salvatore Grimaldi, Bernard De Baets, and Niko Verhoest. 2013. “Multivariate Return Periods in Hydrology : a Critical and Practical Review Focusing on Synthetic Design Hydrograph Estimation.” Hydrology and Earth System Sciences 17 (4): 1281–1296.
APA
Gräler, B., van den Berg, M., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., & Verhoest, N. (2013). Multivariate return periods in hydrology : a critical and practical review focusing on synthetic design hydrograph estimation. HYDROLOGY AND EARTH SYSTEM SCIENCES, 17(4), 1281–1296.
Vancouver
1.
Gräler B, van den Berg M, Vandenberghe S, Petroselli A, Grimaldi S, De Baets B, et al. Multivariate return periods in hydrology : a critical and practical review focusing on synthetic design hydrograph estimation. HYDROLOGY AND EARTH SYSTEM SCIENCES. 2013;17(4):1281–96.
MLA
Gräler, Benedikt et al. “Multivariate Return Periods in Hydrology : a Critical and Practical Review Focusing on Synthetic Design Hydrograph Estimation.” HYDROLOGY AND EARTH SYSTEM SCIENCES 17.4 (2013): 1281–1296. Print.
@article{3223554,
  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.},
  author       = {Gr{\"a}ler, Benedikt and van den Berg, Martinus and Vandenberghe, Sander and Petroselli, Andrea and Grimaldi, Salvatore and De Baets, Bernard and Verhoest, Niko},
  issn         = {1027-5606},
  journal      = {HYDROLOGY AND EARTH SYSTEM SCIENCES},
  language     = {eng},
  number       = {4},
  pages        = {1281--1296},
  title        = {Multivariate return periods in hydrology : a critical and practical review focusing on synthetic design hydrograph estimation},
  url          = {http://dx.doi.org/10.5194/hess-17-1281-2013},
  volume       = {17},
  year         = {2013},
}

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