Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation
By Benedikt Gräler, M. V. D. Berg, Sander Vandenberghe, Andrea Petroselli, Salvatore Grimaldi, B. De Baets, Niko E. C. Verhoest. 2012
301 citations recorded by the source corpus.
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 satis- factory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and ap- plied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivari- ate design events is given and the different approaches are compared. The construction of multivariate distribution func- tions is done through the use of copulas, given their practi- cality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexi- ble way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrat- ing 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, bi- variate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is pre- sented. For a given design return period, the approach chosen clearly affects the calculated design event, and much atten- tion should be given to the choice of the approach used as this depends on the real-world problem at hand.
Subfields: Civil and Structural Engineering, Global and Planetary Change, Water Science and Technology
View Paper: https://www.semanticscholar.org/paper/ea40033c201879a56721f5cc74954608219a6d9e
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In Global and Planetary Change
In Water Science and Technology
Citations in the corpus
- Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model (2016, methodology): “Based on the above discussion, we extend the parametric vine copula model (Gräler et al., 2013) in modeling flood characterizations with the minimum information pair-copula model.”
- Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy) (2017, unknown): “This may be useful when assessing the risk of CEs through, e.g., multivariate return periods of the contributing variables Y (e.g. Graeler et al., 2016, 2013; Salvadori et al., 2016, 2011; Wahl et al., 2015; Aghakouchak et al., 2014; Saghafian and Mehdikhani, 2013; Shiau et al., 2007; Shiau, 2003)…”
- Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River (2015, background): “Joint (primary) return periods called OR and AND were used (Salvadori et al., 2007; Graler et al., 2013): TORu;v ¼ μ 1 Cu;v u; vð Þ; TANDu;v ¼ μ 1 u vþ Cu;v u; vð Þ (8) where μ is the mean interarrival time of the two consecutive events.”
- Uncertainty Analysis of Bivariate Design Flood Estimation and its Impacts on Reservoir Routing (2018, background): “For a given JRP, the corresponding level t can easily be calculated, the most likely combination (MLC) point (q,w) of all possible events at this level can be obtained by selecting the point with the largest joint probability density (Salvadori et al. 2011; Gräler et al. 2013):”