Multivariate modeling of flood characteristics using Vine copulas
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ORIGINAL ARTICLE
Multivariate modeling of flood characteristics using Vine copulas Fatih Tosunoglu1 · Faruk Gürbüz1 · Muhammet Nuri İspirli2 Received: 23 December 2019 / Accepted: 12 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Vine copulas provide a great deal of flexibility in modeling complex dependence structures between the variables. In spite of its importance, very limited attention has been paid in hydrology field. In the present study, multivariate modelling of flood characteristics was performed using traditional Archimedean and Elliptical and Vine copulas. In the first phase, flood characteristics [peak (Q), volume (V) and duration (D)] were computed from daily streamflow of 18 stations located in the Euphrates River Basin, Turkey. Based on various model selection criteria, the gamma and Weibull distributions for Q series, the logistic and generalized extreme value distributions for V series and the logistic, log-logistic and generalized extreme value distributions for D series were mostly found to be the best appropriate univariate models. In the second phase, the considered copulas were evaluated for modeling joint distribution of flood Q–V–D triplets at each station. On evaluating their performance by various copula selection methods, graphical procedures and tail dependence analysis, the Vine copulas have been identified as the most valid models. In last phase, conditional and joint return periods of different flood Q, V and D combinations were estimated and the spatial distribution of the return periods were drawn using Geographic Information Systems tool. Keywords Multivariate modeling · Archimedean · Elliptical and vine copulas · The euphrates river basin · Flood characteristics · Turkey
Introduction Flood frequency analysis is one of the widely used methods for planning, design and management of the hydraulic structures in any region of the world (Baidya et al. 2020; Nagy et al. 2017; Seckin et al. 2011; Zhang et al. 2019). Flood frequency analysis studies typically involve determining the most suitable probability distribution function for annual peak flows observed at gauge stations and flood peak values, which are used in design of hydraulic structures, are then estimated for various return periods. However, univariate methods are adequate if only one flood characteristic (peak Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12665-020-09199-6) contains supplementary material, which is available to authorized users. * Fatih Tosunoglu [email protected] 1
Department of Civil Engineering, Erzurum Technical University, Erzurum, Turkey
Department of Civil Engineering, Atatürk University, Erzurum, Turkey
2
flow or volume) is significant in the design processes. Since floods are multivariate stochastic events having mutually correlated characteristics, such as peak flood flow, corresponding volume and duration, joint distribution properties of these characteristics play an important role
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