Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

Šraj, Mojca; Bezak, Nejc; Brilly, Mitja

doi:10.1002/hyp.10145

Cited by 167 publications

(127 citation statements)

References 52 publications

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“…Given its easy construction, the Archimedean copulas have been extensively applied in bivariate hydrological frequency analysis (e.g., Sraj et al 2015;Salvadori and Michele 2015;Requena et al 2016a, b). Meta-elliptical copulas (Fang et al 2002), as the name suggests, is derived from the elliptical joint distribution.…”

Section: Copula Families and Parameter Estimationmentioning

confidence: 99%

Copula–entropy theory for multivariate stochastic modeling in water engineering

Singh

Zhang

2018

Geosci. Lett.

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The copula-entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) have been applied to multivariate modeling in water engineering. This study evaluates the copula-entropy theory using a sample dataset with known population information and a flood dataset from the experimental watershed at the Walnut Gulch, Arizona. The study finds the following: (1) both univariate and joint distributions can be derived using the entropy theory. (2) The parametric copula fits the true copula better using empirical marginals than using fitted parametric/entropy-based marginals. This suggests that marginals and copula may be identified separately in which the copula is investigated with empirical marginals. (3) For a given set of constraints, the most entropic canonical copula (MECC) is unique and independent of the marginals. This allows the universal solution for the proposed analysis. (4) The MECC successfully models the joint distribution of bivariate random variables. (5) Using the "AND" case return period analysis as an example, the derived MECC captures the change of return period resulting from different marginals.

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Section: Copula Families and Parameter Estimationmentioning

confidence: 99%

Copula–entropy theory for multivariate stochastic modeling in water engineering

Singh

Zhang

2018

Geosci. Lett.

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“…Most of the recent research on statistical models of flood peakvolume relationships revolved around copulas for individual catchments (Bačová Mitková, 2012;Bačová Mitková and Halmová, 2014;Ben-Aissia et al, 2012;Chowdhary et al, 2011;Favre et al, 2004;Ganguli and Reddy, 2013;Genest and Favre, 2007;Karmakar and Simonovic, 2009;Poulin et al, 2007;Reddy and Ganguli, 2012;Shiau et al, 2006;Sraj et al, 2014;Zhang and Singh, 2006). These studies examined parameter estimation methods and the suitability of particular copula types on the basis of a single or a few catchments.…”

Section: Introductionmentioning

confidence: 99%

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Szolgay

Gaál

Bacigál

et al. 2016

Journal of Hydrology and Hydromechanics

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This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical and theoretical copulas in a regional context, with a focus on flood generation processes in general, the regional differentiation of these and the effect of the sample size on reliable discrimination among models. A total of 72 catchments in North-West of Austria are analysed for the period . From the hourly runoff data set, 25 697 flood events were isolated and assigned to one of three flood process types: synoptic floods (including long-and short-rain floods), flash floods or snowmelt floods (both rain-on-snow and snowmelt floods). The first step of the analysis examines whether the empirical peak-volume copulas of different flood process types are regionally statistically distinguishable, separately for each catchment and the role of the sample size on the strength of the statements. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods. The second step examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type across the region. Empirical copulas of synoptic floods are the least similar between the catchments, however with the decrease of the sample size the difference between the performances of the process types becomes small. The third step examines the goodness-of-fit of different commonly used copula types to the data samples that represent the annual maxima of flood peaks and the respective volumes both regardless of flood generating processes (the traditional engineering approach) and also considering the three process-based classes. Extreme value copulas (Galambos, Gumbel and Hüsler-Reiss) show the best performance both for synoptic and flash floods, while the Frank copula shows the best performance for snowmelt floods. It is concluded that there is merit in treating flood types separately when analysing and estimating flood peak-volume dependence copulas; however, even the enlarged dataset gained by the process-based analysis in this study does not give sufficient information for a reliable model choice for multivariate statistical analysis of flood peaks and volumes.

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“…The Copula function has been widely used in recent years to study the synchronous-asynchronous joint probabilities of hydrologic variables due to its ability to accurately predict nonlinear and asymmetric correlations and allow different marginal distributions [15][16][17]. Grimaldi and Serinaldi (2006) [18] used the asymmetric Copula function to investigate the correlation among peak, volume and duration of a flood event.…”

Section: Introductionmentioning

confidence: 99%

Variations in the Runoff-Sediment Relationship of the Weihe River Basin Based on the Copula Function

Guo

Chang

Wang

et al. 2016

Water

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This study investigates the runoff-sediment relationship (RSR) of the Weihe River, a sandy waterway originating from the Loess Plateau, and considers the potential variations in RSR under an evolving environment. The double mass curve method was used to investigate RSR inflection points at six hydrologic stations located in the Weihe River basin (WRB) spanning the period from 1956 to 2010. Because of its ability to accurately define nonlinear and asymmetric correlations between variables, the Copula function provided the joint probability distributions and revealed the joint probabilities of annual runoff and sediment yield through different periods. The results indicated: (1) The sediment yield and runoff exhibit decreasing trends, which was principally related to human activity such as soil and water conservation measures, water projects and industrial and domestic water use, (2) the RSR inflection points principally occurred around 1983 at the Weijiabu, Xianyang, Huaxian and Zhuangtou stations, whereas they were non-significant at the Linjiacun and Zhangjiashan stations. Changes in RSR are attributed to the irregular effect of human activity reducing the runoff and sediment output; and (3) the joint probability distributions of annual runoff and sediment yield varied under an evolving environment and were characterized by spatial variability, which is more evident in the mainstream areas of the Weihe River than in the tributary regions.

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Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

Cited by 167 publications

References 52 publications

Copula–entropy theory for multivariate stochastic modeling in water engineering

Copula–entropy theory for multivariate stochastic modeling in water engineering

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Variations in the Runoff-Sediment Relationship of the Weihe River Basin Based on the Copula Function

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