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Trivariate Frequency Analyses of Peak Discharge, Hydrograph Volume and Suspended Sediment Concentration Data Using Copulas


Copula functions are often used for multivariate frequency analyses, but discharge and suspended sediment concentrations have not yet been modelled together with the use of 3-dimensional copula functions. One hydrological station from Slovenia and five stations from USA with watershed areas from 920 km2 to 24,996 km2 were used for trivariate frequency analyses of peak discharges, hydrograph volumes and suspended sediment concentrations. Different parametric marginal distributions were applied and parameters were estimated with the method of L-moments. Maximum pseudo-likelihood method was used for copula parameters estimation. With the use of statistical and graphical tests we selected the most appropriate copula model. Symmetric and asymmetric versions of Archimedean copulas were applied according to the dependence characteristics of the individual stations. We selected Gumbel-Hougaard copula as the most appropriate model for all discussed stations. Primary joint return periods OR and secondary Kendall’s return periods were calculated and comparison between selected copula functions was made. We can conclude that copula functions are useful mathematical tool, which can also be used for modelling variables that are presented in this paper.

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We wish to thank the Environmental Agency of the Republic of Slovenia (ARSO) for data provision. We would also like to express our thanks to the United States Geological Survey (USGS) for making the hydrological data available to the public on their web site. The results of the study are part of the Faculty of Civil and Geodetic engineering (UL FGG) work on the Slovenian national research project J2-4096 and on the international research project SedAlp, which is financed by the European Union through the Alpine Space program. The critical and useful comments of three anonymous reviewers and associate editor helped to improve this manuscript, for which the authors are very grateful.

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Correspondence to Nejc Bezak.

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Bezak, N., Mikoš, M. & Šraj, M. Trivariate Frequency Analyses of Peak Discharge, Hydrograph Volume and Suspended Sediment Concentration Data Using Copulas. Water Resour Manage 28, 2195–2212 (2014).

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  • Multivariate analysis
  • Symmetric copulas
  • Asymmetric copulas
  • Flood frequency analysis
  • Suspended sediments