<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Flood frequency analysis is usually performed as a univariate analysis of flood peaks using a suitable theoretical probability distribution of the annual maximum flood peaks or peak over threshold values. However, other flood attributes, such as flood volume and duration, are necessary for the design of hydrotechnical projects, too. In this study, the suitability of various copula families for a bivariate analysis of peak discharges and flood volumes has been tested. Streamflow data from selected gauging stations along the whole Danube River have been used. Kendall’s rank correlation coefficient (tau) quantifies the dependence between flood peak discharge and flood volume settings. The methodology is applied to two different data samples: 1) annual maximum flood (AMF) peaks combined with annual maximum flow volumes of fixed durations at 5, 10, 15, 20, 25, 30 and 60 days, respectively (which can be regarded as a regime analysis of the dependence between the extremes of both variables in a given year), and 2) annual maximum flood (AMF) peaks with corresponding flood volumes (which is a typical choice for engineering studies). The bivariate modelling of the extracted peak discharge - flood volume couples is achieved with the use of the Ali-Mikhail-Haq (AMH), Clayton, Frank, Joe, Gumbel, Hüsler-Reiss, Galambos, Tawn, Normal, Plackett and FGM copula families. Scatterplots of the observed and simulated peak discharge - flood volume pairs and goodness-of-fit tests have been used to assess the overall applicability of the copulas as well as observing any changes in suitable models along the Danube River. The results indicate that for the second data sampling method, almost all of the considered Archimedean class copula families perform better than the other copula families selected for this study, and that for the first method, only the upper-tail-flat copulas excel (except for the AMH copula due to its inability to model stronger relationships).</p></abstract>

Flood frequency analysis is usually performed as a univariate analysis of flood peaks using a suitable theoretical probability distribution of the annual maximum flood peaks or peak over threshold values. However, other flood attributes, such as flood volume and duration, are necessary for the design of hydrotechnical projects, too. In this study, the suitability of various copula families for a bivariate analysis of peak discharges and flood volumes has been tested. Streamflow data from selected gauging stations along the whole Danube River have been used. Kendall’s rank correlation coefficient (tau) quantifies the dependence between flood peak discharge and flood volume settings. The methodology is applied to two different data samples: 1) annual maximum flood (AMF) peaks combined with annual maximum flow volumes of fixed durations at 5, 10, 15, 20, 25, 30 and 60 days, respectively (which can be regarded as a regime analysis of the dependence between the extremes of both variables in a given year), and 2) annual maximum flood (AMF) peaks with corresponding flood volumes (which is a typical choice for engineering studies). The bivariate modelling of the extracted peak discharge - flood volume couples is achieved with the use of the Ali-Mikhail-Haq (AMH), Clayton, Frank, Joe, Gumbel, Hüsler-Reiss, Galambos, Tawn, Normal, Plackett and FGM copula families. Scatterplots of the observed and simulated peak discharge - flood volume pairs and goodness-of-fit tests have been used to assess the overall applicability of the copulas as well as observing any changes in suitable models along the Danube River. The results indicate that for the second data sampling method, almost all of the considered Archimedean class copula families perform better than the other copula families selected for this study, and that for the first method, only the upper-tail-flat copulas excel (except for the AMH copula due to its inability to model stronger relationships).

Joint modelling of flood peaks and volumes: A copula application for the Danube River

Journal of Hydrology and Hydromechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Flood frequency analysis is usually performed as a univariate analysis of flood peaks using a suitable theoretical probability distribution of the annual...

Joint modelling of flood peaks and volumes: A copula application for the Danube River

Published Online: Oct 21, 2016

Page range: 382 - 392

Received: Dec 01, 2015

Accepted: Sep 12, 2016

DOI: https://doi.org/10.1515/johh-2016-0049

Keywords
Bivariate frequency analysis, Copulas, Dependence of flood peaks and volumes, Kendall’s rank correlation coefficient, Danube River

© 2016 George Papaioannou et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Joint modelling of flood peaks and volumes: A copula application for the Danube River

Published Online: Oct 21, 2016

Page range: 382 - 392

Received: Dec 01, 2015

Accepted: Sep 12, 2016

DOI: https://doi.org/10.1515/johh-2016-0049

KeywordsBivariate frequency analysis, Copulas, Dependence of flood peaks and volumes, Kendall’s rank correlation coefficient, Danube River

© 2016 George Papaioannou et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Bivariate frequency analysis, Copulas, Dependence of flood peaks and volumes, Kendall’s rank correlation coefficient, Danube River