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

Aronica, G.T., Candela, A., Fabio, P., Santoro, M., 2012. Estimation of flood inundation probabilities using global hazard indexes based on hydrodynamic variables. Phys. Chem. Earth, 42–44, 119–129.10.1016/j.pce.2011.04.001Search in Google Scholar

Bacigál, T., 2013. Modelling dependence with multivariate Archimax (or any user-defined continuous) copulas. Package ‘acopula’, R package – CRAN.10.1007/978-3-642-39165-1_11Search in Google Scholar

Bacigál, T., Mesiar, R., 2012. 3-dimensional Archimax copulas and their fitting to real data. In: Proc. 20th International conference on computational statistics COMPSTAT 2012. The International Statistical Institute, The Hague, The Netherlands, pp. 81–88.Search in Google Scholar

Bačová-Mitková, V., 2002. The relationship between volume of the flood wave and the time duration of flood events. Acta Hydrologica Slovaca, 13, 1, 165–174.Search in Google Scholar

Bačová-Mitková, V., 2011. Different approaches to the flood volumes estimation on the Bodrog River example. Acta Hydrologica Slovaca, 12, 2, 296–303. ISSN 1335-6291 (In Slovak.)Search in Google Scholar

Bačová-Mitková, V., Halmová, D., 2014. Joint modeling of flood peak discharges, volume and duration: a case study of the Danube River in Bratislava. Journal of Hydrology and Hydromechanics, 62, 3, 186–196. doi: 10.2478/johh-2014-0026.10.2478/johh-2014-0026Search in Google Scholar

Balistrocchi, M., Baldassarre, B., 2011. Modelling the statistical dependance of rainfall event variables through copula functions. Hydrol. Earth Syst. Sci., 15, 6, 1959–1977.10.5194/hess-15-1959-2011Search in Google Scholar

Bezak, N., Šraj, M., Mikoš, M., 2016. Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides. Journal of Hydrology. doi:10.1016/j.jhydrol.2016.02.058.10.1016/j.jhydrol.2016.02.058Search in Google Scholar

Cunnane, C., 1988. Methods and merits of regional flood frequency analysis. J. Hydrol., 100, 269–290.10.1016/0022-1694(88)90188-6Search in Google Scholar

Cunnane, C., 1989. Statistical distributions for flood frequency analysis. Operational Hyd. Rep. 33. World Meteorological Organization, Geneva, Switzerland.Search in Google Scholar

Dawdy, D., Griffis, V., Gupta, V., 2012. Regional Flood-Frequency Analysis: How We Got Here and Where We Are Going. J. Hydrol. Eng., 17, 9, 953–959. doi: 10.1061/(ASCE)HE.1943-5584.0000584.10.1061/(ASCE)HE.1943-5584.0000584Search in Google Scholar

De Michele, C., Salvadori, G., 2003. A generalized Pareto intensity-duration model of storm rainfall exploiting 2.- Copulas. J Geophys Res., 108, D2, 4067.10.1029/2002JD002534Search in Google Scholar

De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., Rosso, R., 2005. Bivariate statistical approach to check adequacy of dam spillway. J. Hydrol. Eng., 10, 1, 50–57.10.1061/(ASCE)1084-0699(2005)10:1(50)Search in Google Scholar

Dupuis, D.J., 2007. Using copulas in hydrology; benefits, cautions and issues. J. Hydrol. Eng., 12, 381–393.10.1061/(ASCE)1084-0699(2007)12:4(381)Search in Google Scholar

Favre, A.C., El Adlouni, S., Perreault, L., Thiémonge, N., a Bobeé, B., 2004. Multivariate hydrological frequency analysis using copulas. Water. Resour. Res., 40, W01101.10.1029/2003WR002456Search in Google Scholar

Gaál, L., Szolgay, J., Kohnova, S., Hlavcova, K., Parajka, J., Viglione, A., Merz, R., Bloschl, G., 2015. Dependence between flood peaks and volumes: a case study on climate and hydrological controls. Hydrological Sciences Journal, 60, 6, 968–984. doi: 10.1080/02626667.2014.951361.10.1080/02626667.2014.951361Search in Google Scholar

Gaál, L., Viglione, A., Szolgay, J., Blöschl, G., Bacigál, T., Rogger, M., 2010. Bivariate at-site frequency analysis of simulated flood peak-volume data using copulas. In: CD Rom – EGU General Assembly; Vienna, EGU2010-13441.Search in Google Scholar

Genest, C., Favre, A.C., 2007. Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. ASCE, 12, 4, 347–368.10.1061/(ASCE)1084-0699(2007)12:4(347)Search in Google Scholar

Genest, C., Nešlehová, J., Quessy, J.F., 2012. Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics, 64, 4, 811–834.10.1007/s10463-011-0337-6Search in Google Scholar

Genest, C., Rémillard, B., Beaudoin, D., 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Math. and Economics, 44, 2, 199–213.10.1016/j.insmatheco.2007.10.005Search in Google Scholar

Giustarini, L., Camici, S., Tarpanelli, A., Brocca, L., Melone, F., Moramarco, T., 2010. Dam spillways adequacy evaluation through bivariate flood frequency analysis and hydrological continuous simulation. In: Proc. World Environmental and Water Resources Congress 2010. American Society of Civil Engineers (ASCE), Reston, Virginia, USA, pp. 2328–2339.10.1061/41114(371)241Search in Google Scholar

Goel, N.K., Seth, S.M., Chandra, S., 1998. Multivariate modeling of flood flows. ASCE, J. Hydraul. Eng., 124, 146–155.10.1061/(ASCE)0733-9429(1998)124:2(146)Search in Google Scholar

Groupe de recherche en hydrologie statistique (GREHYS), 1996. Presentation and review of some methods for regional flood frequency analysis. J. Hydrol., 186, 63–84.10.1016/S0022-1694(96)03042-9Search in Google Scholar

Gudendorf, G., Segers, J., 2010. Extreme-value copulas. In: Jaworski, P., Durante, F., Härdle, W.K., Rychlik, T. (Eds.): Copula Theory and its Applications. Springer, Berlin Heidelberg, pp. 127–145.10.1007/978-3-642-12465-5_6Search in Google Scholar

Chowdhary, H., Escobar, L.A., Singh, V.P., 2011. Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data. Hydrology Research, 42, 2–3, 193–216. doi:10.2166/nh.2011.065.10.2166/nh.2011.065Search in Google Scholar

ICPDR, 2009. http://www.icpdr.org/main/activities-projects/danube-river-basin-management-plan-2009Search in Google Scholar

Kendall, M.G., 1955. Rank Correlation Methods. Hafner Publishing Co., New York.Search in Google Scholar

Laio, F., Ganora, D., Claps, P., Galeati, G., 2011. Spatially smooth regional estimation of the flood frequency curve (with uncertainty). J. Hydrol., 408, 67–77. doi:10.1016/j.jhydrol.2011.07.022.10.1016/j.jhydrol.2011.07.022Search in Google Scholar

Ljung, G.M., Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika, 65, 297–303.10.1093/biomet/65.2.297Search in Google Scholar

Mann, H. B., 1945. Nonparametric tests against trend. Econometrica: Journal of the Econometric Society, 13, 3, 245–259.10.2307/1907187Search in Google Scholar

Mediero, L, Jimenez-Alvarez, A., Garrote, L., 2010. Design flood hydrographs from the relationship between flood peak and volume. Hydrol. Earth Syst. Sci., 14, 2495–2505.10.5194/hess-14-2495-2010Search in Google Scholar

Mediero, L., Kjeldsen, T., 2014. Regional flood hydrology in a semi-arid catchment using a GLS regression model. J. Hydrol., 514, 158–171. doi:10.1016/j.jhydrol.2014.04.007.10.1016/j.jhydrol.2014.04.007Search in Google Scholar

Nelsen, R.B., 2006. An introduction to copulas. Lecture notes in statistics. 2^nd ed., Springer, New York.Search in Google Scholar

Pekárová, P., Halmová, D., Bačová Mitková, V., Miklánek, P., Pekár, J., Škoda, P., 2013. Historic flood marks and flood frequency analysis of the Danube River at Bratislava, Slovakia. J. Hydrol. Hydromech., 61, 4, 326–333.10.2478/johh-2013-0041Search in Google Scholar

Pekárová, P., Onderka, M., Pekár, J., Miklanek, P., Halmová, D., Škoda, P., Bačová Mitková, V., 2008. Hydrologic scenarios for the Danube River at Bratislava. Key Publishing, Ostrava, 160 p., http://www.ih.savba.sk/danubeflood.Search in Google Scholar

R Core Team, 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. URL: http://www.R-project.org.Search in Google Scholar

Reddy, M.J., Ganguli, P., 2012. Bivariate flood frequency analysis of Upper Godavari River flows using Archimedean copulas. Water Resour. Manag., 26, 3995–4018. doi:10.1007/s11269-012-0124-z.10.1007/s11269-012-0124-zSearch in Google Scholar

Salvadori, G., De Michele, C., 2004. Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour. Res., 40, 12. doi: 10.1029/2004WR003133.10.1029/2004WR003133Search in Google Scholar

Salvadori, G., De Michele, C., 2010. Multivariate multiparameter extreme value models and return periods: A copula approach. Water Resour. Res., 46, 10. doi: 10.1029/2009WR009040.10.1029/2009WR009040Search in Google Scholar

Shiau, J.T., Wang, H.Y., Tsai, C.T., 2006. Bivariate frequency analysis of floods using copulas. J. Am. Wat. Resour. Assoc., 42, 6, 1549–1564.10.1111/j.1752-1688.2006.tb06020.xSearch in Google Scholar

Singh, K., Singh, V.J., 1991. Derivation of bivariate propability density functions with exponential marginals. Stoch. Hydrol. Hydraulics, 5, 1, 55–68.10.1007/BF01544178Search in Google Scholar

Sommerwerk, N., Baumgartner, C., Blösch, J., Hein, T., Ostojic, A., Paunovic, M., Schneider-Jacoby, M., Siber, R., Tockner, K., 2009. Chapter 3: Danube River basin. In: Tockner, K., Robinson, T.C., Uehlinger, U. (Eds.): Rivers of Europe. Academic Press, London, pp. 59–112.10.1016/B978-0-12-369449-2.00003-5Search in Google Scholar

Sraj, M., Bezak, N., Brilly, M., 2015. Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River. Hydrol. Process., 29, 235–248.10.1002/hyp.10145Search in Google Scholar

Szolgay, J., Gaál, L., Bacigál, T., Kohnová, S., Hlavčová, K., Výleta, R., Blöschl, G., 2016. A regional look at the selection of a process-oriented model for flood peak/volume relationships. In: Proceedings of IAHS, 373, Copernicus Publications, Göttingen, Germany, pp. 61–69. doi: 10.5194/piahs-373-1-2016.10.5194/piahs-373-1-2016Search in Google Scholar

Szolgay, J., Gaál, L., Kohnová, S., Hlavčová, K., Výleta, R., Bacigál, T., Blöschl, G., 2015. A process-based analysis of the suitability of copula types for peak-volume flood relationships. In: Proc. IAHS, 370, Copernicus Publications, Göttingen, Germany, pp. 183–188. doi: 10.5194/piahs-370-183-2015.10.5194/piahs-370-183-2015Search in Google Scholar

Szolgay, J., Kohnová, S., Bacigál, T., Hlavčová, K., 2012. Proposed flood: joint probability analysis of maximum discharges and their pertaining volumes. Acta Hydrologica Slovaca, 13, 2, 297–305.Search in Google Scholar

Tawn, J.A, 1988. Extreme value theory: Models and estimation. Biometrika. 75, 397–415.10.1093/biomet/75.3.397Search in Google Scholar

Willems, P., 2009. A time series tool to support the multicriteria performance evaluation of rainfall-runoff models. Environmental Modelling and Software, 24, 311–321.10.1016/j.envsoft.2008.09.005Search in Google Scholar

Yue, S., Ouarda, T.B.M.J., Bobee, B., 2001. A review of bivariate Gamma distribution for hydrological application. J. Hydrol., 246, 1–4, 1–18.10.1016/S0022-1694(01)00374-2Search in Google Scholar

Zhang, L., Singh, V.P., 2006. Bivariate flood frequency analysis using the copula method. J. Hydrol. Eng., ASCE, 11, 2, 150–164.10.1061/(ASCE)1084-0699(2006)11:2(150)Search in Google Scholar

Zhang, L., Singh, V.P., 2007. Bivariate rainfall frequency distributions using Archimedean copulas. J. Hydrol., 332, 93–109.10.1016/j.jhydrol.2006.06.033Search in Google Scholar