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

AghaKouchak, A., 2014. Entropy-copula in hydrology and climatology. Journal of Hydrometeorology, 15, 2176–2189. doi:10.1175/JHM-D-13-0207.1.10.1175/JHM-D-13-0207.1Search in Google Scholar

Bačová Mitková, V., 2012. Vzájomný vzťah objemu a dĺžky trvania povodňových vĺn. [The relationship between volume of the flood wave and the time duration of flood events]. Acta Hydrologica Slovaca, 13, 1, 165–174. (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

Ben-Aissia, M.-A., Chebana, F., Ouarda, T.B.M.J., Roy, L., Desrochers, G., Chartier, I., Robichaud, É., 2012. Multivariate analysis of flood characteristics in a climate change context of the watershed of the Baskatong reservoir, Province of Québec, Canada. Hydrological Processes, 26, 130–142. doi:10.1002/hyp.8117.10.1002/hyp.8117Search in Google Scholar

Ben Aissia, M.-A., Chebana, F., Ouarda, T.B.M.J., Bruneau, P., Barbet, M., 2015. Bivariate index-flood model: case study in Québec, Canada. Hydrological Sciences Journal, 60, 2, 247–268. doi:10.1080/02626667.2013.875177.10.1080/02626667.2013.875177Search in Google Scholar

Bezak, N., Mikoš, M., Šraj, M., 2014. Trivariate frequency analyses of peak discharge, hydrograph volume and suspended sediment concentration data using copulas. Water Resources Management, 28, 8, 2195–2212. doi:10.1007/s11269-014-0606-2.10.1007/s11269-014-0606-2Search in Google Scholar

Blöschl, G., Viglione, A., Merz, R., Parajka, J., Salinas, J.L., Schöner, W., 2011. Auswirkungen des Klimawandels auf Hochwasser und Niederwasser. [Climate impacts on floods and low flows]. Österreichische Wasser- und Abfallwirtschaft, 63, 1, 21–30. doi:10.1007/s00506-010-0269-z. (In German.)10.1007/s00506-010-0269-zSearch in Google Scholar

Chapman, T.G., Maxwell, A.I., 1996. Baseflow separation—comparison of numerical methods with tracer experiments. In: 23^rd Hydrology and Water Resources Symposium: Water and the Environment, Natl. Conf. Publ., 96/05, Inst. of Eng., Barton, A.C.T., Australia, pp. 539–545.Search in Google Scholar

Chebana, F., Ouarda, T.B.M.J., 2007. Multivariate L-moment homogeneity test. Water Resources Research, 43, W08406. doi:10.1029/2006WR005639.10.1029/2006WR005639Search in Google Scholar

Chebana, F., Ouarda, T.B.M.J., 2009. Index flood-based multivariate regional frequency analysis. Water Resources Research, 45, W10435. doi 10.1029/2008WR007490.10.1029/2008WR007490Search 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

Dalrymple, T., 1960. Flood frequency analysis. U.S. Geological Survey Water-Supply Paper, 1543-A, 80 p.Search in Google Scholar

Favre, A.-C., El Adlouni, S., Perreault, L., Thiémonge, N., Bobée, B., 2004. Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40, W01101. doi:10.1029/2003WR002456.10.1029/2003WR002456Search in Google Scholar

Gaál, L., Szolgay, J., Kohnová, S., Parajka, J., Merz, R., Viglione, A., Blöschl, G., 2012. Flood timescales: Understanding the interplay of climate and catchment processes through comparative hydrology. Water Resources Research, 48, 4, W04511. doi:10.1029/2011WR011509.10.1029/2011WR011509Search in Google Scholar

Gaál, L., Kohnová, S., Szolgay, J., 2013. Regional flood frequency analysis in Slovakia: Which pooling approach suits better? In: Klijn, F., Schweckendiek, T. (Eds.): Comprehensive Flood Risk Management: Research for Policy and Practice. London, CRC Press/Balkema, pp. 27–30.10.1201/b13715-7Search in Google Scholar

Gaál, L., Szolgay, J., Kohnová, S., Hlavčová, K., Parajka, J., Viglione, A., Merz, R., Blöschl, G., 2014. 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

Ganguli, P., Reddy, M.J., 2013. Probabilistic assessment of flood risks using trivariate copulas. Theoretical and Applied Climatology, 111, 341–360. doi:10.1007/s00704-012-0664-4.10.1007/s00704-012-0664-4Search in Google Scholar

Genest, C., Favre, A.-C., 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12, 4, 47–368. doi: 10.1061/(ASCE)1084-0699(2007)12:4(347).10.1061/(ASCE)1084-0699(2007)12:4(347)Search in Google Scholar

Genest, C., Rémillard, B., Beaudoin, D., 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44, 199–213. doi:10.1016/j.insmatheco.2007.10.005.10.1016/j.insmatheco.2007.10.005Search in Google Scholar

Gräler, B., van den Berg, M.J., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., Verhoest, N.E.C., 2013. Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrology and Earth System Sciences, 17, 1281–1296. doi:10.5194/hess-17-1281-2013.10.5194/hess-17-1281-2013Search in Google Scholar

Grimaldi, S., Serinaldi, F., 2006. Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources, 29, 8, 1155–1167. doi: 10.1016/j.advwatres.2005.09.005.10.1016/j.advwatres.2005.09.005Search in Google Scholar

Grimaldi, S., Petroselli, A., Salvadori, G., De Michele, C., 2016. Catchment compatibility via copulas: A nonparametric study of the dependence structures of hydrological responses. Advances in Water Resources, 90, 116–133. doi:10.1016/j.advwatres.2016.02.003.10.1016/j.advwatres.2016.02.003Search in Google Scholar

Hosking, J.R.M., Wallis, J.R., 1997. Regional Frequency Analysis: An Approach Based on L-moments, Cambridge University Press, Cambridge, UK.10.1017/CBO9780511529443Search in Google Scholar

IH, 1999. Flood Estimation Handbook. Institute of Hydrology: Wallingford, UK.Search in Google Scholar

Karmakar, S., Simonovic, S.P., 2009. Bivariate flood frequency analysis. Part 2: A copula-based approach with mixed marginal distributions. Journal of Flood Risk Management, 2, 32–44. doi:10.1111/j.1753-318X.2009.01020.x.10.1111/j.1753-318X.2009.01020.xSearch in Google Scholar

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

Kohnová, S., Szolgay, J., 1999. Regional estimation of design summer flood discharge in small catchments of northern Slovakia. In: Gottschalk, L., Olivry, C., Reed, D., Rosbjerg, D. (Eds.): Hydrological Extremes: Understanding, Predicting, Mitigating. IAHS publ. 255, IAHS Press, Wallingford, pp. 265–268.Search 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. doi:10.1093/biomet/65.2.297.10.1093/biomet/65.2.297Search in Google Scholar

Merz, R., Blöschl, G., 2003. A process typology of regional floods. Water Resources Research, 39, 12, 1340–1347. doi:10.1029/2002WR001952.10.1029/2002WR001952Search in Google Scholar

Merz, R., Blöschl, G., 2009. A regional analysis of event runoff coefficients with respect to climate and catchment characteristics in Austria. Water Resources Research, 45, 1, W01415. doi:10.1029/2008WR007163.10.1029/2008WR007163Search in Google Scholar

Merz, R., Blöschl, G., Parajka, J., 2006. Spatio-temporal variability of event runoff coefficients. Journal of Hydrology, 331, 3–4, 591–604. doi:10.1016/j.jhydrol.2006.06.008.10.1016/j.jhydrol.2006.06.008Search in Google Scholar

Nelsen, R.B., 2006. An Introduction to Copulas. 2^nd edition. Springer-Verlag, New York.Search in Google Scholar

Parajka, J., Merz, R., Blöschl, G., 2007. Uncertainty and multiple objective calibration in regional water balance modelling – Case study in 320 Austrian catchments. Hydrological Processes, 21, 435–446. doi:10.1002/hyp.6253.10.1002/hyp.6253Search in Google Scholar

Parajka, J., Kohnová, S., Bálint, G., Barbuc, M., Borga, M., Claps, P., Cheval, S., Dumitrescu, A., Gaume, E., Hlavčová, K., Merz, R., Pfaundler, M., Stancalie, G., Szolgay, J., Blöschl, G., 2010. Seasonal characteristics of flood regimes across the Alpine–Carpathian range. Journal of Hydrology, 394, 1–2, 78–89. doi:10.1016/j.jhydrol.2010.05.015.10.1016/j.jhydrol.2010.05.015Search in Google Scholar

Pham, M.T., Vernieuwe, H., Baets, B.D., Willems, B., Verhoest, N.E.C., 2015. Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas. Stochastic Environmental Research and Risk Assessment, 18 p. doi: 10.1007/s00477-015-1181-7.10.1007/s00477-015-1181-7Search in Google Scholar

Poulin, A., Huard, D., Favre, A.-C., Pugin, S., 2007. Importance of tail dependence in bivariate frequency analysis. Journal of Hydrologic Engineering, 12, 4, 394–403. doi:10.1061/(ASCE)1084-0699(2007)12:4(394).10.1061/(ASCE)1084-0699(2007)12:4(394)Search in Google Scholar

Reddy, M.J., Ganguli, P., 2012. Bivariate flood frequency analysis of Upper Godavari River flows using Archimedean copulas. Water Resources Management, 26, 14, 3995–4018. doi:10.1007/s11269-012-0124-z.10.1007/s11269-012-0124-zSearch in Google Scholar

Remillard, B., Plante, J.-F., 2012. TwoCop: Nonparametric test of equality between two copulas. R package version 1.0 (19-10-2012). http://cran.r-project.org/web/packages/TwoCop.Search in Google Scholar

Remillard, B., Scaillet, O., 2009. Testing for equality between two copulas. Journal of Multivariate Analysis, 100, 377–386. doi:10.1016/j.jmva.2008.05.004.10.1016/j.jmva.2008.05.004Search in Google Scholar

Requena, A.I., Chebana, F., Mediero, L., 2016. A complete procedure for multivariate index-flood model application. Journal of Hydrology, 535, 559–580. doi:10.1016/j.jhydrol.2016.02.004.10.1016/j.jhydrol.2016.02.004Search in Google Scholar

Rosbjerg, D., Blöschl, G., Burn, D.H., Castellarin, A., Croke, B., DiBaldassarre, G., Iacobellis, V., Kjeldsen, T.R., Kuczera, G., Merz, R., Montanari, A., Morris, D., Ouarda, T.B.M.J., Ren, L., Rogger, M., Salinas, J.L., Toth, E., Viglione, A., 2013. Prediction of floods in ungauged basins. Chapter 9. In: Blöschl, G., Sivapalan, M., Wagener, T., Viglione, A., Savenije, H. (Eds.): Runoff Prediction in Ungauged Basins - Synthesis across Processes, Places and Scales. Cambridge University Press, Cambridge, UK, pp. 135–162.10.1017/CBO9781139235761.012Search in Google Scholar

Salinas, J.L., Castellarin, A., Viglione, A., Kohnová, S., Kjeldsen, T.R., 2014. Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent? Hydrology and Earth System Sciences, 18, 4381–4389. doi:10.5194/hess-18-4381-2014.10.5194/hess-18-4381-2014Search in Google Scholar

Serinaldi, F., 2013. An uncertain journey around the tails of multivariate hydrological distributions. Water Resources Research, 49, 10, 6527–6547. doi:10.1002/wrcr.20531.10.1002/wrcr.20531Search in Google Scholar

Serinaldi, F., 2015. Can we tell more than we can know? The limits of bivariate drought analysis in the United States. Stochastic Environmental Research and Risk Assessment, 14 p. doi:10.1007/s00477-015-1124-3.10.1007/s00477-015-1124-3Search in Google Scholar

Serinaldi, F., Kilsby, C.G., 2013. The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs. Water Resources Research, 49, 3423–3442. doi:10.1002/wrcr.20221.10.1002/wrcr.20221430392425653461Search in Google Scholar

Shiau, J.-T., Wang, H.-Y., Tsai, C.-T., 2006. Bivariate flood frequency analysis of floods using copulas. Journal of the American Water Resources Association, 42, 6, 1549–1564. doi:10.1111/j.1752-1688.2006.tb06020.x.10.1111/j.1752-1688.2006.tb06020.xSearch in Google Scholar

Sraj, M., Bezak, N., Brilly, M., 2014. Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River. Hydrological Processes, 29, 2, 225–238. doi:10.1002/hyp.10145.10.1002/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. IAHS publ. 373. IAHS Press, Wallingford, 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. Proc. IAHS, 370, 183–188. doi: 10.5194/piahs-370-183-2015.10.5194/piahs-370-183-2015Search in Google Scholar

Vernieuwe, H., Vandenberghe, S., De Baets, B., Verhoest, N.E.C., 2015. A continuous rainfall model based on vine copulas. Hydrology and Earth System Sciences, 19, 6, 2685–2699. doi:10.5194/hess-19-2685-2015.10.5194/hess-19-2685-2015Search in Google Scholar

Werner, P.C., Gerstengarbe, F.-W., 2010. Katalog der Grosswetterlagen Europas (1881–2009) nach Paul Hess und Helmut Brezowsky, 7., verbesserte und ergänzte Auflage. [Catalog of Large Weather Conditions of Europe (1881-2009), after Paul Hess and Helmut Brezowsky, 7^th, Improved and Completed Edition]. PIK-Report No. 119, Potsdam Institute for Climate Impact Research, Potsdam, 146 p. (In German.)Search in Google Scholar

Zhang, L., Singh, V.P., 2006. Bivariate flood frequency analysis using the copula method. Journal of Hydrologic Engineering 11, 150–164. doi:10.1061/(asce)1084-0699(2006)11:2(150).10.1061/(ASCE)1084-0699(2006)11:2(150)Search in Google Scholar