Inclusion of historical information in flood frequency analysis using a Bayesian MCMC technique: a case study for the power dam Orlík, Czech Republic

Open access

Inclusion of historical information in flood frequency analysis using a Bayesian MCMC technique: a case study for the power dam Orlík, Czech Republic

The paper deals with at-site flood frequency estimation in the case when also information on hydrological events from the past with extraordinary magnitude are available. For the joint frequency analysis of systematic observations and historical data, respectively, the Bayesian framework is chosen, which, through adequately defined likelihood functions, allows for incorporation of different sources of hydrological information, e.g., maximum annual flood peaks, historical events as well as measurement errors. The distribution of the parameters of the fitted distribution function and the confidence intervals of the flood quantiles are derived by means of the Markov chain Monte Carlo simulation (MCMC) technique.

The paper presents a sensitivity analysis related to the choice of the most influential parameters of the statistical model, which are the length of the historical period h and the perception threshold X0. These are involved in the statistical model under the assumption that except for the events termed as ‘historical’ ones, none of the (unknown) peak discharges from the historical period h should have exceeded the threshold X0. Both higher values of h and lower values of X0 lead to narrower confidence intervals of the estimated flood quantiles; however, it is emphasized that one should be prudent of selecting those parameters, in order to avoid making inferences with wrong assumptions on the unknown hydrological events having occurred in the past.

The Bayesian MCMC methodology is presented on the example of the maximum discharges observed during the warm half year at the station Vltava-Kamýk (Czech Republic) in the period 1877-2002. Although the 2002 flood peak, which is related to the vast flooding that affected a large part of Central Europe at that time, occurred in the near past, in the analysis it is treated virtually as a ‘historical’ event in order to illustrate some crucial aspects of including information on extreme historical floods into at-site flood frequency analyses.

Acreman M. C., Wiltshire S. E., 1989: The regions are dead; long live the regions. Methods of identifying and dispensing with regions for flood frequency analysis. IAHS Publ. 187, 175-188.

Alcoverro J., Corominas J., Gómez M., 1999: The Barranco de Arás flood of 7 August 1996 (Biescas, Central Pyrenees, Spain). Engineering Geology, 51, 237-255.

Bayliss A. C., Reed D. W., 2001: The use of historical data in flood frequency estimation. Report to MAFF. CEH Wallingford, 87 p. Available at: http://nora.nerc.ac.uk/8060/1/BaylissRepN008060CR.pdf

Beable M. E., McKerchar A. I., 1982: Regional flood estimation in New Zealand. In: Water and Soil Division Technical Publication No. 20, Water and Soil Division, Ministry of Works and Development, Wellington, New Zealand.

Bobée B., Rasmussen P. F., 1994: Statistical analysis of annual flood series. In: Menon J. (Ed.): Trends in Hydrology (1). Council of Scientific Research Integration, India, 117-135.

Boháč M., Kulasová B., 2005: Hydrologická studie pro VD Orlík: Průběhy teoretických povodňových vln s kulminačním průtokem s pravděpodobnosti překročení pQ = .0001 a s podmíněnými pravděpodobnostmi překročení objemu. Czech Hydrometeorological Institute. 14 p. (in Czech).

Brunovský P., Lapin M., Melicherčík I., Somorčík J., ševčovič D., 2009: Risks due to variability of K-day extreme precipitation totals and other K-day extreme events. Journal of Hydrology and Hydromechanics, 57, 4, 250-263.

Burn D. H., 1990a: An appraisal of the ‘region of influence’ approach to flood frequency analysis. Hydrological Sciences Journal, 35, 2, 149-165.

Burn D. H., 1990b: Evaluation of regional flood frequency analysis with a region of influence approach. Water Resources Research, 26, 10, 2257-2265.

Burn D. H., 1997: Catchment similarity for regional flood frequency analysis using seasonality measures. Journal of Hydrology, 202, 212-230.

Burn D. H., Goel N. K., 2000: Formation of groups for regional flood frequency analysis. Hydrological Sciences Journal, 45, 97-112.

Castellarin A., 2007: Probabilistic envelope curves for design flood estimation at ungauged sites. Water Resources Research, 43, W04406, doi: 10.1029/2005WR004384.

Coles S., 2001: An introduction to statistical modeling of extreme values. Springer Verlag, London, 208 p.

Costa J. E., 1987: A comparison of the largest rainfall-runoff floods in the United States with those of the People's Republic of China and the World. Journal of Hydrology, 69, 101-115.

Costa J. E., Jarrett R. D., 2008: An evaluation of selected extraordinary floods in the United States reported by the U. S. Geological Survey and implications for future advancement of flood science. Scientific Investigations Report 2008-5164, U. S. Geological Survey, Reston, Virginia, USA.

Cunnane C., 1987: Review of statistical models for flood frequency estimation. In: Singh V. P. (Ed.): Hydrologic frequency modelling. Reidel, Dordrecht, The Netherlands, 49-95.

Dalrymple T., 1960: Flood frequency analyses. Water Supply Paper 1543-A. U. S. Geological Survey, Reston, Virginia, USA.

Drbal K., Hlavínek J., Ošlejšková J., 2003: Evaluation of catastrophic flood in August 2002 - Analysis of effect of waterworks on the flood. (Vyhodnocení katastrofální povodně v srpnu 2002 - Posouzení vlyvu vodních děl na průběh povodně). Research Report. VÚV T. G. Masaryka, 2003, 79 p. (in Czech).

Gaume E., Bain V., Bernardara P., Newinger O., Barbuc M., Bateman A., Blaškovičová L., Blöschl G., Borga M., Dumitrescu A., Daliakopoulos I., Garcia J., Irimescu A., Kohnová S., Koutroulis A., Marchi L., Matreata S., Medina V., Preciso E., Sempere-Torres D., Stancalie G., Szolgay J., Tsanis J., Velasco D., Viglione A., 2009: A collation of data on European flash floods. Journal of Hydrology, 367, 70-78 (doi: 10.1016/j.jhydrol.2008.12.028).

Gaume E., Gaál L., Viglione A., Szolgay J., Kohnová S., Blöschl G., 2010: Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites. Journal of Hydrology (doi: 10.1016/j.jhydrol.2010.01.08).

Gelman A., Carlin J. B., Stern H. S., Rubin D. B., 2004: Bayesian data analysis. Chapman & Hall / CRC, 696 p.

Guse B., Thieken A. H., Castellarin A., Merz B., 2010: Deriving probabilistic regional envelope curves with two pooling methods. Journal of Hydrology, 380, 14-26.

Herschy R. W., 2005: The world's maximum observed floods. Flow Measurement and Instrumentation, 13, 231-235.

Hosking J. R. M., Wallis J. R., 1986: Paleoflood hydrology and flood frequency analysis. Water Resources Research, 22, 4, 543-550.

Hosking J. R. M., Wallis J. R., 1997: Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge, 224 p.

Institute of Hydrology, 1999: Flood Estimation Handbook, Part 3: Statistical procedures for flood frequency estimation. Institute of Hydrology, Wallingford, UK.

Kuczera G., 1999: Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference. Water Resources Research, 35, 5, 1551-1557.

Kundzewicz Z. W., Ulbrich U., Brucher T., Graczyk D., Kruger A., Leckebusch G. C., Menzel L., Pinskwar I., Radziejewski M., Szwed M., 2005: Summer floods in central Europe - Climate change track? Natural Hazards, 36, 165-189.

Leese M. N., 1973: Use of censored data in the estimation of Gumbel distribution parameters for annual maximum flood series. Water Resources Research, 9, 6, 1534-1542.

Meigh J. R., Farquharson F. A. K., Sutcliffe J. V., 1997: A world-wide comparison of regional flood estimation methods and climate. Hydrological Sciences Journal, 42, 2, 225-244.

Merz R., Blöschl G., 2003: A process typology of regional floods. Water Resources Research, 39, 12, 1340 (doi: 10.1029/2002WR001952).

Merz R., Blöschl G., 2008a: Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information. Water Resources Research, 44, W08432 (doi: 10.1029/2007WR006744).

Merz R., Blöschl G., 2008b: Flood frequency hydrology: 2. Combining data evidence. Water Resources Research, 44, W08433 (doi: 10.1029/2007WR006745).

Mimikou M., 1984: Envelope curves for extreme flood events in north-western and western Greece. Journal of Hydrology, 67, 55-66.

NERC (Natural Environment Research Council), 1975: Flood Studies Report, Vol. I.: Hydrological Studies. NERC, London, UK.

Ouarda T. B. M. J., Girard C., Cavadias G. S., Bobée B., 2001: Regional flood frequency estimation with canonical correlation analysis. Journal of Hydrology, 254, 1-4, 157-173.

Parent E., Bernier J., 2002: Bayesian POT modeling for historical data. Journal of Hydrology, 274, 95-108.

Pekárová P., 2009: Flood regime of rivers in the Danube River basin (Režim povodní v povodí rieky Dunaj). Journal of Hydrology and Hydromechanics, 57, 2, 142-150 (in Slovak).

Podolinská J., Šipikalová H., Škoda P., Blaškovičová L., Demeterová B., 2005: N-year maximum discharges on the Slovakia rivers. Conference ‘Hydrological days’, Bratislava.

Rao A. R., Hamed K. H., 1999: Flood frequency analysis. CRC Press, Boca Raton, Florida, USA, 350 p.

Reis D. S., Stedinger J. R., 2005: Bayesian MCMC flood frequency analysis with historical information. Journal of Hydrology, 313, 1-2, 97-116.

Robert C. P., Casella G., 2004: Monte Carlo statistical methods. Springer, New York, 2nd edition, 645 p.

Rodier J. A., Roche M., 1984: World catalogue of maximum observed floods. IASH Publication 143, IASH Press.

Solín L., 2002: Identification of physical regional types for regional flood frequency analysis. In: Weingartner R., Sperafico M. (Eds.): Proceedings of international conference on flood estimation, CHR Report II-17, Bern, Switzerland, 687-697.

Solín L., 2008: Analysis of floods occurrence in Slovakia in the period 1996-2006 (Analýza výskytu povodňových situácií na Slovensku v období rokov 1996-2006). Journal of Hydrology and Hydromechanics, 56, 2, 95-107 (in Slovak).

Stedinger J. R., Cohn T. A., 1986: Flood frequency analysis with historical and paleoflood information. Water Resources Research, 22, 5, 785-793.

Svoboda A., Pekárová P., 1998: The catastrophic flood of July 1998 in the Malá Svinka catchment - its simulation (Katastrofálna povodeň z júla 1998 v povodí Malej Svinky - simulácia jej priebehu). Journal of Hydrology and Hydromechanics, 46, 6, 356-365 (in Slovak).

Szolgay J., Kohnová S., Hlavčová K., Gaál L., Bacigál T., 2008: Assessment of hydrological design values for the hydro-electric power plant Orlík [Final Report] (Posúdenie hydrologických návrhových veličín vodného diela Orlík [Záverečná správa]). Department of Land and Water Resources Management, Faculty of Civil Engineering Slovak University of Technology, Bratislava, 126 p. (in Slovak).

Tierney L., 1994: Markov Chains for exploring posterior distributions. The Annals of Statistics, 22, 4, 1701-1728.

Ulbrich U., Brücher T., Fink A. H., Leckebusch G. C., Krüger A., Pinto J. G., 2003: The central European floods of August 2002. Part I: Rainfall periods and flood development. Weather, 58, 371-377.

UNESCO, 1976: World catalogue of very large floods. The UNESCO Press, 424 p.

Viglione A., 2009. nsRFA: Non-supervised regional frequency analysis. R package. Version 0.6-9. Available at ( cran.r-project.org/web/packages/nsRFA

Wilks D., 1995: Statistical methods in the atmospheric sciences. Academic Press, San Diego, 467 p.

Wiltshire S. E., 1986: Identification of homogeneous regions for flood frequency analysis. Journal of Hydrology, 84, 287-302.

Contributions to Geophysics and Geodesy

The Journal of Geophysical Institute of Slovak Academy of Sciences

Journal Information


CiteScore 2017: 0.36

SCImago Journal Rank (SJR) 2017: 0.199
Source Normalized Impact per Paper (SNIP) 2017: 0.216

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 239 239 28
PDF Downloads 75 75 5