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 whenalso information on hydrological events from the past with extraordinary magnitude areavailable. For the joint frequency analysis of systematic observations and historical data,respectively, the Bayesian framework is chosen, which, through adequately defined likelihoodfunctions, allows for incorporation of different sources of hydrological information,e.g., maximum annual flood peaks, historical events as well as measurement errors. Thedistribution of the parameters of the fitted distribution function and the confidence intervalsof the flood quantiles are derived by means of the Markov chain Monte Carlosimulation (MCMC) technique. The paper presents a sensitivity analysis related to the choice of the most influentialparameters of the statistical model, which are the length of the historical period h and theperception threshold X0. These are involved in the statistical model under the assumptionthat except for the events termed as ‘historical’ ones, none of the (unknown) peak dischargesfrom the historical period h should have exceeded the threshold X0. Both highervalues of h and lower values of X0 lead to narrower confidence intervals of the estimatedflood quantiles; however, it is emphasized that one should be prudent of selecting thoseparameters, in order to avoid making inferences with wrong assumptions on the unknownhydrological events having occurred in the past.The Bayesian MCMC methodology is presented on the example of the maximum dischargesobserved during the warm half year at the station Vltava-Kamýk (Czech Republic)in the period 1877–2002.