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

Abstract

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.