Análise bayesiana de frequência de vazões máximas anuais com informações históricas: aplicação à bacia do rio São Francisco em São Francisco

Abstract

The estimation of the exceedance probability of a rare flood is a current problem in engineering. However, rare floods are associated to high return periods which are much longer than the time span covered by systematic streamflow records. The conventional flood frequency analysis, which is based on the usually short systematic streamflow data samples, may yield unrealistic estimates of the risks associated with extreme events. In order to reduce the uncertainties and to produce more reliable parameter and quantile estimates, every piece of available information should be used. Beyond systematic streamflow data, information on historical floods and paleofloods may be found and incorporated into the flood frequency analysis. Such pieces of information may augment the sample size, thus reducing the range of extrapolation and yielding more reliable inferences in the domain of extreme floods. Bayesian theory is also an important statistical tool for flood frequency analysis. According to the Bayesian approach, the distribution parameters are treated as random variables, being modeled by a prior probability distribution, which may be formulated on the basis, for instance, of a subjective prior knowledge, as provided by a specialized professional, or additional information from regional analysis. By using Bayes theorem, this prior distribution, which may be informative or not, is then updated by the local streamflow data, thus producing the posterior distribution of the parameters. Hence, by using this posterior distribution along with the flood probability distribution, conditioned to the parameters, it is possible to find a marginal probability function to floods, independently of parameter estimates. The present MSc thesis aims to evaluate the gain, in terms of uncertainty reduction, from using theBayesian approach, along with information on historical floods, into the frequency analysis of annual flood maxima. In order to perform it, a case study for the São Francisco river basin, at the location of São Francisco, is presented according to the following scenarios: (1) only the systematic flood records are used; (2) information on historical floods are incorporated; and (3) Bayesian theory is employed, with and without an informative prior distribution on parameters and on the probabilistic model.