Quantificação de incertezas associadas a variáveis intervenientes na modelagem hidrodinâmica por meio de métodos bayesianos.

Abstract

Floods and their effects on riverine populations have been the subject of study of the scientific and technical community all over the world. Despite some improvements in modelling and data acquisition fields, estimates indicate that flood damage tends to increase. Several studies in the water sector over the past two decades have argued that one of the ways to estimate flooding more accurately and to understand the models used is to quantify the different uncertainties, or errors, that affect predictions as estimated by numerical methods and rainfall-runoff models and flood routing. In this sense, this doctorate research prospected different methods available for quantifying uncertainties associated with some parameters, data and variables involved in mathematical modeling of floods and their quantification and propagation on the final result, in this case expressed as hydrographs, as well as water surface elevation profiles and inundation maps. From the bibliographical inspection, it was defined the application of a Bayesian approach scheme, which basically consists of updating the prior knowledge about parameters and variables involved in modeling using observed information related to the phenomenon under consideration, such as flow and stage hydrographs registered in the downstream end of a river reach, and available flood inundation maps. The adoption of Bayesian methods for hydrodynamic modeling, characterized by nonlinear equations of numerical solution, is possible by means of Markov Chain Monte Carlo Methods (MCMC), in order to ensure the approximation of the posterior distribution of parameters, data and variables involved in the inference, that is, obtained after incorporating the observed information available on floods at a given location. For the application and validation of the methodology, a fluvial reach in the upper São Francisco river was selected, located between the Abaeté river outlet and the town of Pirapora, in Minas Gerais state, with daily mean flow data available in the upstream and downstream ends, 22 cross sections and a digital terrain model with horizontal accuracy of 1 m. The results show that the adopted methodology is adequate to quantify the uncertainties arising from the Manning’s roughness coefficients in the channel and floodplains in this type of model and opens a series of possibilities for future studies concerning the subject. The method also ensured the estimation of credibility intervals that characterize the uncertainty in model predictions, such as flow and stage hydrographs in the section used for the Bayesian inference and control of results.