Uncertainty Quantification in Hydrodynamical Modeling as Estimated by Bayesian Techniques

Uncertainty estimation analysis has emerged as a fundamental study to understand the effects of errors inherent to hydraulic modeling processes, of aleatory and epistemic nature, due to input data such as flow, topography and bathymetry, to the structure of the mathematical models used and to boundary and initial conditions. The study reported in this paper sought to apply a Bayesian methodology in order to identify and quantify the uncertainty related to the Manning’s n roughness coefficient in a 1D hydrodynamic model and the total uncertainty involved in the prediction of hydrographs resulting from flood routing through a reach located in the upper São Francisco river, between the Abaeté river outlet and the town of Pirapora. The methodology consists in updating, through the application of Bayes` Theorem, the a priori knowledge about the variability of parameters and data in light of information observed about the modeled phenomenon, such as hydrographs at the downstream end of a river reach. Due to the nonlinear nature of hydrodynamic modeling, the application of this approach is enabled by the approximation of the posterior joint distribution by Markov Chain Monte Carlo (MCMC) methods. In addition, for the use of the Bayesian scheme, a likelihood function was proposed to mathematically represent some expected aspects of the residuals derived from the modeling of non-linear systems, such as heteroscedasticity, serial correlation, asymmetry and kurtosis, at the expense of adding characteristic variables to the process of inference, named latent variables. The results show that the proposed scheme allows to identify the variability of both Manning’s roughness coefficient in the main channel and in the floodplain with a higher quality than that stipulated a priori, in order to express the parametric uncertainty. The other sources of uncertainties, whether associated to the structure of the model or to the input and output data, are expressed using the latent variables. The total predictive uncertainty is presented in the form of credibility intervals for outflow hydrographs and of probabilistic maps at the downstream end of the studied reach.