Uncertainty estimation in hydrodynamic modeling using Bayesian techniques

Abstract

ABSTRACT Uncertainty estimation analysis has emerged as a fundamental study to understand the effects of errors inherent to hydrodynamic modeling processes, of aleatory and epistemic nature, due to input data such as discharge, topography and bathymetry, to the structure and parameterization of the mathematical models used and to their necessary boundary and initial conditions. The study reported in this paper sought to apply a Bayesian-based methodology, associated with thousands of Markov Chain Monte Carlo simulations, 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 and water surface elevation profiles 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 results show that the Bayesian scheme allowed an adequate posterior identification of the parametric uncertainties and of those associated to other sources of errors, with important changes in the prior probability distributions. In addition, the residuals analysis corroborates the applicability of the method to the analysis of uncertainties in hydrodynamic modeling through the use of a more flexible likelihood function than the classical one based on the hypotheses of normality, homoscedasticity and uncorrelated residuals. Future work includes the sensitivity evaluation of the posterior distributions to the addition of lateral inflows, especially concerning the residuals serial correlation, as well as the adoption of other variables to update the prior uncertainties, and the validation of the methodology through the use of the posterior distributions to estimate the total uncertainty involved in the prediction of floods other than the ones used in the inference process.