Bayesian Monte Carlo for evaluation of uncertainty in hydrodynamic models of coastal systems

Uncertainty analysis constitutes the set of procedures and strategies conducted to identify, quantify, and report the impacts of different sources of errors on the predictions of a numerical model. Although during the last couple of decades several investigations in different areas of water resources have explicitly discussed the importance of a new modeling paradigm where model predictions are reported along with uncertainty estimates, uncertainty analysis remains an emerging topic in the field of hydrodynamic modeling. Presently, several unresolved issues remain with regard to the applicability, benefits, and limitations of existing strategies for quantification of uncertainty, and the identification of the principal sources of uncertainty in practical applications. In this document we apply the Bayesian Monte Carlo (BMC) method as a strategy to perform uncertainty analysis in coastal modeling studies. BMC is based on robust principles of Bayesian inference and Monte Carlo simulations, and has been successfully applied for studies of groundwater modeling, hydrologic modeling, and water quality modeling in the past. The procedural aspects of the method are discussed in detail, and the implementation of the method is demonstrated for the hydrodynamic model of the St. Louis Bay estuary, Mississippi (USA) for the evaluation of the impacts of input data errors. Results indicate that BMC is an effective strategy for uncertainty analyses, although in professional practice its use may be limited by computational requirements. We also point out that the effectiveness of the method may be affected by the correct selection of the likelihood function and the model error variance.