Bayesian Analysis for Uncertainty and Risk in a Groundwater Numerical Model's Predictions

Groundwater modeling typically relies on some hypothesis and approximations of reality, as the real hydrologic systems are far more complex than we can mathematically characterize. This kind of a model's errors cannot be neglected in the uncertainty analysis for a model's predictions in practical issues. As the scale and complexity increase, the associated uncertainties boost dramatically. In this study, a Bayesian uncertainty analysis method for a deterministic model's predictions is presented. The geostatistics of hydrogeologic parameters obtained from site characterization are treated as the prior parameter distribution in the Bayes' theorem. Then the Markov-Chain Monte Carlo method is used to generate the posterior statistical distribution of the model's predictions, conditional to the observed hydrologic system behaviors. Finally, a series of synthetic examples are given by applying this method to a MODFLOW pumping test model, to test its capability and efficiency in order to assess various sources of the model's prediction uncertainty. The impacts of the model's parameter sensitivity, simplification, and observation errors to predict uncertainty are evaluated, respectively. The results are analyzed statistically to provide deterministic predictions with associated prediction errors. Risk analysis is also derived from the Bayesian results to draw tradeoff curves for decision-making about exploitation of groundwater resources.