Quantification of the Effect of Model Error on Groundwater Model Predictions and Risk Assessment

Errors arising from the imperfect mathematical representation of the structure of a hydrologic system (model error) do not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. Furthermore, the existence of parameter uncertainty imposes additional difficulties in isolating and evaluating model error because it obscures the impact of model error on model predictions. A Bayesian approach is presented for quantifying model error in the presence of parameter uncertainty. Insight gained in updating the prior information on the model parameters is used to assess the correctness of the model structure, which is defined relative to the accuracy required of the model predictions. Model error is then evaluated for each measurement of the dependent variable through an examination of the correctness of the model structure for different accuracy levels. The effect of model error on each dependent variable is quantified as a function of location and time, and represents a measure of the reliability of the model in terms of each model prediction. Through a synthetic example it is shown that this method may assist in discriminating among models in terms of the correctness of the model structure, as well as in identifying possible causes of model error. Application to a problem of 90Sr migration to water wells at Chernobyl, Ukraine, demonstrates that the Bayesian model error analysis may also offer a more informative description of the uncertainties involved in risk assessments and decision analyses, and an alternative to the practice of adopting a bias towards conservative risk estimates in decision models.