A Bayesian Approach to the quantification of the effect of model error on the predictions of groundwater models

Abstract

Errors arising from the imperfect mathematical representation of the structure of a hydrologic system (model error) are not random but systematic. Their effect on model predictions varies in space and time and differs for the flow and solute transport components of a groundwater model. Such errors do not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. 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 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, which is quantified as a function of location and time, represents a measure of the reliability of the model in terms of each model prediction. This method can be used in identifying possible causes of model error and in discriminating among models in terms of the correctness of the model structure. It also offers an improved description of the uncertainties associated with a modeling exercise that may be useful in risk assessments and decision analyses.