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

Errors arising from the imperfect mathematical representation of the struct ure of a hydrologic system (model error) are not random but systematic. The ir effect on model predictions varies in space and time and differs for the flow and solute transport components of a groundwater model. Such errors d o not necessarily have any probabilistic properties that can be easily expl oited in the construction of a model performance criterion. A Bayesian appr oach 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. Mode l error is evaluated for each measurement of the dependent variable through an examination of the correctness of the model structure for different acc uracy levels. The effect of model error on each dependent variable, which i s quantified as a function of location and time, represents a measure of th e reliability of the model in terms of each model prediction. This method c an be used in identifying possible causes of model error and in discriminat ing among models in terms of the correctness of the model structure. It als o offers an improved description of the uncertainties associated with a mod eling exercise that may be useful in risk assessments and decision analyses .