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On the quantification of the effect of model error on groundwater model predictions and risk assessments Gaganis, Petros

Abstract

Errors arising from an imperfect model structure (model error) may significantly degrade the usefulness of model calibration in predictive modeling and result in misleading uncertainty and risk analyses. Model error is not random but systematic. Its effect on model predictions varies in space and time and differs for the flow and solute transport components of a groundwater model. Model error does not necessarily have any probabilistic properties that can be easily exploited in the construction of a single-objective model performance criterion. The effect of model error on the solution of the inverse problem is evaluated in the parameter space using a per-datum approach to model calibration where a model is calibrated at each data point separately. For each dependent variable, the location of each per-datum parameter estimate in the parameter space is a function of the magnitude of model error at the given sampling location and time. These parameter estimates are translated into a probabilistic description of model output that represents the level of confidence in model performance evaluated in terms of each model prediction. This approach provides useful information regarding the strengths and limitations of a model as well as the performance of classical calibration procedures. The quantification of model error in the presence of parameter uncertainty is also evaluated within the Bayesian framework. Insight gained in updating the prior information on the parameter values is used to assess the correctness of the model structure, which is defined relative to the required accuracy by model predictions. Model error is evaluated in terms of each measurement of the dependent variable through an examination of the correctness of the model structure for different accuracy levels. The spatial and temporal variability of estimated model error can be used in identifying its possible causes, as well as in discriminating among models in terms of model structure correctness. Application of perdatum calibration and the Bayesian model error quantification to a groundwater contamination problem at the Chernobyl site in the Ukraine indicates that evaluating the effect of model error on estimated risks in hydrogeologic decision analysis offers an attractive alternative to adopting a bias towards conservative values.

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