Model calibration/parameter estimation techniques and conceptual model error

Abstract

In a modeling exercise, errors in the model structure cannot be avoided because they arise from our limited capability to exactly describe mathematically the complexity of a physical system. The effect of model error on model predictions is not random but systematic, therefore, it does not necessarily have any probabilistic properties that can be easily exploited in the construction of a model performance criterion. The effect of model error varies in both space and time. It is also different for the flow and the solute transport components of a groundwater model and may have a significant impact on parameter estimation, uncertainty analyses and risk assessments. Structural errors may result in a misleading evaluation of prediction uncertainty associated with parameter error because model sensitivity to uncertain parameters may be quite different than that of the correct model. A substantial model error may significantly degrade the usefulness of model calibration and the reliability of model predictions because parameter estimates are forced to compensate for the existing structural errors. Incorrect uncertainty analyses and estimated parameters that have little value in predictive modeling could potentially lead to an engineering design failure or to a selection of a management strategy that involves unnecessary expenditures. A complementary to classical inverse methods model calibration procedure is presented for assessing the uncertainty in parameter estimates associated with model error. This procedure is based on the concept of a per-datum calibration for capturing the spatial and temporal behavior of model error. A set of per-datum parameter estimates obtained by this new method defines a posterior parameter space that may be translated into a probabilistic description of model predictions. The resulted prediction uncertainty represents a reflection on model predictions of available information regarding the dependent variables and measures the level of confidence in model performance.