On Model Error and Statistical Calibration of Physical Models Habib Najm Sandia National Laboratories Existing methods for representation of model error in the statistical calibration of computational models typically rely on convolving model predictions of select observables with statistical data and model error terms. This strategy is successful in providing a statistical correction to model predictions in a manner that interpolates observations with meaningful uncertainty estimation between points. However, this approach faces a number of challenges when applied in the context of calibration of physical models, where, e.g. auxiliary physical constraints are in force, the model is intended for use outside the calibration regime, and other non-observable model output predictions are of interest. Further, the commonly used additive combination of model and data errors presents challengs for the disambiguation of the two sources of uncertainty. I will outline a calibration strategy that addresses these challenges. The key idea is to embed statistical model error terms inside the model, and not on observable model outputs. In this manner, model error terms can be placed in targeted model components where specific approximations were made. This allows the analyst, e.g. to examine the utility of corrections to one or other suspect model components, to identify the model component where model improvements are relevant for agreement with the data. Our hitherto developments embed model error in specific model parameters, thereby rendering the statistical calibration, at least partly, a density estimation problem. Employing a Bayesian framework, we employ different likelihood constructions, depending on whether there is data noise or not. In particular, for noise free data, as in the case of model-to-model calibration, we rely on approximate Bayesian computation. I will illustrate the use of this construction on simple model problems, with and without data noise, and for calibration of a simplified chemical model for methane-air kinetics against another, more complex, model. Select parameters are encumbered by model error, which translates to uncertainty in predictive model outputs. In cases where there is data noise, the method is seen to enable disambiguation of data and model errors, allowing clear estimation of uncertainty in model predictions resulting from model error.