In this work we highlight the importance of model error assessment in physical model calibration studies. Conventional calibration methods often assume the model is perfect and account for data noise only. Consequently, the estimated parameters typically have biased values that implicitly compensate for model deficiencies. Moreover, improving the amount and the quality of data may not improve the parameter estimates since the model discrepancy is not accounted for. In state-of-the-art methods model discrepancy is explicitly accounted for by enhancing the physical model with a synthetic statistical additive term, which allows appropriate parameter estimates. However, these statistical additive terms do not increase the predictive capability of the model because they are tuned for particular output observables and may even violate physical constraints.
We introduce a framework in which model errors are captured by allowing variability in specific model components and parameterizations for the purpose of achieving meaningful predictions that are both consistent with the data spread and appropriately disambiguate model and data errors. Here we cast model parameters as random variables, embedding the calibration problem within a density estimation framework. Further, we calibrate for the parameters of the joint input density. The likelihood function for the associated inverse problem is degenerate, therefore we use Approximate Bayesian Computation (ABC) to build prediction-constraining likelihoods and illustrate the strengths of the method on synthetic cases. We also apply the ABC-enhanced density estimation to the TransCom 3 CO2 intercomparison study (Gurney, K. R., et al., Tellus, 55B, pp. 555–579, 2003) and calibrate 15 transport models for regional carbon sources and sinks given atmospheric CO2 concentration measurements.