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 taken into account.
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 in general
because they are tuned for particular output observables. Further, the arbitrary
use of standard additive statistical model error terms on model observables may
well violate physical constraints, unless particular care is taken to build in
requisite statistical structure to avoid this.
In order to address these challenges, 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 can potentially disambiguate model and
data errors. To achieve this, select existing or proposed model parameters are
cast as random variables, representing model error, thereby casting the
calibration problem within a density estimation framework. When parameters of
the joint input density are difficult to estimate due to computational expense
or degeneracy of exact likelihoods, we employ Approximate Bayesian Computation
(ABC) to build prediction-constraining approximate likelihoods. We demonstrate
the key strengths of the method on synthetic cases, as well as on two practical
applications of interest, from chemical kinetics and atmospheric transport
modeling.