As a result of conventional inversion, calibrated model parameters are often biased due to unaccounted structural errors. Consequently, the calibrated models have deficient predictive skills due to overconfident and biased inputs. For example, in climate models, structural errors are known to be the largest contributors of predictive uncertainty budget. While augmenting model outputs with statistical correction terms may remove the predictive bias, it can also violate physical laws, or make the calibrated model ineffective for predicting non-observable quantities of interest.
This work will present a framework for representing, quantifying and propagating uncertainties due to model structural errors by embedding stochastic correction terms in the model. Stochastic correction is inferred together with the physical parameters in an inverse modeling task via Bayesian inference and Markov chain Monte Carlo, while likelihood construction and uncertainty propagation benefit from forward modeling tasks of surrogate construction and sensitivity analysis via Polynomial Chaos expansions. The embedded correction approach ensures physical constraints are satisfied, and renders calibrated model predictions meaningful and robust with respect to structural errors. Furthermore, the approach allows differentiating model structural deficiencies from errors associated with data acquisition.
The developed inverse/forward UQ workflow is implemented in UQ Toolkit (www.sandia.gov/uqtoolkit). We will demonstrate the application of the methodology on E3SM Land Model given measurements obtained at select FLUXNET sites.