Department of Earth, Ocean, and Atmospheric Science, Florida State University
"Developing a Data-Driven Error Model for Bayesian Model Error Analysis"
Model structural error is ubiquitous, due to simplification and/or misrepresentation of real-world systems. Due to model structural error, model calibration may lead to biased parameter estimation, because model parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast system responses to new forcing. Taking a groundwater model as an example, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives significantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.