Emulator-enabled approximate Bayesian computation (ABC) and uncertainty analysis for computationally expensive groundwater models

Bayesian inference provides a mathematically elegant and robust approach to constrain numerical model predictions with system knowledge and observations. Technical challenges, such as evaluating a large number of models with long runtimes, have restricted the application of Bayesian inference to groundwater modeling. To overcome such technical challenges, we use Gaussian process emulators to replace a transient regional groundwater MODFLOW model for computing objective functions during model constraining. The regional model is designed to assess the potential impact of a proposed coal seam gas (CSG) development on groundwater levels in the Richmond River catchment, Clarence-Moreton Basin, Australia. The emulators were trained using 4000 snapshots derived from the MODFLOW model and subsequently used to replace the MODFLOW model in an Approximate Bayesian Computation (ABC) scheme. ABC was deemed the more appropriate choice as it relaxes the need to derive an explicit likelihood function that the formal Bayesian analysis requires. The study demonstrated the flexibility of the Gaussian process emulators, which can accurately reproduce the original model behavior at a fraction of the computational cost (from hours to seconds). The gain in computational efficiency using the proposed approach allows the global calibration and uncertainty algorithms to become more feasible for computationally demanding groundwater models. Based on the ABC analysis, the probability for the simulated CSG development causing a water table change of more than 0.2 m was less than 5%. In addition to a probabilistic estimate of the prediction, an added value of emulator-assisted ABC inference is providing information on the extent to which observations can constrain parameters and predictions, as well as the flexibility to include various quantitative and qualitative parameter constraining information.