Bayesian inference provides a mathematically elegant and robust approach to utilize observations to constrain numerical models. However, a formal Bayesian analysis is rarely conducted in practical groundwater modelling, particularly for regional groundwater models. Technical challenges to its implementation include long model runtimes, and the difficulty to define a suitable likelihood function.
To overcome the challenges, we propose a framework to combine model emulating techniques and approximate Bayesian computation (ABC). Highly efficient Gaussian process emulators are trained using thousands of snapshots from the MODFLOW model to replace the computationally demanding process-based groundwater model. ABC relaxes the need to explicitly define a likelihood function, and also allows a powerful and flexible strategy to define multiple objective functions during model constraining. The proposed framework was applied to a newly developed regional groundwater model in the Clarence-Moreton Basin to assess the potential impact of coal seam gas (CSG) development on relevant groundwater systems.
Results: 1. The trained emulators based on 3700 model runs can reproduce the MODFLOW model outputs accurately, which is verified by scatter plots, model mean absolute error (MAE), coefficient of determination (r2), and the root mean square error (RMSE). 2. Although context and prediction specific multiple objective functions were used, the observations did not constrain most parameters significantly. 3. The overall potential impact of the simulated CSG development scheme in the Casino area is minor with extreme drawdown at the water-table of about 1 m within the central area of the development.
Statistical emulators are an efficient tool to replace process-based models when computer efficiency is a critical issue for groundwater model application, such as uncertainty analysis, real-time prediction, and model coupling. The surrogate-based ABC overcomes barriers for applying Bayesian analysis on complex non-linear groundwater models with long runtimes.