Towards Improving the Efficiency of Bayesian Model Averaging Analysis for Flow in Porous Media via the Probabilistic Collocation Method

The characterization of flow in subsurface porous media is associated with high uncertainty. To better quantify the uncertainty of groundwater systems, it is necessary to consider the model uncertainty. Multi-model uncertainty analysis can be performed in the Bayesian model averaging (BMA) framework. However, the BMA analysis via Monte Carlo method is time consuming because it requires many forward model evaluations. A computationally efficient BMA analysis framework is proposed by using the probabilistic collocation method to construct a response surface model, where the log hydraulic conductivity field and hydraulic head are expanded into polynomials through Karhunen–Loeve and polynomial chaos methods. A synthetic test is designed to validate the proposed response surface analysis method. The results show that the posterior model weight and the key statistics in BMA framework can be accurately estimated. The relative errors of mean and total variance in the BMA analysis results are just approximately 0.013% and 1.18%, but the proposed method can be 16 times more computationally efficient than the traditional BMA method