Abstract
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.
Highlights
Groundwater flow and contaminant transport are the key issues in the groundwater resources management
The reference variogram model used to generate the reference random field of log hydraulic conductivity was selected as the truncated power variogram model with Gaussian modes (TpvG) [32,49]:
A Bayesian model averaging framework was developed to deal with the model uncertainty issue
Summary
Groundwater flow and contaminant transport are the key issues in the groundwater resources management. It is challenging to accurately predict the dynamic behavior of groundwater flow and the distribution of the pollutant. This can commonly be attributed to the insufficient knowledge to accurately understand the dynamic process of the groundwater system and the limited size of the error-prone measurement data to fully characterize the properties of the subsurface system. The uncertainty associated with the groundwater modeling can arise from a variety of the factors, such as the mathematical model to represent the physical and chemical processes in the groundwater system, the initial and boundary conditions, the heterogeneity characterization of the hydrogeological parameters, and the static or dynamic observation data to constrain the groundwater model [4,5].
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