Experimental Designs for Model Discrimination and Uncertainty Reduction in Groundwater Modeling

Abstract

Groundwater systems are complex and subject to multiple interpretations due to a lack of sufficient information. Different propositions (or alternatives) are often proposed to represent uncertain model components resulted in many conceptual models using the same data. Yet considering too many models may lead to high prediction uncertainty and may lose the purpose of model development. To decrease the prediction uncertainty due to conceptual model uncertainty, two experimental designs are proposed. The first experimental design intends to identify model propositions in each uncertain model component. A discrimination criterion is developed based on posterior model probability. Bayesian model averaging (BMA) is used to predict future observation data. The experimental design aims to find the optimal number and location of future observations and the number of sampling rounds such that the desired discrimination criterion is met. Hierarchical Bayesian model averaging (HBMA) is adopted to assess if highly probable propositions can be identified. The second experimental design is to discriminate conceptual models and in turn, reduce the number of models. The Box-Hill discrimination function derived for one additional observation was modified to account for multiple independent spatiotemporal observations. The BMA method is used to predict future observation data and quantify conceptual and parametric prediction uncertainty. The design goal is to find optimal locations and the number of sampling rounds such that the Box-Hill discrimination function value is maximized, and the highest posterior probability of a model satisfies a desired probability threshold. The experimental designs are implemented to plan new head observation networks based on existing USGS wells in the Baton Rouge area, Louisiana. The sources of uncertainty that create multiple groundwater models are geological architecture, boundary condition, and fault permeability architecture. All possible design solutions are enumerated using a multi-core supercomputer. The result shows that each highly probable proposition can be identified for each uncertain model component once the discrimination criterion is achieved. Heteroscedasticity (unequal variances) for future groundwater heads should be considered in the design procedure to account for various sources of future observation uncertainty. The variances of head predictions are significantly decreased by reducing posterior model probabilities of unimportant models.