Optimal Observation Network Design for Model Discrimination using Information Theory and Bayesian Model Averaging

Abstract:

Groundwater systems are complex and subject to multiple interpretations and conceptualizations due to a lack of sufficient information. As a result, multiple conceptual models are often developed and their mean predictions are preferably used to avoid biased predictions from using a single conceptual model. Yet considering too many conceptual models may lead to high prediction uncertainty and may lose the purpose of model development. In order to reduce the number of models, an optimal observation network design is proposed based on maximizing the Kullback-Leibler (KL) information to discriminate competing models. The KL discrimination function derived by Box and Hill [1967] for one additional observation datum at a time is expanded to account for multiple independent spatiotemporal observations. The Bayesian model averaging (BMA) method is used to incorporate existing data and quantify future observation uncertainty arising from conceptual and parametric uncertainties in the discrimination function. To consider the future observation uncertainty, the Monte Carlo realizations of BMA predicted future observations are used to calculate the mean and variance of posterior model probabilities of the competing models. The goal of the optimal observation network design is to find the number and location of observation wells and sampling rounds such that the highest posterior model probability of a model is larger than a desired probability criterion (e.g., 95%). The optimal observation network design is implemented to a groundwater study in the Baton Rouge area, Louisiana to collect new groundwater heads from USGS wells. The considered sources of uncertainty that create multiple groundwater models are the geological architecture, the boundary condition, and the fault permeability architecture. All possible design solutions are enumerated using high performance computing systems. Results show that total model variance (the sum of within-model variance and between-model variance) varying over time and space should be considered in the design procedure to account for various sources of the future observation uncertainty. After the optimal design is obtained, the variance of head predictions is significantly reduced by eliminating models that have insignificant posterior model probabilities.