Constructive epistemic modeling of groundwater flow with geological structure and boundary condition uncertainty under the Bayesian paradigm

Abstract

• BMA trees of model weights, prediction and variance serve as a learning tool. • Candidate propositions are tested to learn about individual model components. • Posterior model probability is a degree of belief given our state of knowledge. • Geological structure uncertainty is larger than boundary condition uncertainty. • Model structure uncertainty is larger than parameter uncertainty. Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using hierarchical Bayesian model averaging (BMA), this study shows that segregating different uncertain model components through a BMA tree of posterior model probability, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater flow model of a siliciclastic aquifer-fault system. We consider four uncertain model components. With respect to geological structure uncertainty, we consider three methods for reconstructing the hydrofacies architecture of the aquifer-fault system, and two formation dips. We consider two uncertain boundary conditions, each having two candidate propositions. Through combinatorial design, these four uncertain model components with their candidate propositions result in 24 base models. The study shows that hierarchical BMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models.