Multi-Model Bayesian Analysis of Data Worth and Optimization of Sampling Scheme Design

Abstract

Groundwater is a major source of water supply, and aquifers form major storage reservoirs as well as water conveyance systems, worldwide. The viability of groundwater as a source of water to the world's population is threatened by overexploitation and contamination. The rational management of water resource systems requires an understanding of their response to existing and planned schemes of exploitation, pollution prevention and/or remediation. Such understanding requires the collection of data to help characterize the system and monitor its response to existing and future stresses. It also requires incorporating such data in models of system makeup, water flow and contaminant transport. As the collection of subsurface characterization and monitoring data is costly, it is imperative that the design of corresponding data collection schemes is cost-effective. A major benefit of new data is its potential to help improve one's understanding of the system, in large part through a reduction in model predictive uncertainty and corresponding risk of failure. Traditionally, value-of-information or data-worth analyses have relied on a single conceptual-mathematical model of site hydrology with prescribed parameters. Yet there is a growing recognition that ignoring model and parameter uncertainties render model predictions prone to statistical bias and underestimation of uncertainty. This has led to a recent emphasis on conducting hydrologic analyses and rendering corresponding predictions by means of multiple models. We develop a theoretical framework of data worth analysis considering model uncertainty, parameter uncertainty and potential sample value uncertainty. The framework entails Bayesian Model Averaging (BMA) with emphasis on its Maximum Likelihood version (MLBMA). An efficient stochastic optimization method, called Differential Evolution Method (DEM), is explored to aid in the design of optimal sampling schemes aiming at maximizing data worth. A synthetic case entailing generated log hydraulic conductivity random fields is used to illustrate the procedure. The proposed data worth analysis framework is applied to field pneumatic permeability data collected from unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona.