Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window

Abstract

This study proposes a Bayesian model averaging (BMA) method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods. BMA is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates. Two major issues in applying BMA to hydraulic conductivity estimation are discussed. The first problem is using Occam's window in usual BMA applications to measure approximated posterior model probabilities. Occam's window only accepts models in a very narrow range, tending to single out the best method and discard other good methods. We propose a variance window to replace Occam's window to cope with this problem. The second problem is the Kashyap information criterion (KIC) in the approximated posterior model probabilities, which tends to prefer highly uncertain parameterization methods by considering the Fisher information matrix. With sufficient amounts of observation data, the Bayesian information criterion (BIC) is a good approximation and is able to avoid controversial results from using KIC. This study adopts multiple generalized parameterization (GP) methods such as the BMA models to estimate spatially correlated hydraulic conductivity. Numerical examples illustrate the issues of using KIC and Occam's window and show the advantages of using BIC and the variance window in BMA application. Finally, we apply BMA to the hydraulic conductivity estimation of the “1500‐foot” sand in East Baton Rouge Parish, Louisiana.