Coupling Empirical Bayes and Akaike’s Bayesian Information Criterion to Estimate Aquifer Transmissivity Fields

In this work, an empirical Bayes method was applied to estimate highly parameterized transmissivity fields in 2D aquifers under conditions of steady flow. The Bayesian inverse procedure was coupled with the Akaike’s Bayesian information criterion to identify both the main transmissivity field and the hyperparameters of the prior distribution. The forward problem, solved with a version of MODFLOW, consists in computing hydraulic heads at monitoring points considering fully known boundary conditions, and the transmissivity field. As for the required observations for the inverse problem, the monitored hydraulic head data were used. Due to the nonlinear relationship between the observed data (hydraulic heads) and the unknowns (log transmissivity values in each finite difference cell), the inverse approach is based on a successive linearization method coupled with an adjoint state methodology. At the end, the posterior distribution of the unknowns allows quantifying their uncertainty. The methodology was tested on a well-known literature case study consisting of a confined aquifer, with both Dirichelet- and Neumann-type boundary conditions and considering different degrees of heterogeneities. The inverse approach showed robust, efficient results fully consistent with other methods available in the literature. The methodology was implemented in a free and user-friendly code named ebaPEST.