COUPLED FLOW AND TRANSPORT PARAMETER ESTIMATION AT TROUT LAKE, WISCONSIN: A BAYESIAN APPROACH

An isthmus between Big Muskellunge and Crystal Lakes in the Trout Lake watershed in northern Wisconsin was used to evaluate the practicality of a Bayesian approach to model calibration. This isthmus consists of sandy glacial sediments enveloping a laterally continuous thin layer of silt, a pattern typical of ice-block lake formation in continental glaciated terrain.

Model calibration was a two-phased effort. First, head and head-difference data were used as calibration data with a forward flow model to estimate the hydraulic conductivity field; second, these head and head-difference data were augmented with¹⁸O/¹⁶O and tritium isotope transport data using a coupled flow and transport forward model to refine the hydraulic conductivity estimates. The steady-state stable oxygen isotope data differentiate provenance between lake water and terrestrial recharge. Transient tritium data provides time-of-travel and residence time information within the aquifer.

Rather than enforcing the location of homogeneous zones a priori, we allow each model node to be a free and independent hydraulic conductivity parameter. The number of model nodes greatly exceeds the number of head and concentration measurements resulting in a severely underdetermined problem; thus, regularization is necessary to obtain a meaningful solution. Regularization is accomplished through implementation of the Bayesian geostatistical inverse method. In this approach, variability of the parameter field is characterized by a variogram. The variogram choice reflects general knowledge of the conductivity fields—e.g. enforcing smoothness. Specific variables for the variogram are estimated based on field data. The goal of the Bayesian approach is to allow the model sufficient flexibility to empower the calibration data to guide the balance between parsimony and complexity.

The Bayesian geostatistical inverse results are compared to non-Bayesian regularized inversion using the widely-used parameter estimation software package PEST. A chief advantage to the Bayesian method is the ability to provide a calibration not only the minimum residual variance but also the most likely solution set. These advantages come at a computational cost. Techniques including adjoint state sensitivity calculation alleviating that burden will be presented.