Highly parameterized inverse estimation of hydraulic conductivity and porosity in a three-dimensional, heterogeneous transport experiment

Assessing the impact of parameter estimation accuracy in models of heterogeneous, three-dimensional (3-D) groundwater systems is critical for predictions of solute transport. A unique experimental data set provides concentration breakthrough curves (BTCs) measured at a 0.25(3) cm(3) scale over the 13 x 8 x 8 cm(3) domain (similar to 53,000 measurement locations). Advective transport is used to match the first temporal moments of BTCs (or mean arrival times, m(1)) averaged at 0.25(3) and 1.0 cm(3) scales through simultaneous inversion of highly parameterized heterogeneous hydraulic conductivity (K) and porosity (phi) fields. Pilot points parameterize the fields within eight layers of the 3-D medium, and estimations are completed with six different models of the K-phi relationship. Parameter estimation through advective transport shows accurate estimation of the observed m(1) values. Results across the six different K-phi relationships have statistically similar fits to the observed m(1) values and similar spatial estimates of m(1) along the main flow direction. The resulting fields provide the basis for forward transport modeling of the advection-dispersion equation (ADE). Using the estimated K and phi fields demonstrates that advective transport coupled with inversion using dense spatial field parameterization provides an efficient surrogate for the ADE. These results indicate that there is not a single set of model parameters, or a single K-phi relationship, that leads to a best representation of the actual experimental sand packing pattern (i.e., nonuniqueness). Additionally, knowledge of the individual sand K and phi values along with their arrangement in the 3-D experiment does not reproduce the observed transport results at small scales. Small-scale variation in the packing and mixing of the sands causes large deviations from the expected transport results as highlighted in forward ADE simulations. Highly parameterized inverse estimation is able to identify those regions where variations in mixing and packing alter the expected property values and significantly improve results relative to the naive application of the experimentally derived property values. Impacts of the observation scale, the scale over which results are averaged and the number of observations and parameters on the final estimations are also examined. Results indicate existence of a representative element volume (REV) at 0.25 cm(3), the existence of subgrid scale heterogeneity that impacts transport and the accuracy of highly parameterized models with even relatively small amounts of observations. Finally, this work suggests that local-heterogeneity features below the REV scale are difficult to incorporate into parameterized models, highlighting the importance of addressing prediction uncertainty for small-scale variability (i.e., uncaptured variability) in modeling practice.