A Bayesian Approach to Estimate Aquifer Heterogeneity with Generalized Parameterization

The research proposes a generalized parameterization (GP) method and Bayesian estimation for parameter heterogeneity characterization and identification in groundwater modeling. GP unifies zonation and interpolation through a set of weighting coefficients, and is capable of creating a zonation structure, a continuous distribution, or a mixed structure. GP shows greater flexibility not only in manipulating the highly complex spatial distribution but also in identifying the parameter structure. With GP, parameter structure identification seeks to identify the parameter dimension, parameter pattern, parameter values as well as the values of the weighting coefficients simultaneously through a set of basis points. Additionally, this study develops an embedded genetic algorithm (GA) for solving the structure identification problem. A Bayesian estimator that estimates the basis point values as well as the values of the weighing coefficients is embedded in the GA, which searches for the best basis point locations. We demonstrate the inverse methodology by a numerical example in which the distributed transmissivity in a two-dimensional confined aquifer is identified. We calculate the Jacobian matrix by the adjoint state method. With GP, we have successfully identified the transmissivity structure with four basis points that results in a good fitting in groundwater heads and captures the non-smooth characteristic as well as the trend of the true transmissivity field. We compare GP with Voronoi tessellation (zonation) and natural neighbor interpolation. Results show that GP outperforms the other two parameterization methods in that GP identified the transmissivity field with a smaller parameter uncertainty along with a sufficiently small fitting residual and without over parameterization.