Enhancing Aquifer Characterization With Position-Encoded Hyperparameters: A Novel ES-SIFG Approach

Abstract

To accurately predict groundwater flow and solute transport, it is essential to precisely characterize the highly heterogeneous aquifer conditions. Ensemble smoother with multiple data assimilation (ESMDA), though widely applied to identify aquifer properties and spatial features, encounters severe problems in practice due its fundamental assumptions of linearity and Gaussianity. To tackle this challenge, we first use a spatially-informed field generator (SIFG) to hyperparameterize the conductivity field and encode position information into the hyperparameters, and then combine it with ensemble smoother to form a new inversion framework called ensemble smoother with SIFG (ES-SIFG). In ES-SIFG, followed by utilizing an ensemble smoother to update the hyperparameters rather than the aquifer parameters. The main innovation of ES-SIFG is integrating positional information into hyperparameters, enabling the use of distance-based covariance localization (CL) and significantly reducing the number of model simulations. The proposed method has been tested on parameter identification problems in 2-D and 3-D non-Gaussian aquifers and compared to ESMDA with normal score transformation. Results indicate that ES-SIFG outperforms ESMDA and is capable of accurately identifying non-Gaussian aquifer parameters and reconstructing contaminant release history, particularly in resolving equifinality and preserving prior geological structure. Furthermore, SIFG allows usage of CL between hyperparameters and observations, which ensures the stable convergence of data assimilation processes even with very small ensemble sizes.