A novel sampling-free algorithm for subsurface data assimilation using Gaussian process-derived sensitivities.

Accurate characterization of hydraulic parameters is vital for modeling subsurface flow and transport. In the past decade, ensemble-based methods have been widely applied in estimating unknown parameters from state measurements. However, these methods require sufficiently large ensemble sizes to guarantee the accuracy of the ensemble averaged parameter sensitivities, leading to heavy computational burdens especially in large-scale problems. Although different surrogates have been introduced to alleviate the computational burden, the sensitivity information therein is still calculated by sampling the surrogate. Therefore, the sampling error is still inevitable. In this study, we propose an adaptive Gaussian process (GP) based iterative smoother (GPIS) algorithm in which the parameter sensitivity indices are analytically derived from the GP surrogate. During the iterations, the GP surrogate is adaptively refined by taking the updated parameter realizations as new base points. Both numerical and experimental cases are conducted to test the effectiveness of GPIS. We also compare its performance in estimating the heterogeneous hydraulic conductivity field with that of its prototype iterative ensemble smoother (IES) and our previously developed GP based iterative ensemble smoother (GPIES). Results show that, using the GP-derived sensitivity indices, GPIS shows advantages over GPIES in terms of both estimation accuracy and computational efficiency. Although subsurface flow and transport problems are considered in this work, the proposed method can be equally applied in other hydrological problems.