Parameter Identification by High-Resolution Inverse Numerical Model Based on LBM/CMA-ES: Application to Chalk Aquifer (North of France)

Abstract

The present paper proposes the numerical solution of an inverse problem in groundwater flow (Darcy’s equation). This solution was achieved by combining a high-resolution new code HYSFLO-LBM (Hydrodynamic of Subsurface Flow by Lattice Boltzmann Method), based on LBM, to solve the direct problem, and the metaheuristic optimization algorithm CMA-ES ES (Covariance Matrix Adaptation-Evolution Strategy) to solve the optimization step. The integrated optimization algorithm which resulted from this combination, HYSFLO-LBM/CMA-ES, was applied to the hydrogeological experimental site of Beauvais (Northern France), instrumented by a set of sensors distributed over 20 hydrogeological wells. Hydrogeological parameters measured by the sensors are necessary to understand the aquifer functioning and to serve as input data for the identification of the transmissivity field by the HYSFLO-LBM/CMA-ES code. Results demonstrated an excellent concordance between the integrated optimization algorithm and hydrogeological applied methods (pumping test and magnetic resonance sounding). The spatial distribution of the transmissivity and hydraulic conductivity are related to the heterogeneous distribution of aquifer formations. The LBM and CMA-ES were chosen for their proven excellent performance and lesser cost, in terms of both money and time, unlike the geophysical survey and pumping test. The model can be used and developed as a decision support tool for integrated water resources management in the region.