Groundwater Parameter Inversion Using Topographic Constraints and a Zonal Adaptive Multiscale Procedure: A Case Study of an Alluvial Aquifer

Abstract

The identification of aquifer parameters (i.e., specific yield and hydraulic conductivity) and forcing terms (recharge) is crucial for the process of modeling groundwater flow and contamination. Inversion techniques allow the unravelling of complex systems’ heterogeneity with more ease than manual calibration by computing parameter fields through an automated minimization between simulated and measured data (i.e., water head or measured aquifer parameters). It also allows the iterative search of multiple, equally plausible solutions, depending on system complexity (e.g., aquifer heterogeneity and variability of the forcing terms such as recharge). A Zoned Adaptive Multiscale Triangulation (ZAMT) is used for parameter estimation. ZAMT is the extension of an adaptive multiscale parameter estimation procedure already applied on different field cases. This extension consists of adding constraints varying over the domain. The ZAMT dissociates the parameter grid from the calculation mesh and allows local parameter grid refinement depending on local criteria, addressing the ill-posedness of inversion problems, decreasing computation time by reducing the amount of possible solutions and local minima, and ensuring flexibility in the parameter’s distribution. Each parameter is defined per vertex of the parameter grid; it can be set with a different range of values in order to integrate more pedo-geological information and help the optimization process by reducing the number of local minima. For the same purpose, a plausibility term based on topological characteristics of the aquifer or minimal and maximal water levels is added to the objective function. Groundwater flow is described by a classical nonlinear diffusion-type equation (unconfined aquifer), which is discretized with a two-dimensional nonconforming finite element method because water head data is unsuitable to invert three-dimensional parameter fields. Therefore, flow is considered mainly horizontal, and the parameters are obtained as average values on the saturated thickness. The study area is an alluvial (unconfined) aquifer of 6.64 km², situated in the southern, Mediterranean part of France. The simulation runs with a chronicle of 191 piezometers over 7 years (2012–2019), using a calibration period of 5 years (2012–2016). The optimization threshold is set to ensure a mean absolute error below 40 cm. The ZAMT and the additional plausibility criterion were found to produce an ensemble of realistic parameter sets with low parameter standard deviation. The model is considered robust as the water head error remains at the same level during the verification period, which includes an exceptionally dry year (2017). Overall, the calibration is best near the rivers (Dirichlet boundaries), while the terraced portion of the site challenges the limits of the 2D approach and the inversion procedure.