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.

中文翻译：

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使用地形约束和分区自适应多尺度程序的地下水参数反演：冲积含水层的案例研究

含水层参数（即比产量和水力传导率）和强迫项（补给）的识别对于模拟地下水流和污染的过程至关重要。通过模拟和测量数据（即水头或测量的含水层参数）之间的自动最小化计算参数场，反演技术允许比手动校准更容易地解开复杂系统的异质性。它还允许根据系统复杂性（例如，含水层异质性和诸如补给等强迫项的可变性）迭代搜索多个同样合理的解决方案。分区自适应多尺度三角测量 (ZAMT) 用于参数估计。ZAMT 是已应用于不同现场情况的自适应多尺度参数估计程序的扩展。此扩展包括添加在域上变化的约束。ZAMT 将参数网格与计算网格分离，并允许根据局部标准对局部参数网格进行细化，解决反演问题的不适定性，通过减少可能的解和局部最小值的数量来减少计算时间，并确保参数的灵活性分配。每个参数定义为参数网格的每个顶点；它可以设置为不同的值范围，以便整合更多的土壤地质信息，并通过减少局部最小值的数量来帮助优化过程。出于同样的目的，基于含水层拓扑特征或最小和最大水位的合理性项被添加到目标函数中。地下水流由经典的非线性扩散型方程（无承压含水层）描述，由于水头数据不适合反演三维参数场，因此采用二维非一致有限元方法对其进行离散化。因此，流动主要被认为是水平的，并且参数作为饱和厚度的平均值获得。研究区是一个 6.64 平方公里的冲积（非承压）含水层，位于法国南部的地中海部分。模拟运行了 7 年（2012-2019 年）内 191 个渗压计的编年史，校准期为 5 年（2012-2016 年）。设置优化阈值以确保平均绝对误差低于 40 cm。发现 ZAMT 和附加合理性标准产生了一组具有低参数标准偏差的现实参数集。该模型被认为是稳健的，因为在验证期间水头误差保持在同一水平，其中包括一个异常干旱的年份（2017 年）。总的来说，校准最好靠近河流（狄利克雷边界），而场地的梯田部分挑战了二维方法和反演程序的限制。