The prediction of water table height in unconfined layered porous media is a difficult modelling problem that typically requires numerical simulation. This paper proposes an analytical model to approximate the exact solution based on a steady-state Dupuit–Forchheimer analysis. The key contribution in relation to a similar model in the literature relies in the ability of the proposed model to consider more than two layers with different thicknesses and slopes, so that the existing model becomes a special case of the proposed model herein. In addition, a model assessment methodology based on the Bayesian inverse problem is proposed to efficiently identify the values of the physical parameters for which the proposed model is accurate when compared against a reference model given by MODFLOW-NWT, the open-source finite-difference code by the U.S. Geological Survey. Based on numerical results for a representative case study, the ratio of vertical recharge rate to hydraulic conductivity emerges as a key parameter in terms of model accuracy so that, when appropriately bounded, both the proposed model and MODFLOW-NWT provide almost identical results.

中文翻译：

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倾斜层状多孔介质中无侧限水流近似模型的贝叶斯评估

无侧限层状多孔介质中地下水位高度的预测是一个困难的建模问题，通常需要数值模拟。本文提出了一种基于稳态 Dupuit-Forchheimer 分析来近似精确解的分析模型。与文献中类似模型相关的关键贡献依赖于所提出模型考虑具有不同厚度和坡度的两层以上的能力，因此现有模型成为本文所提出模型的特例。此外，提出了一种基于贝叶斯逆问题的模型评估方法，以有效地识别物理参数的值，当与 MODFLOW-NWT 给出的参考模型进行比较时，该模型是准确的，开源有限差分美国的代码 地理调查。基于代表性案例研究的数值结果，垂直补给率与水力传导率的比率成为模型精度方面的关键参数，因此，如果有适当的界限，所提出的模型和 MODFLOW-NWT 都提供几乎相同的结果。