Transport in Porous Media, Vol.126, No.1, 177-197, 2019
A Bayesian Assessment of an Approximate Model for Unconfined Water Flow in Sloping Layered Porous Media
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.
Keywords:Dupuit-Forchheimer analysis;Layered porous media;Bayesian hypothesis testing;Railway track drainage