A Bayesian Assessment of an Approximate Model for Unconfined Water Flow in Sloping Layered Porous Media

Juan Chiachío,Manuel Chiachío,Shankar Sankararaman,Darren Prescott

doi:10.1007/s11242-018-1094-2

Abstract

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.

Highlights

The modelling of unconfined water flow in layered porous media is a challenging problem with important applications in Earth sciences and engineering
Of the unconfined boundary condition and the fact that the location of this boundary is unknown (Bear 1972). This modelling complexity is accentuated when dealing with sloping layered porous media with recharge (Rushton and Youngs 2010), which typically requires the use of numerical methods such as finite-difference (FD) (Wang and Anderson 1982; Todsen 1971; Lee and Leap 1997) or finite element (FE) models (Shamsai and Narasimhan 1991; Rulon et al 1985; Chen et al 2008; Zheng et al 2009) to approximate the exact solution
In addition to the three-layered porous media considered in this case study, a variation of the system configuration consisting of splitting the 0.5-m-thick porous material into two and four equal-thickness layers is considered as a way to provide insight about the influence of the number of layers on the plausibility of those subspaces

Summary

Introduction

The modelling of unconfined water flow in layered porous media is a challenging problem with important applications in Earth sciences and engineering. An exact analytical solution to the problem is virtually impossible due to the nonlinearity of the unconfined boundary condition and the fact that the location of this boundary is unknown (Bear 1972) This modelling complexity is accentuated when dealing with sloping layered porous media with recharge (Rushton and Youngs 2010), which typically requires the use of numerical methods such as finite-difference (FD) (Wang and Anderson 1982; Todsen 1971; Lee and Leap 1997) or finite element (FE) models (Shamsai and Narasimhan 1991; Rulon et al 1985; Chen et al 2008; Zheng et al 2009) to approximate the exact solution.

Methods

Results

Conclusion