A Bayesian assessment of an approximate model for unconfined water flow in sloping layered porous media

Juan Chiachío, Manuel Chiachío, Shankar Sankararaman, Darren Prescott

Research output: Contribution to journalArticle

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.
LanguageEnglish
Number of pages21
JournalTransport in Porous Media
Early online date9 Jun 2018
DOIs
StateE-pub ahead of print - 9 Jun 2018

Fingerprint

Approximate Model
Porous Media
Porous materials
Water
Model
Hydraulic Conductivity
Geological surveys
Reference Model
Hydraulic conductivity
Open Source
Analytical Model
Inverse problems
Slope
Table
Finite Difference
Inverse Problem
Exact Solution
Analytical models
Vertical
Numerical Simulation

Keywords

  • Dupuit–Forchheimer analysis
  • layered porous media
  • Bayesian hypothesis testing
  • railway track drainage

Cite this

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title = "A Bayesian assessment of an approximate model for unconfined water flow in sloping layered porous media",
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.",
keywords = "Dupuit–Forchheimer analysis , layered porous media, Bayesian hypothesis testing, railway track drainage",
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month = "6",
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doi = "10.1007/s11242-018-1094-2",
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A Bayesian assessment of an approximate model for unconfined water flow in sloping layered porous media. / Chiachío, Juan; Chiachío, Manuel; Sankararaman, Shankar; Prescott, Darren.

In: Transport in Porous Media, 09.06.2018.

Research output: Contribution to journalArticle

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AB - 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.

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