Improving the numerical solution of soil moisture-based Richards equation for land models with a deep or shallow water table

Xubin Zeng, Mark Decker

Research output: Contribution to journalArticle

78 Citations (Scopus)

Abstract

The soil moisture-based Richards equation is widely used in land models for weather and climate studies, but its numerical solution using the mass-conservative scheme in the Community Land Model is found to be deficient when the water table is within the model domain. Furthermore, these deficiencies cannot be reduced by using a smaller grid spacing. The numerical errors are much smaller when the water table is below the model domain. These deficiencies were overlooked in the past, most likely because of the more dominant influence of the free drainage bottom boundary condition used by many land models. They are fixed here by explicitly subtracting the hydrostatic equilibrium soil moisture distribution from the Richards equation. This equilibrium distribution can be derived at each time step from a constant hydraulic (i.e., capillary plus gravitational) potential above the water table, representing a steady-state solution of the Richards equation. Furthermore, because the free drainage condition has serious deficiencies, a new bottom boundary condition based on the equilibrium soil moisture distribution at each time step is proposed that also provides an effective and direct coupling between groundwater and surface water.

Original languageEnglish (US)
Pages (from-to)308-319
Number of pages12
JournalJournal of Hydrometeorology
Volume10
Issue number1
DOIs
StatePublished - 2009

Fingerprint

Richards equation
water table
shallow water
deep water
soil moisture
boundary condition
drainage
hydrostatics
spacing
land
hydraulics
weather
surface water
groundwater
climate
distribution

ASJC Scopus subject areas

  • Atmospheric Science

Cite this

Improving the numerical solution of soil moisture-based Richards equation for land models with a deep or shallow water table. / Zeng, Xubin; Decker, Mark.

In: Journal of Hydrometeorology, Vol. 10, No. 1, 2009, p. 308-319.

Research output: Contribution to journalArticle

@article{984a7d64dbea4345b19f75be8ba2d074,
title = "Improving the numerical solution of soil moisture-based Richards equation for land models with a deep or shallow water table",
abstract = "The soil moisture-based Richards equation is widely used in land models for weather and climate studies, but its numerical solution using the mass-conservative scheme in the Community Land Model is found to be deficient when the water table is within the model domain. Furthermore, these deficiencies cannot be reduced by using a smaller grid spacing. The numerical errors are much smaller when the water table is below the model domain. These deficiencies were overlooked in the past, most likely because of the more dominant influence of the free drainage bottom boundary condition used by many land models. They are fixed here by explicitly subtracting the hydrostatic equilibrium soil moisture distribution from the Richards equation. This equilibrium distribution can be derived at each time step from a constant hydraulic (i.e., capillary plus gravitational) potential above the water table, representing a steady-state solution of the Richards equation. Furthermore, because the free drainage condition has serious deficiencies, a new bottom boundary condition based on the equilibrium soil moisture distribution at each time step is proposed that also provides an effective and direct coupling between groundwater and surface water.",
author = "Xubin Zeng and Mark Decker",
year = "2009",
doi = "10.1175/2008JHM1011.1",
language = "English (US)",
volume = "10",
pages = "308--319",
journal = "Journal of Hydrometeorology",
issn = "1525-755X",
publisher = "American Meteorological Society",
number = "1",

}

TY - JOUR

T1 - Improving the numerical solution of soil moisture-based Richards equation for land models with a deep or shallow water table

AU - Zeng, Xubin

AU - Decker, Mark

PY - 2009

Y1 - 2009

N2 - The soil moisture-based Richards equation is widely used in land models for weather and climate studies, but its numerical solution using the mass-conservative scheme in the Community Land Model is found to be deficient when the water table is within the model domain. Furthermore, these deficiencies cannot be reduced by using a smaller grid spacing. The numerical errors are much smaller when the water table is below the model domain. These deficiencies were overlooked in the past, most likely because of the more dominant influence of the free drainage bottom boundary condition used by many land models. They are fixed here by explicitly subtracting the hydrostatic equilibrium soil moisture distribution from the Richards equation. This equilibrium distribution can be derived at each time step from a constant hydraulic (i.e., capillary plus gravitational) potential above the water table, representing a steady-state solution of the Richards equation. Furthermore, because the free drainage condition has serious deficiencies, a new bottom boundary condition based on the equilibrium soil moisture distribution at each time step is proposed that also provides an effective and direct coupling between groundwater and surface water.

AB - The soil moisture-based Richards equation is widely used in land models for weather and climate studies, but its numerical solution using the mass-conservative scheme in the Community Land Model is found to be deficient when the water table is within the model domain. Furthermore, these deficiencies cannot be reduced by using a smaller grid spacing. The numerical errors are much smaller when the water table is below the model domain. These deficiencies were overlooked in the past, most likely because of the more dominant influence of the free drainage bottom boundary condition used by many land models. They are fixed here by explicitly subtracting the hydrostatic equilibrium soil moisture distribution from the Richards equation. This equilibrium distribution can be derived at each time step from a constant hydraulic (i.e., capillary plus gravitational) potential above the water table, representing a steady-state solution of the Richards equation. Furthermore, because the free drainage condition has serious deficiencies, a new bottom boundary condition based on the equilibrium soil moisture distribution at each time step is proposed that also provides an effective and direct coupling between groundwater and surface water.

UR - http://www.scopus.com/inward/record.url?scp=65349171003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65349171003&partnerID=8YFLogxK

U2 - 10.1175/2008JHM1011.1

DO - 10.1175/2008JHM1011.1

M3 - Article

AN - SCOPUS:65349171003

VL - 10

SP - 308

EP - 319

JO - Journal of Hydrometeorology

JF - Journal of Hydrometeorology

SN - 1525-755X

IS - 1

ER -