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The Soil Moisture Velocity Equation
Journal of Advances in Modeling Earth Systems (2017)
  • Fred L. Ogden
  • Craig C. Douglas
Numerical solution of the one-dimensional Richards’ equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyper-resolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards’ equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards’ equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.
  • Richards' Equation,
  • Numerical,
  • Solution,
  • Infiltration,
  • PDE,
  • ODE
Publication Date
June 14, 2017
doi:10.1002/ 2017MS000931
Publisher Statement
Copyright (C) The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Citation Information
Ogden, F. L., M. B. Allen, W. Lai, J. Zhu, M. Seo, C. C. Douglas, and C. A. Talbot (2017), The soil moisture velocity equation, J. Adv. Model. Earth Syst., 9, 1473–1487, doi:10.1002/2017MS000931.
Creative Commons license
Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC-ND International License.