Unsaturated flow in heterogeneous soils with spatially distributed uncertain hydraulic parameters

Daniel M. Tartakovsky, Zhiming Lu, Alberto Guadagnini, Alexandre M. Tartakovsky

Research output: Contribution to journalArticlepeer-review


Uncertain soil properties are often modeled as random fields. This renders the unsaturated flow equations stochastic. Determining statistics of pressure head statistics, ψ, is nontrivial, since the Richards equation is highly nonlinear. The prevalent approach is to linearize relative hydraulic conductivity, Kr(ψ), around the ensemble mean pressure head, 〈ψ〉, which often leads to significant errors. Recently, an approach has been proposed to avoid such a linearization for the Gardner model, Kr = exp(αψ), with the soil parameter α being a random variable. We generalize this approach by allowing α to be a random field. This is achieved by means of a partial mean-field approximation with respect to α(x). Using two-dimensional infiltration into a heterogeneous soil with uncertain hydraulic parameters as an example, we demonstrate that our predictions of the mean pressure head and its variance remain accurate for moderately variable αs. The robustness of our solutions increases with the correlation length of α.

Original languageEnglish (US)
Pages (from-to)182-193
Number of pages12
JournalJournal of Hydrology
Issue number3-4
StatePublished - May 1 2003
Externally publishedYes


  • Moment equations
  • Nonlinear
  • Porous media
  • Random
  • Stochastic

ASJC Scopus subject areas

  • Water Science and Technology


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