Conditional moment analysis of steady state unsaturated flow in bounded, randomly heterogeneous soils

Zhiming Lu, Shlomo P Neuman, Alberto Guadagnini, Daniel M. Tartakovsky

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We consider steady state unsaturated flow in bounded, randomly heterogeneous soils under the influence of random boundary and source terms. Our aim is to predict pressure heads and fluxes without resorting to Monte Carlo simulation, upscaling, or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. We represent this relationship through Gardner's exponential model while treating its exponent α as a random constant and saturated hydraulic conductivity Ks as a spatially correlated random field. We linearize the steady state unsaturated flow equations by means of the Kirchhoff transformation and integrate them in probability space to obtain exact integro-differential equations for the conditional mean and variance-covariance of transformed pressure head and flux. After approximating these equations recursively to second order in the standard deviation σY of Y = ln Ks, we solve them by finite elements for superimposed mean uniform and divergent flows in the vertical plane, with and without conditioning on measured Y values. Comparison with Monte Carlo solutions demonstrates that whereas our nonlocal solution is nominally restricted to mildly nonuniform media with σY2 ≪ 1, it yields remarkably accurate results for strongly nonuniform media with σY2 at least as large as 2. This accords well with a previous theoretical analysis, which shows that the solution may remain asymptotic for values of σY2 as large as 2.

Original languageEnglish (US)
Pages (from-to)91-916
Number of pages826
JournalWater Resources Research
Volume38
Issue number4
StatePublished - Apr 2002

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unsaturated flow
Hydraulic conductivity
Soils
hydraulic conductivity
Fluxes
soil
unsaturated hydraulic conductivity
Integrodifferential equations
upscaling
saturated hydraulic conductivity
Linearization
conditioning
simulation
analysis

Keywords

  • Conditioning
  • Heterogeneity
  • Randomness
  • Uncertainty
  • Unsaturated flow

ASJC Scopus subject areas

  • Environmental Science(all)
  • Environmental Chemistry
  • Aquatic Science
  • Water Science and Technology

Cite this

Conditional moment analysis of steady state unsaturated flow in bounded, randomly heterogeneous soils. / Lu, Zhiming; Neuman, Shlomo P; Guadagnini, Alberto; Tartakovsky, Daniel M.

In: Water Resources Research, Vol. 38, No. 4, 04.2002, p. 91-916.

Research output: Contribution to journalArticle

Lu, Zhiming ; Neuman, Shlomo P ; Guadagnini, Alberto ; Tartakovsky, Daniel M. / Conditional moment analysis of steady state unsaturated flow in bounded, randomly heterogeneous soils. In: Water Resources Research. 2002 ; Vol. 38, No. 4. pp. 91-916.
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