Flow in unsaturated random porous media, nonlinear numerical analysis and comparison to analytical stochastic models

Thomas Harter, T. C. Jim Yeh

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably saturated flow in actual or realistic hypothetical heterogeneous porous media. Statistical properties of unsaturated hydraulic conductivity, soil water tension, and soil water flux in heterogeneous soils are investigated through high resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in analytical stochastic models of unsaturated flow, hydraulic conductivity and soil water tension are found to be lognormally and normally distributed, respectively. In contrast, simulations indicate that in moderate to strong variable conductivity fields, longitudinal flux is highly skewed. Transverse flux distributions are leptokurtic, the moments of the probability distributions obtained from Monte Carlo simulations are compared to modified first-order analytical models. Under moderate to strong heterogeneous soil flux conditions (σ2y 1), analytical solutions overestimate variability in soil water tension by up to 40% as soil heterogeneity increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well with the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flow in heterogeneous soils.

Original languageEnglish (US)
Pages (from-to)257-272
Number of pages16
JournalAdvances in Water Resources
Issue number3
StatePublished - Nov 1998


  • Flow modeling
  • Heterogeneity
  • Soil water
  • Stochastic analysis
  • Vadose zone

ASJC Scopus subject areas

  • Water Science and Technology


Dive into the research topics of 'Flow in unsaturated random porous media, nonlinear numerical analysis and comparison to analytical stochastic models'. Together they form a unique fingerprint.

Cite this