Conditioning mean study state flow on hydraulic head and conductivity through geostatistical inversion

A. F. Hernandez, S. P. Neuman, A. Guadagnini, J. Carrera

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.

Original languageEnglish (US)
Pages (from-to)329-338
Number of pages10
JournalStochastic Environmental Research and Risk Assessment
Issue number5
StatePublished - Nov 2003


  • Aquifer characteristics
  • Geostatistics
  • Groundwater flow
  • Inverse problem
  • Regression analysis
  • Steady-state conditions
  • Stochastic processes
  • Uncertainty

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)


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