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WATER RESOURCES RESEARCH, VOL. 39, NO. 2, 1028, doi:10.1029/2001WR000544, 2003

Error in unsaturated stochastic models parameterized with field data

Robert M. Holt

Department of Geology and Geological Engineering, University of Mississippi, University, Mississippi, USA


John L. Wilson

Department of Earth and Environmental Science, New Mexico Institute of Mining and Technology, Socorro, New Mexico, USA


Robert J. Glass

Flow Visualization and Processes Laboratory, Sandia National Laboratories, Albuquerque, New Mexico, USA


Abstract

We use Monte Carlo error analysis to illustrate the impact of measurement errors in field-estimated hydraulic properties on predictions made with 1D and 3D unconditional stochastic models of unsaturated flow and transport. Monte Carlo simulations are conducted across a series of simplified artificial realities completely described by the Gardner–Russo parametric model. The mean values of properties are varied between simulations to elucidate the relationship between true properties and prediction errors. Hydraulic properties are reestimated by simulating tension infiltrometer measurements in the presence of small simple errors. Two types of observation error are considered, along with one inversion-model error resulting from poor contact between the instrument and the medium. Errors in the spatial statistics of hydraulic properties cause critical stochastic model assumptions to be violated, limiting the usable parameter space for model predictions. Even where critical assumptions are valid, stochastic model predictions show significant error, and the magnitude and pattern of error changes with the true property means, the flow conditions, and the type of measurement error. Mean velocities may show errors up to an order of magnitude. The velocity variance is overestimated by up to three orders of magnitude during 3D flow and eight orders of magnitude during 1D flow. The 1D velocity integral scale is underestimated by as much as five orders of magnitude. The estimates for 1D longitudinal macrodispersivity are surprisingly robust and show relatively small error across most of the parameter space.

Published 8 February 2003.

Index Terms: 1869 Hydrology: Stochastic processes; 1875 Hydrology: Unsaturated zone; 1829 Hydrology: Groundwater hydrology; 1832 Hydrology: Groundwater transport.

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Citation: Holt, R. M., J. L. Wilson, and R. J. Glass (2003), Error in unsaturated stochastic models parameterized with field data, Water Resour. Res., 39(2), 1028, doi:10.1029/2001WR000544.