Gaussian analysis of one-dimensional unsaturated flow in randomly heterogeneous soils

Amir, Orna; Neuman, Shlomo P.

doi:10.1130/0-8137-2348-5.105

Cited by 17 publications

(27 citation statements)

References 13 publications

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“…Moreover, moment equations are applicable to either mildly heterogeneous or wellcharacterized soils. Unless the use of the Kirchhoff transformation is warranted [36,33,17], they also require linearization of the constitutive relations, K r = K r (h) and h = h(w), in the Richards equation (1). This limits the range of their applicability and introduces modeling errors that cannot be quantified a priori.…”

Section: Introductionmentioning

confidence: 98%

“…An alternative is to assume that a system state, e.g., pressure head w(x, t) in (1), has a Gaussian PDF p w (W; x, t) [1,2]. This approach provides a full probabilistic description of w required for risk assessment-it can be used, for example, to compute Pr½wðx; tÞ 6 W ¼ R W w min p w ðW 0 ; x; tÞdW 0 , the probability of uncertain (random) pressure head w at point x and time t not exceeding a given value W-once its mean wðx; tÞ and variance r 2 w ðx; tÞ are obtained from the corresponding deterministic moment equations [1,2]. Unfortunately, PDFs of w(x, t) are in general non-Gaussian [35].…”

Section: Introductionmentioning

confidence: 99%

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Reduced complexity models for probabilistic forecasting of infiltration rates

Wang

Tartakovsky

2011

Advances in Water Resources

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Reduced complexity models for probabilistic forecasting of infiltration rates

Wang

Tartakovsky

2011

Advances in Water Resources

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“…Examples of such ''parametric solutions'' include assumed Gaussian PDF for hydraulic head in steady-state and transient saturated flows (Nachabe and Morel-Seytoux 1995) and pressure in steady-state (Amir and Neuman 2001) and transient (Amir and Neuman 2004) unsaturated flow, and b-distributions for concentration of conservative (Bellin and Tonina 2007) and reactive (Cirpka et al 2008) solutes migrating in groundwater flow. While promising, such approaches are akin to guessing a solution of a differential equation, except the validity of assumed PDFs as solutions of SPDEs cannot be verified by direct substitution and requires, instead, extensive numerical testing.…”

Section: Introductionmentioning

confidence: 99%

Probability density functions for advective–reactive transport in radial flow

Broyda

Dentz

Tartakovsky

2010

Stoch Environ Res Risk Assess

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We study transport of a reactive solute in a chemically heterogeneous porous medium whose chemical properties are uncertain. The dissolved substance undergoes a heterogeneous chemical reaction with a solid phase in the presence of advection caused by extraction/injection from a point source. We present semi-analytical solutions for the probability density function of the solute concentration, which allows us to quantify predictive uncertainty associated with uncertain reaction rate constants for both linear and nonlinear reactions. This enables one to compute probabilities of rare events, which are required for quantitative risk analyses.

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“…The comparison shows excellent agreement between the two sets of results over a remarkably broad range of constitutive parameters. A paper that describes this part of Dr. Amir's work has appeared in the journal (Amir and Neuman, 2001a). An earlier, less complete version has appeared in a book published as a Geological Society of America Special Paper (Amir and Neuman, 2000).…”

Section: Analysis Based On Gaussian Approximationmentioning

confidence: 99%

“…During the last year, Dr. Amir was able to improve substantially the quality of pressure head variance and covariance assessments based on her one-dimensional Gaussian approach. A paper summarizing her most recent work on this topic has been submitted for publication in the journal Transport in Porous Media (Amir and Neuman, 2002b).…”

Section: Extension Of Gaussian Approach To Transient Flowmentioning

confidence: 99%

Conditional Analysis of Unsaturated Flow in Randomly Heterogeneous Soils Without Monte Carlo Simulation or Upscaling

Neuman¹

2002

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This study focused on flow in the unsaturated or vadose zone, which forms a major hydrologic link between the ground surface and underlying groundwater aquifers. To properly understand its role in protecting groundwater from surface and near surface sources of contamination, one must be able to analyze quantitatively fluid flow in unsaturated soils. The difficulty is that such soils are ubiquitously heterogeneous, with hydraulic properties that fluctuate from point to point in a seemingly erratic manner. The common approach has been to delineate this variation, and analyze unsaturated flow in randomly heterogeneous soils, deterministically. Yet with increasing frequency, the popular deterministic approach is proving to be inadequate. Our project aimed at developing theoretical and computational methods to predict, in an optimum fashion, unsaturated flow in randomly heterogeneous soils under the action of uncertain forcing terms and to assess the corresponding prediction errors. Previously, such predictions and assessments required the conduct of numerous Monte Carlo simulations on a fine grid, which was computationally demanding and therefore seldom used in practice. An alternative is to conduct Monte Carlo simulations on a coarse grid, which is still computationally intensive (due to the need for many repetitions) and leads to a loss of accuracy due to the need to average (upscale) the flow equations over relatively large grid cells. Our objective was to avoid the need for either Monte Carlo simulation or upscaling by developing ways to render predictions and uncertainty assessments directly, in a computationally efficient and accurate manner. This final technical report describes our accomplishment in the development of two novel approaches, one based on the Kirchhoff transformation and the other on a Gaussian method of approximation. The report also describes some initial ideas about how to extend the applicability of these two approaches to multidimensional and transient flows in a broader class of soils than we have considered previously. The report cites publications based on research supported in part by this ARO grant.

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Gaussian analysis of one-dimensional unsaturated flow in randomly heterogeneous soils

Cited by 17 publications

References 13 publications

Reduced complexity models for probabilistic forecasting of infiltration rates

Reduced complexity models for probabilistic forecasting of infiltration rates

Probability density functions for advective–reactive transport in radial flow

Conditional Analysis of Unsaturated Flow in Randomly Heterogeneous Soils Without Monte Carlo Simulation or Upscaling

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