Identification of aquifer dispersivities in two‐dimensional transient groundwater Contaminant transport: An optimization approach

Umari, Amjad M. J.; Willis, Robert; Liu, Philip L.‐F.

doi:10.1029/wr015i004p00815

Cited by 35 publications

(5 citation statements)

References 17 publications

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“…Methods of parameter estimation have been applied to distributed parameter groundwater flow models (for a review, see Yeh [1986]) and solute transport studies [Kipp, 1978;Umari et al, 1979;Parker and van Genuchten, 1984;Strecker and Chu, 1986;Wagner and Gorelick, 1986;Knopman andVoss, 1987, 1988] when the correct physical model is assumed to be known. With the important exception of the work of Cooley et al [1986] on discrimination among flow models, little attention in the groundwater literature has been given to applying methods of parameter estimation to the problem of discrimination among physically based models.…”

Section: Nonlinear Regressionmentioning

confidence: 99%

Discrimination among one‐dimensional models of solute transport in porous media: Implications for sampling design

Knopman¹,

Voss²

1988

Water Resources Research

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A methodology is developed for discrimination among models of transient solute transport in porous media. The method utilizes nonlinear regression on observations of solute concentration. Discrimination requires comparisons of model predictions to observations, systematic error in residuals, stability in parameter estimates from regression on different observation sets, and other measures of model fit among hypothesized models of transport. The set of observations of solute concentration to which models are fitted strongly influences the assessment of these discrimination criteria. The most desirable observation set for discrimination amplifies the weaknesses of those models that appear to describe existing conditions but are in fact unsuitable for prediction. The inadequacies of various observation sets are illustrated in four examples of discrimination between one‐dimensional models of solute transport. Our purpose in these examples is to understand the physical, deterministic basis of sampling design for model discrimination. In addition to physical attributes such as transport processes, boundary conditions, and flow geometry, the assumed distribution of random error in the regression model is also treated as a model attribute to be tested by the designed experiment. A common problem in field studies occurs when the set of available observations does not include sufficient information with which to discriminate among hypothesized models, hence supporting the need to design a second round of sampling specifically for discrimination. A proposed objective function in the sampling design problem favors design points at locations and times when two hypothesized transport models display the greatest differences in predicted concentration. Two hypothetical examples demonstrate the effectiveness of the objective function and the application of the discrimination criteria.

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Section: Nonlinear Regressionmentioning

confidence: 99%

Discrimination among one‐dimensional models of solute transport in porous media: Implications for sampling design

Knopman¹,

Voss²

1988

Water Resources Research

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“…The magnitude of the perturbations and their correlation structure reflected the combined effect of model and observation errors. Using the synthetic observations, the model parameters (transmissivity, in a predetermined set of zones, and dispersivity) were determined using a parameter identification (PI) technique [Bard, 1974;Neuman, 1973;Yeh, 1975Yeh, , 1986Cooley, 1977Cooley, , 1982Cooley, , 1983Umari et al, 1979;Neuman and Yakowitz, 1979;Yeh and Yoon, 1981;Sadeghipour and Yeh, 1984;Yeh, 1986] developed by $trecker and Chu [1986]. The PI scheme was formulated as an ordinary constrained least squares problem which minimizes the discrepancies between model solutions and observations.…”

confidence: 99%

An evaluation of data requirements for groundwater contaminant transport modeling

Chu¹,

Strecker²,

Lettenmaier³

1987

Water Resources Research

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Groundwater flow and contaminant transport models have been widely used for planning and design purposes in the past decade. Two of the most significant limitations for application of these models are data availability and parameter estimation. By use of a parameter identification algorithm and synthesized data, it is possible to isolate the effects of data availability and data uncertainty. This approach was implemented using the U.S. Geological Survey's method of characteristics (USGS-MOC) model for a hypothetical aquifer. A parameter identification scheme attached to the USGS-MOC model was used to determine unknown transmissivities and dispersivities. The study results showed that the predictive ability of the USGS-MOC model (and, by implication, similar models) is limited unless relatively extensive and good quality data are available. For the example tested, it was found that extending the length of the observation series was more effective in improving parameter estimates and resolution of the contaminant plume prediction than adding observation wells. Further, when the boundary conditions were known, the contaminant predictions were much more sensitive to accurate estimation of transmissivity than to the estimation of dispersivities. The numerical results also showed that after a relatively short simulation period (less than 4 years), predicted contaminant concentrations could be significantly in error. This suggests the importance of integrating uncertainty analysis into the prediction of long-term contaminant transport.

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“…A review paper on this topic was presented recently by Yeh (25). In comparison, the body of published research for parameter estimation for mass transport problems is still small (26)(27)(28)(29)(30)(31)(32)(33)(34). In the solution of inverse problems, the primary obstacle is their ill-posed nature, i.e., the existence, uniqueness, and stability of the solution may not be satisfied.…”

Section: Introductionmentioning

confidence: 99%

Applications of numerical methods to simulate the movement of contaminants in groundwater.

Sun

1989

Environ Health Perspect

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This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model.

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Identification of aquifer dispersivities in two‐dimensional transient groundwater Contaminant transport: An optimization approach

Cited by 35 publications

References 17 publications

Discrimination among one‐dimensional models of solute transport in porous media: Implications for sampling design

Discrimination among one‐dimensional models of solute transport in porous media: Implications for sampling design

An evaluation of data requirements for groundwater contaminant transport modeling

Applications of numerical methods to simulate the movement of contaminants in groundwater.

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