State of the Art Report on Mathematical Methods for Groundwater Pollution Source Identification

Atmadja, Juliana; Bagtzoglou, Amvrossios C.

doi:10.1080/15275920127949

Cited by 51 publications

(66 citation statements)

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“…To resolve the groundwater pollution source problem in heterogeneous media, Atmadja [3] and Atmadja and Bagtzoglou [4][5][6] have proposed the method of marching-jury backward beam equation (MJBBE), which dealt with the recovery of the spatial distribution of contaminant concentration and was not an optimization method. Judged from by calculating the recovery of the spatial distribution of contaminant concentration in a homogeneous media, the MJBBE method obtains smaller numerical errors than that in the heterogeneous media (see Figures 5 and 8-11 of Atmadja and Bagtzoglou [5]).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the groundwater pollution identification problem has become a very important issue, which involves the location of a contaminant source, the recovery of the release history, and spatial distribution of the contaminant concentration. For a mathematical model of the problem, Gorelick et al [1], Wagner [2], Atmadja [3], and Atmadja and Bagtzoglou [4][5][6] employed the backward in time advection-dispersion equation (ADE) to govern the problem. By accurately identifying those groundwater pollution source characteristics, one can resolve the threat effectively.…”

Section: Introductionmentioning

confidence: 99%

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The backward group preserving scheme for 1D backward in time advection‐dispersion equation

Liu

Chang

2008

Numerical Methods Partial

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In this article, we propose a backward group preserving scheme (BGPS) on the advection-dispersion equation (ADE) for tackling of the contamination problems. The BGPS has been successfully applied on the backward heat conduction problems as well as the backward in time Burgers equation, but it has never been applied to solve the ADE. The BGPS is able to recover the spatial distribution of groundwater contaminant concentration in this work. Several numerical examples are worked out, and we show, based on those numerical examples, that the BGPS is applicable to the ADE and the method can also handle the ADE with piecewise constant dispersion coefficients. When a steep gradient is appeared in the solution, several steps of the BGPS can be used to retrieve the desired initial data and its result is better than the marching-jury backward beam equation (MJBBE) method as far as our examples are concerned.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The backward group preserving scheme for 1D backward in time advection‐dispersion equation

Liu

Chang

2008

Numerical Methods Partial

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“…The transport physical processes are simulated 'backward' to localize the source and identify the release history. It regroups classes 2 and 4 as defined 15 by Atmadja and Bagtzoglou (2001a). In that case, both flow-field and contaminated plume are assumed perfectly known.…”

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confidence: 99%

“…Parameter models are proposed and used as input in forward solver to simulate concentration breakthrough curves at the sample locations; when the mismatch between the simulated concentrations and the observed ones is within an acceptable level of error, the proposed model is 20 accepted as a solution. This class of methods contains optimization methods as described by Atmadja and Bagtzoglou (2001a); Amirabdollahian and Datta (2013) but also posterior sampling methods which provide posterior probabilities of the solutions.…”

mentioning

confidence: 99%

“…Firstly, to assess the performance of an inverse problem formulation to identify contaminant source characteristics on a synthetic case that presents realistic hydrogeological property contrasts and connected 15 structures, because 1) in spite of its advantages, inverse problem formulation to identify contaminant source characteristics has been employed only on multi-Gaussian type heterogeneities and 2) the type of heterogeneities strongly influences mass transport. Secondly, to verify the efficiency of an EI algorithm to identify contaminant source characteristics because such optimizers offer parameter space exploration possibilities that prevent being trapped in local minima at a much lower cost than with simulated annealing.…”

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confidence: 99%

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Contaminant source localization via Bayesian global optimization

Pirot¹,

Krityakierne²,

Ginsbourger³

et al. 2017

Preprint

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Abstract. A Bayesian optimization approach to localize a contaminant source is proposed. The localization problem is illustrated with two 2D synthetic cases which display sharp transmissivity contrasts and specific connectivity patterns. These cases generate highly non-linear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian Process model and on the Expected Improvement criterion is used to efficiently localize the minimum of the objective function which identifies the contaminant source. In addition, the generated objective functions 5 are made available as a benchmark to further allow the comparison of optimization algorithms on functions characterized by multiple minima and inspired by concrete field applications.

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Efficient Bayesian experimental design for contaminant source identification

et al. 2015

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In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

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State of the Art Report on Mathematical Methods for Groundwater Pollution Source Identification

Cited by 51 publications

References 0 publications

The backward group preserving scheme for 1D backward in time advection‐dispersion equation

The backward group preserving scheme for 1D backward in time advection‐dispersion equation

Contaminant source localization via Bayesian global optimization

Efficient Bayesian experimental design for contaminant source identification

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