Stochastic management of pump-and-treat strategies using surrogate functions

Baù, Domenico; Mayer, Alex

doi:10.1016/j.advwatres.2006.01.008

Cited by 67 publications

(40 citation statements)

References 32 publications

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“…Yan and Minsker [2006] developed a methodology for reducing the number of full-model calls using a dynamic learning technique. A technique similar to ANN modeling is a method proposed by Baú and Mayer [2006] in which the objective functions are approximated using kriging interpolation, resulting in surrogate functions which reduce the computational burden of the management problem presented in their work.…”

Section: Introductionmentioning

confidence: 99%

Snapshot selection for groundwater model reduction using proper orthogonal decomposition

Siade

Putti

Yeh

2010

Water Resources Research

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[1] Water resources systems management often requires complex mathematical models whose use may be computationally infeasible for many advanced analyses, e.g., optimization, data assimilation, model uncertainty, etc. The computational demand of these analyses can be reduced by approximating the model with a simpler reduced model. Proper Orthogonal Decomposition (POD) is an efficient model reduction technique based on the projection of the original model onto a subspace generated by full-model snapshots. In order to implement this method, an appropriate number of snapshots of the full model must be taken at the appropriate times such that the resulting reduced model is as accurate as possible. Since confined aquifers reach steady state in an exponential manner, we present a simple exponential function that can be used to select snapshots for these types of models. This selection method is then employed to determine the optimal snapshot set for a unit, dimensionless model. The optimal snapshot set is found by maximizing the minimum eigenvalue of the snapshot covariance matrix, a criterion similar to those used in experimental design. The resulting snapshot set can then be translated to any complex, real world model based on a simple, approximate relationship between dimensionless and real-world times. This translation is illustrated using a basin scale model of Central Veneto, Italy. We show that this method is very easy to implement and produces an accurate reduced model that, in the case of Central Veneto, Italy, runs approximately 1,000 times faster than the full model.

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Section: Introductionmentioning

confidence: 99%

Snapshot selection for groundwater model reduction using proper orthogonal decomposition

Siade

Putti

Yeh

2010

Water Resources Research

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“…Although they have some merit when handling uncertain groundwater environmental issues, these optimization approaches have serious drawbacks: they require enormous computational resources, including computing time and memory (Baú and Mayer 2006). Various techniques have been suggested to improve this computational efficiency.…”

Section: Introductionmentioning

confidence: 98%

Information effect on remediation design of contaminated aquifers using the pump and treat method

Lee

2009

Stoch Environ Res Risk Assess

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We examine the effect of uncertainty due to limited information on the remediation design of a contaminated aquifer using the pump and treat method. The hydraulic conductivity and contaminant concentration distributions for a fictitious contaminated aquifer are generated assuming a limited number of sampling locations. Stochastic optimization with multiple realizations is used to account for aquifer uncertainty. The optimization process involves a genetic algorithm (GA). As the number of realizations increases, a greater extraction rate and more wells are needed. There was a total cost increase, but the optimal remediation designs became more reliable. Stochastic optimization analysis also determines the locations for extraction wells, the variation in extraction rates as a function of the change of well locations, and the reliability of the optimal designs. The number of realizations (stack number) that caused the design factors to converge could be determined. Effective stochastic optimization may be achieved by reducing computational resources. An increase in the variability of the conductivity distribution requires more extraction wells. Information about potential extraction wells can be used to prevent failure of the remediation task.

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“…Although the multiple realization approach has some merits in its solutions to uncertain groundwater environmental problems, the stochastic optimization approach generally requires enormous computational resources, such as computing time or memory (Freeze and Gorelick 1999;Baú and Mayer 2006). In order to improve computational efficiency, several methods have been suggested.…”

Section: Introductionmentioning

confidence: 99%

Convergence of deterministic and stochastic approaches in optimal remediation design of a contaminated aquifer

Lee

2008

Stoch Environ Res Risk Assess

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The comparison between two series of optimal remediation designs using deterministic and stochastic approaches showed a number of converging features. Limited sampling measurements in a supposed contaminated aquifer formed the hydraulic conductivity field and the initial concentration distribution used in the optimization process. The deterministic and stochastic approaches employed a single simulation-optimization method and a multiple realization approach, respectively. For both approaches, the optimization model made use of a genetic algorithm. In the deterministic approach, the total cost, extraction rate, and the number of wells used increase when the design must satisfy the intensified concentration constraint. Growing the stack size in the stochastic approach also brings about same effects. In particular, the change in the selection frequency of the used extraction wells, with increasing stack size, for the stochastic approach can indicate the locations of required additional wells in the deterministic approach due to the intensified constraints. These converging features between the two approaches reveal that a deterministic optimization approach with controlled constraints is achievable enough to design reliable remediation strategies, and the results of a stochastic optimization approach are readily available to real contaminated sites.

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Stochastic management of pump-and-treat strategies using surrogate functions

Cited by 67 publications

References 32 publications

Snapshot selection for groundwater model reduction using proper orthogonal decomposition

Snapshot selection for groundwater model reduction using proper orthogonal decomposition

Information effect on remediation design of contaminated aquifers using the pump and treat method

Convergence of deterministic and stochastic approaches in optimal remediation design of a contaminated aquifer

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