Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory: 1. Model development

Ahlfeld, David P.; Mulvey, John M.; Pinder, George F.; Wood, Eric F.

doi:10.1029/wr024i003p00431

Cited by 185 publications

(77 citation statements)

References 29 publications

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“…The main computational effort required for the evaluation of the derivatives lies in the solution of the linear problem (38) or (39). The solution of these problems is equivalent to the solution of N or k linear systems respectively, one for each column of the matrix B or C. The strategy proposed by Ahlfeld et al (1988a) is therefore to choose the first approach if the number of wells (N) is smaller or equal to the number of constraints (k), the second one otherwise.…”

Section: / Tucciarelli Karatzas and Pindermentioning

confidence: 99%

“…These derivatives can be efficiently obtained with the aid of sensitivity analysis (Ahlfeld et al 1988a and1988b), using one of two alternative approaches.…”

Section: The Sensitivity Analysismentioning

confidence: 99%

“…The GW2SEN code (Ahlfeld et al 1988a and1988b) has been used for the transport and sensitivity computations. The problem has been solved using 196 potential well locations, one at each node inside the rectangle.…”

Section: A Model Examplementioning

confidence: 99%

“…In (4) through (8), (4) through (8) is achieved using the GW2SEN numerical simulator (Ahlfeld et al 1988a), which is a two-dimensional finite element code that provides the nodal concentration values as well as the sensitivities of the concentration with respect to the pumping rates. These sensitivities form the "response matrix" of the concentrations that is used in the optimization model (Gorelick et al 1984).…”

mentioning

confidence: 99%

“…The pumping rates are assumed to be constant within a finite number of stages (Ahlfeld 1990), each one long enough to neglect transient head effects. The formulation of the above optimization problem is based on the "response matrix" or "implicit method" approach wherein the number of optimization design variables is equal to the number of controllable parameters (Ahlfeld et al 1988a, Gorelick et al 1984.…”

mentioning

confidence: 99%

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A Primal Method for the Solution of the Groundwater Quality Management Problem

Tucciarelli¹,

Karatzas²,

Pinder³

1998

Operations Research

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A new algorithm for the solution of the groundwater quality management problem is presented. The method assumes that most of the computational effort in such problems involves evaluation of the concentrations and their derivatives with respect to the pumping rates at the control points. The methodology proposed herein is a combination of the cutting plane method and the primal method. In this approach each line search moves from a feasible point towards the solution of a subproblem with linear constraints and the same objective function as the original problem. Sensitivity analysis is used to compute the derivative of a single concentration with respect to all the pumping rates by solving only one linear system at each time step. The method has been tested with analytical convex problems and a model example. A comparison of the algorithm's performance was conducted using MINOS 5.1. For the case of a linear cost function the method shows a computational growth rate almost linearly proportional to the number of decision variables.

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Section: / Tucciarelli Karatzas and Pindermentioning

confidence: 99%

“…These derivatives can be efficiently obtained with the aid of sensitivity analysis (Ahlfeld et al 1988a and1988b), using one of two alternative approaches.…”

Section: The Sensitivity Analysismentioning

confidence: 99%

Section: A Model Examplementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A Primal Method for the Solution of the Groundwater Quality Management Problem

Tucciarelli¹,

Karatzas²,

Pinder³

1998

Operations Research

Self Cite

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Global change and the groundwater management challenge

Gorelick

Chen

2015

Water Resources Research

351

142

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With rivers in critical regions already exploited to capacity throughout the world and groundwater overdraft as well as large-scale contamination occurring in many areas, we have entered an era in which multiple simultaneous stresses will drive water management. Increasingly, groundwater resources are taking a more prominent role in providing freshwater supplies. We discuss the competing fresh groundwater needs for human consumption, food production, energy, and the environment, as well as physical hazards, and conflicts due to transboundary overexploitation. During the past 50 years, groundwater management modeling has focused on combining simulation with optimization methods to inspect important problems ranging from contaminant remediation to agricultural irrigation management. The compound challenges now faced by water planners require a new generation of aquifer management models that address the broad impacts of global change on aquifer storage and depletion trajectory management, land subsidence, groundwater-dependent ecosystems, seawater intrusion, anthropogenic and geogenic contamination, supply vulnerability, and long-term sustainability. The scope of research efforts is only beginning to address complex interactions using multiagent system models that are not readily formulated as optimization problems and that consider a suite of human behavioral responses.

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Interactive design of experiments: A priori global versus sequential optimization, revised under changing states of knowledge

Geiges

Rubin

Nowak

2015

Water Resources Research

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Predicting hydro(geo)logical or environmental systems is subject to high levels of uncertainties, especially if appropriate data for model calibration are lacking. For subsurface systems, where data acquisition is cost intensive and time demanding, it is especially important to collect only those data that provide the largest amount of relevant information. The high expenses call for optimal experimental design, which is widely recognized for maximizing the efficiency of experiments. In model‐based design of experiments, the analysis of the design efficiency and the resulting optimal design are based on the initial state of knowledge about the modeled system. Joint optimization of multimeasurement designs is a well‐known challenge, and the usefulness of global optimization approaches is widely recognized in this context. However, we will show that the benefit for such global optimization becomes questionable when measurement data become available sequentially. Instead, the optimization effort should be invested within an interactive design approach. Today's fast telecommunication, global connectivity, and high‐performance computing allow to consider such interactive coupling. This study will use a synthetic case study to compare the standard en‐bloc global optimization approach to two interactive design approaches. The approaches are implemented in a Bayesian framework and are compared based on their complexity and overall performance. The key conclusion confirms a previously untested presumption: for models that trigger nonlinear parameter inference problems, interaction (which may come at a loss of global optimization) is more beneficial than global optimization based on the initial state of knowledge (which typically implies the impossibility of interactivity).

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Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory: 1. Model development

Cited by 185 publications

References 29 publications

A Primal Method for the Solution of the Groundwater Quality Management Problem

A Primal Method for the Solution of the Groundwater Quality Management Problem

Global change and the groundwater management challenge

Interactive design of experiments: A priori global versus sequential optimization, revised under changing states of knowledge

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