Monte Carlo techniques for estimating solution quality in stochastic groundwater management models

David W. Watkins*, David P. Morton, Daene C. McKinney

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

For computational purposes, a stochastic groundwater management model with minimizing value z* is often approximately solved by randomly sampling n realizations of the model's stochastic parameters, and then solving the resulting `approximating problem' for (x*n, z*n). It can be shown that, in expectation, z*n is a lower bound on z* and that this lower bound monotonically improves as n increases. Using this result, an approach based on Monte Carlo sampling and solution of multiple instances of the n-scenario approximating problem is applied to construct confidence intervals on the optimality gap for any candidate solution x, such as x = x*n. A sampling procedure based on common random numbers ensures non-negative estimates of the optimality gap and provides significant variance reduction over naive sampling on a test problem involving the location of pumping wells for contaminant plume containment.

Original languageEnglish (US)
Title of host publicationComputational Methods in Contamination and Remediation of Water Resources
EditorsV.N. Burganos, G.P. Karatzas, A.C. Payatakes, C.A. Brebbia, W.G. Gray, G.F. Pinder
PublisherComputational Mechanics Publ
Pages67-74
Number of pages8
Volume1
StatePublished - Jan 1 1998
EventProceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) - Crete, Greece
Duration: Jun 1 1998Jun 1 1998

Other

OtherProceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2)
CityCrete, Greece
Period6/1/986/1/98

ASJC Scopus subject areas

  • Engineering(all)

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