Groundwater Management Using Model Reduction via Empirical Orthogonal Functions
Publication: Journal of Water Resources Planning and Management
Volume 134, Issue 2
Abstract
This work presents a novel approach for solving groundwater management problems with reduced computational effort. We replace a groundwater flow model governed by a partial differential equation with a simple model governed by an ordinary differential equation. Model reduction is achieved with empirical orthogonal functions, i.e., principal components. Replacement of the full-scale model by a reduced model allows implementation of the embedding approach for optimal groundwater management. Comparing the results obtained with the full-scale simulation model, preliminary analyses show that the reduced model is able to reproduce head variations in the flow domain with good accuracy and, to a certain degree, the sensitivities of head with respect to pumping. A key advantage of the reduced model is that it is simple and easy to solve, and in many instances captures the dominating characteristics of the original model. In view of the many sources of uncertainty influencing groundwater simulation, the accuracy provided by a reduced model may be sufficient for planning purposes. As with other examples of model reduction presented in recent research efforts, the methodology shows promise in presenting general trends, but does not eliminate the need for the original model when more detailed analyses are needed.
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Acknowledgments
This material is based upon work supported by NSF under Agreement No. NSFEAR-0336952 and USGS under Grant No. UNSPECIFIED05HQGR0161. The writers wish to thank two anonymous reviewers for their in-depth reviews and constructive comments.
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© 2008 ASCE.
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Received: Mar 8, 2006
Accepted: May 30, 2007
Published online: Mar 1, 2008
Published in print: Mar 2008
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