A statistical parameter estimation method using singular value decomposition with application to Avra Valley aquifer in southern Arizona

Persistent Link:
http://hdl.handle.net/10150/191092
Title:
A statistical parameter estimation method using singular value decomposition with application to Avra Valley aquifer in southern Arizona
Author:
Jacobson, Elizabeth A.
Issue Date:
1985
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Inverse modeling of aquifers usually involves identification of effective parameters such as transmissivities over a finite number of subregions, or zones. Theoretical restrictions on the maximum size of a zone for which such effective transmissivities can be properly defined and the desire to obtain a good resolution of the spatial variability of transmissivity may suggest that the aquifer be divided into numerous small zones. Considerations of parameter identifiability, on the other hand, may require that the number of unknown transmissivities be limited. To satisfy both requirements, an inverse approach has been developed in which the number of zones can be as large as deemed necessary on the basis of hydrogeological considerations. However, instead of trying to estimate a similar number of transmissivities, a smaller number of surrogate parameters, which are defined as linear combinations of the original log transmissivities, is estimated. The optimum number and definition of the surrogate parameters are determined through a singular value decomposition of a matrix arising from the linearization of the inverse problem. A "resolution matrix" and an "information density matrix" can also be obtained from the singular value decomposition. The resolution matrix is indicative of parameter identifiability and is valuable in deciding whether specific log-transmissivity zones should be lumped with their neighbors or left intact. The information density matrix shows how well the model can reproduce each measured hydraulic head value and may be used to determine the relative worth of each datum point for parameter estimation. This, in turn, may suggest discontinuing the collection of certain data and/or starting to collect data at other points in the aquifer. The methodology is illustrated by using data from the Avra Valley aquifer of southern Arizona.
Type:
Dissertation-Reproduction (electronic); text
Keywords:
Hydrology.; Groundwater flow -- Models.; Groundwater flow -- Models -- Arizona -- Avra Valley.
Degree Name:
Ph. D.
Degree Level:
doctoral
Degree Program:
Hydrology and Water Resources; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Neuman, Shlomo P.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA statistical parameter estimation method using singular value decomposition with application to Avra Valley aquifer in southern Arizonaen_US
dc.creatorJacobson, Elizabeth A.en_US
dc.contributor.authorJacobson, Elizabeth A.en_US
dc.date.issued1985en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractInverse modeling of aquifers usually involves identification of effective parameters such as transmissivities over a finite number of subregions, or zones. Theoretical restrictions on the maximum size of a zone for which such effective transmissivities can be properly defined and the desire to obtain a good resolution of the spatial variability of transmissivity may suggest that the aquifer be divided into numerous small zones. Considerations of parameter identifiability, on the other hand, may require that the number of unknown transmissivities be limited. To satisfy both requirements, an inverse approach has been developed in which the number of zones can be as large as deemed necessary on the basis of hydrogeological considerations. However, instead of trying to estimate a similar number of transmissivities, a smaller number of surrogate parameters, which are defined as linear combinations of the original log transmissivities, is estimated. The optimum number and definition of the surrogate parameters are determined through a singular value decomposition of a matrix arising from the linearization of the inverse problem. A "resolution matrix" and an "information density matrix" can also be obtained from the singular value decomposition. The resolution matrix is indicative of parameter identifiability and is valuable in deciding whether specific log-transmissivity zones should be lumped with their neighbors or left intact. The information density matrix shows how well the model can reproduce each measured hydraulic head value and may be used to determine the relative worth of each datum point for parameter estimation. This, in turn, may suggest discontinuing the collection of certain data and/or starting to collect data at other points in the aquifer. The methodology is illustrated by using data from the Avra Valley aquifer of southern Arizona.en_US
dc.description.notehydrology collectionen_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.typetexten_US
dc.subjectHydrology.en_US
dc.subjectGroundwater flow -- Models.en_US
dc.subjectGroundwater flow -- Models -- Arizona -- Avra Valley.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineHydrology and Water Resourcesen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairNeuman, Shlomo P.en_US
dc.contributor.committeememberDavis, Stanley N.en_US
dc.contributor.committeememberWangsness, R. K.en_US
dc.contributor.committeememberEmrick, Royen_US
dc.contributor.committeememberMaddock III, Thomasen_US
dc.identifier.oclc213394907en_US
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