Conditioning nonlocal steady-state flow on hydraulic head and conductivity through geostatistical inversion

Persistent Link:
http://hdl.handle.net/10150/280279
Title:
Conditioning nonlocal steady-state flow on hydraulic head and conductivity through geostatistical inversion
Author:
Hernandez-Ochoa, Abel F.
Issue Date:
2003
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:
Nonlocal moment equations allow one to render optimum predictions of flow in randomly heterogeneous media deterministically conditional on measured values of medium properties and to assess the corresponding predictive uncertainty. I present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head and (or) flux. My algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Computational efficiency is enhanced through the use of a direct sparse matrix solver. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Correlation among parameter estimates (or priors) is considered in the universal kriging equations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a calibration criterion, composed of residuals of head or (and) flux and (possibly) log conductivity, using the Levenberg-Marquardt algorithm. Statistical parameters characterizing the natural variability of hydraulic conductivity can also be estimated using this algorithm. I illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain under various conditions for a range of parameters. My examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty. Over-parameterization is seen to create zones of high mean conductivity, in which flux prediction is more uncertain than is in other regions. It is found that a regular distribution of pilot points works better than does an irregular layout and that the number of pilot points should be as close as possible to the number of head data while maintaining parameters reasonably uncorrelated. Head and flux predictions are very satisfactory for cases with either log conductivity variance or integral scale between one and four, though prediction quality deteriorates with either larger variances or shorter integral scales. The method may perform satisfactorily in cases with no conductivity measurements and only a few head data.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Hydrology.; Environmental Sciences.; Engineering, Environmental.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Hydrology and Water Resources
Degree Grantor:
University of Arizona
Advisor:
Neuman, Shlomo P.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleConditioning nonlocal steady-state flow on hydraulic head and conductivity through geostatistical inversionen_US
dc.creatorHernandez-Ochoa, Abel F.en_US
dc.contributor.authorHernandez-Ochoa, Abel F.en_US
dc.date.issued2003en_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.abstractNonlocal moment equations allow one to render optimum predictions of flow in randomly heterogeneous media deterministically conditional on measured values of medium properties and to assess the corresponding predictive uncertainty. I present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head and (or) flux. My algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Computational efficiency is enhanced through the use of a direct sparse matrix solver. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Correlation among parameter estimates (or priors) is considered in the universal kriging equations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a calibration criterion, composed of residuals of head or (and) flux and (possibly) log conductivity, using the Levenberg-Marquardt algorithm. Statistical parameters characterizing the natural variability of hydraulic conductivity can also be estimated using this algorithm. I illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain under various conditions for a range of parameters. My examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty. Over-parameterization is seen to create zones of high mean conductivity, in which flux prediction is more uncertain than is in other regions. It is found that a regular distribution of pilot points works better than does an irregular layout and that the number of pilot points should be as close as possible to the number of head data while maintaining parameters reasonably uncorrelated. Head and flux predictions are very satisfactory for cases with either log conductivity variance or integral scale between one and four, though prediction quality deteriorates with either larger variances or shorter integral scales. The method may perform satisfactorily in cases with no conductivity measurements and only a few head data.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectHydrology.en_US
dc.subjectEnvironmental Sciences.en_US
dc.subjectEngineering, Environmental.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineHydrology and Water Resourcesen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNeuman, Shlomo P.en_US
dc.identifier.proquest3089947en_US
dc.identifier.bibrecord.b44420973en_US
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