# Calibration and validation of aquifer model.

http://hdl.handle.net/10150/190993
Title:
Calibration and validation of aquifer model.
Author:
Sagar, Budhi,1943-
Issue Date:
1973
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:
The main aim of this study is to develop a suitable method for the calibration and validation of mathematical models of large and complex aquifer systems. Since the calibration procedure depends on the nature of the model to be calibrated and since many kinds of models are used for groundwater, the question of model choice is broached first. Various aquifer models are critically reviewed and a table to compare them as to their capabilities and limitations is set up. The need for a general calibration method for models in which the flow is represented by partial differential equations is identified from this table. The calibration problem is formulated in the general mathematical framework as the inverse problem. Five types of inverse problems that exist in modeling aquifers by partial differential equations are identified. These are, to determine (1) parameters, (2) initial conditions, (3) boundary conditions, (4) inputs, and (5) a mixture of the above. Various methods to solve these inverse problems are reviewed, including those from fields other than hydrology. A new direct method to solve the inverse problem (DIMSIP) is then developed. Basically, this method consists of transforming the partial differential equations of flow to algebraic equations by substituting in them the values of the various derivatives of the dependent variable (which may be hydraulic pressure, chemical concentration or temperature). The parameters are then obtained by formulating the problem in a nonlinear optimization framework. The method of sequential unconstrained minimization is used. Spline functions are used to evaluate the derivatives of the dependent variable. Splines are functions defined by piecewise polynomial arcs in such a way that derivatives up to and including the order one less than the degree of polynomials used are continuous everywhere. The natural cubic splines used in this study have the additional property of minimum curvature which is analogous to minimum energy surface. These and the derivative preserving properties of splines make them an excellent tool for approximating the dependent variable surfaces in groundwater flow problems. Applications of the method to both a test situation as well as to real-world data are given. It is shown that the method evaluates the parameters, boundary conditions and inputs; that is, solves inverse problem type V. General conditions of heterogeneity and anisotropy can be evaluated. However, the method is not applicable to steady flows and has the limitation that flow models in which the parameters are functions of the dependent variable cannot be calibrated. In addition, at least one of the parameters has to be preassigned a value. A discussion of uncertainties in calibration procedures is given. The related problems of model validation and sampling of aquifers are also discussed.
Type:
Dissertation-Reproduction (electronic); text
Keywords:
Hydrology.; Aquifers -- Mathematical models.; Groundwater flow -- Mathematical models.
Degree Name:
Ph. D.
Degree Level:
doctoral
Degree Program:
Hydrology and Water Resources; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Kisiel, Chester C.

DC FieldValue Language
dc.language.isoenen_US
dc.titleCalibration and validation of aquifer model.en_US
dc.creatorSagar, Budhi,1943-en_US
dc.contributor.authorSagar, Budhi,1943-en_US
dc.date.issued1973en_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.abstractThe main aim of this study is to develop a suitable method for the calibration and validation of mathematical models of large and complex aquifer systems. Since the calibration procedure depends on the nature of the model to be calibrated and since many kinds of models are used for groundwater, the question of model choice is broached first. Various aquifer models are critically reviewed and a table to compare them as to their capabilities and limitations is set up. The need for a general calibration method for models in which the flow is represented by partial differential equations is identified from this table. The calibration problem is formulated in the general mathematical framework as the inverse problem. Five types of inverse problems that exist in modeling aquifers by partial differential equations are identified. These are, to determine (1) parameters, (2) initial conditions, (3) boundary conditions, (4) inputs, and (5) a mixture of the above. Various methods to solve these inverse problems are reviewed, including those from fields other than hydrology. A new direct method to solve the inverse problem (DIMSIP) is then developed. Basically, this method consists of transforming the partial differential equations of flow to algebraic equations by substituting in them the values of the various derivatives of the dependent variable (which may be hydraulic pressure, chemical concentration or temperature). The parameters are then obtained by formulating the problem in a nonlinear optimization framework. The method of sequential unconstrained minimization is used. Spline functions are used to evaluate the derivatives of the dependent variable. Splines are functions defined by piecewise polynomial arcs in such a way that derivatives up to and including the order one less than the degree of polynomials used are continuous everywhere. The natural cubic splines used in this study have the additional property of minimum curvature which is analogous to minimum energy surface. These and the derivative preserving properties of splines make them an excellent tool for approximating the dependent variable surfaces in groundwater flow problems. Applications of the method to both a test situation as well as to real-world data are given. It is shown that the method evaluates the parameters, boundary conditions and inputs; that is, solves inverse problem type V. General conditions of heterogeneity and anisotropy can be evaluated. However, the method is not applicable to steady flows and has the limitation that flow models in which the parameters are functions of the dependent variable cannot be calibrated. In addition, at least one of the parameters has to be preassigned a value. A discussion of uncertainties in calibration procedures is given. The related problems of model validation and sampling of aquifers are also discussed.en_US
dc.description.notehydrology collectionen_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.typetexten_US
dc.subjectHydrology.en_US
dc.subjectAquifers -- Mathematical models.en_US
dc.subjectGroundwater flow -- Mathematical models.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineHydrology and Water Resourcesen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairKisiel, Chester C.en_US
dc.contributor.committeememberDuckstein, Lucienen_US
dc.contributor.committeememberSanders, J. L.en_US
dc.contributor.committeememberEvans, Daniel D.en_US
dc.contributor.committeememberSimpson, Eugene S.en_US
dc.identifier.oclc213094058en_US