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A modular three-dimensional finite-difference ground-water flow model
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detail presented in some examples is cumbersome. Moreover, the depth of probabilistic background is shallow. I must wonder if the reader looking for a techniques manual will be left with 'just enough information to be dangerous'. ! would use this chapter to identify specific techniques to be studied independently with increased attention to the formal background material. This book suffers from weak editing and presentation. I suspect it was prepared in the so-called 'camera-ready' format. Unfortunately, the minor inconsistencies in style and quality of reproduction detract from the information Riggs has assembled. Finally, a caution to the beginner wishing to go further into the probabilistic background. In my opinion, the transition from reading this book to further study of a probability text will require attention to shades of differences in definitions. The language of this book is in a couple of instances quite loose compared to formally developed definitions. Perhaps this situation reflects the sources of material for the discussion. In the statistics chapter, 19 of the 22 references are more than 20 years old. K.E. BENCALA (Menlo Park, Calif.)
A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model. Michael G. McDonald and Arlen W. Harbaugh. U.S. Geological Survey, National Center, Reston, Va., 1984, 528 pp. Copies available from Scientific Publications Co., P.O. Box 23041, Washington, DC 20026-3041. Price Report $39,/ computer program tape $35 (paperback). Some fifteen years ago, Allan Freeze, backed by the resources of the IBM Thomas J Watson Research Center at Yorktown Heights, published one of the first three-dimensional groundwater flow models. Since that time an increasing appreciation of the real problems posed by the utilisation of groundwater resources has maintained interest in techniques of numerical modelling in both the research and consulting communities. Groundwater models are now used widely in resource evaluation and management and with the advent of more and more powerful microcomputers will be used more widely still. The models that fifteen years ago required the largest IBM mainframe computers to run, will now be available on the groundwater hydrologist's desk top. Not all such model users will fully appreciate the techniques of numerical analysis that underlie any program, particularly those involved in handling boundary conditions and solving the matrix equations for a fully three-dimensional system. It follows that there is an onus on the model developer to write clearly understood programs, backed up by clearly understood documentation. This has been the aim of the current authors. In rewriting the USGS groundwater model code, they have aimed to avoid problems encountered in the past with modifying earlier programs by writing the code in a completely modular form. All the major modules are completely independent so that future improvements or special modifications by individual users should be made with-
388 out major changes to other parts of the program. The program is written in standard FORTRAN 66 and should be easily portable between different machines. The program will handle steady state and transient, two and three-dimensional groundwater flow problems. The programmers have been at pains to allow considerable flexibility in setting up a particular flow domaim The underlying equations are developed in a block-centred finite difference formulation involving a bulk conductance term between blocks. The program allows this conductance to take account of variations in thickness of different geological strata as well as differences in nodal spacing in plan and hydraulic properties. In this way other features of the model, such as anisotropy in hydraulic properties, thin impermeable layers and interactions through a river bed covering only part of a block are easily implemented by specifying an appropriate conductance. The program is organised as a collection of packages, each consisting of a number of modules and sub-modules. Each of these is implemented as a single subroutine in the program. A subroutine naming convention is used to clearly reflect the overall structure of the program. The manual is organised in a similarly modular form, with one chapter for each of the packages. Data requirements and output options for each module are clearly indicated and a listing of each subroutine is given. In any run of the module the user need only include those packages and modules required by the problem under study. Three packages are required for all runs: a "basic" package that controls the calling of the individual modules; a block-centred flow package that assembles the matrix equations; and a solver package that solves the equations. The other packages included are a river package, a recharge package, a well package, a drain package, an evapotranspiration package, and a "general-head" boundary package to handle situations not covered by the other boundary-condition packages. The authors have provided two solver algorithms, either of which may be used to solve the large sparse matrix equations that arise in two- and threedimensional problems. These are a strongly implicit procedure (SIP) and a slice successive over-relaxation method (SSOR). Both methods use an iterative technique to calculate the change in heads at each time step. In reviewing the program I have had access only to the manual, and have not been able to actually run the program. However, I have tried to evaluate the program and manual from the point of view of a new and non-expert user. The authors have been generally successful in the presentation of their program to such a user. The modular structure and block-centred formulation provide a natural and simple introduction to the concepts underlying the model. The presentation is generally clear and examples of inputs and outputs are clearly described. However, there are some program limitations that, although noted in the manual, may not be immediately obvious to such a user. In particular, although flexibility in allowing geological strata to vary in thickness is allowed, the
389 calculated heads will be in error unless those strata are nearly horizontal. Dipping strata might be better handled by a finite element program. Another limitation arises where the water table changes in elevation sufficiently to cross block boundaries. Only falling water tables can be handled, in which case when the water table leaves a block it takes no further part in the simulation. This change is allowed to take place at the end of each iteration, which may lead to error due to the approximate nature of the solution at early iterations. There is also one major point which really requires further clarification for the user's benefit, that is the choice of solution algorithm. No indication is given as to whether the SIP or SSOR procedure will be appropriate for any given problem, nor of the relative efficiency on comparable problems. Some guarded comments about the SIP procedure concerning the choice of the (multiple) iteration parameters, together with the more complex mathematics, might lead the inexperienced user towards the SSOR package. Clearly it may be difficult to generalise about the relative merits of the alternatives, but the authors could at least have provided the benefits of their experience in this respect, together with some pointers to the literature. In summary, I feel this has been a successful exercise. The authors have provided a well written, well documented program which, although having some limitations, will be of wide applicability. Subject to the comments above concerning the solution algorithms, it could certainly serve as a good introduction to finite difference modelling techniques for both student and practicing groundwater hydrologists. Finally, however, it is worth noting that the authors give no guidance as to how to convert the limited field data that is usually available for a particular application, into the large number of parameter values required by the model. The inexperienced user cannot be reminded too often that, however good the implementation, the predictions of groundwater models are only as good as the field data on which they are based. KEITH BEVEN (Lancaster) Flow to Wells in Intrusive Dikes. W.K. Boehmer and J. Boonstra. ILRI, Wageningen, 1986, x ÷ 260 pp., Dfl. 50.00. Flow to Wells in Intrusive Dikes is a Ph.D thesis written jointly by Willem K. Boehmer, hydrogeologist at Euroconsult, Arnhem, and Johannes Boonstra, hydrologist at the International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. The book has its roots in South Africa where, in the late sixties and early seventies, Boehmer was engaged in the exploration and exploitation of waterbearing fractured dikes for drinking water supplies. Wells in such dikes were found to yield many times more water than wells in the surrounding country rock. That rock is composed of alternating series of the Karroo System's sedimentary rocks (sandstones, siltstones, mudstones) and represents a reservoir from which a dike can draw water when it is pumped.
detail presented in some examples is cumbersome. Moreover, the depth of probabilistic background is shallow. I must wonder if the reader looking for a techniques manual will be left with 'just enough information to be dangerous'. ! would use this chapter to identify specific techniques to be studied independently with increased attention to the formal background material. This book suffers from weak editing and presentation. I suspect it was prepared in the so-called 'camera-ready' format. Unfortunately, the minor inconsistencies in style and quality of reproduction detract from the information Riggs has assembled. Finally, a caution to the beginner wishing to go further into the probabilistic background. In my opinion, the transition from reading this book to further study of a probability text will require attention to shades of differences in definitions. The language of this book is in a couple of instances quite loose compared to formally developed definitions. Perhaps this situation reflects the sources of material for the discussion. In the statistics chapter, 19 of the 22 references are more than 20 years old. K.E. BENCALA (Menlo Park, Calif.)
A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model. Michael G. McDonald and Arlen W. Harbaugh. U.S. Geological Survey, National Center, Reston, Va., 1984, 528 pp. Copies available from Scientific Publications Co., P.O. Box 23041, Washington, DC 20026-3041. Price Report $39,/ computer program tape $35 (paperback). Some fifteen years ago, Allan Freeze, backed by the resources of the IBM Thomas J Watson Research Center at Yorktown Heights, published one of the first three-dimensional groundwater flow models. Since that time an increasing appreciation of the real problems posed by the utilisation of groundwater resources has maintained interest in techniques of numerical modelling in both the research and consulting communities. Groundwater models are now used widely in resource evaluation and management and with the advent of more and more powerful microcomputers will be used more widely still. The models that fifteen years ago required the largest IBM mainframe computers to run, will now be available on the groundwater hydrologist's desk top. Not all such model users will fully appreciate the techniques of numerical analysis that underlie any program, particularly those involved in handling boundary conditions and solving the matrix equations for a fully three-dimensional system. It follows that there is an onus on the model developer to write clearly understood programs, backed up by clearly understood documentation. This has been the aim of the current authors. In rewriting the USGS groundwater model code, they have aimed to avoid problems encountered in the past with modifying earlier programs by writing the code in a completely modular form. All the major modules are completely independent so that future improvements or special modifications by individual users should be made with-
388 out major changes to other parts of the program. The program is written in standard FORTRAN 66 and should be easily portable between different machines. The program will handle steady state and transient, two and three-dimensional groundwater flow problems. The programmers have been at pains to allow considerable flexibility in setting up a particular flow domaim The underlying equations are developed in a block-centred finite difference formulation involving a bulk conductance term between blocks. The program allows this conductance to take account of variations in thickness of different geological strata as well as differences in nodal spacing in plan and hydraulic properties. In this way other features of the model, such as anisotropy in hydraulic properties, thin impermeable layers and interactions through a river bed covering only part of a block are easily implemented by specifying an appropriate conductance. The program is organised as a collection of packages, each consisting of a number of modules and sub-modules. Each of these is implemented as a single subroutine in the program. A subroutine naming convention is used to clearly reflect the overall structure of the program. The manual is organised in a similarly modular form, with one chapter for each of the packages. Data requirements and output options for each module are clearly indicated and a listing of each subroutine is given. In any run of the module the user need only include those packages and modules required by the problem under study. Three packages are required for all runs: a "basic" package that controls the calling of the individual modules; a block-centred flow package that assembles the matrix equations; and a solver package that solves the equations. The other packages included are a river package, a recharge package, a well package, a drain package, an evapotranspiration package, and a "general-head" boundary package to handle situations not covered by the other boundary-condition packages. The authors have provided two solver algorithms, either of which may be used to solve the large sparse matrix equations that arise in two- and threedimensional problems. These are a strongly implicit procedure (SIP) and a slice successive over-relaxation method (SSOR). Both methods use an iterative technique to calculate the change in heads at each time step. In reviewing the program I have had access only to the manual, and have not been able to actually run the program. However, I have tried to evaluate the program and manual from the point of view of a new and non-expert user. The authors have been generally successful in the presentation of their program to such a user. The modular structure and block-centred formulation provide a natural and simple introduction to the concepts underlying the model. The presentation is generally clear and examples of inputs and outputs are clearly described. However, there are some program limitations that, although noted in the manual, may not be immediately obvious to such a user. In particular, although flexibility in allowing geological strata to vary in thickness is allowed, the
389 calculated heads will be in error unless those strata are nearly horizontal. Dipping strata might be better handled by a finite element program. Another limitation arises where the water table changes in elevation sufficiently to cross block boundaries. Only falling water tables can be handled, in which case when the water table leaves a block it takes no further part in the simulation. This change is allowed to take place at the end of each iteration, which may lead to error due to the approximate nature of the solution at early iterations. There is also one major point which really requires further clarification for the user's benefit, that is the choice of solution algorithm. No indication is given as to whether the SIP or SSOR procedure will be appropriate for any given problem, nor of the relative efficiency on comparable problems. Some guarded comments about the SIP procedure concerning the choice of the (multiple) iteration parameters, together with the more complex mathematics, might lead the inexperienced user towards the SSOR package. Clearly it may be difficult to generalise about the relative merits of the alternatives, but the authors could at least have provided the benefits of their experience in this respect, together with some pointers to the literature. In summary, I feel this has been a successful exercise. The authors have provided a well written, well documented program which, although having some limitations, will be of wide applicability. Subject to the comments above concerning the solution algorithms, it could certainly serve as a good introduction to finite difference modelling techniques for both student and practicing groundwater hydrologists. Finally, however, it is worth noting that the authors give no guidance as to how to convert the limited field data that is usually available for a particular application, into the large number of parameter values required by the model. The inexperienced user cannot be reminded too often that, however good the implementation, the predictions of groundwater models are only as good as the field data on which they are based. KEITH BEVEN (Lancaster) Flow to Wells in Intrusive Dikes. W.K. Boehmer and J. Boonstra. ILRI, Wageningen, 1986, x ÷ 260 pp., Dfl. 50.00. Flow to Wells in Intrusive Dikes is a Ph.D thesis written jointly by Willem K. Boehmer, hydrogeologist at Euroconsult, Arnhem, and Johannes Boonstra, hydrologist at the International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. The book has its roots in South Africa where, in the late sixties and early seventies, Boehmer was engaged in the exploration and exploitation of waterbearing fractured dikes for drinking water supplies. Wells in such dikes were found to yield many times more water than wells in the surrounding country rock. That rock is composed of alternating series of the Karroo System's sedimentary rocks (sandstones, siltstones, mudstones) and represents a reservoir from which a dike can draw water when it is pumped.