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Modeling 75
Book Reviews The book is essentially interdisciplinary in nature; a specialist in one area could find much of relevance in the work presented in the other fields. As with any such conference proceedings, the individual papers vary greatly in originality, clarity and mathematical complexity. However, this collection provides such a wide selection of work being undertaken throughout the world on environmental modelling that anyone involved in this will find much of interest. The section on regional models is concerned with a variety of topics ranging from a discussion of the factors influencing the delay before a price change affects energy consumption to a mathematical model for zooplankton production, grazing and loss. One paper tackles what must be the central dilemma of every environmental planner--the need to compromise between the requirements of low pollution and low cost. A technique for combining these conflicting objectives by a method of vector valued optimization is presented and illustrated by a study of the choice of power station sites on the Rhine. In the next section, most branches of hydraulic engineering are represented. The design of sewer networks, the design and operation of a multi-reservoir flood control system and the prediction of failure of levee flood protection structures are all discussed. Two papers include interesting comparisons of their models with practice. The first of these uses finite elements to model tidal effects and applies the technique to the North Sea and the Solent. The second combines the use of analogue and digital computers to predict groundwater flow in limestone aquifers, demonstrating the advantages of this approach in a parametric sensitivity analysis, when a very large number of trial solutions are required for the same problem. Two of the papers on air pollution argue for a change in the current practice of basing pollution legislation on the average concentration reaching the ground. One paper suggests that it would be preferable to set limits on the total pollutant emitted and the other proposes a probabilistic approach with a polluted area being defined by a grid square in which the probability of pollution exceeds a given value. The other papers in this section each construct a mathematical model to describe the existing pattern of pollution. These cover pollution in the Forth Valley, carbon monoxide pollution in Los Angeles and a time series representation of the changes over a number of years in the smoke and sulphur dioxide pollution at Kew in London. The fact that the section on water pollution is the longest in the book probably reflects the great interest in this problem in recent years. A number of investigations into the pollution in
rivers and lakes are described including an experiment in which a model based on statistical records is used in conjunction with telemetry monitoring to give short term forecasts of pollution levels in the Lower Fox River. Different approaches to the solution of the advection-dispersion equation are presented, ranging from the use of a moving coordinate system to a fractional step integration technique. One paper traces pollution to its source and shows the importance of run-off from streets, especially after a storm following a long dry spell of weather. The final two sections cover thermal problems and modelling techniques. Models are given for the thermal discharge into a river and from a power station into a fjord. The effect of different standards of insulation on various designs of house is discussed. One paper classifies the various types of mathematical model and discusses the problem of parameter sensitivity. The difficulty of finding an effective rule for stopping iteration in an optimizing process is examined and finally a discussion is given on the solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers. On reading through the book one is struck by the range and complexity of environmental problems to which mathematical modelling is being applied. Although it lacks the unity of a textbook, this book does provide a useful review of current work on environmental modelling. It should enable the researcher to relate his work to that being undertaken in other fields and enable the planner to appreciate better the more accurate prediction methods that are becoming available.
R. R. Wilson
Modeling 75 2nd Annual Symposium of the Waterways Harbors and Coastal Engineering Division of ASCE American Society of Civil Engineers, New York, 1975. 1686 pp. (2 Vols). $30.00 These two volumes of Modeling 75 contain 96 papers given at a civil engineering symposium in California in September 1975. Each volume runs to some 800 pages and is intended to convey the state-of-the-art of various types of models. The aim of the symposium was to provide a forum in which not only the relative merits of mathematical and small-scale physical models could be reviewed but also, and more fundamentally, a forum in which the applicability of models to specific engineering problems could be evaluated. The papers are grouped by subject area into the following divisions: navigation and port facilities, wave dynamics, environmental modelling,
inlets, jets and mixing, mathematical river models, river structures, estuaries, water quality models, harbour resonance, coastal movable-bed models, coastal hydrodynamic processes, coastal sediment processes, finite element models, storm surges, and wave structure interaction. The material presented will be of use to hydraulic engineers concerned with modelling coastal or estuarine processes and also to others interested in seeing the kind of numerical and physical techniques which are currently being used to solve specific engineering problems. A balance is maintained between papers dealing with purely small-scale physical models and 'scale effects', and those dealing with numerical or analytical models. A significant number of papers describe a mixed approach in which both numerical and physical models are used to investigate a specific problem. A large number of interesting case studies are also presented which serve to illustrate the diversity of hydraulic phenomena as they occur under natural conditions. The scope of the numerical modelling techniques range from the three-dimensional time-dependent models through to the various applications of the one-dimensional case. Those familiar with the work of Abbott of the Danish Hydraulic Institute and Leendertse of the Rand Corporation, will find useful, the examples illustrating their highlydeveloped modelling systems. The twodimensional vertically integrated model also finds much application. Those concerned with methodology will need to regroup the papers according to modelling methods rather than subject area, as it is possible to find several examples from separate sections of the symposium based on a similar modelling approach. Those looking for a general review of the mathematical techniques will not find much material in evidence, although there are several papers reviewing the general aspects of physical modelling techniques. It is a pity that three out of the four keynote addresses on modelling are not included in the symposium proceedings. The emphasis throughout is very much on application, although details of cost comparison between the different modelling systems are invariably lacking. The problems associated with the acquisition of suitable field data are also only briefly mentioned in the majority of papers. Despite these criticisms, those concerned with solving engineering coastal problems will find these two volumes a very useful addition to the literature which is available in this subject area.
D. W. Knight
Appl. Math. Modelling, 1976, Vol 1, December
167
rivers and lakes are described including an experiment in which a model based on statistical records is used in conjunction with telemetry monitoring to give short term forecasts of pollution levels in the Lower Fox River. Different approaches to the solution of the advection-dispersion equation are presented, ranging from the use of a moving coordinate system to a fractional step integration technique. One paper traces pollution to its source and shows the importance of run-off from streets, especially after a storm following a long dry spell of weather. The final two sections cover thermal problems and modelling techniques. Models are given for the thermal discharge into a river and from a power station into a fjord. The effect of different standards of insulation on various designs of house is discussed. One paper classifies the various types of mathematical model and discusses the problem of parameter sensitivity. The difficulty of finding an effective rule for stopping iteration in an optimizing process is examined and finally a discussion is given on the solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers. On reading through the book one is struck by the range and complexity of environmental problems to which mathematical modelling is being applied. Although it lacks the unity of a textbook, this book does provide a useful review of current work on environmental modelling. It should enable the researcher to relate his work to that being undertaken in other fields and enable the planner to appreciate better the more accurate prediction methods that are becoming available.
R. R. Wilson
Modeling 75 2nd Annual Symposium of the Waterways Harbors and Coastal Engineering Division of ASCE American Society of Civil Engineers, New York, 1975. 1686 pp. (2 Vols). $30.00 These two volumes of Modeling 75 contain 96 papers given at a civil engineering symposium in California in September 1975. Each volume runs to some 800 pages and is intended to convey the state-of-the-art of various types of models. The aim of the symposium was to provide a forum in which not only the relative merits of mathematical and small-scale physical models could be reviewed but also, and more fundamentally, a forum in which the applicability of models to specific engineering problems could be evaluated. The papers are grouped by subject area into the following divisions: navigation and port facilities, wave dynamics, environmental modelling,
inlets, jets and mixing, mathematical river models, river structures, estuaries, water quality models, harbour resonance, coastal movable-bed models, coastal hydrodynamic processes, coastal sediment processes, finite element models, storm surges, and wave structure interaction. The material presented will be of use to hydraulic engineers concerned with modelling coastal or estuarine processes and also to others interested in seeing the kind of numerical and physical techniques which are currently being used to solve specific engineering problems. A balance is maintained between papers dealing with purely small-scale physical models and 'scale effects', and those dealing with numerical or analytical models. A significant number of papers describe a mixed approach in which both numerical and physical models are used to investigate a specific problem. A large number of interesting case studies are also presented which serve to illustrate the diversity of hydraulic phenomena as they occur under natural conditions. The scope of the numerical modelling techniques range from the three-dimensional time-dependent models through to the various applications of the one-dimensional case. Those familiar with the work of Abbott of the Danish Hydraulic Institute and Leendertse of the Rand Corporation, will find useful, the examples illustrating their highlydeveloped modelling systems. The twodimensional vertically integrated model also finds much application. Those concerned with methodology will need to regroup the papers according to modelling methods rather than subject area, as it is possible to find several examples from separate sections of the symposium based on a similar modelling approach. Those looking for a general review of the mathematical techniques will not find much material in evidence, although there are several papers reviewing the general aspects of physical modelling techniques. It is a pity that three out of the four keynote addresses on modelling are not included in the symposium proceedings. The emphasis throughout is very much on application, although details of cost comparison between the different modelling systems are invariably lacking. The problems associated with the acquisition of suitable field data are also only briefly mentioned in the majority of papers. Despite these criticisms, those concerned with solving engineering coastal problems will find these two volumes a very useful addition to the literature which is available in this subject area.
D. W. Knight
Appl. Math. Modelling, 1976, Vol 1, December
167