The Mathematics of Marine Modelling
The Mathematics of Marine Modelling

Author: Henk Schuttelaars

Publisher: Springer Nature

Published: 2022-11-30

Total Pages: 324

ISBN-13: 3031095596

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Over the past few decades, numerical simulation has become instrumental in understanding the dynamics of seas, coastal regions and estuaries. The decision makers rely more and more frequently on model results for the management of these regions. Some modellers are insufficiently aware of the theoretical underpinning of the simulation tools they are using. On the other hand, a number of applied mathematicians tend to view marine sciences as a domain in which they would like to use the tools they have a good command of. Bridging the gap between model users and applied mathematicians is the main objective of the present book. In this respect a vast number of issues in which mathematics plays a crucial role will be addressed.

Modeling Methods for Marine Science
Modeling Methods for Marine Science

Author: David M. Glover

Publisher: Cambridge University Press

Published: 2011-06-02

Total Pages: 589

ISBN-13: 1139500716

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This advanced textbook on modeling, data analysis and numerical techniques for marine science has been developed from a course taught by the authors for many years at the Woods Hole Oceanographic Institute. The first part covers statistics: singular value decomposition, error propagation, least squares regression, principal component analysis, time series analysis and objective interpolation. The second part deals with modeling techniques: finite differences, stability analysis and optimization. The third part describes case studies of actual ocean models of ever increasing dimensionality and complexity, starting with zero-dimensional models and finishing with three-dimensional general circulation models. Throughout the book hands-on computational examples are introduced using the MATLAB programming language and the principles of scientific visualization are emphasised. Ideal as a textbook for advanced students of oceanography on courses in data analysis and numerical modeling, the book is also an invaluable resource for a broad range of scientists undertaking modeling in chemical, biological, geological and physical oceanography.

Aspects of Mathematical Modelling
Aspects of Mathematical Modelling

Author: Roger J. Hosking

Publisher: Springer Science & Business Media

Published: 2008-03-02

Total Pages: 373

ISBN-13: 376438591X

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The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

Inverse Modeling of the Ocean and Atmosphere
Inverse Modeling of the Ocean and Atmosphere

Author: Andrew F. Bennett

Publisher: Cambridge University Press

Published: 2005-10-20

Total Pages: 260

ISBN-13: 1139434535

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Inverse Modeling of the Ocean and Atmosphere is a graduate-level book for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, and applications to contemporary research models, together with elaborate observing systems, are examined in detail. The book offers a review of the various alternative approaches, and further advanced research topics are discussed. Derived from the author's lecture notes, this book constitutes an ideal course companion for graduate students, as well as being a valuable reference source for researchers and managers in theoretical earth science, civil engineering and applied mathematics.

Mathematical Models in Biology
Mathematical Models in Biology

Author: Leah Edelstein-Keshet

Publisher: SIAM

Published: 1988-01-01

Total Pages: 629

ISBN-13: 9780898719147

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Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

The Mathematics of Models for Climatology and Environment
The Mathematics of Models for Climatology and Environment

Author: Jesus I. Diaz

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 486

ISBN-13: 3642606032

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This book is the culmination of the NATO Advanced Study Institute on The Mathematics of Models for Climatology and Environment which was held at Puerto de la Cruz ,Tenerife, Spain during 11-21 January 1995. One of the main goals of the ASI was to establish a bridge between mathematical modellers on the one hand and physical oceanographers and climatologists on the other. The book is divided into fourth parts containing a total of 16 chapters: Parts I, II and III are devoted to general models and Part IV to models related to some local problems. Most of the mathematical models here considered involve systems of nonlinear partial differential equations. The mathemat ical treatment cover a large list of subjects: existence and uniqueness for well-possed problems, large time behaviour, stability, bifurcation,diagrams of equilibria, conditions for the occurrence of interfaces or free boundaries, numerical algorithms and its implementation, controllability of the problems, etc. I thank Jacques- Louis Lions and Cornelius Johannes van Duijn for their guidance and collaboration as co-directors of the AS!. I also thank J.F.Padial and G. Diaz for their help in the planning and conduct of the ASI as well as in the preparation of this book.

Mathematics for Dynamic Modeling
Mathematics for Dynamic Modeling

Author: Edward J. Beltrami

Publisher:

Published: 1987

Total Pages: 302

ISBN-13:

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This new edition of Mathematics for Dynamic covers tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. Each chapter includes exercises, many of which expand on the material in the text.

Coastal and Shelf Sea Modelling
Coastal and Shelf Sea Modelling

Author: Philip P. G. Dyke

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 266

ISBN-13: 1475747861

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Since the computing revolution, modelling has become the most important way in which we further our knowledge about how the sea moves and how the processes in the sea operate. The coast and the continental shelf are two of the most important areas of the sea to understand. Coastal and Shelf Sea Modelling is therefore very timely and important. In this text, modelling the processes that occur in the sea is motivated continually through real life examples. Sometimes these are incorporated naturally within the text, but there are also a number of case studies taken from the recent research literature. These will be particularly valuable to students as they are presented in a style more readily accessible than that found in a typical research journal. The motivation for modelling is care for the environment. The well publicised problem of global warming, the phenomenon of El Niño, more localised pollution scares caused by tanker accidents and even smaller scale coastal erosion caused by storms all provide motivation for modelling and all get coverage in this text. Particularly novel features of the book include a systematic treatment of the modelling process in a marine context, the inclusion of diffusion in some detail, ecosystems modelling and a brief foray into wave prediction. The final chapter provides the reader with the opportunity to do some modelling; there are many worked examples followed by exercises that readers can try themselves. All answers are provided. Throughout, the style is informal and the technicalities in term of mathematics are kept to a minimum. Coastal and Shelf Sea Modelling is particularly suitable for graduate marine and oceanographic modelling courses, but will also prove useful to coastal engineers and students at any level interested in the quantitative modelling of marine processes. It is stressed that only a minimal level of mathematics (first year calculus or less) is required; the style and content is introductory.

Applied Turbulence Modelling in Marine Waters
Applied Turbulence Modelling in Marine Waters

Author: Hans Burchard

Publisher: Springer

Published: 2007-08-15

Total Pages: 224

ISBN-13: 3540454195

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The simulation of turbulent mixing processes in marine waters is one of the most pressing tasks in oceanography. It is rendered difficult by the various complex phenomena occurring in these waters like strong stratification, ex ternal and internal waves, wind generated turbulence, Langmuir circulation etc. The need for simulation methods is especially great in this area because the physical processes cannot be investigated in the laboratory. Tradition ally, empirical bulk type models were used in oceanography, which, however, cannot account for many of the complex physical phenomena occurring. In engineering, statistical turbulence models describing locally the turbulence mixing processes were introduced in the early seventies, such as the k E model which is still one of the most widely used models in Computational Fluid Dy namics. Soon after, turbulence models were applied more and more also in the atmospheric sciences, and here the k kL model of Mellor and Yamada became particularly popular. In oceanography, statistical turbulence mod els were introduced rather late, i. e. in the eighties, and mainly models were taken over from the fields mentioned above, with some adjustments to the problems occurring in marine waters. In the literature on turbulence model applications to oceanography problems controversial findings and claims are reported about the various models, creating also an uncertainty on how well the models work in marine water problems.