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Global Atmospheric and Oceanic Modelling: Fundamental Equations [Hardback]

  • Formāts: Hardback, 816 pages, height x width x depth: 260x207x43 mm, weight: 2000 g, Worked examples or Exercises
  • Izdošanas datums: 28-Apr-2022
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108838332
  • ISBN-13: 9781108838337
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  • Formāts: Hardback, 816 pages, height x width x depth: 260x207x43 mm, weight: 2000 g, Worked examples or Exercises
  • Izdošanas datums: 28-Apr-2022
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108838332
  • ISBN-13: 9781108838337
Citas grāmatas par šo tēmu:
Meteorologists and oceanographers build global atmospheric and oceanic models for weather and climate prediction using fundamental equations of fluid flow. This book provides a comprehensive account of such equations to improve understanding of the formulation of existing forecast models and encourage the development of more accurate models.

Combining rigorous theory with practical application, this book provides a unified and detailed account of the fundamental equations governing atmospheric and oceanic fluid flow on which global, quantitative models of weather and climate prediction are founded. It lays the foundation for more accurate models by making fewer approximations and imposing dynamical and thermodynamical consistency, moving beyond the assumption that the Earth is perfectly spherical. A general set of equations is developed in a standard notation with clearly stated assumptions, limitations, and important properties. Some exact, non-linear solutions are developed to promote further understanding and for testing purposes. This book contains a thorough consideration of the fundamental equations for atmospheric and oceanic models, and is therefore invaluable to both theoreticians and numerical modellers. It also stands as an accessible source for reference purposes.

Recenzijas

'Andrew Staniforth has produced a comprehensive and insightful book on the mathematical foundation of global atmosphere and oceanic modelling. For different geophysical fluid applications, he guides us masterfully from the first principles of fluid physics to their evolution equations. The book covers all the fundamental aspects of these equations including conservation laws and exact nonlinear solutions. This brilliant book is ideal for introducing graduate students to the subject matter as much as it is relevant for experts as a reference book.' Gilbert Brunet, Bureau of Meteorology, Melbourne 'Well, this is an impressive book. It covers both the equations of motion and how those equations and their approximations can be used in models of the ocean and atmosphere. It is clearly written, careful and thorough, with a range and a depth that is unmatched elsewhere. It will be of immense value both to those interested in the fundamentals and those wishing to build models that have a sound foundation. It will be a standard for years to come.' Geoffrey K. Vallis, University of Exeter 'This is the textbook I wish I'd had as a graduate student and course instructor! This is an incredibly comprehensive resource for students and researchers alike. I am confident the book will become the go to reference on atmospheric and oceanic modelling for the 2020s and beyond.' Andrew Weaver, University of Victoria 'Global Atmospheric and Oceanic Modelling is bound to become a classic in the literature of Geophysical Fluid Dynamics. Written by a multi-decade insider to the design of the numerical dynamical cores that are at the heart of the models employed for both weather prediction and climate change projection, the book provides a meticulously documented development of dynamically and thermodynamically self-consistent sets of equations that are employed to describe the evolution of these geophysical fluids. Highlights of the book include a careful development of the influence of the ellipsoidal shape of the planet which acts through the gravitational field on the evolution of these fluid domains.' W. Richard Peltier, University of Toronto 'This text is a tremendous resource for anyone looking for a rigorous, thorough treatment of the fundamental equations needed for the development of dynamical cores of numerical models for weather and climate, especially for those interested and/or involved in model design and development. The treatment is detailed, general, and exact without ad-hoc approximations or simplifications. This includes a more truthful representation of variations in gravity due to the geometry of the system. Andrew Staniforth offers the reader unique insights from his experience of an entire career as a leading scholar in the field.' Thomas Birner, University of Munich ' comprehensive and rigorous Graduate students and advanced researchers with interests in atmospheric, oceanic, or general climate modeling will find this treatise invaluable Highly recommended.' M. Alam, Choice

Papildus informācija

A unified and comprehensive account of the fundamental equations of atmospheric and oceanic models for climate and weather forecasting.
Preface xiii
Notation and Acronyms xvii
I FOUNDATIONS
1(494)
1 Introduction
3(11)
1.1 A Very Brief History of Time
3(1)
1.2 Dynamical Cores
4(1)
1.3 Gravity
5(1)
1.4 Fluid Composition of Earth's Atmosphere and Oceans
6(6)
1.5 Organisation of
Chapters
12(2)
2 Governing Equations for Motion of a Dry Atmosphere: Vector Form
14(24)
2.1 Preamble
14(1)
2.2 Fluid Dynamics
15(14)
2.3 Thermodynamics of an Ideal Gas
29(7)
2.4 The Governing Equations for Motion of an Ideal Gas
36(1)
2.5 Concluding Remarks
37(1)
3 Governing Equations for Motion of a Cloudy Atmosphere: Vector Form
38(30)
3.1 Preamble
38(1)
3.2 Representation of Water and Other Substances in the Atmosphere
39(10)
3.3 The Equation of State for Cloudy Air
49(3)
3.4 The Momentum Equation for Cloudy Air
52(1)
3.5 The Thermodynamic-Energy Equation for Cloudy Air
53(3)
3.6 Alternative Forms for the Thermodynamic-Energy Equation
56(6)
3.7 The Governing Equations for Motion of a Cloudy Atmosphere
62(1)
3.8 Concluding Remarks
63(5)
Appendix: Derivation of the Equation of State for Cloudy Air from First Principles
65(3)
4 Governing Equations for Motion of Geophysical Fluids: Vector Form
68(29)
4.1 Preamble
68(1)
4.2 More General Thermodynamics
69(17)
4.3 Functional Forms for a Cloudy-Air Parcel
86(6)
4.4 The Governing Equations for Motion of a Geophysical Fluid
92(1)
4.5 Concluding Remarks
93(4)
Appendix: Specific Heat Capacities for an Ideal Gas
94(3)
5 Orthogonal-Curvilinear Coordinate Systems
97(22)
5.1 Preamble
97(1)
5.2 Deep Orthogonal-Curvilinear Coordinates
98(13)
5.3 Shallow Orthogonal-Curvilinear Coordinates
111(7)
5.4 Concluding Remarks
118(1)
6 Governing Equations for Motion of Geophysical Fluids: Curvilinear Form
119(14)
6.1 Preamble
119(1)
6.2 The Governing Equations in Vector Form
120(1)
6.3 Axial-Orthogonal-Curvilinear Coordinates
121(1)
6.4 Coriolis Terms
122(4)
6.5 The Governing Equations in Axial-Orthogonal-Curvilinear Coordinates
126(2)
6.6 The Governing Equations in Spherical-Polar and Cylindrical-Polar Coordinates
128(1)
6.7 Euler--Lagrange Forms of the Momentum Components
128(1)
6.8 Concluding Remarks
129(4)
Appendix A The Governing Equations in Spherical-Polar Coordinates
130(1)
Appendix B The Governing Equations in Cylindrical-Polar Coordinates
131(2)
7 Representation of Gravity: Basic Theory and Spherical Planets
133(41)
7.1 Preamble
133(8)
7.2 A Guide to This
Chapter and to the Next One
141(2)
7.3 Equilibrium States for Unaccelerated Flow
143(4)
7.4 The Geopotential at and near Earth's Surface
147(2)
7.5 Newtonian Gravity and Potential Theory
149(1)
7.6 A Spherical Planet of Constant Density
150(6)
7.7 Avenues for Investigation
156(1)
7.8 A Spherical Planet of Variable Density
156(15)
7.9 Concluding Remarks
171(3)
Appendix: Some Spherical Relations
172(2)
8 Representation of Gravity: Further Theory and Spheroidal Planets
174(42)
8.1 Preamble
174(2)
8.2 Functional Forms for Spheroidal Planets
176(6)
8.3 An Ellipsoidal Planet of Constant Density
182(7)
8.4 Reformulation of the Procedure to Determine Newtonian Gravity Outside a Planet
189(2)
8.5 An Ellipsoidal Planet of Variable Density
191(20)
8.6 Spherical Geopotential Approximation as an Asymptotic Limit
211(3)
8.7 Concluding Remarks
214(2)
9 Thermodynamic Potentials and Thermodynamical Consistency
216(22)
9.1 Preamble
216(2)
9.2 Thermodynamic Potentials
218(5)
9.3 Basic Gibbs Thermodynamic Potentials
223(5)
9.4 Composite Gibbs Potentials
228(9)
9.5 Concluding Remarks
237(1)
10 Moist Thermodynamics
238(56)
10.1 Preamble
238(1)
10.2 Humid Air
239(4)
10.3 Latent Internal Energy and Phase Transitions
243(4)
10.4 Water Substance in a Vacuum
247(12)
10.5 Cloudy Air, Possibly Containing Liquid and/or Frozen Water
259(16)
10.6 The Triple Point of Water in the Presence of Dry Air
275(11)
10.7 Definition of Some Thermodynamic Quantities
286(6)
10.8 Concluding Remarks
292(2)
11 Ocean Thermodynamics
294(34)
11.1 Preamble
294(2)
11.2 Oceanic Gibbs Potentials
296(3)
11.3 Derivation of Vallis (2017)'s Prototypical Gibbs Potential
299(13)
11.4 An Alternative Prototypical Gibbs Potential for an Ocean
312(7)
11.5 The TEOS-10 Gibbs Potential
319(8)
11.6 Concluding Remarks
327(1)
12 Geopotential Coordinates for Modelling Planetary Atmospheres and Oceans
328(43)
12.1 Preamble
328(2)
12.2 Geodesy and the World Geodetic System
330(8)
12.3 The Classical Spherical Geopotential Approximation Revisited
338(2)
12.4 Geopotential Approximation for Ellipsoidal Planets
340(5)
12.5 Further Geopotential Approximation above Earth's Geoid
345(4)
12.6 Further Geopotential Approximation below Earth's Geoid
349(4)
12.7 Interlude
353(1)
12.8 Orthogonal Trajectories to the Geopotential Surfaces
354(3)
12.9 GREAT Coordinates
357(9)
12.10 Concluding Remarks
366(5)
Appendix: The Equilibrium Depth of an Ocean Covering a Planet
369(2)
13 Vertical Coordinates and Boundary Conditions
371(42)
13.1 Preamble
371(2)
13.2 The Deep-Fluid Equations and Boundary Conditions
373(15)
13.3 Mass Conservation
388(1)
13.4 Energetics
389(4)
13.5 Axial-Angular-Momentum Conservation
393(2)
13.6 Boundary Conditions in the Vertical and Global Conservation
395(8)
13.7 Conservation with the Shallow Approximation
403(1)
13.8 An Energy-Like Invariant for Elastic Lids at Finite Pressure
403(2)
13.9 An Atmospheric State with Zero Pressure at Finite Height
405(5)
13.10 Concluding Remarks
410(3)
Appendix: Some Useful Identities
411(2)
14 Variational Methods and Hamilton's Principle of Stationary Action
413(50)
14.1 Preamble
413(1)
14.2 Eulerian versus Lagrangian Viewpoints for Fluid Dynamics
414(3)
14.3 Mass Conservation
417(2)
14.4 Functionals and Variational Principles
419(8)
14.5 Hamilton's Principle of Stationary Action
427(4)
14.6 Gravitational Attraction between Two Particles Revisited
431(4)
14.7 A System of Point Particles
435(4)
14.8 Governing Equations for Global Fluids: Vector Form
439(10)
14.9 Governing Equations for Global Fluids: Curvilinear Form
449(3)
14.10 Euler-Lagrange Equations for Global Fluids
452(4)
14.11 Concluding Remarks
456(7)
Appendix: Variations in Axial-Orthogonal-Curvilinear Coordinates
456(7)
15 Conservation
463(32)
15.1 Preamble
463(1)
15.2 Governing Equations
464(1)
15.3 Conservation Principles: Vector Form
465(15)
15.4 Conservation Principles: Curvilinear Form
480(7)
15.5 Noether's Theorem, Symmetries, and Conservation
487(7)
15.6 Concluding Remarks
494(1)
II DYNAMICALLY CONSISTENT EQUATION SETS
495(158)
16 Deep and Shallow, Dynamically Consistent Equation Sets in 3D
497(34)
16.1 Preamble
497(3)
16.2 A Unified Quartet of Dynamically Consistent Equation Sets
500(11)
16.3 Derivation Methodologies for Approximate Equation Sets
511(1)
16.4 Classical Eulerian Derivation
511(1)
16.5 Lagrangian Derivation Using Hamilton's Principle
512(4)
16.6 Lagrangian Derivation Using Euler-Lagrange Equations
516(1)
16.7 Equation Transition from Deep Fluids to Shallow Fluids
517(3)
16.8 Concluding Remarks
520(11)
Appendix A Four Equation Sets in Spherical-Polar Coordinates
522(4)
Appendix B Four Equation Sets in Axial-Orthogonal-Curvilinear Coordinates
526(5)
17 Quasi-Shallow, Dynamically Consistent Equation Sets in 3D
531(31)
17.1 Preamble
531(2)
17.2 Classical Eulerian Derivation
533(10)
17.3 Lagrangian Derivation
543(6)
17.4 A Unified Sextet of Equation Sets in Spheroidal Geometry
549(4)
17.5 A Unified Sextet of Equation Sets in Spherical Geometry
553(4)
17.6 Concluding Remarks
557(5)
Appendix A Quasi-Shallow Equation Sets in Axial-Orthogonal-Curvilinear Coordinates
557(2)
Appendix B Variations for Quasi-Shallow Contributions
559(3)
18 Shallow-Water Equation Sets in 2D
562(69)
18.1 Preamble
562(4)
18.2 Eulerian Derivation of the Basic Shallow-Water Equations
566(9)
18.3 Horizontal Coordinate Systems and Models of Gravity
575(9)
18.4 Lagrangian Density for the Basic Shallow-Water Equations
584(7)
18.5 Quasi-Shallow Enhancement of Lagrangian Density
591(4)
18.6 Euler-Lagrange Derivation of the Quasi-Shallow Enhanced Set
595(4)
18.7 `Quasi-Shallow' Shallow-Water Conservation Principles
599(3)
18.8 The `Quasi-Shallow' Shallow-Water Equations in Spherical Geometry
602(3)
18.9 Derivation of a Unified Quartet of Equation Sets
605(9)
18.10 The Unified Quartet in Spherical Geometry
614(4)
18.11 Concluding Remarks
618(13)
Appendix A Derivation of 2D Quasi-Shallow Lagrangian Density by Vertically Averaging the 3D One
621(3)
Appendix B Conservation Principles for the `Quasi-Shallow' Shallow-Water Equations
624(7)
19 A Barotropic Potential Vorticity (BPV) Equation for Flow over a Spheroidal Planet
631(22)
19.1 Preamble
631(1)
19.2 The Momentum and Mass-Continuity Equations in Curvilinear Form
632(2)
19.3 Inviscid, Horizontal, Shallow Flow in Spheroidal Geometry
634(5)
19.4 Global Conservation
639(4)
19.5 The BPV Equation for a Spheroidal Planet
643(3)
19.6 An Alternative Derivation of the BPV Equation
646(1)
19.7 Dynamical Consistency
647(1)
19.8 The Poisson Problem for Pressure
648(1)
19.9 Variational Derivation of the Momentum Equations
649(1)
19.10 Concluding Remarks
650(3)
III EXACT STEADY AND UNSTEADY NON-LINEAR SOLUTIONS
653(120)
20 Exact Steady Solutions of the Global Shallow-Water Equations
655(43)
20.1 Preamble
655(2)
20.2 The Shallow-Water Equations in Spheroidal Geometry
657(1)
20.3 A Derivation Methodology
658(1)
20.4 A Physical Interpretation of hS1 (ξ2)
659(2)
20.5 Some Illustrative Solutions
661(7)
20.6 Rotated Solutions in Spherical Geometry
668(1)
20.7 Interlude
669(2)
20.8 The Stability of Exact Solutions to Linear Perturbation
671(11)
20.9 Illustrative Examples of the Application of the Stability Analysis
682(13)
20.10 Concluding Remarks
695(3)
Appendix: Rotated Coordinate Transformations
695(3)
21 Exact 3D Steady Solutions of Global Equation Sets
698(25)
21.1 Preamble
698(1)
21.2 A Unified Quartet of Governing Equations
699(1)
21.3 Simplification for Steady, Axially Symmetric Flow
700(1)
21.4 Compatibility Constraints for Balance
701(2)
21.5 A Change of Dependent Variable
703(2)
21.6 Construction of Exact Steady Solutions
705(3)
21.7 A Generalised Thermal-Wind Equation
708(2)
21.8 Three Illustrative Examples
710(11)
21.9 Concluding Remarks
721(2)
22 Exact Unsteady Solutions of the Barotropic Potential Vorticity Equation over an Ellipsoid
723(23)
22.1 Preamble
723(2)
22.2 Derivation of Exact Unsteady Solutions
725(12)
22.3 A Complementary Derivation of Exact Unsteady Solutions
737(2)
22.4 Diagnosis of Pressure for a Particular Solution
739(3)
22.5 Diagnosis of Pressure for a Family of Solutions
742(2)
22.6 Concluding Remarks
744(2)
23 Exact Unsteady Solutions in 3D over an Ellipsoidal Planet
746(27)
23.1 Preamble
746(1)
23.2 A Quartet of Equation Sets for Unforced 3D Fluid Flow over a Rotating Ellipsoidal Planet
747(3)
23.3 Preparatory Steps
750(6)
23.4 Exact Barotropic Solutions over an Ellipsoid
756(4)
23.5 A Family of Exact, Unsteady 3D Solutions
760(1)
23.6 A Particular Exact, Unsteady, 3D Solution
761(1)
23.7 The Top Boundary Condition
762(1)
23.8 Test Cases for Validating 3D Dynamical Cores
762(9)
23.9 Concluding Remarks
771(2)
Appendix: Vector Identities 773(4)
References 777(7)
Index 784
Andrew N. Staniforth now retired led the development of dynamical cores for weather and climate prediction at two national centres (Canada and the UK). He has published over 100 peer-reviewed journal articles, and is the recipient of various prizes and awards including: the Editor's Award (American Meteorological Society, 1990); the Andrew Thompson Prize (Canadian Meteorological and Oceanographic Society, 1993); and the Buchan and Adrian Gill Prizes (Royal Meteorological Society, 2007 and 2009).