Global Atmospheric and Oceanic Modelling
Fundamental Equations

A unified and comprehensive account of the fundamental equations of atmospheric and oceanic models for climate and weather forecasting.

Andrew N. Staniforth (Author)

9781108838337, Cambridge University Press

Hardback, published 28 April 2022

816 pages
26 x 20.7 x 4.3 cm, 2 kg

'… 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

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.

Preface. Notation and acronyms. Part I. Foundations: 1. Introduction
2. Governing equations for motion of a dry atmosphere: Vector form
3. Governing equations for motion of a cloudy atmosphere: Vector form
4. Governing equations for motion of geophysical fluids: Vector form
5. Orthogonal curvilinear coordinate systems
6. Governing equations for motion of geophysical fluids: Curvilinear form
7. Representation of gravity: Basic theory and spherical planets
8. Representation of gravity: Further theory and spheroidal planets
9. Thermodynamic potentials and thermodynamical consistency
10. Moist thermodynamics
11. Ocean thermodynamics
12. Geopotential coordinates for modelling planetary atmospheres and oceans
13. Vertical coordinates and boundary conditions
14. Variational methods and Hamilton's principle of stationary action
15. Conservation. Part II. Dynamically Consistent Equation Sets: 16. Deep and shallow equation sets in 3D
17. Quasi-shallow equation sets in 3D
18. Shallow water equation sets in 2D
19. A barotropic potential vorticity (BPV) equation for flow over a spheroidal planet. Part III. Exact Steady and Unsteady Nonlinear Solutions: 20. Exact steady solutions of the global shallow water equations
21. Exact 3D steady solutions of global equation sets
22. Exact unsteady solutions of the barotropic potential vorticity equation over an ellipsoid
23. Exact unsteady solutions in 3D over an ellipsoidal planet. Appendix. References. Index.

Subject Areas: Mechanics of fluids [TGMF], Climate change [RNPG], Meteorology & climatology [RBP], Oceanography [seas RBKC], Atmospheric physics [PHVJ], Fluid mechanics [PHDF]