Description 
1 online resource 
Contents 
Preface  1. Introduction  2. The governing equations and asymptotic approximations to them. 2.1. The governing equations. 2.2. Key asymptotic regimes. 2.3. Derivation of the semigeostrophic approximation. 2.4. Various approximations to the shallow water equations. 2.5. Various approximations to the threedimensional hydrostatic Boussinesq equations  3. Solution of the semigeostrophic equations in plane geometry. 3.1. The solution as a sequence of minimum energy states. 3.2. Solution as a mass transportation problem. 3.3. The shallow water semigeostrophic equations. 3.4. A discrete solution of the semigeostrophic equations. 3.5. Rigorous results on existence of solutions  4. Solution of the semigeostrophic equations in more general cases. 4.1. Solution of the semigeostrophic equations for compressible flow. 4.2. Spherical semigeostrophic theory. 4.3. The shallow water spherical semigeostrophic equations. 4.4. The theory of almost axisymmetric flows  5. Properties of semigeostrophic solutions. 5.1. The applicability of semigeostrophic theory. 5.2. Stability theorems for semigeostrophic flow. 5.3. Numerical methods for solving the semigeostrophic equations  6. Application of semigeostrophic theory to the predictability of atmospheric flows. 6.1. Application to shallow water flow on various scales. 6.2. The Eady wave. 6.3. Simulations of baroclinic waves. 6.4. Semigeostrophic flows on the sphere. 6.5. Orographic flows. 6.6. Inclusion of friction. 6.7. Inclusion of moisture  7. Summary 
Summary 
This book counteracts the current fashion for theories of "chaos" and unpredictability by describing a theory that underpins the surprising accuracy of current deterministic weather forecasts, and it suggests that further improvements are possible. The book does this by making a unique link between an exciting new branch of mathematics called "optimal transportation" and existing classical theories of the largescale atmosphere and ocean circulation. It is then possible to solve a set of simple equations proposed many years ago by Hoskins which are asymptotically valid on large scales, and use them to derive quantitative predictions about many largescale atmospheric and oceanic phenomena. A particular feature is that the simple equations used have highly predictable solutions, thus suggesting that the limits of deterministic predictability of the weather may not yet have been reached. It is also possible to make rigorous statements about the largescale behaviour of the atmosphere and ocean by proving results using these simple equations and applying them to the real system allowing for the errors in the approximation. There are a number of other titles in this field, but they do not treat this largescale regime 
Subject 
Dynamic meteorology.


Dynamic meteorology  Mathematics


Rossby waves.


Rossby waves  Mathematics


Atmospheric circulation  Mathematics


Ocean circulation  Mathematics


Atmospheric circulation  Mathematics


Dynamic meteorology


Rossby waves

Form 
Electronic book

ISBN 
1281867144 

9781281867148 

9781860949197 

1860949193 
