An Introduction to Global Spectral Modeling

by Krishnamurti, T. N.; Bedi, H. S.; Hardiker, V. M.

• ISBN13: 9780195094732
• ISBN10: 0195094735
• Format: Hardcover
• Copyright: 1998-02-05
• Publisher: Oxford University Press

Summary

This introductory book on numerical weather prediction utilizes thespectral transform method. It is an indispensable guide to the methods beingused by nearly all major weather forecast centers in the United States, England,Japan, India, France, and Australia.

Table of Contents

1 Introduction	1	(3)
2 An Introduction to Finite Differencing	4	(33)
2.1 Introduction	4	(1)
2.2 Application of Taylor's Series to Finite Differencing	5	(1)
2.3 Forward and Backward Differencing	6	(1)
2.4 Centered Finite Differencing	7	(1)
2.5 Fourth-Order Accurate Formulas	8	(2)
2.6 Second-Order Accurate Laplacian	10	(5)
2.7 Fourth-Order Accurate Laplacian	15	(2)
2.8 Elliptic Partial Differential Equations in Meteorology	17	(1)
2.9 Direct Method	18	(3)
2.10 Relaxation Method	21	(5)
2.11 Sequential Relaxation Versus Simultaneous Relaxation	26	(2)
2.12 Barotropic Vorticity Equation	28	(2)
2.13 The 5-Point Jacobian	30	(1)
2.14 Arakawa Jacobian	30	(5)
2.15 Exercises	35	(2)
3 Time-Differencing Schemes	37	(17)
3.1 Introduction	37	(1)
3.2 Amplification Factor	38	(2)
3.3 Stability	40	(9)
3.4 Shallow-Water Model	49	(5)
4 What Is a Spectral Model?	54	(6)
4.1 Introduction	54	(1)
4.2 The Galerkin Method	55	(3)
4.3 A Meteorological Application	58	(1)
4.4 Exercises	59	(1)
5 Lower-Order Spectral Model	60	(11)
5.1 Introduction	60	(1)
5.2 Maximum Simplification	61	(3)
5.3 Conservation of Mean-Square Vorticity and Mean Kinetic Energy	64	(2)
5.4 Energy Transformations	66	(2)
5.5 Mapping the Solution	68	(1)
5.6 An Example of Chaos	68	(2)
5.7 Exercises	70	(1)
6 Mathematical Aspects of Spectral Models	71	(33)
6.1 Introduction	71	(2)
6.2 Legendre Equation and Associated Legendre Equation	73	(3)
6.3 Laplace's Equation	76	(1)
6.4 Orthogonality Properties	77	(4)
6.5 Recurrence Relations	81	(1)
6.6 Gaussian Quadrature	82	(7)
6.7 Spectral Representation of Physical Fields	89	(4)
6.8 Barotropic Spectral Model on a Sphere	93	(3)
6.9 Shallow-Water Spectral Model	96	(4)
6.10 Semi-implicit Shallow-Water Spectral Model	100	(2)
6.11 Inclusion of Bottom Topography	102	(1)
6.12 Exercises	103	(1)
7 Multilevel Global Spectral Model	104	(34)
7.1 Introduction	104	(1)
7.2 Truncation in a Spectral Model	105	(2)
7.3 Aliasing	107	(1)
7.4 Transform Method	108	(4)
7.5 The x-y-XXX Coordinate System	112	(6)
7.6 A Closed System of Equations in XXX Coordinates on a Sphere	118	(9)
7.7 Spectral Form of the Primitive Equations	127	(7)
7.8 Examples	134	(4)
8 Physical Processes	138	(45)
8.1 Introduction	138	(1)
8.2 The Planetary Boundary Layer	138	(8)
8.3 Cumulus Parameterization	146	(13)
8.4 Large-Scale Condensation	159	(4)
8.5 Parameterization of Radiative Processes	163	(20)
9 Initialization Procedures	183	(21)
9.1 Introduction	183	(1)
9.2 Normal Mode Initialization	183	(10)
9.3 Physical Initialization	193	(8)
9.4 Initialization of the Earth's Radiation Budget	201	(3)
10 Spectral Energetics	204	(40)
10.1 Introduction	204	(1)
10.2 Energy Equations on a Sphere	204	(15)
10.3 Energy Equations in Wavenumber Domain	219	(13)
10.4 Energy Equations in Two-Dimensional Wavenumber Domain	232	(12)
References	244	(5)
Index	249