An Introduction to Global Spectral Modeling

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

• ISBN13: 9780387302546
• ISBN10: 0387302549
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-04-30
• Publisher: Springer Verlag

Summary

This introductory book on numerical weather prediction focuses on the spectral transform method, which is an important component for global weather forecasts at numerous operational centers. Therefore, it is an indispensable guide to the methods being used by nearly all major weather forecast centers in the United States, England, Japan, India, France, and Australia. The objectives of this book are to provide a systematic and sequential background for students, researchers, and operational weather forecasters in order to develop comprehensive weather forecast models. The chapter exercises allow it to be used as a graduate textbook for courses in meteorology as well.

Author Biography

T.N. Krishnamurti is professor of meteorology at Florida State University. He obtained his PhD in 1959 at the University of Chicago. His research interests are in the following areas: high resolution hurricane forecast (tracks, landfall, and intensity), monsoon forecasts on short, medium range, and monthly time scale and studies of interseasonal and interannual variability of the tropical atmosphere. As a participant in the meteorology team in tropical field projects, he has been responsible for the acquisition and analysis of meteorological data, which extends over most of the tropical atmosphere over several years and is now being assembled and analyzed. These data are unique; it is unlikely that a meteorological data record will be available for decades. Phenomenological interests include hurricanes, monsoons, jet streams, and the meteorology of arid zones.H.S. Bedi is affiliated with Florida State University.V.M. Hardiker is a research associate at Florida State University.L. Ramaswamy is a graduate research assistant in the Department of Meteorology at Florida State University.

Table of Contents

Preface	v
1 Introduction	1	(3)
2 An Introduction to Finite Differencing	4	(36)
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	(3)
2.6 Second-Order Accurate Laplacian	11	(4)
2.7 Fourth-Order Accurate Laplacian	15	(4)
2.8 Elliptic Partial Differential Equation in Meteorology	19	(1)
2.9 Direct Method	19	(4)
2.10 Relaxation Method	23	(4)
2.11 Sequential Relaxation Versus Simultaneous Relaxation	27	(2)
2.12 Advective Nonlinear Dynamics	29	(4)
2.13 The 5-Point Jacobian	33	(1)
2.14 Arakawa Jacobian	33	(6)
2.15 Exercises	39	(1)
3 Time-Differencing Schemes	40	(20)
3.1 Introduction	40	(1)
3.2 Amplification Factor	40	(3)
3.3 Stability	43	(11)
3.4 Shallow-Water Model	54	(6)
4 What Is a Spectral Model?	60	(5)
4.1 Introduction	60	(1)
4.2 The Galerkin Method	60	(3)
4.3 A Meteorological Application	63	(1)
4.4 Exercises	64	(1)
5 Lower-Order Spectral Model	65	(11)
5.1 Introduction	65	(1)
5.2 Maximum Simplification	66	(2)
5.3 Conservation of Mean-Square Vorticity and Mean Kinetic Energy	68	(3)
5.4 Energy Transformations	71	(1)
5.5 Mapping the Solution	72	(1)
5.6 An Example of Chaos	73	(1)
5.7 Exercises	74	(2)
6 Mathematical Aspects of Spectral Models	76	(36)
6.1 Introduction	76	(3)
6.2 Legendre Equation and Associated Legendre Equation	79	(3)
6.3 Laplace's Equation	82	(1)
6.4 Orthogonality Properties	83	(4)
6.5 Recurrence Relations	87	(2)
6.6 Gaussian Quadrature	89	(6)
6.7 Spectral Representation of Physical Fields	95	(5)
6.8 Barotropic Spectral Model on a Sphere	100	(4)
6.9 Shallow-Water Spectral Model	104	(4)
6.10 Semi-implicit Shallow-Water Spectral Model	108	(2)
6.11 Inclusion of Bottom Topography	110	(1)
6.12 Exercises	110	(2)
7 Multilevel Global Spectral Model	112	(34)
7.1 Introduction	112	(1)
7.2 Truncation in a Spectral Model	112	(3)
7.3 Aliasing	115	(1)
7.4 Transform Method	115	(4)
7.5 The x-y-σ Coordinate System	119	(7)
7.6 A Closed System of Equations in σ Coordinates on a Sphere	126	(10)
7.7 Spectral Form of the Primitive Equations	136	(6)
7.8 Examples	142	(4)
8 Physical Processes	146	(46)
8.1 Introduction	146	(1)
8.2 The Planetary Boundary Layer	146	(9)
8.3 Cumulus Parameterization	155	(12)
8.4 Large-Scale Condensation	167	(6)
8.5 Parameterization of Radiative Processes	173	(19)
9 Initialization Procedures	192	(21)
9.1 Introduction	192	(1)
9.2 Normal Mode Initialization	192	(10)
9.3 Physical Initialization	202	(8)
9.4 Initialization of the Earth's Radiation Budget	210	(3)
10 Spectral Energetics	213	(39)
10.1 Introduction	213	(1)
10.2 Energy Equations on a Sphere	213	(15)
10.3 Energy Equations in Wavenumber Domain	228	(13)
10.4 Energy Equations in Two-Dimensional Wavenumber Domain	241	(11)
11 Limited Area Spectral Model	252	(11)
11.1 Introduction	252	(1)
11.2 Map Projection	253	(1)
11.3 Model Equations	254	(4)
11.4 Orography and Lateral Boundary Relaxation	258	(1)
11.5 Spectral Representation and Lateral Boundary Conditions	258	(1)
11.6 Spectral Truncation	259	(1)
11.7 Model Physics and Vertical Structure	260	(1)
11.8 Regional Model Forecast Procedure	261	(2)
12 Ensemble Forecasting	263	(32)
12.1 Introduction	263	(1)
12.2 Monte Carlo Method	263	(2)
12.3 National Center for Environmental Prediction Method	265	(3)
12.4 Florida State University Method	268	(5)
12.5 European Center for Medium Range Forecasts Method	273	(4)
12.6 Superensemble Methodology and Results	277	(18)
13 Adaptive Observational Strategies	295	(8)
13.1 Introduction	295	(1)
13.2 Techniques for Targeted Observations	296	(7)
Appendix A	303	(1)
Appendix B	304	(1)
References	305	(8)
Index	313