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E-grāmata: Introduction to Global Spectral Modeling

(Research Assistant, Meteorology, all at Florida State University, USA), (Research Assistant, Meteorology), (Department of Meteorology)
  • Formāts: PDF+DRM
  • Izdošanas datums: 05-Feb-1998
  • Izdevniecība: Oxford University Press Inc
  • Valoda: eng
  • ISBN-13: 9780198025498
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Introduction to Global Spectral ModelingPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 05-Feb-1998
  • Izdevniecība: Oxford University Press Inc
  • Valoda: eng
  • ISBN-13: 9780198025498
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This book is an indispensable guide to the methods used by nearly all major weather forecast centers in the United States, England, Japan, India, France, and Australia. Designed for senior-level undergraduates and first-year graduate students, the book provides an introduction to global spectral modeling. It begins with an introduction to elementary finite-difference methods and moves on towards the gradual description of sophisticated dynamical and physical models in spherical coordinates. Topics include computational aspects of the spectral transform method, the planetary boundary layer physics, the physics of precipitation processes in large-scale models, the radiative transfer including effects of diagnostic clouds and diurnal cycle, the surface energy balance over land and ocean, and the treatment of mountains. The discussion of model initialization includes the treatment of normal modes and physical processes, and the concluding chapter covers the spectral energetics as a diagnostic tool for model evaluation.

Recenzijas

"[ P]resents thoroughly the mathematics involved in modeling . . . storms, forecasting their paths, and understanding associated atmospheric dynamics. This book is intensively mathematical, with a focus on differential and integral calculus. . . . With respect to integral calculus, the section of the book on Gauss quadrature is interesting and unique . . . The two chapters on physical processes and initialization procedures are equally well written and explain the physical processes that must be accounted for in models . . . [ I]f at all intrigued by how sophisticated weather forecasting has become . . . , then a reader will find this book not only interesting, but thorough enough to enable model development if that is a goal. Problems are presented at the end of each chapter, so this book can be used as a text in the classroom. Researchers involved in the modeling of turbulence, ocean systems, and tectonic systems may also value the presentations in this book."--Mathematical Geology

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


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