An Introduction to Global Spectral Modeling.

By: Krishnamurti, T. NContributor(s): Bedi, H. S | Hardiker, V. MMaterial type: TextTextPublisher: Cary : Oxford University Press USA - OSO, 1998Copyright date: ©1998Description: 1 online resource (266 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780198025498Subject(s): Numerical weather forecasting | Weather forecastingGenre/Form: Electronic books.Additional physical formats: Print version:: An Introduction to Global Spectral ModelingDDC classification: 551.63/4 LOC classification: QC996 -- .K73 1998ebOnline resources: Click to View
Contents:
Intro -- Contents -- 1 Introduction -- 2 An Introduction to Finite Differencing -- 2.1 Introduction -- 2.2 Application of Taylor's Series to Finite Differencing -- 2.3 Forward and Backward Differencing -- 2.4 Centered Finite Differencing -- 2.5 Fourth-Order Accurate Formulas -- 2.6 Second-Order Accurate Laplacian -- 2.7 Fourth-Order Accurate Laplacian -- 2.8 Elliptic Partial Differential Equations in Meteorology -- 2.9 Direct Method -- 2.10 Relaxation Method -- 2.11 Sequential Relaxation Versus Simultaneous Relaxation -- 2.12 Barotropic Vorticity Equation -- 2.13 The 5-Point Jacobian -- 2.14 Arakawa Jacobian -- 2.15 Exercises -- 3 Time-Differencing Schemes -- 3.1 Introduction -- 3.2 Amplification Factor -- 3.3 Stability -- 3.4 Shallow-Water Model -- 4 What Is a Spectral Model? -- 4.1 Introduction -- 4.2 The Galerkin Method -- 4.3 A Meteorological Application -- 4.4 Exercises -- 5 Lower-Order Spectral Model -- 5.1 Introduction -- 5.2 Maximum Simplification -- 5.3 Conservation of Mean-Square Vorticity and Mean Kinetic Energy -- 5.4 Energy Transformations -- 5.5 Mapping the Solution -- 5.6 An Example of Chaos -- 5.7 Exercises -- 6 Mathematical Aspects of Spectral Models -- 6.1 Introduction -- 6.2 Legendre Equation and Associated Legendre Equation -- 6.3 Laplace's Equation -- 6.4 Orthogonality Properties -- 6.5 Recurrence Relations -- 6.6 Gaussian Quadrature -- 6.7 Spectral Representation of Physical Fields -- 6.8 Barotropic Spectral Model on a Sphere -- 6.9 Shallow-Water Spectral Model -- 6.10 Semi-implicit Shallow-Water Spectral Model -- 6.11 Inclusion of Bottom Topography -- 6.12 Exercises -- 7 Multilevel Global Spectral Model -- 7.1 Introduction -- 7.2 Truncation in a Spectral Model -- 7.3 Aliasing -- 7.4 Transform Method -- 7.5 The x-y-σ Coordinate System -- 7.6 A Closed System of Equations in σ Coordinates on a Sphere.
7.7 Spectral Form of the Primitive Equations -- 7.8 Examples -- 8 Physical Processes -- 8.1 Introduction -- 8.2 The Planetary Boundary Layer -- 8.3 Cumulus Parameterization -- 8.4 Large-Scale Condensation -- 8.5 Parameterization of Radiative Processes -- 9 Initialization Procedures -- 9.1 Introduction -- 9.2 Normal Mode Initialization -- 9.3 Physical Initialization -- 9.4 Initialization of the Earth's Radiation Budget -- 10 Spectral Energetics -- 10.1 Introduction -- 10.2 Energy Equations on a Sphere -- 10.3 Energy Equations in Wavenumber Domain -- 10.4 Energy Equations in Two-Dimensional Wavenumber Domain -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- V -- Z.
Summary: This introductory book on numerical weather prediction utilizes the spectral transform method. 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.
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Intro -- Contents -- 1 Introduction -- 2 An Introduction to Finite Differencing -- 2.1 Introduction -- 2.2 Application of Taylor's Series to Finite Differencing -- 2.3 Forward and Backward Differencing -- 2.4 Centered Finite Differencing -- 2.5 Fourth-Order Accurate Formulas -- 2.6 Second-Order Accurate Laplacian -- 2.7 Fourth-Order Accurate Laplacian -- 2.8 Elliptic Partial Differential Equations in Meteorology -- 2.9 Direct Method -- 2.10 Relaxation Method -- 2.11 Sequential Relaxation Versus Simultaneous Relaxation -- 2.12 Barotropic Vorticity Equation -- 2.13 The 5-Point Jacobian -- 2.14 Arakawa Jacobian -- 2.15 Exercises -- 3 Time-Differencing Schemes -- 3.1 Introduction -- 3.2 Amplification Factor -- 3.3 Stability -- 3.4 Shallow-Water Model -- 4 What Is a Spectral Model? -- 4.1 Introduction -- 4.2 The Galerkin Method -- 4.3 A Meteorological Application -- 4.4 Exercises -- 5 Lower-Order Spectral Model -- 5.1 Introduction -- 5.2 Maximum Simplification -- 5.3 Conservation of Mean-Square Vorticity and Mean Kinetic Energy -- 5.4 Energy Transformations -- 5.5 Mapping the Solution -- 5.6 An Example of Chaos -- 5.7 Exercises -- 6 Mathematical Aspects of Spectral Models -- 6.1 Introduction -- 6.2 Legendre Equation and Associated Legendre Equation -- 6.3 Laplace's Equation -- 6.4 Orthogonality Properties -- 6.5 Recurrence Relations -- 6.6 Gaussian Quadrature -- 6.7 Spectral Representation of Physical Fields -- 6.8 Barotropic Spectral Model on a Sphere -- 6.9 Shallow-Water Spectral Model -- 6.10 Semi-implicit Shallow-Water Spectral Model -- 6.11 Inclusion of Bottom Topography -- 6.12 Exercises -- 7 Multilevel Global Spectral Model -- 7.1 Introduction -- 7.2 Truncation in a Spectral Model -- 7.3 Aliasing -- 7.4 Transform Method -- 7.5 The x-y-σ Coordinate System -- 7.6 A Closed System of Equations in σ Coordinates on a Sphere.

7.7 Spectral Form of the Primitive Equations -- 7.8 Examples -- 8 Physical Processes -- 8.1 Introduction -- 8.2 The Planetary Boundary Layer -- 8.3 Cumulus Parameterization -- 8.4 Large-Scale Condensation -- 8.5 Parameterization of Radiative Processes -- 9 Initialization Procedures -- 9.1 Introduction -- 9.2 Normal Mode Initialization -- 9.3 Physical Initialization -- 9.4 Initialization of the Earth's Radiation Budget -- 10 Spectral Energetics -- 10.1 Introduction -- 10.2 Energy Equations on a Sphere -- 10.3 Energy Equations in Wavenumber Domain -- 10.4 Energy Equations in Two-Dimensional Wavenumber Domain -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- V -- Z.

This introductory book on numerical weather prediction utilizes the spectral transform method. 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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