An Introduction to Global Spectral Modeling

Inhaltsverzeichnis

Introduction

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 Elliptical 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 Low-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-s Coordinate System
7.6 A Closed System of Equations in s 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
11 Limited Area Spectral Model
11.1 Introduction
11.2 Map Projection
11.3 Model Equations
11.4 Orography and Lateral Boundary Relaxation
11.5 Spectral Representation and Lateral Boundary Conditions
11.6 Spectral Truncation
11.7 Model Physics and Vertical Structure
11.8 Regional Model Forecast Procedure
12 Ensemble Forecasting
12.1 Introduction
12.2 Monte Carlo Method
12.3 National Center for

Portrait

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.

Pressestimmen

James Russell Carr in Mathematical Geology, Vol. 31, No. 8, 1999 on the book's first edition:

In summary, the mathematical treatment is quite intense and demands patience of readers, at least in the case of this one. But if at all intrigued by how sophisticated weather forecasting has become (certainly strom forecasting) then a reader will find this book not only interesting, but thorough enough to enable model development if that is a goal. Problems are presneted at the end of each chapter, so this book can be used as a texct in the class room. Reserachers involved in the modeling of turbulence, ocean systems and tectonic systems may also value the presentation of this book.