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Earth Sciences & Geography - Atmospheric Sciences | An Introduction to Global Spectral Modeling

An Introduction to Global Spectral Modeling

Krishnamurti, T.N., Bedi, H.S., Hardiker, V., Watson-Ramaswamy, L.

Originally published by Oxford University Press, 1988

2nd, rev. and enlarged ed. 2006, X, 320 p.

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Numerical weather prediction is receiving increased attention as weather forecasters aim to improve the numerical models used to forecast the weather. This is a textbook on global spectral modeling, which is an important component for global weather forecasts at numerous operational centers. This book covers all areas of model development including numerical analysis, treatment of clouds, mountains, radiation, precipitation processes, and the surface layers over land and the ocean. 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. This is designed for a one semester introductory graduate level course on weather prediction methodologies. As a prerequisite it requires a basic background in meteorology, applied mathematics, and numerical analysis.

Content Level » Research

Keywords » Global Spectral Modeling - Meteorology - Numerical weather prediction - Scale - Weather forecasting - digital elevation model

Related subjects » Atmospheric Sciences - Earth Sciences & Geography - Environmental Engineering and Physics - Geophysics & Geodesy - Meteorology - Monitoring & Environmental Analysis

Table of contents 

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

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