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Numerical Methods in Weather Prediction - 1st Edition - ISBN: 9780124706507, 9780323157469

Numerical Methods in Weather Prediction

1st Edition

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Author: G Marchuk
eBook ISBN: 9780323157469
Imprint: Academic Press
Published Date: 1st January 1974
Page Count: 288
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Numerical Methods in Weather Prediction focuses on the numerical methods for solving problems of weather prediction and explains the aspect of the general circulation of the atmosphere. This book explores the development in the science of meteorology, which provides investigators with improved means of studying physical processes by mathematical stimulation. Organized into eight chapters, this book starts with an overview of the significant physical factors that are instrumental in enriching the theoretical models of weather prediction. This text then examines the system of hydrodynamic equations and the equation of heat transfer related to large-scale atmospheric processes. Other chapters consider the quasigeostrophic approximation model, which is the basis for concepts of the dynamics of atmospheric motions and instrumental in establishing the basic features and laws of evolution of meteorological variables as applied to large-scale processes. The final chapter deals with the adjustment of the humidity field. This book is a valuable resource for meteorologists.

Table of Contents

Preface to the English Edition

Preface to the Russian Edition


1 Basic Equations of Atmospheric Dynamics

1.1 The System of Equations of Atmospheric Dynamics

1.2 The Free Convection Approximation

1.3 Equations of Dynamics in the (x,y,p) Coordinate System

2 The Quasigeostrophic Approximation

2.1 The Basic Quasigeostrophic System of Equations

2.2 The Equation for Pressure Variation

2.3 The Equation for Temperature Variations

2.4 The Equation for the Vertical Velocity

2.5 The Effect of Surface Friction on the Evolution of Meteorological Variables in the Free Atmosphere

3 The Splitting-Up Method

3.1 Basic Principles of the Relaxation Method Applied to Stationary Problems

3.2 The Splitting-up Method Applied to Stationary Problems

3.3 A Scheme for the Splitting up of Nonstationary Problems

3.4 Hydrodynamic Equations of Transport along Trajectories

4 The Splitting-Up Method Applied to the Weather Prediction Equations

4.1 Splitting up the System of Hydrodynamic Equations

4.2 Investigation of the Equations of Dynamic Adjustment of Fields for Simple Models

4.3 A General Approach to the Dynamic Adjustment of Fields

4.4 Investigation of the Stability of an Algorithm

4.5 Numerical Methods of Solution of Spectral Problems

4.6 Construction of a General Splitting-up Scheme

5 A Weather Prediction Scheme Based on Conservation Laws

5.1 The Hydrothermodynamic Equations in the Form of Conservation Laws

5.2 Equations for the Deviations of Meteorological Variables from their Standard Values in the Quasistatic Approximation

5.3 The Complete Set of Equations of Atmospheric Dynamics in Terms of Deviations

5.4 The Splitting-up Method

5.5 Construction of the Equations for Pressure Variation

5.6 Difference Schemes Based on the Conservation Laws

5.7 New Difference Schemes for Solving Weather Prediction Problems

6 Humidity Prediction in the Atmosphere

6.1 Basic Equations

6.2 Boundary Conditions and Initial Data

6.3 The Splitting-up Method

6.4 Difference Schemes for Solving the Equations of Humidity Transport

7 The Radiation Field in Weather Prediction

7.1 Basic Characteristics of the Radiation Field

7.2 The Equation of Radiant Energy Transfer

7.3 Approximate Solution of the Radiation Transfer Equations

7.4 The Splitting-up Method for Solving the Radiation Transfer Problem

8 Objective Analysis of Meteorological Fields

8.1 Methods of Optimal Interpolation

8.2 Adjustment of the Meteorological Fields

8.3 Objective Analysis of the Humidity Field


Subject Index


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© Academic Press 1974
1st January 1974
Academic Press
eBook ISBN:

About the Author

G Marchuk

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