Numerical Methods in Weather Prediction

Preface to the English EditionPreface to the Russian EditionIntroduction1 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 System2 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 Atmosphere3 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 Trajectories4 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 Scheme5 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 Problems6 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 Transport7 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 Problem8 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 FieldReferencesSubject Index