Preface |
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xv | |
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1 | (3) |
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1.2 Conservation of Momentum |
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4 | (5) |
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1.2.1 Pressure Gradient Force |
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5 | (1) |
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6 | (2) |
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1.2.3 Gravitational Force |
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8 | (1) |
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1.3 Noninertial Reference Frames and "Apparent" Forces |
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9 | (9) |
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1.3.1 Centripetal Acceleration and Centrifugal Force |
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10 | (1) |
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11 | (3) |
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1.3.3 The Coriolis Force and the Curvature Effect |
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14 | (3) |
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1.3.4 Constant Angular Momentum Oscillations |
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17 | (1) |
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1.4 Structure of the Static Atmosphere |
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18 | (5) |
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1.4.1 The Hydrostatic Equation |
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18 | (2) |
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1.4.2 Pressure as a Vertical Coordinate |
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20 | (2) |
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1.4.3 A Generalized Vertical Coordinate |
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22 | (1) |
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23 | (2) |
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25 | (6) |
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26 | (1) |
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26 | (2) |
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28 | (3) |
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2 Basic Conservation Laws |
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2.1 Total Differentiation |
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31 | (4) |
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2.1.1 Total Differentiation of a Vector in a Rotating System |
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33 | (2) |
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2.2 The Vectorial Form of the Momentum Equation in Rotating Coordinates |
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35 | (2) |
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2.3 Component Equations in Spherical Coordinates |
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37 | (4) |
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2.4 Scale Analysis of the Equations of Motion |
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41 | (4) |
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2.4.1 Geostrophic Approximation and Geostrophic Wind |
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42 | (1) |
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2.4.2 Approximate Prognostic Equations: The Rossby Number |
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43 | (1) |
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2.4.3 The Hydrostatic Approximation |
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44 | (1) |
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2.5 The Continuity Equation |
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45 | (5) |
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2.5.1 A Eulerian Derivation |
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46 | (1) |
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2.5.2 A Lagrangian Derivation |
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47 | (1) |
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2.5.3 Scale Analysis of the Continuity Equation |
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48 | (2) |
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2.6 The Thermodynamic Energy Equation |
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50 | (3) |
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2.7 Thermodynamics of the Dry Atmosphere |
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53 | (4) |
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2.7.1 Potential Temperature |
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53 | (1) |
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2.7.2 The Adiabatic Lapse Rate |
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54 | (1) |
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54 | (2) |
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2.7.4 Scale Analysis of the Thermodynamic Energy Equation |
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56 | (1) |
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2.8 The Boussinesq Approximation |
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57 | (1) |
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2.9 Thermodynamics of the Moist Atmosphere |
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58 | (9) |
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2.9.1 Equivalent Potential Temperature |
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59 | (2) |
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2.9.2 The Pseudoadiabatic Lapse Rate |
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61 | (1) |
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2.9.3 Conditional Instability |
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62 | (2) |
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64 | (1) |
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65 | (1) |
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66 | (1) |
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3 Elementary Applications of the Basic Equations |
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3.1 Basic Equations in Isobaric Coordinates |
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67 | (2) |
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3.1.1 The Horizontal Momentum Equation |
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67 | (1) |
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3.1.2 The Continuity Equation |
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68 | (1) |
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3.1.3 The Thermodynamic Energy Equation |
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69 | (1) |
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69 | (9) |
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3.2.1 Natural Coordinates |
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70 | (1) |
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71 | (1) |
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72 | (1) |
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73 | (1) |
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3.2.5 The Gradient Wind Approximation |
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74 | (4) |
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3.3 Trajectories and Streamlines |
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78 | (3) |
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81 | (3) |
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3.4.1 Barotropic and Baroclinic Atmospheres |
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84 | (1) |
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84 | (3) |
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3.5.1 The Kinematic Method |
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85 | (2) |
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3.5.2 The Adiabatic Method |
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87 | (1) |
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3.6 Surface Pressure Tendency |
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87 | (8) |
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89 | (3) |
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92 | (3) |
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4 Circulation, Vorticity, and Potential Vorticity |
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4.1 The Circulation Theorem |
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95 | (5) |
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100 | (4) |
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4.2.1 Vorticity in Natural Coordinates |
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102 | (2) |
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4.3 The Vorticity Equation |
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104 | (6) |
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4.3.1 Cartesian Coordinate Form |
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104 | (2) |
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4.3.2 The Vorticity Equation in Isobaric Coordinates |
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106 | (1) |
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4.3.3 Scale Analysis of the Vorticity Equation |
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107 | (3) |
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110 | (5) |
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4.5 Shallow Water Equations |
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115 | (5) |
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4.5.1 Barotropic Potential Vorticity |
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118 | (2) |
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4.6 Ertel Potential Vorticity in Isentropic Coordinates |
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120 | (7) |
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4.6.1 Equations of Motion in Isentropic Coordinates |
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120 | (1) |
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4.6.2 The Potential Vorticity Equation |
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121 | (1) |
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4.6.3 Integral Constraints on Isentropic Vorticity |
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121 | (1) |
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122 | (1) |
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122 | (2) |
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124 | (3) |
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5 Atmospheric Oscillations |
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5.1 The Perturbation Method |
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127 | (1) |
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128 | (8) |
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130 | (1) |
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5.2.2 Dispersion and Group Velocity |
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131 | (2) |
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5.2.3 Wave Properties in Two and Three Dimensions |
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133 | (2) |
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5.2.4 A Wave Solution Strategy |
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135 | (1) |
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136 | (8) |
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5.3.1 Acoustic or Sound Waves |
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136 | (3) |
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5.3.2 Shallow Water Waves |
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139 | (5) |
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5.4 Internal Gravity (Buoyancy) Waves |
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144 | (6) |
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5.4.1 Pure Internal Gravity Waves |
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145 | (5) |
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5.5 Linear Waves of a Rotating Stratified Atmosphere |
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150 | (6) |
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5.5.1 Pure Inertial Oscillations |
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150 | (2) |
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5.5.2 Rossby and Inertia-Gravity Waves |
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152 | (4) |
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5.6 Adjustment to Geostrophic Balance |
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156 | (3) |
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159 | (12) |
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5.7.1 Free Barotropic Rossby Waves |
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161 | (2) |
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5.7.2 Forced Topographic Rossby Waves |
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163 | (2) |
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165 | (1) |
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166 | (2) |
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168 | (3) |
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6 Quasi-geostrophic Analysis |
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6.1 The Observed Structure of Extratropical Circulations |
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171 | (7) |
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6.2 Derivation of the Quasi-Geostrophic Equations |
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178 | (5) |
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181 | (2) |
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6.3 Potential Vorticity Derivation of the QG Equations |
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183 | (4) |
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6.4 Potential Vorticity Thinking |
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187 | (10) |
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6.4.1 PV Inversion, Induced Flow, and Piecewise PV Inversion |
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188 | (6) |
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6.4.2 PV Conservation and the QG "Height Tendency" Equation |
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194 | (3) |
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6.5 Vertical Motion (w) Thinking |
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197 | (7) |
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6.6 Idealized Model of a Baroclinic Disturbance |
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204 | (2) |
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6.7 Isobaric Form of the QG Equations |
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206 | (7) |
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208 | (1) |
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208 | (2) |
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210 | (3) |
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7.1 Hydrodynamic Instability |
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213 | (2) |
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7.2 Normal Mode Baroclinic Instability: A Two-Layer Model |
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215 | (12) |
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7.2.1 Linear Perturbation Analysis |
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217 | (6) |
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7.2.2 Vertical Motion in Baroclinic Waves |
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223 | (4) |
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7.3 The Energetics of Baroclinic Waves |
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227 | (7) |
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7.3.1 Available Potential Energy |
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227 | (2) |
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7.3.2 Energy Equations for the Two-Layer Model |
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229 | (5) |
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7.4 Baroclinic Instability of a Continuously Stratified Atmosphere |
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234 | (11) |
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7.4.1 Log-Pressure Coordinates |
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235 | (2) |
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7.4.2 Baroclinic Instability: The Rayleigh Theorem |
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237 | (4) |
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7.4.3 The Eady Stability Problem |
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241 | (4) |
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7.5 Growth and Propagation of Neutral Modes |
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245 | (11) |
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7.5.1 Transient Growth of Neutral Waves |
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247 | (3) |
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7.5.2 Downstream Development |
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250 | (1) |
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251 | (1) |
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251 | (2) |
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253 | (3) |
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8 The Planetary Boundary Layer |
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8.1 Atmospheric Turbulence |
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256 | (3) |
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256 | (3) |
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8.2 Turbulent Kinetic Energy |
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259 | (2) |
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8.3 Planetary Boundary Layer Momentum Equations |
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261 | (9) |
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8.3.1 Well-Mixed Boundary Layer |
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262 | (2) |
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8.3.2 The Flux-Gradient Theory |
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264 | (1) |
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8.3.3 The Mixing Length Hypothesis |
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264 | (2) |
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266 | (2) |
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268 | (1) |
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8.3.6 The Modified Ekman Layer |
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269 | (1) |
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8.4 Secondary Circulations and Spin Down |
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270 | (9) |
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275 | (1) |
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275 | (1) |
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276 | (3) |
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9.1 Energy Sources for Mesoscale Circulations |
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279 | (1) |
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9.2 Fronts and Frontogenesis |
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280 | (10) |
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9.2.1 The Kinematics of Frontogenesis |
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281 | (4) |
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9.2.2 Semigeostrophic Theory |
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285 | (2) |
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9.2.3 Cross-Frontal Circulation |
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287 | (3) |
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9.3 Symmetric Baroclinic Instability |
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290 | (4) |
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294 | (8) |
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9.4.1 Waves over Sinusoidal Topography |
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294 | (3) |
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9.4.2 Flow over Isolated Ridges |
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297 | (1) |
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298 | (1) |
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9.4.4 Downslope Windstorms |
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299 | (3) |
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302 | (4) |
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9.5.1 Convective Available Potential Energy |
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302 | (1) |
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303 | (3) |
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306 | (6) |
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9.6.1 Development of Rotation in Supercell Thunderstorms |
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306 | (4) |
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9.6.2 The Right-Moving Storm |
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310 | (2) |
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312 | (14) |
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9.7.1 Dynamics of Mature Hurricanes |
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314 | (4) |
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9.7.2 Hurricane Development |
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318 | (3) |
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321 | (1) |
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321 | (1) |
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322 | (4) |
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10 The General Circulation |
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10.1 The Nature of the Problem |
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326 | (2) |
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10.2 The Zonally Averaged Circulation |
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328 | (13) |
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10.2.1 The Conventional Eulerian Mean |
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330 | (7) |
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10.2.2 The Transformed Eulerian Mean |
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337 | (3) |
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10.2.3 The Zonal-Mean Potential Vorticity Equation |
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340 | (1) |
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10.3 The Angular Momentum Budget |
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341 | (8) |
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343 | (2) |
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10.3.2 The Zonal-Mean Angular Momentum |
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345 | (4) |
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10.4 The Lorenz Energy Cycle |
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349 | (7) |
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10.5 Longitudinally Dependent Time-Averaged Flow |
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356 | (5) |
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10.5.1 Stationary Rossby Waves |
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356 | (3) |
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10.5.2 Jet Stream and Storm Tracks |
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359 | (2) |
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10.6 Low-Frequency Variability |
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361 | (6) |
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362 | (2) |
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364 | (1) |
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10.6.3 Sea Surface Temperature Anomalies |
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364 | (3) |
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10.7 Numerical Simulation of the General Circulation |
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367 | (3) |
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10.7.1 Dynamical Formulation |
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368 | (1) |
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10.7.2 Physical Processes and Parameterizations |
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369 | (1) |
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10.8 Climate Sensitivity, Feedbacks, and Uncertainty |
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370 | (8) |
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373 | (1) |
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374 | (1) |
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375 | (3) |
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11.1 The Observed Structure of Large-Scale Tropical Circulations |
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378 | (14) |
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11.1.1 The Intertropical Convergence Zone |
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378 | (3) |
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11.1.2 Equatorial Wave Disturbances |
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381 | (3) |
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11.1.3 African Wave Disturbances |
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384 | (2) |
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386 | (3) |
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11.1.5 The Walker Circulation |
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389 | (1) |
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11.1.6 El Nino and the Southern Oscillation |
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390 | (2) |
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11.1.7 Equatorial Intraseasonal Oscillation |
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392 | (1) |
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11.2 Scale Analysis of Large-Scale Tropical Motions |
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392 | (6) |
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11.3 Condensation Heating |
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398 | (3) |
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11.4 Equatorial Wave Theory |
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401 | (5) |
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11.4.1 Equatorial Rossby and Rossby-Gravity Modes |
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401 | (3) |
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11.4.2 Equatorial Kelvin Waves |
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404 | (2) |
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11.5 Steady Forced Equatorial Motions |
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406 | (7) |
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409 | (1) |
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409 | (1) |
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410 | (3) |
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12 Middle Atmosphere Dynamics |
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12.1 Structure and Circulation of the Middle Atmosphere |
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413 | (4) |
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12.2 The Zonal-Mean Circulation of the Middle Atmosphere |
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417 | (9) |
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12.2.1 Lagrangian Motion of Air Parcels |
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418 | (2) |
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12.2.2 The Transformed Eulerian Mean |
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420 | (4) |
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12.2.3 Zonal-Mean Transport |
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424 | (2) |
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12.3 Vertically Propagating Planetary Waves |
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426 | (4) |
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12.3.1 Linear Rossby Waves |
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426 | (2) |
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12.3.2 Rossby Wavebreaking |
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428 | (2) |
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12.4 Sudden Stratospheric Warmings |
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430 | (5) |
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12.5 Waves in the Equatorial Stratosphere |
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435 | (5) |
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12.5.1 Vertically Propagating Kelvin Waves |
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436 | (1) |
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12.5.2 Vertically Propagating Rossby-Gravity Waves |
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437 | (1) |
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12.5.3 Observed Equatorial Waves |
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438 | (2) |
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12.6 The Quasi-Biennial Oscillation |
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440 | (6) |
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12.7 Trace Constituent Transport |
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446 | (7) |
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446 | (1) |
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447 | (1) |
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12.7.3 Transport in the Stratosphere |
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448 | (2) |
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450 | (1) |
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450 | (2) |
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452 | (1) |
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13 Numerical Modeling and Prediction |
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13.1 Historical Background |
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453 | (2) |
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13.2 Numerical Approximation of the Equations of Motion |
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455 | (9) |
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13.2.1 Finite Differences |
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455 | (2) |
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13.2.2 Centered Differences: Explicit Time Differencing |
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457 | (1) |
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13.2.3 Computational Stability |
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458 | (2) |
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13.2.4 Implicit Time Differencing |
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460 | (2) |
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13.2.5 The Semi-Lagrangian Integration Method |
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462 | (1) |
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463 | (1) |
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13.3 The Barotropic Vorticity Equation in Finite Differences |
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464 | (3) |
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467 | (5) |
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13.4.1 The Barotropic Vorticity Equation in Spherical Coordinates |
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468 | (2) |
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13.4.2 Rossby-Haurwitz Waves |
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470 | (1) |
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13.4.3 The Spectral Transform Method |
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471 | (1) |
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13.5 Primitive Equation Models |
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472 | (3) |
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473 | (1) |
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13.5.2 Physical Parameterizations |
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474 | (1) |
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475 | (6) |
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13.6.1 Data Assimilation for a Single Variable |
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476 | (3) |
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13.6.2 Data Assimilation for Many Variables |
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479 | (2) |
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13.7 Predictability and Ensemble Forecasting |
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481 | (10) |
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486 | (1) |
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487 | (1) |
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488 | (3) |
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A Useful Constants and Parameters |
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491 | (2) |
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493 | (6) |
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499 | (1) |
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499 | (1) |
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C.3 Vector Operations in Various Coordinate Systems |
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500 | (3) |
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D.1 Equivalent Potential Temperature |
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503 | (1) |
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D.2 Pseudoadiabatic Lapse Rate |
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504 | (3) |
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E Standard Atmosphere Data |
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507 | (2) |
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F Symmetric Baroclinic Oscillations |
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509 | (2) |
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G Conditional Probability and Likelihood |
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511 | (2) |
Bibliography |
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513 | (6) |
Index |
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519 | |