Contents 6
Preface 12
1. Introduction 14
1.1 THE ATMOSPHERIC CONTINUUM 14
1.2 PHYSICAL DIMENSIONS AND UNITS 15
1.3 SCALE ANALYSIS 17
1.4 FUNDAMENTAL FORCES 17
1.4.1 Pressure Gradient Force 18
1.4.2 Gravitational Force 20
1.4.3 Viscous Force 21
1.5 NONINERTIALREFERENCEFRAMESAND\u201cAPPARENT\u201d FORCES 23
1.5.1 Centripetal Acceleration and Centrifugal Force 24
1.5.2 Gravity Force 25
1.5.3 The Coriolis Force and the Curvature Effect 27
1.5.4 Constant Angular Momentum Oscillations 32
1.6 STRUCTURE OF THE STATIC ATMOSPHERE 32
1.6.1 The Hydrostatic Equation 33
1.6.2 Pressure as a Vertical Coordinate 34
1.6.3 A Generalized Vertical Coordinate 36
PROBLEMS 1 37
MATLAB EXERCISES 1 39
Suggested References 1 40
2. Basic Conservation Laws 41
2.1 TOTAL DIFFERENTIATION 42
2.1.1 Total Differentiation of a Vector in a Rotating System 44
2.2 THE VECTORIAL FORM OF THE MOMENTUM EQUATION IN ROTATING COORDINATES 46
2.3 COMPONENT EQUATIONS IN SPHERICAL COORDINATES 47
2.4 SCALE ANALYSIS OF THE EQUATIONS OF MOTION 51
2.4.1 Geostrophic Approximation and GeostrophicWind 53
2.4.2 Approximate Prognostic Equations; the Rossby Number 53
2.4.3 The Hydrostatic Approximation 54
2.5 THE CONTINUITY EQUATION 55
2.5.1 An Eulerian Derivation 56
2.5.2 A Lagrangian Derivation 57
2.5.3 Scale Analysis of the Continuity Equation 58
2.6 THE THERMODYNAMIC ENERGY EQUATION 59
2.7 THERMODYNAMICS OF THE DRY ATMOSPHERE 62
2.7.1 Potential Temperature 63
2.7.2 The Adiabatic Lapse Rate 64
2.7.3 Static Stability 64
2.7.4 Scale Analysis of the Thermodynamic Energy Equation 66
PROBLEMS 2 67
MATLAB EXERCISES 2 68
Suggested References 2 69
3. Elementary Applications of the Basic Equations 70
3.1 BASIC EQUATIONS IN ISOBARIC COORDINATES 70
3.1.1 The Horizontal Momentum Equation 70
3.1.2 The Continuity Equation 71
3.1.3 The Thermodynamic Energy Equation 72
3.2 BALANCED FLOW 73
3.2.1 Natural Coordinates 73
3.2.2 Geostrophic Flow 75
3.2.3 Inertial Flow 75
3.2.4 Cyclostrophic Flow 76
3.2.5 The GradientWind Approximation 78
3.3 TRAJECTORIES AND STREAMLINES 81
3.4 THE THERMAL WIND 83
3.4.1 Barotropic and Baroclinic Atmospheres 87
3.5 VERTICAL MOTION 88
3.5.1 The Kinematic Method 89
3.5.2 The Adiabatic Method 90
3.6 SURFACE PRESSURE TENDENCY 90
PROBLEMS 3 92
MATLAB EXERCISES 3 96
4. Circulation and Vorticity 99
4.1 THE CIRCULATION THEOREM 99
4.2 VORTICITY 104
4.2.1 Vorticity in Natural Coordinates 106
4.3 POTENTIAL VORTICITY 108
4.4 THE VORTICITY EQUATION 113
4.4.1 Cartesian Coordinate Form 114
4.4.2 The Vorticity Equation in Isobaric Coordinates 116
4.4.3 Scale Analysis of the Vorticity Equation 116
4.5 VORTICITY IN BAROTROPIC FLUIDS 119
4.5.1 The Barotropic (Rossby) Potential Vorticity Equation 120
4.5.2 The Barotropic Vorticity Equation 121
4.6 THEBAROCLINIC (ERTEL) POTENTIALVORTICITYEQUATION 121
4.6.1 Equations of Motion in Isentropic Coordinates 122
4.6.2 The Potential Vorticity Equation 123
4.6.3 Integral Constraints on Isentropic Vorticity 123
PROBLEMS 4 124
MATLAB EXERCISES 4 126
Suggested References 4 127
5. The Planetary Boundary Layer 128
5.1 ATMOSPHERIC TURBULENCE 129
5.1.1 The Boussinesq Approximation 130
5.1.2 Reynolds Averaging 131
5.2 TURBULENT KINETIC ENERGY 133
5.3 PLANETARY BOUNDARY LAYER MOMENTUM EQUATIONS 135
5.3.1 Well-Mixed Boundary Layer 136
5.3.2 The Flux\u2013Gradient Theory 137
5.3.3 The Mixing Length Hypothesis 139
5.3.4 The Ekman Layer 140
5.3.5 The Surface Layer 142
5.3.6 The Modified Ekman Layer 143
5.4 SECONDARY CIRCULATIONS AND SPIN DOWN 144
PROBLEMS 5 149
MATLAB EXERCISES 5 150
Suggested References 5 151
6. Synoptic-Scale Motions I: Quasi- Geostrophic Analysis 152
6.1 THE OBSERVED STRUCTURE OF EXTRATROPICAL CIRCULATIONS 153
6.2 THE QUASI-GEOSTROPHIC APPROXIMATION 159
6.2.1 Scale Analysis in Isobaric Coordinates 160
6.2.2 The Quasi-Geostrophic Vorticity Equation 164
6.3 QUASI-GEOSTROPHIC PREDICTION 168
6.3.1 Geopotential Tendency 170
6.3.2 The Quasi-Geostrophic Potential Vorticity Equation 172
6.3.3 Potential Vorticity Inversion 174
6.3.4 Vertical Coupling Through Potential Vorticity 175
6.4 DIAGNOSIS OF THE VERTICAL MOTION 177
6.4.1 The Traditional Omega Equation 177
6.4.2 The Q Vector 181
6.4.3 The Ageostrophic Circulation 185
6.5 IDEALIZED MODEL OF A BAROCLINIC DISTURBANCE 187
PROBLEMS 6 189
MATLAB EXERCISES 6 191
Suggested References 6 193
7. Atmospheric Oscillations: Linear Perturbation Theory 195
7.1 THE PERTURBATION METHOD 196
7.2 PROPERTIES OFWAVES 196
7.2.1 Fourier Series 198
7.2.2 Dispersion and Group Velocity 199
7.3 SIMPLEWAVE TYPES 201
7.3.1 Acoustic or SoundWaves 202
7.3.2 ShallowWater GravityWaves 205
7.4 INTERNAL GRAVITY (BUOYANCY) WAVES 209
7.4.1 Pure Internal GravityWaves 209
7.4.2 TopographicWaves 214
7.5 GRAVITYWAVES MODIFIED BY ROTATION 217
7.5.1 Pure Inertial Oscillations 217
7.5.2 Inertia\u2013GravityWaves 219
7.6 ADJUSTMENT TO GEOSTROPHIC BALANCE 221
7.7 ROSSBYWAVES 226
7.7.1 Free Barotropic RossbyWaves 228
7.7.2 Forced Topographic RossbyWaves 230
PROBLEMS 7 233
MATLAB EXERCISES 7 237
Suggested References 7 239
8. Synoptic-Scale Motions II: Baroclinic Instability 241
8.1 HYDRODYNAMIC INSTABILITY 242
8.2 NORMAL MODE BAROCLINIC INSTABILITY: A TWO-LAYER MODEL 243
8.2.1 Linear Perturbation Analysis 245
8.2.2 Vertical Motion in BaroclinicWaves 251
8.3 THE ENERGETICS OF BAROCLINICWAVES 255
8.3.1 Available Potential Energy 255
8.3.2 Energy Equations for the Two-Layer Model 258
8.4 BAROCLINIC INSTABILITY OFA CONTINUOUSLY STRATIFIED ATMOSPHERE 263
8.4.1 Log-Pressure Coordinates 264
8.4.2 Baroclinic Instability: The Rayleigh Theorem 266
8.4.3 The Eady Stability Problem 270
8.5 GROWTHAND PROPAGATION OF NEUTRAL MODES 273
8.5.1 Transient Growth of NeutralWaves 273
8.5.2 Downstream Development 276
PROBLEMS 8 277
MATLAB EXERCISES 8 279
Suggested References 8 280
9. Mesoscale Circulations 281
9.1 ENERGY SOURCES FOR MESOSCALE CIRCULATIONS 282
9.2 FRONTS AND FRONTOGENESIS 282
9.2.1 The Kinematics of Frontogenesis 283
9.2.2 Semigeostrophic Theory 287
9.2.3 Cross-Frontal Circulation 290
9.3 SYMMETRIC BAROCLINIC INSTABILITY 292
9.4 MOUNTAINWAVES 297
9.4.1 Flow over Isolated Ridges 297
9.4.2 LeeWaves 298
9.4.3 DownslopeWindstorms 299
9.5 CUMULUS CONVECTION 302
9.5.1 Equivalent Potential Temperature 303
9.5.2 The Pseudoadiabatic Lapse Rate 304
9.5.3 Conditional Instability 305
9.5.4 Convective Available Potential Energy (CAPE) 308
9.5.5 Entrainment 309
9.6 CONVECTIVE STORMS 311
9.6.1 Development of Rotation in Supercell Thunderstorms 312
9.6.2 The Right-Moving Storm 315
9.7 HURRICANES 317
9.7.1 Dynamics of Mature Hurricanes 318
9.7.2 Hurricane Development 320
PROBLEMS 9 322
MATLAB EXERCISES 9 323
Suggested References 9 324
10. The General Circulation 326
10.1 THE NATURE OF THE PROBLEM 327
10.2 THE ZONALLY AVERAGED CIRCULATION 329
10.2.1 The Conventional Eulerian Mean 331
10.2.2 The Transformed Eulerian Mean (TEM) 338
10.2.3 The Zonal-Mean Potential Vorticity Equation 340
10.3 THE ANGULAR MOMENTUM BUDGET 342
10.3.1 Sigma Coordinates 344
10.3.2 The Zonal-Mean Angular Momentum 346
10.4 THE LORENZ ENERGY CYCLE 350
10.5 LONGITUDINALLY DEPENDENT TIME-AVERAGED FLOW 356
10.5.1 Stationary RossbyWaves 357
10.5.2 Jetstream and Storm Tracks 360
10.6 LOW-FREQUENCY VARIABILITY 362
10.6.1 Climate Regimes 362
10.6.2 Annular Modes 365
10.6.3 Sea Surface Temperature Anomalies 366
10.7 LABORATORYSIMULATIONOFTHEGENERALCIRCULATION 367
10.8 NUMERICAL SIMULATION OF THE GENERAL CIRCULATION 373
10.8.1 The Development of AGCMs 373
10.8.2 Dynamical Formulation 374
10.8.3 Physical Processes and Parameterizations 375
10.8.4 The NCAR Climate System Model 378
PROBLEMS 10 379
MATLAB EXERCISES 10 381
Suggested References 10 382
11. Tropical Dynamics 383
11.1 THE OBSERVED STRUCTURE OF LARGE-SCALE TROPICAL CIRCULATIONS 384
11.1.1 The Intertropical Convergence Zone 384
11.1.2 EquatorialWave Disturbances 387
11.1.3 AfricanWave Disturbances 390
11.1.4 Tropical Monsoons 393
11.1.5 TheWalker Circulation 395
11.1.6 El Ni 藴 no and the Southern Oscillation 396
11.1.7 Equatorial Intraseasonal Oscillation 398
11.2 SCALE ANALYSIS OF LARGE-SCALE TROPICAL MOTIONS 400
11.3 CONDENSATION HEATING 404
11.4 EQUATORIALWAVE THEORY 407
11.4.1 Equatorial Rossby and Rossby\u2013Gravity Modes 408
11.4.2 Equatorial KelvinWaves 411
11.5 STEADY FORCED EQUATORIAL MOTIONS 413
PROBLEMS 11 416
MATLAB EXERCISES 11 417
Suggested References 11 419
12. Middle Atmosphere Dynamics 420
12.1 STRUCTURE AND CIRCULATION OF THE MIDDLE ATMOSPHERE 421
12.2 THE ZONAL-MEAN CIRCULATION OF THE MIDDLE ATMOSPHERE 424
12.2.1 Lagrangian Motion of Air Parcels 426
12.2.2 The Transformed Eulerian Mean 428
12.2.3 Zonal-Mean Transport 432
12.3 VERTICALLY PROPAGATING PLANETARYWAVES 434
12.3.1 Linear RossbyWaves 434
12.3.2 RossbyWavebreaking 435
12.4 SUDDEN STRATOSPHERICWARMINGS 437
12.5 WAVES IN THE EQUATORIAL STRATOSPHERE 442
12.5.1 Vertically Propagating KelvinWaves 444
12.5.2 Vertically Propagating Rossby\u2013GravityWaves 444
12.5.3 Observed EquatorialWaves 446
12.6 THE QUASI-BIENNIAL OSCILLATION 448
12.7 TRACE CONSTITUENT TRANSPORT 453
12.7.1 Dynamical Tracers 453
12.7.2 Chemical Tracers 455
12.7.3 Transport in the Stratosphere 456
PROBLEMS 12 458
MATLAB EXERCISES 12 459
Suggested References 12 460
13. Numerical Modeling and Prediction 461
13.1 HISTORICAL BACKGROUND 462
13.2 FILTERING METEOROLOGICAL NOISE 463
13.3 NUMERICAL APPROXIMATION OF THE EQUATIONS OF MOTION 465
13.3.1 Finite Differences 465
13.3.2 Centered Differences: Explicit Time Differencing 467
13.3.3 Computational Stability 468
13.3.4 Implicit Time Differencing 471
13.3.5 The Semi-Lagrangian Integration Method 472
13.3.6 Truncation Error 473
13.4 THE BAROTROPIC VORTICITY EQUATION IN FINITE DIFFERENCES 475
13.5 THE SPECTRAL METHOD 477
13.5.1 The Barotropic Vorticity Equation in Spherical Coordinates 478
13.5.2 Rossby\u2013HaurwitzWaves 480
13.5.3 The Spectral Transform Method 481
13.6 PRIMITIVE EQUATION MODELS 483
13.6.1 The Ecmwf Grid Point Model 483
13.6.2 Spectral Models 485
13.6.3 Physical Parameterizations 487
13.7 DATA ASSIMILATION 488
13.7.1 The Initialization Problem 488
13.7.2 Nonlinear Normal Mode Initialization 490
13.7.3 Four-Dimensional Data Assimilation 492
13.8 PREDICTABILITY AND ENSEMBLE PREDICTION SYSTEMS 494
PROBLEMS 13 498
MATLAB EXERCISES 13 500
Suggested References 13 503
Appendix A: Useful Constants and Parameters 504
Appendix B: List of Symbols 506
Appendix C: Vector Analysis 511
C.1 VECTOR IDENTITIES 511
C.2 INTEGRAL THEOREMS 512
C.3 VECTOR OPERATIONS IN VARIOUS COORDINATE SYSTEMS 512
Appendix D: Moisture Variables 514
D.1 EQUIVALENT POTENTIAL TEMPERATURE 514
D.2 PSEUDOADIABATIC LAPSE RATE 516
Appendix E: Standard Atmosphere Data 517
Appendix F: Symmetric Baroclinic Oscillations 519