The Earth's Atmosphere (eBook)

Preface 7
Contents 9
About the Book and the Author 19
Guide to Systems of Numbering Diagrams and Equations in Text and Appendices 21
Text 21
Appendices 21
Part I Physics of the Earth’s Atmosphere 23
The Sun and the Earth – The Solar System and the Earth’s Gravitation 24
1.1 Introduction 24
1.2 Earth’s Gravitational Force – Gravity 25
1.3 Geopotential Surfaces 27
1.4 Motion in the Earth’s Gravitational Field – The Law of Central Forces 27
The Earth’s Atmosphere – Its Origin, Composition and Properties 30
2.1 Introduction: Origin of the Earth’s Atmosphere 30
2.2 Composition of the Atmosphere 31
2.3 Properties and Variables of the Atmosphere 33
2.4 Gas Laws – Equations of State 44
Heat and Thermodynamics of the Atmosphere 48
3.1 Introduction. The Nature of Heat and Kinetic Theory 48
3.2 The First Law of Thermodynamics 48
3.3 Specific Heats of Gases 49
3.4 Adiabatic Changes in the Atmosphere 51
3.5 The Concept of Entropy 54
3.6 The Second Law of Thermodynamics 57
3.7 Thermodynamic Equilibrium of Systems: Thermodynamic Potentials 61
3.8 The Third Law of Thermodynamics 62
3.9 The Atmosphere as a Heat Engine 63
Water Vapour in the Atmosphere: Thermodynamics of Moist Air 64
4.1 Introduction 64
4.2 Humidity of the Air – Definitions 65
4.3 Density of Moist Air – Virtual Temperature 66
4.4 Measurement of Humidity – Hygrometers/Psychrometers 67
4.5 Ascent of Moist Air in the Atmosphere – Pseudo-Adiabatic Process 69
4.6 Saturated Adiabatic Lapse Rate of Temperature 71
4.7 Equivalent Potential Temperature 71
4.8 Variation of Saturation Vapour Pressure with Temperature 72
4.9 Co-existence of the Three Phases ofWater – the Triple Point 74
4.10 Stability of Moist Air 76
Physics of Cloud and Precipitation 80
5.1 Introduction – Historical Perspective 80
5.2 Cloud-Making in the Laboratory – Condensation Nuclei 81
5.3 Atmospheric Nuclei – Cloud Formation in the Atmosphere 83
5.4 Drop-Size Distribution in Clouds 85
5.5 Rate of Fall of Cloud and Rain Drops 86
5.6 Supercooled Clouds and Ice-Particles – Sublimation 87
5.7 Clouds in the Sky: Types and Classification 89
5.8 From Cloud to Rain 89
5.9 Meteorological Evidence – Rainfall from Cold andWarm Clouds 96
5.10 Climatological Rainfall Distribution over the Globe 97
Physics of Radiation – Fundamental Laws 100
6.1 Introduction – the Nature of Thermal Radiation 100
6.2 Radiation and Absorption – Heat Exchanges 100
6.3 Properties of Radiation 102
6.4 Laws of Radiation – Emission and Absorption 103
6.5 Spectral Distribution of Radiant Energy 107
6.6 Some Practical Uses of Electromagnetic Radiation 109
The Sun and its Radiation 110
7.1 Introduction 110
7.2 Physical Characteristics of the Sun 111
7.3 Structure of the Sun – its Interior 111
7.4 The Photosphere 115
7.5 The Solar Atmosphere 116
7.6 The Solar Wind 118
7.7 The Search for Neutrinos 119
The Incoming Solar Radiation – Interaction with the Earth’s Atmosphere and Surface 120
8.1 Introduction – the Solar Spectrum 120
8.2 Interactions with the Upper Atmosphere (Above 80 km) 121
8.3 The Mesosphere (50–80km Layer) 123
8.4 Interaction with Ozone: the Ozonosphere (20–50 km) 123
8.5 Scattering, Reflection and Absorption of Solar Radiation in the Atmosphere 128
8.6 Incoming Solar Radiation (Insolation) at the Earth’s Surface 129
8.7 Reflection of Solar Radiation at the Earth’s Surface – The Albedo 134
Heat Balance of the Earth’s Surface – Upward and Downward Transfer of Heat 136
9.1 Introduction: General Considerations 136
9.2 Heat Balance on a PlanetWithout an Atmosphere 137
9.3 Heat Balance on a Planet with an Atmosphere: The Greenhouse Effect 138
9.4 Vertical Transfer of Radiative Heating – Diurnal TemperatureWave 140
9.5 Sensible Heat Flux 141
9.6 Evaporation and Evaporative Heat Flux from a Surface 144
9.7 Exchange of Heat Between the Earth’s Surface and the Underground Soil 146
9.8 Radiative Heat Flux into the Ocean 150
9.9 The Thermohaline Circulation – Buoyancy Flux 155
9.10 Photosynthesis in the Ocean: Chemical and Biological Processes 156
Heat Balance of the Earth-Atmosphere System – Heat Sources and Sinks 158
10.1 Introduction – definition of heat sources and sinks 158
10.2 Physical Processes Involved in Heat Balance 159
10.3 Simpson’s Computation of Heat Budget 160
10.4 Heat Balance from Satellite Radiation Data 162
10.5 Heat Sources and Sinks from the Energy Balance Equation 166
10.6 Computation of Atmospheric Heating from Mass Continuity Equation 170
Part II Dynamics of the Earth’s Atmosphere – The General Circulation 174
Winds on a Rotating Earth – The Dynamical Equations and the Conservation Laws 176
11.1 Introduction 176
11.2 Forces Acting on a Parcel of Air 177
11.3 Acceleration of Absolute Motion 179
11.4 Acceleration of Relative Motion 180
11.5 The Equations of Motion in a Rectangular Co- ordinate System 183
11.6 A System of Generalized Vertical Co-ordinates 183
11.7 The Equations of Motion in Spherical Co-ordinate System 185
11.8 The Equation of Continuity 188
11.9 The Thermodynamic Energy Equation 189
11.10 Scale Analysis and Simplification of the Equations of Motion 190
Simplified Equations of Motion – Quasi- Balanced Winds 194
12.1 Introduction 194
12.2 The Basic Equations in Isobaric Co-ordinates 194
12.3 Balanced Flow in Natural Co-ordinates 196
12.4 Trajectories and Streamlines 201
12.5 Streamline-Isotach Analysis 203
12.6 Variation of Wind with Height – The ThermalWind 204
Circulation, Vorticity and Divergence 208
13.1 Definitions and Concepts – Circulation and Vorticity 208
13.2 The Circulation Theorem 209
13.3 Absolute and Relative Vorticity 212
13.4 Vorticity and Divergence in Natural Co-ordinates 212
13.5 Potential Vorticity 214
13.6 The Vorticity Equation in Frictionless Adiabatic Flow 217
13.7 The Vorticity Equation from the Equations of Motion 217
13.8 Circulation and Vorticity in the Real Atmosphere ( In Three Dimensions) 220
13.9 Vertical Motion in the Atmosphere 221
13.10 Differential Properties of aWind Field 223
13.11 Types of Wind Fields – Graphical Representation 226
The Boundary Layers of the Atmosphere and the Ocean 228
14.1 Introduction 228
14.2 The Equations of Turbulent Motion in the Atmosphere 229
14.3 The Mixing-Length Hypothesis – Exchange Co-efficients 232
14.4 The Vertical Structure of the Frictionally-Controlled Boundary Layer 233
14.5 The Secondary Circulation – The Spin-Down Effect 238
14.6 The Boundary Layer of the Ocean – Ekman Drift and Mass Transport 243
14.7 Ekman Pumping and Coastal Upwelling in the Ocean 245
Waves and Oscillations in the Atmosphere and the Ocean 248
15.1 Introduction 248
15.2 The Simple Pendulum 249
15.3 Representation of Waves by Fourier Series 250
15.4 Dispersion of Waves and Group Velocity 251
15.5 The Perturbation Technique 252
15.6 SimpleWave Types 253
15.7 Internal Gravity (or Buoyancy) Waves in the Atmosphere 260
15.8 Dynamics of Shallow Water Gravity Waves 265
Equatorial Waves and Oscillations 274
16.1 Introduction 274
16.2 The Governing Equations in Log-Pressure Co- ordinate System 275
16.3 The Kelvin Wave 276
16.4 The Mixed Rossby-Gravity Wave 278
16.5 Observational Evidence 280
16.6 The Quasi-Biennial Oscillation (QBO) 281
16.7 The Madden-Julian Oscillation (MJO) 283
16.8 El Nino-Southern Oscillation (ENSO) 287
Dynamical Models and Numerical Weather Prediction ( N. W. P.) 296
17.1 Introduction – Historical Background 296
17.2 The Filtering of Sound and Gravity Waves 297
17.3 Quasi-Geostrophic Models 299
17.4 Nondivergent Models 300
17.5 Hierarchy of Simplified Models 303
17.6 Primitive Equation Models 305
17.7 Present Status of NWP 311
Dynamical Instability of Atmospheric Flows – Energetics and Energy Conversions 314
18.1 Introduction 314
18.2 Inertial Instability 315
18.3 Baroclinic Instability 316
18.4 Vertical Motion in Baroclinically UnstableWaves 321
18.5 Energetics and Energy Conversions in Baroclinic Instability 323
18.6 Barotropic Instability 327
18.7 Conditional Instability of the Second Kind (CISK) 329
The General Circulation of the Atmosphere 332
19.1 Introduction – Historical Background 332
19.2 Zonally-Averaged Mean Temperature and Wind Fields Over the Globe 334
19.3 Observed Distributions of Mean Winds (Streamlines) and Circulations Over the Globe During Winter and Summer 338
19.4 Maintenance of the Kinetic Energy and Angular Momentum of the General Circulation 340
19.5 Eddy-Transports 345
19.6 Laboratory Simulation of the General Circulation 348
19.7 Numerical Experiment on the General Circulation 352
Appendices 354
Appendix-1(A) Vector Analysis-Some Important Vector Relations 1.1 The Concept of a Vector 354
1.2 Addition and Subtraction of Vectors: Multiplication of a Vector by a Scalar 355
1.3 Multiplication of Vectors 356
1.4 Differentiation of Vectors: Application to the Theory of Space Curves 358
1.5 Space Derivative of a Scalar Quantity. The Concept of a Gradient Vector 359
1.6 Del Operator, 360
1.7 Use of Del Operator in Different Co-ordinate Systems 361
x, y, z) 361
Appendix-1(B) Motion Under Earth’s Gravitational Force 362
Appendix-2 Adiabatic Propagation of SoundWaves 363
Appendix-3 Some Selected Thermodynamic Diagrams 364
Appendix-4 Derivation of the Equation for Saturation Vapour Pressure Curve Taking into Account the Temperature Dependence of the Specific Heats ( Joos and Freeman ( 1967)) 365
Appendix-5 Theoretical Derivation of Kelvin’s Vapour Pressure 367
Relation for 367
Appendix-6 Values of Thermal Conductivity Constants for a Few Materials, Drawn from Sources, Including ‘ International Critical Tables’( 1927), ‘ Smithsonian Physical Tables’ ( 1934), ‘ Landholt- Bornstein’ ( 1923 – 1936), ‘ McAdams’ ( 1942) and others 369
Appendix-7 Physical Units and Dimensions 370
Appendix-8 Some Useful Physical Constants and Parameters 371
References 374
Author Index 380
Subject Index 384