Basics of
Atmospheric Science

A. Chandrasekar
Senior Professor and Head
Department of Earth and Space Sciences
Indian Institute of Space Science and Technology
Thiruvananthapuram

PHI Learning Private Limited
New Delhi-110001
2010


BASICS OF ATMOSPHERIC SCIENCE
A. Chandrasekar
© 2010 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book may
be reproduced in any form, by mimeograph or any other means, without permission in writing from
the publisher.
ISBN-978-81-203-4022-0
The export rights of this book are vested solely with the publisher.
Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,
New Delhi-110001 and Printed by Mohan Makhijani at Rekha Printers Private Limited,
New Delhi-110020.


In memory of
My respected teacher
Padmashri (Late) Professor R. Ananthakrishnan
Former Director, Institute of Tropical Meteorology, Pune

Contents

Foreword
Preface

................................................................................................................................. xv
.............................................................................................................................. xvii

1. Introductory Survey of the Atmosphere .................................................. 1–15
1.1
1.2
1.3
1.4
1.5

Introduction
1
Origin and Composition of the Atmosphere
2
Distribution of Pressure and Density
4
Ionosphere, Atmospheric Electric Field and Magnetosphere
Distribution of Temperature and Winds
8
1.5.1
Distribution of Temperature
8
1.5.2

Distribution of Winds
11
1.6 Atmosphere as a Fluid and Fluid Continuum
13
1.7 Physical Laws
13
1.8 Determinism and Chaos
14
Review Questions
15

2.

6

Atmospheric Observations...................................................................... 16–34
2.1
2.2
2.3
2.4
2.5

Overview and Importance of Meteorological Observation
Measurement of Temperature and Humidity
18
2.2.1
Temperature Measurement
18
2.2.2
Humidity Measurement

21
Measurement of Wind and Pressure
22
2.3.1
Wind Measurement
22
2.3.2
Atmospheric Pressure Measurement
24
Measurement of Precipitation
25
Modern Meteorological Instruments
26
v

17


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CONTENTS

2.6

Surface and Upper Air Observational Network
27
2.6.1
Surface Observational Network

27
2.6.2
Radar Network
28
2.6.3
Upper Air Observational Network
28
2.7 Satellite Observation
31
Review Questions
33

3.

Atmospheric Thermodynamics .............................................................. 35–75
3.1
3.2

3.3
3.4

3.5

3.6

3.7

3.8

Gas Laws and Equation of State for a Mixture of Ideal Gases

36
3.1.1
Mixture of Gases
37
Work, Heat and First Law of Thermodynamics
38
3.2.1
Work
38
3.2.2
Work Done by a System Expanding against External Forces
3.2.3
Heat
41
3.2.4
First Law of Thermodynamics
41
3.2.5
Internal Energy and Enthalpy
42
3.2.6
Specific Heat Capacity
44
Adiabatic Processes
46
Moist Thermodynamics and Latent Heats
47
3.4.1
Measures of Water Vapour in Air
47

3.4.2
Equation of State of Moist Air
48
3.4.3
Latent Heat
49
Hydrostatic Equilibrium
49
3.5.1
Geopotential
50
3.5.2
Scale Height and Height Computations Using the
Hypsometric Equation
51
3.5.3
Reduction of Pressure to Sea Level
54
Thermodynamic Diagram
55
3.6.1
Emagram
55
3.6.2
Tephigram
55
3.6.3
Skew T–log p Diagram
56
3.6.4

Stuve Diagram
56
Hydrodynamic Stability—Parcel and Slice Methods
56
3.7.1
Saturated Adiabatic and Pseudoadiabatic Processes
56
3.7.2
Saturated Adiabatic Lapse Rate
57
3.7.3
Equivalent Potential Temperature
57
3.7.4
Stability Criteria Using Parcel Method
59
3.7.5
Stability Criteria Using Slice Method
63
3.7.6
Entrainment Effects
65
Entropy and Second Law of Thermodynamics
67
3.8.1
Entropy
67
3.8.2
Second Law of Thermodynamics
68

3.8.3
Heat Engines and Refrigeration Cycles
69

39


CONTENTS

3.9

Carnot Cycle and Clausius Clapeyron Equation
3.9.1
Carnot Cycle
70
3.9.2
Clausius Clapeyron Equation
71
Solved Examples
72
Review Questions
74

4.

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70


Radiation ................................................................................................ 76–104
4.1

Spectrum of Radiation
76
4.1.1
Overview
77
4.1.2
Electromagnetic Spectrum of Radiation
78
4.2 Black Body Radiation
78
4.2.1
Planck’s Law
79
4.2.2
Local Thermodynamical Equilibrium
81
4.2.3
Radiometric Quantities
82
4.3 Atmospheric Absorption of Solar Radiation
85
4.3.1
Absorption and Emission of Radiation by Molecules
4.3.2
Absorptivity and Emissivity
85

4.3.3
Kirchhoff’s Law
87
4.3.4
Reflectivity and Transmittivity
87
4.3.5
Absorption of Solar Radiation by Atmosphere
87
4.3.6
Indirect Estimate of Solar Irradiance at the Top of the
Atmosphere
89
4.3.7
Vertical Profile of Absorption
90
4.4 Scattering of Solar Radiation
91
4.5 Atmospheric Absorption and Emission of Infrared Radiation
4.6 Remote Temperature Sounding from Space
94
4.6.1
Calculation of the Surface Temperature
95
4.6.2
Two-layer Atmospheric Temperature Profile
96
4.6.3
Multi-layer Atmospheric Temperature Profile
97

Solved Examples
100
Review Questions
103

5.

85

92

Clouds and Precipitation ..................................................................... 105–148
5.1
5.2

5.3

Atmospheric Aerosols
105
5.1.1
Aerosol Size and Concentration
106
5.1.2
Sources and Sinks of Atmospheric Aerosol
108
Nucleation of Water Vapour Condensation
109
5.2.1
Thermodynamic Potentials
109

5.2.2
Nucleation Theory of Water Vapour Condensation
5.2.3
Cloud Condensation Nuclei
117
Droplet Growth in Warm Clouds
118
5.3.1
Overview
118
5.3.2
Growth of Cloud Droplets in Warm Clouds
by Condensation
119

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5.3.3
Growth of Cloud Droplets by Collision and Coalescence
5.3.4
The Continuous Collision Model
124
5.3.5

The Stochastic Collision Model
126
5.4 Formation and Growth of Ice Crystals in Cold Clouds
127
5.4.1
Homogeneous Nucleation of Ice Particles
127
5.4.2
Ice Nuclei
128
5.4.3
Bergeron Process
128
5.4.4
Growth Rate of Ice Crystals by Deposition
129
5.4.5
Hail Formation
130
5.4.6
Radiative Effects of Clouds
131
5.5 Mechanisms of Cloud Formation and Cloud Seeding
132
5.5.1
Mechanisms of Cloud Formation
132
5.5.2
Types of Clouds
133

5.5.3
Convective Clouds
135
5.5.4
Cloud Seeding
137
5.6 Role of Clouds and Precipitation Products in Charge Separation
5.6.1
Distribution of Charges in a Thunderstorm
138
5.6.2
Mechanisms for Charge Separation
139
5.6.3
Lightning Discharge
141
Solved Examples
142
Review Questions
147

6.

122

138

Governing Laws of Atmospheric Motion .......................................... 149–186
6.1


6.2

6.3

Equation in a Rotating Coordinate System—Centripetal and
Coriolis Acceleration
150
6.1.1
Introduction
150
6.1.2
Rotating Frame of Reference
151
6.1.3
Equation of Motion in an Inertial Frame of Reference
153
Gravity and Pressure Gradient Forces
154
6.2.1
Pressure Gradient Force
154
6.2.2
Gravitational Force
155
6.2.3
Equation of Motion in a Rotating Coordinate System
155
6.2.4
Effects of Coriolis Force
156

6.2.5
Flow of Rivers on the Surface of the Earth
156
6.2.6
Effects of Coriolis Force Due to Relative Motion
along a Latitude Circle
157
6.2.7
Effects of Coriolis Force Due to Relative Motion
along a Meridian
158
6.2.8
Effects of Coriolis Force Due to Vertical Motion
159
6.2.9
Rossby Number
159
6.2.10 Gravity
160
Total, Local and Convective Derivatives
161


CONTENTS

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6.4


Continuity Equation
162
6.4.1
Eulerian Approach
162
6.4.2
Lagrangian Approach
164
6.5 Equations of Motion and Equations for Horizontal Flow
165
6.5.1
Equations of Motion in Spherical Coordinates
165
6.5.2
Scale Analysis of the Equations of Motion
167
6.5.3
f-plane and b-plane Approximations
168
6.5.4
Geostrophic Wind
169
6.5.5
Isallobaric Wind
170
6.5.6
Natural Coordinate System
170
6.5.7

Inertial Flow
172
6.5.8
Cyclostrophic Flow
173
6.5.9
Gradient Flow
174
6.6 Thermal Wind
176
6.7 Thermodynamic Energy Equation
178
Solved Examples
180
Review Questions
185

7.

Atmospheric Motion ............................................................................ 187–213
7.1

Circulation and Vorticity
188
7.1.1
Vorticity
188
7.1.2
Decomposition of a Linear Velocity Field
188

7.1.3
Circulation
190
7.1.4
Kelvin’s Circulation Theorem
192
7.1.5
Bjerknes’ Circulation Theorem
193
7.1.6
Applications of Circulation Theorem
194
7.1.7
Vorticity in the Natural Coordinate System
195
7.2 Isobaric Coordinate System
196
7.2.1
Horizontal and Time Derivates in Isobaric
Coordinate System
197
7.2.2
Continuity Equation in Isobaric Coordinate System
7.2.3
Horizontal Equation of Motion in Isobaric
Coordinate System
200
7.2.4
Geostrophic and Thermal Wind Equations in
Isobaric Coordinates

200
7.3 Vorticity and Divergence Equations
201
7.3.1
Vorticity Equation
201
7.3.2
Divergence Equation
203
7.4 Absolute and Potential Vorticity
203
7.4.1
Absolute Vorticity
204
7.4.2
Potential Vorticity
204
Solved Examples
207
Review Questions
212

199


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8.


CONTENTS

Atmospheric Boundary Layer ............................................................ 214–238
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9

Brief Consideration
214
Definition of Viscosity
214
Expression for Viscosity from Kinetic Theory
215
Viscous Forces in the Equation of Motion
217
Turbulence
219
Turbulence and Diffusion
220
Equations of Mean Motion in Turbulent Flow
221
Mixing Length
223

Surface and Ekman Layers
225
8.9.1
Surface Layer
225
8.9.2
Ekman Layer
227
8.10 Secondary Circulations and Spin-down in the Atmosphere
8.11 Secondary Circulations and Spin-down in a Teacup
231
Solved Examples
233
Review Questions
238

9.

229

Waves in the Atmosphere .................................................................... 239–267
9.1

Rossby Waves
239
9.1.1
Perturbation Method
240
9.1.2
Some Basic Properties of Waves

240
9.1.3
Rossby Waves in a Barotropic Atmosphere
241
9.2 Gravity Waves in Shallow Water
244
9.3 Orographic and Sound Waves
246
9.3.1
Orographic Waves
246
9.3.2
Sound Waves
248
9.4 Internal Gravity Waves
250
9.5 Equatorial Waves
252
9.5.1
Shallow Water Equations
252
9.5.2
Equatorial Rossby and Rossby Gravity Waves
256
9.5.3
Mixed Rossby Gravity Waves
260
9.5.4
Equatorial Kelvin Wave
261

Solved Examples
263
Review Questions
266

10.

Large-scale Meteorological Systems in Mid-Latitudes .................... 268–279

10.1 General
10.1.1
10.2 Fronts
10.2.1
10.2.2
10.2.3
10.2.4

Considerations
268
Air Masses
269
270
Warm Front
270
Cold Front
272
Stationary Front
272
Occluded Front
273



CONTENTS

10.3 Extratropical Cyclone
10.4 Jet Streams
275
Review Questions
278

11.

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273

Meteorological Systems in Low Latitudes ......................................... 280–326
11.1 General Considerations
280
11.2 Monsoons
281
11.2.1 Differential Heating of Land and Sea
287
11.2.2 Compressibility, Rotation and Moisture Effects
288
11.2.3 Tropical and Oceanic Convergent Zones
289
11.2.4 Intraseasonal and Interannual Variability of the

Indian Monsoon
290
11.3 Monsoon Disturbances and Semipermanent Monsoon Systems
Over India
295
11.3.1 Monsoon Disturbances
295
11.3.2 Semipermanent Monsoon Systems Over India
298
11.4 Tropical Cyclones
300
11.4.1 Factors Responsible for the Formation of
Tropical Cyclone
301
11.4.2 Climatology of Tropical Cyclones
302
11.4.3 Movement of Tropical Cyclones
303
11.4.4 Life Cycle of a Tropical Cyclone
306
11.4.5 Tropical Cyclone Structure
308
11.4.6 Eye and the Eyewall
311
11.5 Thunderstorms and Tornadoes
312
11.5.1 Thunderstorms
312
11.5.2 Life Cycle of Thunderstorms
313

11.5.3 Severe Thunderstorms and Squall Lines
315
11.5.4 Tornadoes
316
11.6 El Nino-Southern Oscillation
316
11.6.1 Overview of ENSO
317
11.6.2 Indian Ocean Dipole
323
11.6.3 ENSO and Indian Monsoon
323
Review Questions
324

12.

Global Energy Balance ........................................................................ 327–344
12.1 Globally-averaged Atmospheric Energy Balance
327
12.1.1 Global Energy Balance Requirement for the
Earth’s Atmosphere
328
12.1.2 Global Energy Balance at the Earth Surface
330
12.1.3 Estimates of the Global Energy Balance for the
Earth–Atmospheric System
332
12.1.4 Energy Processes in the Upper Atmosphere
333



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CONTENTS

12.2 Internal, Potential and Kinetic Energy
334
12.2.1 Internal and Potential Energy
334
12.2.2 Kinetic Energy
335
12.3 Conversion of Potential and Internal Energies to Kinetic Energy
12.3.1 Available Potential Energy
336
12.4 Generation and Frictional Dissipation of Kinetic Energy
338
12.4.1 Generation of Kinetic Energy
338
12.4.2 Frictional Dissipation of Kinetic Energy
340
12.5 Atmosphere as a Heat Engine
343
Review Questions
343

13.


336

General Circulation ............................................................................. 345–359
13.1 General Consideration
346
13.1.1 Overview
346
13.1.2 Observed Meridional Cross-section of Longitudinallyaveraged Zonal Wind and Temperature
347
13.1.3 Longitudinally-dependent Flow
349
13.1.4 Requirement on Theories of General Circulation
350
13.2 Meridional Circulation Model—Hadley Circulation
351
13.3 Angular Momentum Balance
353
13.4 Dishpan Experiments
358
Review Questions
359

14.

Numerical Modelling of the Atmosphere ........................................... 360–389
14.1 General Considerations
360
14.1.1 Overview
361
14.1.2 The Finite Difference Method

362
14.1.3 Partial Differential Equations
363
14.2 Modern Numerical Weather Prediction
370
14.2.1 Overview
370
14.2.2 Observations
371
14.3 Data Assimilation
371
14.3.1 Overview
371
14.3.2 Objective Analysis
372
14.3.3 Initialization
373
14.3.4 Data Assimilation Cycle
374
14.4 Spectral and Finite Element Methods
375
14.4.1 Galerkin Method
375
14.4.2 Spectral Method
377
14.4.3 Finite Element Method
378
14.5 Challenges in Weather and Climate Forecasts
380
14.5.1 Weather Forecasting—A Historical Perspective

14.5.2 Ensemble Forecasting
383
14.5.3 Climate Forecasting
385
Review Questions
388

380


CONTENTS

15.

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Chaos in the Atmosphere .................................................................... 390–409
15.1 Illustrative Example of Chaos—Forced Pendulum
15.2 Poincare Section and Lyapunov Exponents
393
15.3 Period Doubling and Route to Chaos
397
15.4 Bouncing Ball Problem
400
15.5 Lorenz Attractor
403
15.6 Limits of Deterministic Predictability
407

Review Questions
408

391

Appendix 1

Useful Universal Physical Constants ................................................. 411–412

Appendix 2

Vector Identities ..................................................................................413–415

Appendix 3

Atmospheric Ozone .............................................................................416–418

Appendix 4

Equations of Motion in Spherical Coordinates .................................419–420

Appendix 5

Relaxation Methods ............................................................................421–422

Appendix 6

Von Neumann Stability Analysis ........................................................423–425

Appendix 7


Fortran Computer Program for Numerical
Solution of the Barotropic Vorticity Equation ...................................426–429

Appendix 8

Fortran Computer Program for Numerical
Solution of the Shallow Water Equation ...........................................430–434

Appendix 9

Fortran Computer Program for Numerical
Solution of the Forced Damped Pendulum .......................................435–436

Appendix 10 Fortran Computer Program for Numerical
Solution of the Lorenz System ...........................................................437–438
Bibliography................................................................................................................439–440
Index ...........................................................................................................................441–446


Foreword

I consider it a great privilege to write this Foreword to this extremely timely and useful book
on “Basics of Atmospheric Science” by Prof. A. Chandrasekar. There are many introductory
books in the market on Atmospheric Science that are very attractive with coloured
illustrations, but lack in depth. On the other hand, there are books that deal in depth only on
certain aspects of Atmospheric Science. During my long teaching career, I felt the need of a
book on Atmospheric Science that will not only introduce the different aspects of the field
with some depth, but also highlight the exciting challenges. This book by Prof. Chandrasekar
is going to fill the much needed gap for such an introductory textbook for undergraduate and

postgraduate students in Atmospheric Science.
The book does a great job of laying the foundation of all aspects of atmospheric science
related to weather and climate. While the first few chapters (Chapters 1–5) discuss the
fundamental processes such as the origin of the atmosphere, atmospheric thermodynamics,
atmospheric radiation and cloud and precipitation, the next few chapters (Chapters 6–8) lay
the foundation for theoretical understanding of weather and climate. The following few
chapters (Chapters 9–11) deal with large scale systems such as waves and synoptic
disturbances in both tropics and extra-tropics, while the driving factors for the observed
climate and the general circulation are introduced in Chapters 12 and 13. Finally, the book
ends with discussing advanced numerical modelling of the atmosphere and the challenging
problem of deterministic limit on weather predictability.
Today, the atmospheric science has emerged as a highly quantitative science. I am very
happy to see that Prof. Chandrasekar’s book attempts to make the learning quantitative by
introducing questions at the end of every chapter together with some model solutions. Also
for any student of meteorology, it is fundamental to learn and understand the differences
between the tropical and extra-tropical systems. I am happy to see that the book introduces
the students to both tropical and extra-tropical systems.
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FOREWORD

I was responsible for introducing atmospheric science to Prof. Chandrasekar. After
completion of his Ph.D. in Applied Mathematics, we worked together for a couple of years at
the Centre for Atmospheric and Oceanic Sciences, IISc Bangalore. He then joined IIT
Kharagpur and taught Atmospheric Science for nearly two decades. I am very happy to see

that he took time off to write this book that will be extremely valuable for the students.

B.N. Goswami
Indian Institute of Tropical Meteorology
Dr. Homi Bhabha Road
Pashan, Pune-411008


Preface

Atmospheric Science over the years has evolved into an exciting field of study with farreaching scientific, economic and societal implications. In recent times too, there has been a
greater appreciation of the importance of this branch of science. This is understandable
considering the grave issues which confront mankind, ranging from global warming arising
from man-induced activities affecting climate change to depleting food resources for the evergrowing world population. Although many of us in the field of atmospheric science, had for
long, felt the need for a book on atmospheric science, dealing with not only the different
aspects of the field in depth, but also providing the readers with a comprehensive treatment of
the underlying physical principles. I did not imagine that I would indeed venture into writing
such a book.
I am indebted to numerous persons including my teachers, colleagues, students and
others who have played an important role in my career and development. I have dedicated this
book in memory of my teacher Prof. (Late) R. Ananthakrishnan, an inspiring teacher and a
person who epitomized both the desirable qualities of “high thinking” and “simple living”.
I have also benefited immensely from my association with Prof. G. Nath, my Ph.D. supervisor
at the Indian Institute of Science, Bangalore. I acknowledge with gratitude the help and
encouragement I received from Prof. B.N. Goswami, Director, Indian Institute of Tropical
Meteorology, Pune, over the years. After my Ph.D., I worked with Prof. B.N. Goswami at the
Indian Institute of Science, Bangalore during 1987–1988 and got introduced to some very
interesting research problems in the area of atmospheric science. Prof. B.N. Goswami, despite
his very busy schedule, has been kind enough to write the Foreword for this book and I thank
him for the same. Prof. B.N. Goswami provided several helpful suggestions on the contents as

well as the subject matter to be covered in this book. His timely comments and
encouragement finally led to the fruitful completion of the book.
I would be failing in my duty if I did not acknowledge the help and assistance I received
from Professor J. Srinivasan, Centre for Atmospheric and Oceanic Sciences, Indian Institute
of Science, Bangalore, Prof. T.S. Murty, University of Ottawa, Canada and Dr. Suresh,
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PREFACE

India Meteorological Department, Chennai, in the preparation of this book. Both
Prof. Srinivasan and Prof. Murty were kind enough to go through the contents of this book
and provide pertinent and useful suggestions which helped in the overall improvement of the
book. Dr. Suresh took time off in going through the entire book and besides providing useful
comments, he also patiently corrected the errors which appeared in the equations as well as in
the text. I wish to thank my Ph.D. student Dr. S. Sandeep, Mr. Liju and Mr. Sai of
the Indian Institute of Technology Kharagpur who all helped in the preparation of the figures
in this book. But for their help, this book project would not have been completed in time. I
wish to acknowledge the help and assistance which I received from DGM, TERLS, VSSC,
Thiruvananthapuram and Dr. K.V.S. Namboodiri and his group at Meteorological facility at
VSSC, Head TDAD, VSSC and the members of the photography unit of VSSC for their help
in the preparation of the photos for the cover page. I also acknowledge the help I received
from Ms. Mary Maxine Browne, Purdue University who read the first few chapters and
carefully edited the contents.
I take this opportunity to thank Prof. B.K. Mathur and Prof. R.N.P. Chowdhury (the
earlier and the present) Head of the Department of Physics and Meteorology, Indian Institute

of Technology Kharagpur and Prof. S.K. Dube and Prof. D. Acharya (the earlier and the
present) Director, Indian Institute of Technology Kharagpur for their unstinted support and
encouragement in this book project. I took leave from the Indian Institute of Technology
Kharagpur and joined the Indian Institute of Space Science and Technology (IIST),
Thiruvananthapuram in July 2009 during the final stages of this book project. I acknowledge
with gratitude the help and encouragement I since received from Dr. B.N. Suresh, Director,
IIST towards this project.
I wish to place on record the excellent help and encouragement I received from the editors
of PHI Learning, the publishers of this book. In this connection I would like to specially
thank Mr. Surajit Sarkar, Ms. Babita Mishra, Mr. Darshan Kumar and Mr. K.K. Chaturvedi, all
of PHI Learning, who have been very supportive during the period of this project.
I have also received support and encouragement from well wishers, collaborators,
friends and colleagues, a list too long to mention here. However, I wish to acknowledge the
encouragement I received from Mr. G. Srinivas, Prof. P.C. Pandey, Dr. A. Gambheer,
Dr. Kiran Alapaty, Dr. D. Niyogi, Dr. K. Srinivasan, Dr. D. Lohar, Dr. S.P. Namboodiri,
Dr. Akio Kitoh and Dr. Panos G. Georgopoulos. I also wish to acknowledge the quiet support
I received from my family members and thank them for their forbearance. And finally, I seek
the blessings from ALMIGHTY and hope that the book will be well received.
A. Chandrasekar


1

Introductory Survey
of the Atmosphere

In recent times there has been a pronounced increase and appreciation of the importance of
the science of the atmosphere. The reasons for such increased interests in the earth’s
atmosphere are due to the increasing concern of man’s role in the emerging global warming
scenario as well as issues related to world food resources in the light of the increasing human

population. This chapter presents an introductory survey and overview of the study of the
earth’s atmosphere in eight sections. Section 1.1 introduces the various disciplines of
atmospheric science, and Section 1.2 summarizes the origin and composition of the earth’s
atmosphere. While Section 1.3 explains the basic elements of (vertical) distribution of
pressure and density, Section 1.4 outlines the components of the ionosphere, the earth’s
electric field, and the magnetosphere. Section 1.5 reviews the (vertical) distribution of
temperature and winds, while Section 1.6 outlines the behaviour of the atmosphere as a fluid.
Section 1.7 introduces the fundamental physical laws on which the science of the atmosphere
is based. Chapter 1 concludes with Section 1.8, which introduces the concepts of determinism
and chaos as these are understood in atmospheric science.

1.1

INTRODUCTION

The study of the atmospheric sciences is primarily devoted to the description and
understanding of phenomena in the earth’s atmosphere and to a lesser extent on that of the
other planets in the solar system. Atmospheric Sciences refer to the study of the physical,
chemical and dynamical aspects of the earth’s atmosphere, which extends upwards several
hundred kilometres from the earth’s surface. The term “atmospheric sciences” is usually used
in a broad sense and it includes atmospheric chemistry, aeronomy, magnetospheric physics,
and solar influences on the entire atmospheric system of the earth. The underlying postulate in
the study of the atmospheric sciences is that the atmospheric phenomena can be understood in
terms of the basic laws of physics. The physical laws of fluid dynamics, radiation and
thermodynamics are the most readily applicable to the study of atmospheric phenomena.
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Meteorology can be defined as the scientific study of the earth’s atmosphere that
focuses on weather processes and forecasting. Meteorological phenomena are primarily
observable weather events, which are explained by the science of meteorology. Atmospheric
Sciences and Meteorology have been traditionally divided into the following three broad
disciplines: physical, synoptic and dynamic meteorology. Physical meteorology is devoted to
the study of atmospheric structure and composition, atmospheric optics, atmospheric
electricity as well as the physical processes involving radiation, cloud and rain formation.
Both, synoptic and dynamic meteorology deal with atmospheric motion and their evolution in
time. However, while the former employs empirical approaches to forecast large-scale
atmospheric motion, the latter utilizes approaches based on the physical laws of fluid
dynamics. In this book an effort has been made to provide an overview of the various facets
of the behaviour of the atmosphere in combination with an emphasis on the fundamental laws
of physics that aid in the understanding of the atmospheric behaviour.

1.2

ORIGIN AND COMPOSITION OF THE ATMOSPHERE

The earth’s atmosphere, in contrast to the sun’s atmosphere, is very much deficient in noble
gases such as helium, neon, argon, xenon and krypton. Atmospheric scientists generally agree
that during the early history of the earth the gaseous material (most probably hydrogen and
helium) which formed part of the original atmosphere of the earth was lost into space due to

(i) the earth’s weak gravity that was not strong enough to retain these lighter gases, and
(ii) the lack of differentiation between the earth’s solid inner and liquid outer core. The earth’s
first atmosphere apparently did not exist for a long period of time, and was followed by a
second atmosphere, which had formed due to volcanic out gassing. Volcanic eruptions and
their violent expulsion of volcanic substances from the earth’s interior gave rise to the second
atmosphere. The constituents of this atmosphere were quite similar to the gases emitted by
modern volcanoes, and were composed of 85% water vapour, 10% carbon dioxide, and a few
per cent nitrogen and sulphur together with sulphur compounds such as sulphur dioxide and
hydrogen sulphide, as well as very small amounts of carbon monoxide, hydrogen, chlorine,
ammonia and methane. It is to be noted that no evidence exists of free oxygen being present
in these volcanic emissions, and consequently free oxygen was absent in this second
atmosphere. Since the atmosphere is capable of holding only a very small amount of the mass
of water vapour released through volcanic eruptions, it can be easily surmised that a large part
of the water vapour present in the second atmosphere must have condensed as clouds. This
would have led to torrential rains and the formation of large water bodies on the earth’s
surface. The formation of the hydrosphere, however, does not explain the presence of oxygen
in our present atmosphere.
Two possible sources of atmospheric oxygen are associated with the absorption of solar
radiation: (i) the photodissociation of water due to the absorption of ultraviolet radiation, and
(ii) the action of plants through photosynthetic reaction due to the absorption of visible
radiation. Oxygen formation using the photodissociation process is less likely to be the chief
cause of oxygen formation as studies indicate that not more than 1–2% of the oxygen
presently seen in our atmosphere could have been produced using the photodissociation
process. However, it is generally agreed that the photosynthesis reaction (CO2 + H2O +


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visible sunlight = organic compounds + O2) by cyanobacteria and eventually higher plants is
the main source of production of significant amounts of the present oxygen. While there were
two sources of oxygen production in the atmosphere, three oxygen sinks have been identified
which occurred at different stages of the earth’s evolution. The first sink of oxygen, which
happened in the early stages of the earth’s atmospheric evolution, is attributed to chemical
weathering through the oxidation of surface materials. Both animal respirations as well as the
burning of fossil fuels, the latter happening in very recent times, are the other additional sinks
of oxygen. If the atmospheric oxygen did form due to photosynthesis reaction, then the
possibility exists for plant life to form in an oxygen-free atmosphere. Scientists believe that in
the initial stages, single-celled organisms existed that did not require oxygen. Subsequently
primitive forms of plant life formed, which released oxygen through photosynthesis. Since
nitrogen is chemically inert and has low solubility in water, most of the nitrogen released
during the early volcanic eruptions has managed to remain in the atmosphere. Due to the
nearly complete removal of water vapour and carbon dioxide associated with the process of
condensation and photosynthesis, nitrogen has become the dominant constituent of the earth’s
atmosphere. Quite striking is the fact that the atmospheres of the earths nearest neighbours,
Venus and Mars, are entirely different from that of the earth. In contrast to the earth’s
nitrogen–oxygen dominated atmosphere, the atmospheres of both Venus and Mars are
composed primarily of carbon dioxide. Also, the atmosphere of Venus is one hundred times
more massive than the earth, and the atmosphere of Mars is one hundred times less massive
than the Earth’s atmosphere. The differences between the atmospheric histories of these
planets are indeed intriguing because, despite sharing a common birth, the atmospheres of all
these planets have evolved along very different paths.
Table 1.1 presents the composition of the earth’s atmosphere in the well-mixed region

up to a height of 100 km. Nitrogen contributes up to 78% by volume, while oxygen and
argon contribute 21% and 0.93% by volume. The earth’s atmosphere also contains a variable
amount of water vapour (accounting for a maximum of 4%) as well as very small amounts of
carbon dioxide and ozone. Due to the effective mixing associated with the turbulent fluid
TABLE 1.1

Composition of earth’s atmosphere in the homosphere
(ppmv is parts per million by volume)

Gas
Nitrogen (N2)

Volume mixing ratio

Molecular weight

0.78

28.02

Oxygen (O2)

0.21

32.0

Argon (Ar)

0.0093


39.95

Water vapour (H2O)

< 0.04

18.02

Carbon dioxide (CO2)

360 ppmv

44.01

Neon (Ne)

18 ppmv

20.18

Ozone (O3)

12 ppmv

48.0

Helium (He)

5 ppmv


4.0

Krypton (Kr)

1 ppmv

83.7

Hydrogen (H2)

0.5 ppmv

2.02


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motion of the atmosphere up to a height of 100 km, the atmosphere has a uniform
composition; this atmospheric layer is known as the homosphere. Above 100 km, the mean
free path is no longer small, and the process of molecular diffusion by random molecular
motion dominates more than the macroscopic turbulent mixing of air parcels, therefore,
random molecular motion determines the composition of the earth’s atmosphere. The region

of the atmosphere above 100 km is known as the heterosphere and is characterized by a
gradual decrease with the height of the mean molecular weight of the mixture of the gases.
The earth’s atmosphere above 120 km is predominantly atomic oxygen; at heights above
100 km, helium and hydrogen dominate. Unlike the other constituents, both water vapour and
ozone are known to vary widely both in space and time even within the homosphere.

1.3

DISTRIBUTION OF PRESSURE AND DENSITY

Atmospheric pressure at a given point is defined as the height of the overlying atmosphere of
a column of unit cross-sectional area around that point extending to the top of the atmosphere.
The above definition of pressure implies a decrease of pressure with increase in height, and
hence it is not surprising that pressure is observed to decrease with height. Also, the vertical
variation of pressure with height is large in comparison with its horizontal and temporal
variations. Hence, for the sake of convenience, a standard atmosphere is defined; representing
the horizontal and time-averaged structure of the atmosphere as a function of height only.
Table 1.2 presents the details of pressure, temperature, and density variation based on the US
Standard Atmosphere.
TABLE 1.2
Height (km)
0
1
2
3
4
5
6
7
8

9
10
11
12
13
14
15

US Standard Atmosphere

Temperature (°C)
15.0
8.5
2.0
–4.5
–11.0
–17.5
–24.0
–30.5
–37.0
–43.5
–50.0
–56.5
–56.5
–56.5
–56.5
–56.5

Pressure (hPa)
1013.15

900.0
800.0
700.0
620.0
540.0
470.0
410.0
360.0
310.0
260.0
230.0
190.0
170.0
140.0
120.0

Density (kg m–3)
1.225
1.1
1.0
0.91
0.82
0.74
0.66
0.59
0.53
0.47
0.41
0.36
0.31

0.27
0.23
0.19
(Contd.)


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TABLE 1.2
Height (km)
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

40
46
50
56
60
66
70
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U.S. Standard Atmosphere (Contd.)

Temperature (°C)
–56.5
–56.5
–56.5
–56.5
–56.5
–55.5
–54.5
–53.5

–52.5
–51.5
–50.5
–49.5
–48.5
–47.5
–46.5
–45.5
–44.5
–41.7
–38.9
–36.1
–22.75
–6.25
–2.55
–15.15
–26.15
–42.65
–53.55
–66.75
–74.55
–86.25

Pressure (hPa)
100.0
90.0
75.0
65.0
55.0
47.0

40.0
34.0
29.0
25.0
22.0
18.0
16.0
14.0
12.0
10.0
8.7
7.5
6.5
5.6
2.87
1.31
0.79
0.37
0.22
0.09
0.05
0.02
0.01
0.003

Density (kg m–3)
0.17
0.14
0.12
0.10

0.088
0.075
0.064
0.054
0.046
0.039
0.034
0.029
0.025
0.021
0.018
0.015
0.013
0.011
0.0096
0.0082
0.0039
0.0017
0.0010
0.0005
0.0003
0.0001
0.00008
0.00003
0.000018
0.000007

In an isothermal atmosphere, both the pressure and density decrease exponentially with
height. In the real atmosphere, up to a height of 100 km, the logarithm of pressure is nearly
linear with height. The atmospheric pressure averaged over the surface of the earth at mean

sea level has a value of 1.0132 × 105 Pa or 1013.2 hPa. The averaged value of density of the
air at mean sea level has a value of 1.225 kg m–3. The vertical distribution of air density in
the earth’s atmosphere closely follows the vertical distribution of pressure. As is commonly
known, density depends on both pressure and temperature. Consequently, if density variations
with height closely follow pressure variations with height, the variations of air temperature in


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the vertical are logically much less smaller than pressure variation in the vertical. Also, the
horizontal and temporal variation of the air density is much smaller compared to the vertical
variation.

1.4

IONOSPHERE, ATMOSPHERIC ELECTRIC FIELD AND
MAGNETOSPHERE

On December 12, 1901, Marconi successfully demonstrated trans-Atlantic communication by
receiving a radio signal in St. John’s Newfoundland that had been sent from Cornwall,
England. A year later, Oliver Heaviside and Arthur Kennelly independently proposed the
existence of a conducting layer—the ionosphere—in the upper atmosphere that would allow

an electromagnetic signal to be reflected back to the earth. At heights of 80 km or above, the
atmospheric density is so low that free electrons can exist for short periods of time before
they are captured by a nearby positive ion. The existence of charged particles at this altitude
(80 km and above) indicates the beginning of the ionosphere, a region having both the
properties of a gas and of plasma. Solar radiations at ultraviolet (UV) and shorter wavelengths
(X-rays) are considered to be ionizing because photons of energy at these frequencies are
capable of dislodging an electron from a neutral gas atom or molecule during a collision. In
the above process, known as photoionization, the interaction of electromagnetic radiation such
as solar UV and X-ray radiation with matter results in the dissociation of that matter into
electrically charged particles made up of a free electron and a positively charged ion. Cosmic
rays and solar wind particles are also known to play a role in the photoionization process, but
their effect is minor compared with the effect of the sun’s electromagnetic radiation on photoionization. At the highest levels of the earth’s outer atmosphere, (greater than 300–400 km),
solar radiation is very strong, but only a few atoms exist with which to interact, so the amount
of ionization is small. As the altitude decreases, more gas atoms are present, so the
photoionization process increases. However, at the same moment an opposing process known
as recombination begins, wherein a free electron is “captured” by a positive ion if it moves
close enough to it. Since the density of the atmosphere increases at lower altitudes, the
recombination process becomes dominant, since the ions are at this lower altitude relatively
closer to each other. Ultimately, the balance between these two conflicting processes
determines the degree of ionization present at any given time. At still lower altitudes (80 km
or lower), the number of gas atoms (and molecules) increases further, and more opportunity
exists for absorption of energy from a photon of UV or X-ray solar radiation. However, the
intensity of the above-mentioned solar radiations is less at these lower altitudes because some
of UV and X-ray solar radiation have been absorbed at the higher altitude levels. Finally a
situation is reached where the lower radiation intensity, greater gas density, and greater
recombination rates balance out, and the ionization rate begins to decrease with decreasing
altitude. This leads to the formation of several distinct ionization peaks or layers, such as the
D, E, F1, and F2 layers centred approximately at 80 km, 105 km, 175 km and 250 km,
respectively. The ionosphere is still used by international broadcasters to reflect radio signals
back to the earth, so that programs can be heard around the entire world. The ionosphere

provides long-range capabilities for commercial ship-to-shore communications, trans-oceanic
aircraft links, and military communication and surveillance systems. Also, all signals


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transmitted to and from satellites for communication and navigation purposes must pass
through the ionosphere; hence ionospheric irregularities (disturbances) can have a major
impact on system performance and the reliability of satellite equipment. Since the ionosphere
is almost entirely made up of plasma, also known as the fourth state of matter, research on
the ionosphere can increase our understanding of plasma.
The region of the atmosphere—extending upwards from a few tens of kilometres to the
top of the ionosphere—is characterized by very large electrical conductivity at a constant
electric potential and is known as the electrosphere. Under conditions of fair weather,
a downwardly directed atmospheric electric field exists with an averaged magnitude of
120 V m–1 near the earth’s surface. The downwardly directed electric field, under fair weather
conditions, implies that the electrosphere carries a net positive charge and an average
potential of 300 kV with respect to the earth’s surface. To maintain the above voltage, the
earth has a negative charge of about a million coulombs on its surface and an equal net
positive charge is distributed throughout the atmosphere. Careful measurements have indicated
that the earth’s negative charge remains roughly constant over time. Considering the
magnitude of the leakage current flowing in the air, which amounts to 2 to 4 × 10–12 A m–2,

the electrosphere together with the earth both constitute a spherical capacitor, and should get
discharged in a matter of minutes. However, the fact the fair weather electric field is by and
large constant suggests the existence of electrical generators, which maintain the fair weather
electric field. Atmospheric scientists generally agree that thunderstorms serve as electrical
generators and maintain the fair weather field by separating the electric charges with positive
and negative charges concentrated at the top and the base of the thunderstorm cloud. While
the positive charges found in the upper regions of the thunderstorm cloud get leaked to the
electrosphere, lightning flashes ensure that negative charges are transported to the ground
from the base of the thunderstorm cloud. The point discharge current and the precipitation
current account for the remaining two components of the global electrical circuit. Point
discharge currents transport positive charges from pointed obstacles on the earth’s surface
upward through the air beneath and above a thunderstorm. Precipitation currents bring
positive charges to the earth’s surface with thunderstorm precipitation. The approximate values
of the various components of the electrical budget for the earth in units of C km–2 yr–1 are:
90 units of positive charge gained during the fair weather conditions, 100 units of positive
charge lost due to point discharge current, 30 units of positive charge gained due to
precipitation current and 20 units of negative charge gained due to the lightning discharge.
At very high levels of 500 km and more, the motion of the charged particles is very
much influenced by the presence of the earth’s magnetic field; hence this region of the
atmosphere at and above 500 km is known as the magnetosphere. In the magnetosphere, very
little interaction occurs between the charged particles and the neutral atoms/molecules due to
the infrequent collisions between them. The sun’s extremely hot atmosphere consists of
nothing but plasma—a gas consisting of charged particles—mostly electrons and protons.
Solar plasma streams radially into space at high speed and pulls the sun’s magnetic field
along with it. The electrified particles, and the solar magnetic field that they pull along, is
called the solar wind. These solar wind particles come streaming towards the earth at very
high velocities at 450 km s–1 or more and take about 2–3 days to reach the earth. The solar
wind particles flowing directly from the sun towards the earth come across the



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magnetosphere, which acts as an obstacle, which the solar wind particles must go around.
Due to their high speed, however, they have no time for an orderly detour. Instead, their
direction is changed abruptly in the so-called bow shock region just outside the sunward
magnetic field. The abrupt passage of the solar wind particles through the bow shock region
reduces the speed and changes the motion of the particles. Most of these solar wind particles
are deflected around the magnetosphere through an area known as the magnetosheath. Acting
as a shield, the magnetosphere effectively screens the earth from most of the direct solar wind
particles. These charged solar wind particles do not travel readily across the magnetosphere,
but are deflected at angles to the magnetic field. Some of the solar wind particles, however,
can travel along the earth’s magnetic field lines, and leak through the earth’s magnetic screen.
These particles cause disturbances within the earth’s magnetosphere and are associated with
the structure of the interplanetary magnetic field, which rotates with the sun.

1.5

DISTRIBUTION OF TEMPERATURE AND WINDS

The earth’s atmosphere is mostly transparent to the incoming solar radiation, and hence the
above radiation from the sun is absorbed by the earth surface. The earth’s atmosphere in turn
absorbs the terrestrial long wave radiation from the earth surface resulting in a situation,

where the atmosphere is primarily heated, from below. This results in a vertical distribution of
air temperature, wherein the air temperature decreases with height. In addition to the vertical
distribution of air temperature, there also exists horizontal distribution of air temperature, due
to the differential heating of the incoming solar radiation between the low and high latitudes.
Typically, the air temperature decreases poleward in the troposphere. In addition to giving rise
to the horizontal distribution of air temperature, the differential heating between the low and
high latitudes also results in atmospheric motions of various scales. The thermally direct
circulations associated with the differential heating also give rise to vertical distribution of winds.

1.5.1

Distribution of Temperature

Vertical Distribution of Temperature
Figure 1.1 depicts the vertical distribution of air temperature for the standard atmosphere, for
typical mid-latitude conditions. Four distinct layers can be identified in the figure and these
are known as troposphere, stratosphere, mesosphere and thermosphere, respectively. The
boundaries (transitions) between the different layers are known as tropopause, stratopause,
and mesopause, respectively. The heights of these boundaries vary in both time and space,
primarily with latitude and season. The observed, globally averaged surface temperature for
the earth is about 15°C. Incoming solar radiation entering the earth’s atmosphere has a short
wavelength with a maximum energy centred around the wavelength range of 0.2 mm to 2 mm.
The radiation emitted by the earth and its atmosphere have longer wavelengths, known as
infrared radiation, with its maximum energy centred on > 4 mm. The earth’s atmosphere is
mostly transparent to the solar radiation in the wavelength range of 0.2 mm to 2 mm, but absorbs
infrared radiation due to the properties of water vapour, carbon dioxide, methane, and other
trace gases. While the incoming solar radiation and outgoing infrared radiation tend to remain
nearly in balance, the net effect of the earth’s opacity to infrared radiation and its near