Salby M.L. Fundamentals of Atmospheric Physics
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X Contents
2.2 The First Law
2.2.1 Internal Energy
2.2.2 Diabatic Changes of State
2.3 Heat Capacity
2.4 Adiabatic Processes
2.4.1 Potential Temperature
2.4.2 Thermodynamic Behavior Accompanying Vertical Motion
2.5 Diabatic Processes
2.5.1 Polytropic Processes
Suggested Reading
Problems
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Chapter 3 The Second Law and Its Implications
3.1 Natural and Reversible Processes
3.1.1 The Carnot Cycle
3.2 Entropy and the Second Law
3.3 Restricted Forms of the Second Law
3.4 The Fundamental Relations
3.4.1 The Maxwell Relations
3.4.2 Noncompensated Heat Transfer
3.5 Conditions for Thermodynamic Equilibrium
3.6 Relationship of Entropy to Potential Temperature
3.6.1 Implications for Vertical Motion
Suggested Reading
Problems
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Chapter 4 Heterogeneous Systems
4.1 Description of a Heterogeneous System
4.2 Chemical Equilibrium
4.3 Fundamental Relations for a Multicomponent System
4.4 Thermodynamic Degrees of Freedom
4.5 Thermodynamic Characteristics of Water
4.6 Equilibrium Phase Transformations
4.6.1 Latent Heat
4.6.2 Clausius-Clapeyron Equation
Suggested Reading
Problems
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Chapter 5 Transformations of Moist Air
5.1 Description of Moist Air
5.1.1 Properties of the Gas Phase
5.1.2 Saturation Properties
5.2 Implications for the Distribution of Water Vapor
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5.3 State Variables of the Two-Component System
5.3.1 Unsaturated Behavior
5.3.2 Saturated Behavior
5.4 Thermodynamic Behavior Accompanying Vertical Motion
5.4.1 Condensation and the Release of Latent Heat
5.4.2 The Pseudo-Adiabatic Process
5.4.3 The Saturated Adiabatic Lapse Rate
5.5 The Pseudo-Adiabatic Chart
Surface Relative Humidity
Surface Potential Temperature
Surface Dew Point
Cumulus Cloud Base
Equivalent Potential Temperature at the Surface
Freezing Level of Surface Air
Liquid Water Content at the Freezing Level
Temperature inside Cloud at 650 mb
Mixing Ratio inside Cloud at 650 mb
Suggested Reading
Problems
Chapter 6
Hydrostatic Equilibrium
6.1 Effective Gravity
6.2 Geopotential Coordinates
6.3 Hydrostatic Balance
6.4 Stratification
6.4.1 Idealized Stratification
Layer of Constant Lapse Rate
Isothermal Layer
Adiabatic Layer
6.5 Lagrangian Interpretation of Stratification
6.5.1 Adiabatic Stratification
6.5.2 Diabatic Stratification
Suggested Reading
Problems
Chapter 7 Hydrostatic Stability
7.1 Reaction to Vertical Displacement
7.2 Stability Categories
7.2.1 Stability in Terms of Temperature
7.2.2 Stability in Terms of Potential Temperature
7.2.3 Moisture Dependence
7.3 Implications for Vertical Motion
7.4 Finite Displacements
7.4.1 Conditional Instability
7.4.2 Entrainment
7.4.3 Potential Instability
7.4.4 Modification of Stability under Unsaturated Conditions
7.5 Stabilizing and Destabilizing Influences
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7.6 Turbulent Dispersion
7.6.1 Convective Mixing
7.6.2 Inversions
7.6.3 Life Cycle of the Nocturnal Inversion
Suggested Reading
Problems
Chapter 8 Atmospheric Radiation
8.1 Shortwave and Longwave Radiation
8.1.1 Spectra of Observed SW and LW Radiation
8.2 Description of Radiative Transfer
8.2.1 Radiometric Quantities
8.2.2 Absorption
Lambert's Law
8.2.3 Emission
Planck's Law
Wien's Displacement Law
The Stefan-Boltzmann Law
Kirchhof-f's Law
8.2.4 Scattering
8.2.5 The Equation of Radiative Transfer
8.3 Absorption Characteristics of Gases
8.3.1 Interactions between Radiation and Molecules
8.3.2 Line Broadening
8.4 Radiative Transfer in a Plane Parallel Atmosphere
8.4.1 Transmission Function
8.4.2 Two-Stream Approximation
8.5 Thermal Equilibrium
8.5.1 Radiative Equilibrium in a Gray Atmosphere
8.5.2 Radiative-Convective Equilibrium
8.5.3 Radiative Heating
8.6 Thermal Relaxation
8.7 The Greenhouse Effect
Suggested Reading
Problems
Chapter 9 Aerosol and Clouds
9.1 Morphology of Atmospheric Aerosol
9.1.1 Continental Aerosol
9.1.2 Marine Aerosol
9.1.3 Stratospheric Aerosol
9.2 Microphysics of Clouds
9.2.1 Droplet Growth by Condensation
9.2.2 Droplet Growth by Collision
9.2.3 Growth of Ice Particles
9.3 Macroscopic Characteristics of Clouds
9.3.1 Formation and Classification of Clouds
9.3.2 Microphysical Properties of Clouds
9.3.3 Cloud Dissipation
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9.4 Radiative Transfer in Aerosol and Cloud
9.4.1 Scattering by Molecules and Particles
Rayleigh Scattering
Mie Scattering
9.4.2 Radiative Transfer in a Cloudy Atmosphere
9.5 Roles of Clouds and Aerosol in Climate
9.5.1 Involvement in the Global Energy Budget
Influence of Cloud Cover
Influence of Aerosol
9.5.2 Involvement in Chemical Processes
Suggested Reading
Problems
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Chapter 10 Atmospheric Motion
10.1 Descriptions of Atmospheric Motion
10.2 Kinematics of Fluid Motion
10.3 The Material Derivative
10.4 Reynolds' Transport Theorem
10.5 Conservation of Mass
10.6 The Momentum Budget
10.6.1 Cauchy's Equations of Motion
10.6.2 Momentum Equations in a Rotating Reference Frame
10.7 The First Law of Thermodynamics
Suggested Reading
Problems
Chapter 11 Atmospheric Equations of Motion
11.1 Curvilinear Coordinates
11.2 Spherical Coordinates
11.2.1 The Traditional Approximation
11.3 Special Forms of Motion
11.4 Prevailing Balances
11.4.1 Motion-Related Stratification
11.4.2 Scale Analysis
11.5 Thermodynamic Coordinates
11.5.1 Isobaric Coordinates
11.5.2 Log-Pressure Coordinates
11.5.3 Isentropic Coordinates
Suggested Reading
Problems
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Chapter 12 Large-Scale Motion
12.1
Geostrophic Equilibrium
12.1.1 Motion on an f Plane
The Helmholtz Theorem
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12.2 Vertical Shear of the Geostrophic Wind
12.2.1 Classes of Stratification
12.2.2 Thermal Wind Balance
12.3 Frictional Geostrophic Motion
12.4 Curvilinear Motion
12.4.1 Inertial Motion
12.4.2 Cyclostrophic Motion
12.4.3 Gradient Motion
12.5 Weakly Divergent Motion
12.5.1 Barotropic Nondivergent Motion
12.5.2 Vorticity Budget under Baroclinic Stratification
12.5.3 Quasi-Geostrophic Motion
Suggested Reading
Problems
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Chapter 13 The Planetary Boundary Layer
13.1 Description of Turbulence
13.1.1 Reynolds Decomposition
13.1.2 Turbulent Diffusion
13.2 Structure of the Boundary Layer
13.2.1 The Ekman Layer
13.2.2 The Surface Layer
13.3 Influence of Stratification
13.4 Ekman Pumping
Suggested Reading
Problems
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Chapter 14 Atmospheric Waves
14.1 Description of Wave Propagation
14.1.1 Surface Water Waves
14.1.2 Fourier Synthesis
14.1.3 Limiting Behavior
14.1.4 Wave Dispersion
14.2 Acoustic Waves
14.3 Buoyancy Waves
14.3.1 Shortwave Limit
14.3.2 Propagation of Gravity Waves in a Nonhomogeneous Medium
14.3.3 The WKB Approximation
14.3.4 Method of Geometric Optics
Turning Level
Critical Level
14.4 The Lamb Wave
14.5 Rossby Waves
14.5.1 Barotropic Nondivergent Rossby Waves
14.5.2 Rossby Wave Propagation in Three Dimensions
14.5.3 Planetary Wave Propagation in Sheared Mean Flow
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14.6 Wave Absorption
14.7 Nonlinear Considerations
Suggested Reading
Problems
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Chapter 15 The General Circulation
15.1 Forms of Atmospheric Energy
15.1.1 Moist Static Energy
15.1.2 Total Potential Energy
15.1.3 Available Potential Energy
Adiabatic Adjustment
15.2 Heat Transfer in an Axisymmetric Circulation
15.3 Heat Transfer in a Laboratory Analogue
15.4 Tropical Circulations
Suggested Reading
Problems
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Chapter
16 Hydrodynamic Instability
16.1 Inertial Instability
16.2 Shear Instability
16.2.1 Necessary Conditions for Instability
16.2.2 Barotropic and Baroclinic Instability
16.3 The Eady Problem
16.4 Nonlinear Considerations
Suggested Reading
Problems
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Chapter
17 The Middle Atmosphere
17.1 Ozone Photochemistry
17.1.1 The Chemical Family
17.1.2 Photochemical Equilibrium
17.2 Involvement of Other Species
17.2.1 Nitrous Oxide
17.2.2 Chlorofluorocarbons
17.2.3 Methane
17.3 Air Motion
17.3.1 The Brewer-Dobson Circulation
17.3.2 Wave Driving of the Mean Meridional Circulation
17.4 Sudden Stratospheric Warmings
17.5 The Quasi-Biennial Oscillation
17.6 Direct Interactions with the Troposphere
17.7 Heterogeneous Chemical Reactions
Suggested Reading
Problems
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xvi Contents
Appendix A: Conversion to SI Units
Appendix B: Thermodynamic Properties of Air and Water
Appendix C: Physical Constants
Appendix D: Vector Identities
Appendix E: Curvilinear Coordinates
Appendix F." Pseudo-Adiabatic Chart
References
Answers to Selected Problems
Index
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Preface
Global satellite observations coupled with increasingly sophisticated com-
puter simulation have led to rapid advances in our understanding of the at-
mosphere. While opening many doors, these tools have also raised new and
increasingly complex questions about atmospheric behavior. At the same time,
environmental issues have brought atmospheric science to the center of sci-
ence and technology, where it now plays a key role in shaping national and
international policy.
An amalgam of several disciplines, atmospheric science is, by its very nature,
interdisciplinary. It therefore requires one to master a wide range of skills and
attracts students from varied backgrounds. Current environmental issues, like
global warming and ozone depletion, have drawn increased attention to inter-
disciplinary problems, which involve interactions between traditional subjects
like dynamics, radiation, and chemistry. Yet, the demands of specialization
often make the introductory course in atmospheric science the only formal
opportunity to develop a broad foundation in basic physical principles and
how they interact to shape atmospheric behavior.
This book is intended to serve as a text for a graduate core course in
atmospheric science. Modern research problems require a unified treatment
of material that, historically, has been separated into physical and dynamical
meteorology, one which establishes the interrelationship of these subjects. It is
in this spirit that this book develops the fundamental principles of atmospheric
physics.
The text concentrates on four major themes:
1. Atmospheric thermodynamics
2. Hydrostatic equilibrium and stability
3. Atmospheric radiation and clouds
4. Atmospheric dynamics,
which represent the cornerstones of modern atmospheric research. The global
energy budget, hydrological cycle, and photochemistry are also treated, but
as applications of the major themes. This material has been integrated by
cross-referencing subject matter, with applications drawn from a wide range
of topics in global research.
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xviii
Preface
The text is targeted at first-year graduate students with diverse backgrounds
in physics, chemistry, mathematics, or engineering, but not necessarily for-
mal training in thermodynamics, radiation, and fluid mechanics. It emphasizes
physical concepts, which are developed from first principles. Therefore, the
student without formal exposure to a subject is not at a disadvantage, the
only prerequisites being a solid grounding in basic undergraduate physics and
advanced calculus and some exposure to partial differential equations. The
material can also be digested by undergraduates with similar preparation.
The presentation is from a Lagrangian perspective, which considers trans-
formations of an individual air parcel moving through the circulation. In addi-
tion to its conceptual advantages, this framework affords a powerful diagnostic
tool for interpreting atmospheric behavior. Each chapter opens with a devel-
opment of basic principles and closes with applications from topical problems
in global research. Many are illustrated with behavior on a particular day,
which enables the atmosphere to be dissected in contemporaneous properties,
like thermal structure, motion, trace species, and clouds, and therefore brings
to light interactions among them.
Chapters 2 through 5 are devoted to atmospheric thermodynamics. Em-
phasis is placed on heterogeneous systems, which figure centrally in cloud
formation, its interaction with radiation, and the roles of water vapor in global
energetics and chemistry. Atmospheric hydrostatics are treated in Chapters
6 and 7, which interpret stratification from a Lagrangian perspective and at-
mospheric heating in terms of stabilizing and destabilizing influences. Chap-
ters 8 and 9 concentrate on atmospheric radiation and cloud processes. After
developing the fundamental laws governing radiative transfer, the text con-
siders energetics under radiative and radiative-convective equilibrium. Cloud
behavior is discussed in relation to the greenhouse effect, climate feedback
mechanisms, and chemical processes. Chapters 10 through 16 are devoted to
atmospheric dynamics. The perspective is transformed from the Lagrangian to
the Eulerian description of atmospheric behavior via Reynolds' transport the-
orem, from which the equations of motion follow directly. Large-scale motion
is treated first in terms of geostrophic and hydrostatic equilibrium and then ex-
tended to higher order to introduce vorticity dynamics and quasi-geostrophic
motion. Wave propagation is developed from the paradigm of surface water
waves. The general circulation is motivated by a zonally symmetric model of
heat transfer in the presence of rotation, which, through its laboratory ana-
logue, the rotating annulus, sets the stage for baroclinic instability. The book
closes in Chapter 17 with an overview of the middle atmosphere that synthe-
sizes topics developed in earlier chapters. Problems at the end of each chapter
are of varied sophistication, ranging in difficulty from direct applications of
the development to small computer projects.
One of the challenges in integrating material of this scope is to unify nomen-
clature, in which an individual quantity can be referred to by as many as half
a dozen different expressions (e.g., in radiation). In defining quantities, I have
Preface
xix
adopted nomenclature that conforms to their physical meaning, for example,
to distinguish scalar quantities, like trace speed, from vector quantities, like
group velocity, to distinguish between properties referenced to unit mass ver-
sus to a particle, and to clearly distinguish between frames of reference. SI
units and terminology have been adopted almost throughout. Exceptional are
units of mb, which remain the most familiar specification of pressure, chemical
reaction rates, for which cgs units are the accepted standard, and the radia-
tive terms
intensity
and flux, which are preferred over
radiance
and
irradiance
to conform to more general concepts discussed elsewhere in the text.
This book has benefited from my interaction with a number of individuals.
Constructive criticism on earlier versions of the text was selflessly provided by
David G. Andrews, Rolando R. Garcia, Dennis L. Hartmann, Raymond Hide,
David J. Hoffman, Brian J. Hoskins, James R. Holton, Julius London, Roland
A. Madden, John. A. McGinley, and Gerald R. North. Thanks also go to those
who supplied data and illustrations. Figures and the supporting calculations
were skillfully prepared by Patrick Callaghan, Jacqueline Gratrix, and Kenneth
Tanaka, several of which were organized with the guidance of Harry Hendon
while I was away on sabbatical. Many of the problems evolved through inter-
action with John Bergman, Patrick Callaghan, Gil Compo, Gene Francis, and
Andrew Fusco, from whom I learned a lot. I am grateful to the National Aero-
nautics and Space Administration for its continued support during the book's
construction and to the Lady Davis Foundation at Hebrew University, which
provided support during a sabbatical when I began this exercise. I am also
grateful to Atmospheric Systems and Analysis for support to produce several
of the illustrations. Last, but surely not least, I am indebted to my wife Eva
for enduring the last years, so that this project could be completed.
MURRY L. SALBY