Table Of ContentDynamical and Physical
METEOROLOGY
GEORGE J. HALTINER, Ph.D.
and FRANK L. MARTIN, Ph.D.
Professors^ L .S. Naval Postgraduate School^ Slonterey^ California
McGRAW-HILL BOOK COMPANY, INC.
New York Toronto London
1957
DYNAMICAL AND PHYSICAL METEOROLOGY
Copyright © 1957 by the McGraw-Hill Book Company, Inc. Printed in the
United States of America. All rights reserved. This book, or parts thereof,
may not be reproduced in any form without permission of the publishers.
Library of Congress Catalog Card Number 57-8005
THE MAPLE PRESS COMPANY, YORK, PA.
PREFACE
The rapid advance in the fields of dynamical and physical meteorology
during the last decade has created a need for texts incorporating the
results of recent research. These fields have become so broad that to con
fine a text of this kind to a reasonable size it is necessary to make a
selection of topics. In general only those phases of physical meteorology
that are more closely linked with dynamic meteorology are included. The
authors endeavor to develop most topics from first principles and to bring
the subject to a point near its present stage. However, the detailed de
velopment of any topic is carried only as far as the limited mathematics
required of the reader permits. Beyond this point, a qualitative discussion
of further advances is frequently made. Probably no two instructors
would agree exactly on a list of subjects to be covered in a text of limited
size; nevertheless the authors feel, on the basis of their experience in teach
ing meteorology, that the selection of topics here should afford a suf
ficiently broad basis from which more detailed discussions may proceed.
The scope of the text is somewhat restricted by the fact that little
mathematics beyond differential and integral calculus is assumed. Some
vector calculus is employed, but the object here is mainly to simplify the
mathematical equations and the physical interpretations. Since the vector
operations used in this text are relatively few in number, they are re
viewed in Chapter 1, so that the student may gain adequate facility with
them. The experience of the authors indicates that the student, even
though unfamiliar with the vector notation at first, soon becomes accus
tomed to it and ultimately benefits greatly through the simplification
achieved. It should also be mentioned that brief reference to the termi
nology of statistics is made occasionally. However, these references occur
so infrequently that the meaning, in general, is evident even if the student
has no previous knowledge of statistics.
No attempt has been made to give the reference for original authors in
every case, especially in connection with classical material. However, ap
propriate credit is generally given to the contributors of more recent re
search. The authors are indebted to the American Meteorological Society
for permission to reproduce Figs. 6-2, 7-7, 8-10, 9-1, 14-5, 14-6, 19-7, 21-2,
21-3, 22-5, 23-1, 23-2, 23-4, 23-5, 23-6, 23-7a, b, 23-9, 23-10, 23-11, 23-12,
VI PREFACE
and Plate II; to the Royal Meteorological Society for Figs. 14-11 and
22-4; to the editor of Tellus for Figs. 23-8, 23-lG, 23-17, 23-21; to Dr.
B. Haurwitz for Figs. 7-5 and 8-1; to Dr. P. J. Kiefer for Plate I; to the
Smithsonian Institution for Fig. 7-3; and to Harvard University Press
for Fig. 15-3 and Plate II.
It should be mentioned that, in every sense, this text represents a joint
contribution by the authors. We wish to thank our respective families
for their patience while the work proceeded. We would like to express
our thanks to Professor W. D. Duthie, Chairman, Department of Aer
ology, U.S. Naval Postgraduate School, for his cooperation during the
preparation of the text. Our thanks also go to Mrs. Maurine McDonald
for her assistance in typing the manuscript.
George J. Haltiner
Frank L. Martin
CONTENTS
PREFACE V
CHAPTER 1. VECTOR OPERATIONS 1
1.1. Dimensions, Units, and Time 1.2. Vector Notation 1.3. Addition and Sub
traction of Vectors 1.4. Dot Product 1.5. Cross Product 1.6. Differentiation of
Vectors 1.7. Del Operator 1.8. Nondivergence and the Stream Function 1.9. To
tal Differential; Local Change
CHAPTER 2. THERMODYNAMICS OF DRY AIR 8
2.1. Physical Variables 2.2. Equation of State 2.3. Composition of the Atmos
phere 2.4. Mixtures of Gases 2.5. Work Done by an Expanding Gas 2.6. Specific
Heat 2.7. First Law of Thermodynamics 2.8. Internal Energy 2.9. Adiabatic
Processes; Potential Temperature 2.10. Stuve Diagram 2.11. Clapeyron, or (p,a).
Diagram 2.12. Emagram 2.13. Linear Representation of Energy Integrals on the
Emagram 2.14. T-ln 6 Chart 2.15. Thermodynamic Diagrams
CHAPTER 3. MOIST AIR 21
3.1. Introduction 3.2. Saturation Vapor Pressure 3.3. Latent Heat 3.4. Equa
tion of State for Water Vapor 3.5. Moist Air; Measures of Water-vapor Content
3.6. Equation of State; Virtual Temperature 3.7. Specific Heats for Moist Air
3.8. Adiabatic Expansion of Unsaturated Air 3.9. Isobaric Cooling or Warming
of Moist Air; Dew Point 3.10. Wet-bulb Temperature; Equivalent Temperature
3.11. Hygrometric Chart 3.12. Fog 3.13. Adiabatic Expansion of Saturated Air
3.14. Irreversible Ascent Bi 3.15. Reversible Ascent A2 3.16. Critique of the
Types of Ascent 3.17. Pseudo-wet-bulb Temperature and Potential Temperature
3.18. Conservatism of Air-mass Properties 3.19. Horizontal Mixing of Air Masses
3.20. Vertical Mixing of Air Masses; Mixing Condensation Level 3.21. Convection
and Vertical Mixing; Convective Condensation Level 3.22. The Condensation
Process 3.23. Some Factors Influencing Saturation Vapor Pressure 3.24. Cloud
Droplets 3.25. Bergeron-Findeisen Theory 3.26. Accretion Theory 3.27. Cloud
Seeding
CHAPTER 4. HYDROSTATIC EQUILIBRIUM; GEOPOTENTIAL
DETERMINATIONS 46
4.1. Gravity 4.2. Geopotential 4.3. Hydrostatic Equilibrium 4.4. Geopotential
Determinations 4.5. Pressure-Height Curves 4.6. Lapse Rate 4.7. ^‘Adiabatic”
Atmosphere; Adiabatic Lapse Rates 4.8. Homogeneous Atmosphere 4.9. Stand
ard Atmosphere 4.10. Barometric Altimetry 4.11. Pastagram 4.12. Precipitable
Water Vapor; Rate of Precipitation
vii
vill CONTENTS
CHAPTER 5. VERTICAL STABILITY AND CONVECTION 57
5.1. Parcel Method 5.2. Adiabatic Displacements 5.3. Stability Criteria in Terms
of Potential Temperature 5.4. Vertical Stretching; Potential Instability 5.5. Con
vergence and Vertical Stretching 5.6. Latent Instability; Stability Index 5.7. Slice
Method of Stability Analysis 5.8. Entrainment 5.9. Recent Theoretical Advances
5.10. Thunderstorms
CHAPTER 6. THE NATURE OF RADIATION 74
6.1. Definition of Radiation 6.2. The Electromagnetic Spectrum 6.3. The Em
pirical Nature of Absorption 6.4. Definitions 6.5. Emissive Properties of Black
Bodies 6.6. The Definitions of Monochromatic Reflectivity, Transmissivity, and
Absorptivity 6.7. Kirchhoff’s Law 6.8. Radiative Transfer through an Absorbing
Medium 6.9. The Flux of Terrestrial Radiation at a Reference Level
CHAPTER 7. SOLAR RADIATION AND THE EARTH-ATMOSPHERE
SYSTEM 87
7.1. The Sun as an Energy Source 7.2. Some Characteristics of the Sun 7.3. The
Sun as a Black Body 7.4. Undepleted Insolation 7.5 Direct-beam Insolation with
Clear Skies 7.6. The Smithsonian Technique of Solar Constant Measurement
7.7. The Clear Sky, Direct-beam Insolation at the Earth’s Surface 7.8. A De
scription of Scattering 7.9. Scattering Depletion of the Solar Beam by Water Vapor
7.10. Disposition of Solar Radiation Incident on the Troposphere with Clear Skies
7.11. Disposition of Solar Radiation Incident on the Troposphere with Cloudy Skies
CHAPTER 8. TERRESTRIAL RADIATION 106
8.1. Some Comparative Absorptivities in Solar and Terrestrial Wavelengths 8.2. Ab
sorption by the Atmospheric Gases in the Terrestrial Wavelengths 8.3. Simpson’s
Treatment of the Flux of Terrestrial Radiation 8.4. Intensity Transmission by
Water Vapor 8.5. Pressure and Temperature Corrections; Corrected Optical Depth
8.6. Water Vapor and CO2 Fluxes; Elsasser’s Method 8.7. Upward Flux; Net Flux
8.8. Divergence of Flux and Radiative Heating or Cooling of Air 8.9. Flux Compu
tations by the Method of Isothermal Emissivities 8.10. The Kew Chart 8.11. Flux-
divergence Tables
CHAPTER 9. SOME SYNOPTIC CONSEQUENCES OF TERRESTRIAL
RADIATION 125
9.1. Radiative Temperature Changes in the Atmosphere 9.2. Maintenance of In
versions 9.3. Terrestrial Radiative Transfer at Cloud Bases and Tops 9.4. Cloud
Destabilization 9.5. Heat-transfer Processes at the Ground 9.6. Some Minimum-
temperature Formulas 9.7. Applications to Minimum-temperature Forecasting
9.8. Effects of Variations of Certain Meteorological Parameters on the Nocturnal-
temperature Fall 9.9. A Modification to Include Turbulent Heat Transport
9.10. The Radiative Transformation of a Maritime-polar to a Continental-polar
Air Mass
CHAPTER 10. THE MEAN HEAT BALANCE OF THE EARTH-
ATMOSPHERE SYSTEM 142
10.1. Introduction 10.2. The Mean Heat Balance of the Earth-Troposphere System
10.3. Discussion of the Items of the Mean Heat Balance 10.4. The Atmospheric
Greenhouse Effect 10.5. The Mean Heat Balance in Latitudinal Belts of the Tropo
sphere 10.6. The Role of the General Circulation in the Heat Balance 10.7. Cer-
CONTENTS IX
tain General Circulation Characteristics 10.8. Radiative and Convective Equi
librium in the Atmosphere 10.9. Radiative Heating and Cooling in the Ozone Layer
CHAPTER 11. THE EQUATION OF MOTION 158
11.1. Absolute and Relative Motion 11.2. Equation of Motion 11.3. Gravitation
and Gravity 11.4. The Pressure Force 11.5. The Relative Equation of Motion
11.6. Zonal Flow 11.7. Tangential Rectangular (Local) Coordinates 11.8. Spheri
cal Polar Coordinates 11.9. Some Approximations 11.10. Acceleration in Natural
Coordinates 11.11. Horizontal Spherical Flow 11.12. The Coriolis Force in Natural
Coordinates 11.13. The Equations of Horizontal Motion in Natural Coordinates
11.14. Mapping the Horizontal Motion 11.15. Energy Equations
CHAPTER 12. HORIZONTAL FRICTIONLESS FLOW 178
12.1. Introduction 12.2. Classification of Flow 12.3. Changes in Speed 12.4. Geo-
strophic Flow 12.5. The Inertial Wind 12.6. The Adjustment of the Pressure Force
to the Wind 12.7. Eulerian Flow 12.8. Gradient Flow 12.9. Trajectories and
Streamlines 12.10. An Example of Sinusoidal Streamlines and Trajectories 12.11.
Blaton’s Equation 12.12. Further Properties of Gradient Flow 12.13. Gradient
Wind Scales 12.14. General Horizontal Frictionless Motion 12.15. Wind Esti
mates 12.16. Factors Associated with Horizontal Accelerations and Ageostrophic
Flow 12.17. The Local Contribution to Horizontal Acceleration and the Ageo
strophic Wind 12.18. Downwind Contributions to Horizontal Acceleration and the
Ageostrophic Wind 12.19. Vertical-motion Contributions to Horizontal Acceleration
and the Ageostrophic Wind
CHAPTER 13. VARIATION OF THE WIND AND PRESSURE FIELDS
IN THE VERTICAL 200
13.1. Introduction 13.2. Quasi-Lagrangian Coordinates (rr,7/,^,0 13.3. Co
ordinates; Constant-pressure Analysis 13.4. Vertical Variation of the Wind; Thermal
Wind 13.5. Vertical Shear of the Geostrophic Wind 13.6. The Vertical Variation
of the Gradient Wind 13.7. Local Temperature Variations 13.8. Horizontal Ad-
vection and the Local Temperature Variation 13.9. The Thermal Wind and Rela
tive Stability 13.10. Vertical Variation of Pressure Systems
CHAPTER 14. WIND STRUCTURE IN THE FRICTION LAYER 214
14.1. Introduction 14.2. Viscous Stresses 14.3. Equations of Motion for a Vis
cous Fluid 14.4. The Reynolds Number 14.5. Turbulent Fluctuations; Reynolds
Stresses 14.6. Molecular Viscosity 14.7. Exchange Coefficients 14.8. Gustiness
14.9. The Surface Layer 14.10. The Wind Profile in the Neutral Surface Layer
14.11. The Wind Profile in the Nonneutral Surface Layer 14.12. The Layers of
Frictional Influence 14.13. The Vertical Variation of the Wind in the Spiral Layer
14.14. The Balance of Forces 14.15. Generalizations of the Taylor Spiral 14.16.
The Variation of Cross-isobar Angle with Stability in the Friction Layer
CHAPTER 15. DIFFUSION OF HEAT AND WATER VAPOR 244
15.1. Introduction 15.2. Application of the Prandtl Mixing-length Principle 15.3.
Diffusion of Water Vapor in the Ocean’s Surface Layer; Evaporation 15.4. The
Diurnal Variation of Vapor Pressure in Continental Areas 15.5. The Diurnal Vari
ation of Temperature near the Ground 15.6. A Theory of the Diurnal Variation
of Temerature, Usipng a Variable Eddy-diffusion Coefficient 15.7. Terrestrial
Radiative Warming-Cooling in the Diurnal Variation of Temperature near the Ground
X CONTENTS
15.S. Steady-state Air Mass Transformation cP mP 15.9. Forced and Free Con-
veetion and the Flux of Sensible Heat
CHAPTER 16. DIFFUSION OF ATMOSPHERIC POLLUTANTS 264
16.1. Introduction 16.2. The Partial Differential Equation of Turbulent Diffusion
16.3. Diffusion from Instantaneous Point and Line Sources in the Case of Constant
Diffusion Coefficients 16.4. Diffusion from Continuous Point Sources 16.5. Steady
state Diffusion from Infinite Line Sources 16.6. Some Conclusions Regarding
Atmospheric Diffusive Power 16.7. Steady-state Diffusion Pattern from a Point
Source 16.8. Statistical Theory of Turbulence 16.9. Steady-state Diffusion from
Continuous Point Sources 16.10. Applications of the Continuous point-source
Theory 16.11. Other Factors Affecting Concentration of Pollutants
CHAPTER 17. FRONTOGENESIS 287
17.1. The Frontogenetical Function 17.2. Frontogenesis in the Horizontal Velocity
Field 17.3. Linear Velocity Fields 17.4. Elementary Streamline Patterns 17.5.
Frontogenetical and Frontolytical Sectors 17.6. Streamline Patterns 17.7. Syn
optic Evidence of Frontogenesis
CHAPTER 18. SURFACES OF DISCONTINUITY 297
18.1. Introduction 18.2. Pressure Distribution near Fronts 18.3. Pressure Tend
encies Associated with Fronts 18.4. Temperature Distribution at Fronts 18.5.
Wind Distribution at Fronts; Kinematic Boundary Condition 18.6. Classification
of Fronts 18.7. Margules’ Formula 18.8. Nongeostrophic Front 18.9. The Geo-
strophic Front 18.10. Tropopause 18.11. Pressure Jumps
CHAPTER 19. THE MECHANISM OF PRESSURE CHANGE 308
19.1. Introduction 19.2. Kinematics of Pressure Systems 19.3. Intensification of
Pressure Systems 19.4. Equation of Continuity 19.5. Velocity Divergence 19.6.
Divergence in Horizontal Spherical Flow. 19.7. The Measurement of Horizontal
Divergence 19.8. Computation of Large-scale Vertical Motion 19.9. The Equation
of Continuity in Other Coordinate Systems 19.10. Pressure-tendency Equations
19.11. Empirical Results on Pressure Changes 19.12. Further Results on Horizontal
and Isobaric Divergence 19.13. Horizontal Mass Divergence in Wave-shaped Isobar
Patterns 19.14. Horizontal Mass Divergence in Closed Cyclonic Circulations 19.15.
Movement and Deepening of the Extratropical Cyclone 19.16. The Speed of Long
and Short Waves 19.17. Evolution of the Extratropical Cyclone 19.18. Some
Empirical Considerations
CHAPTER 20. VORTICITY AND CIRCULATION 342
20.1. Introduction: Definition of the Vorticity Vector 20.2. The Vertical Compo
nent of Vorticity 20.3. Relative and Absolute Vorticity 20.4. Circulation and Its
Relationship to Vorticity 20.5. The Principle of Solenoids 20.6. Applications of
the Circulation Theorem 20.7. The Vorticity Equation 20.8. The Vorticity Equa
tion in Other Coordinate Systems 20.9. Constant Absolute Vorticity (CAV)
Trajectories 20.10. Applications to Wave-speed Computations 20.11. Effect of
Velocity Divergence (Convergence) on Trajectories 20.12. Development of the Lee-
side Trough 20.13. Relative and Absolute Vorticity Patterns 20.14. An Applica
tion to Pressure Change 20.15. Sutcliffe’s Approach to the Problem of Development.
CHAPTER 21. THE PERTURBATION THEORY 366
21.1. Introduction 21.2. Waves 21.3. The Perturbation Equations 21.4. The
CONTENTS XI
Perturbation Equations for the Autobarotropic, Incompressible Atmosphere 21.5.
Boundary Conditions 21.6. Gravity Waves in a Homogeneous, Incompressible
Fluid Having a Free Surface 21.7. Shearing-gravitational Waves on an Internal
Surface of Discontinuity 21.8. Long Waves in Zonal Currents; the Autobarotropic
Incompressible Atmosphere 21.9. Jet Stream Waves 21.10. Waves in a Baroclinic
Current 21.11. Hydrodynamic Instability; Inertial Instabihty 21.12. Dispersion
of Energy 21.13. Examples of Dispersion
CHAPTER 22. DYNAMIC FORECASTING BY NUMERICAL
METHODS 387
22.1. Introduction 22.2. The Barotropic Model 22.3. Numerical Methods 22.4.
The Relaxation Method Applied to the Barotropic Model 22.5. A Graphical Tech
nique 22.6. Baroclinic Effects; Equivalent Barotropic Model 22.7. Baroclinic
Effects; Advective Model 22.8. Two-parameter Model 22.9. Baroclinic Effects;
Two-level Model 22.10. Further Refinements 22.11. Stability Properties and
Structure of Baroclinic Waves
CHAPTER 23. THE GENERAL CIRCULATION 415
23.1. Definition of the Problem 23.2. Mean Circulation of the Troposphere and
Lower Stratosphere 23.3. Latitudinal and Seasonal Variations in the Mean Circu
lation 23.4. Comparison between the Northern and Southern Hemispheres 23.5.
Extension of the Meridional Cross Sections to 100,000 Ft 23.6. A Model of the
General Circulation 23.7. Experimental Approaches to the General Circulation
23.8. The Maintenance of the Mean Circulation; the Kinetic-energy Balance of the
Atmosphere 23.9. The Maintenance of the Mean Zonal Circulation; Angular-
momentum Considerations 23.10. Maintenance of the Zonal Circulation; Absolute-
vorticity Considerations 23.11. A Theory of Index-cycle Variations 23.12. A
Numerical Experiment on the General Circulation 23.13. Statistical Studies of the
General Circulation
INDEX 455
