Table Of ContentT H E
U P P E R
A T M O S P H E R E
Meteorology and Physics
BY
RICHARD A. CRAIG
DEPARTMENT OF METEOROLOGY
THE FLORIDA STATE UNIVERSITY
TALLAHASSEE, FLORIDA
1965
@
ACADEMIC PRESS New York and London
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Preface
During the past fifteen years, knowledge of the upper atmosphere of our
planet has increased at a tremendous rate. The use of improved balloons, of
rockets, and of satellites has resulted in a vast collection of observations and
has greatly stimulated related research. New contributions appear in the scientific
journals at the rate of many thousand pages per year. As a result, it is no longer
practical to attempt a comprehensive book that will do justice to all or most of
the specialized topics involved, as Professor Mitra was able to do in 1948.
Instead a book must be written with a specific objective which will influence
the choice of and relative emphasis on the topics treated. The objective of this
book is to provide a suitable introduction to what I choose to call the meteorology
of the upper atmosphere.
Neither “upper atmosphere” nor “meteorology” has an unambiguous
meaning. I have found it convenient in this book to refer to the atmosphere
above the tropopause as the “upper atmosphere,” although the expression is
often used elsewhere to refer to the atmosphere above some higher level. The
word “meteorology” is quite broadly defined in dictionaries, but in practice
is usually associated with studies of the atmosphere below some ill-defined
limit. This limit has been moving upward in recent years and might now be
taken as about 30 km. Meteorologists are, collectively, concerned with a broad
range of difficult problems connected with this part of the atmosphere and have
made relatively few contributions to studies of the upper atmosphere above,
say, 30 km. The scientists who have contributed to such studies have been
mostly physicists, chemists, and astronomers by training, and are often called
“aeronomers.”
However, I happen to feel that a distinction based on any altitude limit is a
poor one, especially if it hinders understanding and communication. Meteorology
embraces many different kinds of problems, from turbulence and diffusion to
the general circulation, from cloud physics to numerical weather prediction.
But most meteorologists would agree that our central problem is the under-
standing, prediction, and eventual control of the behavior of a fluid atmosphere
subject to certain forces and boundary conditions on a rotating planet. This
implies a basic interest in the structure, circulation, and interactions of the
atmosphere as a whole, and especially in the time variations that occur, whether
these are determined observationally or theoretically. This central underlying
V
vi Preface
theme, however poorly I may have described it, distinguishes meteorology as
I use the word. In this sense, there is no good reason why meteorology should
be confined to the troposphere or even the troposphere and lower stratosphere.
I should like to predict that during the next ten to twenty years there will
develop an active identifiable branch of atmospheric science that is concerned
with the upper atmosphere from the point of view described above. Whether
it will be called “meteorology of the upper atmosphere” I do not know, nor
do I particularly care. Its development will require the cooperation of scientists
who are presently labeled as meteorologists, aeronomers, atmospheric scientists,
or perhaps something else. I hope that this book will to some extent stimulate
and accelerate this development.
The difficulties, though, are formidable and the objective is correspondingly
ambitious. Interdisciplinary studies are much easier to advocate in general
terms than to carry out in practice. The meteorologist who attempts to extend
his interests to the upper atmosphere must first of all learn that the astronomical,
physical, and chemical background problems are quite different from those
of the troposphere. Although he need not become an expert in all of these,
he must understand and appreciate them and be able to communicate with
people who are experts. Correspondingly, the aeronomer who wants to apply
his observations to meteorology (or meteorology to an interpretation of his
observations) must learn that a rotating, compressible, turbulent fluid is an
extremely complex system not described satisfactorily by some of the sim-
plifications of classical physics.
I have written this book with the meteorological reader primarily in mind.
This means that I have emphasized those topics that I think might interest
him the most. It also means that I have elaborated on related physical and
chemical problems that I think might be the most unfamiliar to him, and at
the same time, important for him to appreciate. On the other hand, I have
assumed a mature reader with a good background in applied mathematics and
in basic aspects of physics and chemistry, such as a graduate student or research
worker in meteorology should have. Not all will agree with specific applications
of these intentions, because no two readers will have the same interests and
background. I have therefore thought it very important to include large numbers
of references which will enable the reader to follow up subjects for which he
finds my treatment deficient for his purposes. For various reasons the emphasis
is on the atmosphere between the tropopause and 100 km, although a good
deal of material is also included about the atmosphere between 100 and 300 km.
Very little is said about the important problems at still higher levels, which
are now the subject of active and vigorous research.
Despite a certain preoccupation with the difficulties of a meteorologist
seeking to extend his view upward, I do hope that the book will be useful to
all scientists interested in the upper atmosphere. The aeronomer who specializes
Preface Vii
in a certain branch of upper-atmospheric research will undoubtedly find short-
comings in the treatment of his specialty. But he should find it profitable to
read about other aspects of the upper atmosphere from the point of view
adopted here.
As always with a book of this sort, the author has been dependent on many
other people for help and has incurred many debts in its preparation. First of
all, I am very grateful to the following friends and colleagues who took the
time to read various portions of the manuscript: R. M. Goody, B. Haurwitz,
W. S. Hering, L. G. Jacchia, F. S. Johnson, J. London, and R. J. Reed. Their
perceptive comments and helpful suggestions resulted in a considerable im-
provement of the manuscript over an earlier version. However, not all portions
of the manuscript were reviewed, and I was unable for various reasons to take
advantage of all suggestions about the portions that were reviewed. Therefore,
responsibility for the faults that remain is clearly mine.
A majority of the figures in the text have been adapted from figures published
elsewhere. The publishers involved have been most considerate in granting
me the right to do this. Reference to sources is in all cases made in the captions.
Here at The Florida State University a number of people have contributed
greatly to the preparation of the book. These include many graduate students
who struggled through early course-note versions of the text. In particular,
Dr. M. A. Lateef and Messrs. W. A. Bowman, S. Y. K. Li, and J. Bell have
helped with text, figures, and references. Above all, I am indebted to Mrs. Janina
Richards who has expertly typed the manuscript through several versions,
perhaps a total of 3000 pages, and always without a word of complaint. In fact
she somehow managed to make me feel guilty whenever progress was slow
and there was no typing to be done. Without her help, the book would certainly
have been delayed and perhaps never have been completed.
RICHARDA . CRAIG
December I964
C H A P T E R 1
In t ro duc tion
The term “upper atmosphere” is commonly used to designate the earth’s
atmosphere above some explicitly or implicitly defined altitude. However,
the choice of altitude to separate “lower atmosphere” or “middle atmosphere”
from “upper atmosphere” is not uniform. For example, some may regard air
30 km above the earth as being in the upper atmosphere while others may
consider this air to be part of the lower atmosphere or middle atmosphere.
Here the expression “upper atmosphere” refers to air above the tropopause.
Thus, only air in the troposphere, which has the most direct thermal interaction
with the earth‘s surface, is excluded. This is a rather more general use of the
term than is customary, but there seems to be no better single expression to
describe the part of the atmosphere with which we shall deal.
For purposes of reference, the upper atmosphere is often divided into sub-
regions, each with a different name. The fact that several systems of nomen-
clature have been used has resulted in a good deal of unfortunate confusion
and ambiguity. Most of these systems are based on the vertical temperature
distribution, and it will be convenient to defer a detailed discussion of nomen-
clature (to Section 1.3) until after we have considered the broad outline of
upper-atmosphere structure.
Since the end of World War 11, several exciting developments have tended
to focus broad scientific attention on the upper atmosphere of our planet. The
increased ceiling and greater reliability of sounding balloons; the use of rockets
to probe the upper atmosphere; cooperative international efforts during the
International Geophysical Year; and especially the successes of Soviet and
American scientists in launching instrumented satellites-all have broadened
the horizons of upper-atmospheric research and uncovered significant new
information. Nevertheless, it is a fact that the broad outlines of our knowledge
of the upper atmosphere were already sketched before this era by a small group
of dedicated men who were limited by the technology of their time to various
indirect and ingenious methods of probing. As examples, one might mention
the use of radio waves to study the ionized regions, the use of sound waves to
deduce the vertical temperature distribution, the deduction of density distri-
bution from meteor observations, measurements of solar ultraviolet radiation
to learn about ozone, spectroscopic studies of aurora and airglow, and analyses
of atmospheric tides and magnetic variations. These studi‘es not only furnished
1
2 1. Introduction
a broad and generally accurate body of knowledge in the prerocket days, but
also played a vital role in dictating the emphasis and direction of the recent
research. Many of these techniques are still very useful.
Study of the upper atmosphere involves so many interrelated problems that
it is difficult to discuss one without assuming some knowledge of the others.
This introductory chapter deals in broad outline with the structure and compo-
sition of the upper atmosphere (Sections 1.1 and 1.2), covers nomenclature
(Section 1.3), and, in Section 1.4, outlines the principal topics to be discussed
in greater detail later. It is intended to define, to orient, and to facilitate cross-
referencing in the more detailed chapters to follow.
1.1 Variables Describing Structure and Composition
The physical and chemical state of the atmosphere is partially described by
the structure variables-temperature, pressure, and density. Much effort has
been devoted to measuring, by various methods, how these parameters vary
in space and time. Indeed, a significant portion of this book will be devoted to
discussions of those methods and their results. Some methods of probing the
upper atmosphere measure temperature directly, some measure pressure, and
some measure density. The equation of state and the hydrostatic equation relate
the three, and Subsection 1.1.1 considers how these relationships are usually
written and used in the meteorological and aeronomical literature.
Two complications, not generally familiar to meteorologists, become impor-
tant at high enough levels in the upper atmosphere. One is variable composition,
which begins to affect the mean molecular weight of air above 80 km. This is
discussed briefly in Subsection 1.1.2. The other is the variation with altitude
of the acceleration of gravity, which must be considered in the upper atmos-
phere. This is discussed briefly in Subsection 1.1.3.
1.1.1 THEE QUATIOONF STATEA ND THE HYDROSTATEIQCU ATION
The constituents of air obey the equation of state for an ideal gas very closely
at the pressures existing in the atmosphere. Air itself therefore behaves very
nearly as an ideal gas, provided that it is assigned a properly defined mean
molecular weight. We can write
p = pRT/m (1.1)
where p is the pressure, p the density, T the kinetic temperature, R the universal
gas constant, and m the mean molecular weight. The value of R is 8.317 x
lo7 erg mole-l deg-l; the gram-molecular weight (for dry air) has the value
28.966 at sea level and is known to be essentially constant up to about 80 km.
Above that level it undoubtedly decreases with altitude (see Subsection 1.1.2).
1.1 Variables Describing Structure and Composition 3
To a very good degree of approximation, air is in hydrostatic equilibrium,
so that the downward-directed gravity force balances the upward-directed
pressure-gradient force. Coriolis and acceleration terms are several orders of
magnitude smaller, except perhaps occasionally, in the case of the latter, for
small scales of motion. Therefore
aplaz = -pg (1-2)
where z is the vertical coordinate directed outward perpendicular to the earth’s
surface and g is the acceleration of gravity. The acceleration of gravity, by
convention, combines the effect of Newtonian gravitation and centripetal
acceleration due to the earth’s rotation. It varies somewhat with both latitude
and altitude (see Subsection 1.1.3).
Throughout the lower atmosphere and in some of the upper atmosphere,
it is permissible to neglect variations of g and m with height. Then, according
to (1.1) and (1.2), the pressure p at a height x above the bottom of an isothermal
layer is related to the pressure po at the bottom of the layer by
(1.3a)
It is often convenient (although not so common with reference to the lower
atmosphere as to the upper atmosphere) to introduce the scale height H, where
H = RT/mg. In terms of H, (1.3a) may be written
(1.3b)
Also, for an isothermal layer,
P = Po exp(--zlH) (1.4)
Another case of considerable interest is a layer where the temperature varies
linearly with z. In this case, for a temperature To at the bottom of the layer
and a lapse rate* I‘,
rz
T = T, -
p = Po( T/T0)OmfRr
A convenient parameter, used frequently in the upper-atmosphere literature,
is the number density n, the number of particles per unit volume. In a mixture
of gases
n = z n i (1.8)
I
*In common meteorological usage, the lapse rate r is defined to be positive when
temperature decreases with height; r = -aT/az.
4 1. Introdzrction
where ni is the number density of the ith constituent. The equation of state if
conveniently written for the mixture
p = nkT (1 -9)
or, for an individual constituent,
pi = nikT (1.10)
where k is Boltzmann’s constant (k = 1.380 x 10-l6 erg deg-l) and pi is
the partial pressure of the ith constituent.
The density pi of the ith constituent is given by nipi ,w here pii s the molecular
mass and is related to the gram-molecular weight mi by pi = mi/N. Here N
is Avogadro’s constant, N = 6.025 x loz3( g mok-l. Obviously, the universal
gas constant R is related to k by R = Nk. The density of a mixture of gases
may be written
P = n7p.i = nCL (I .11)
where p, the mean molecular mass, is defined by p = &zipi/&.
The hydrostatic equation in this notation may be written
appz = -npg ;1.12)
and clearly (1.3a) and (1.6) may be used with k/p substituted for Rlm.
1.1.2 VARIATIOONF MEANM OLECULAWRE IGHTW ITH HEIGHT;
SCALEH EIGHTM, OLECULAR-SCATLEEM PERATURE
At high enough elevations, the atmosphere is not mixed and p (or m) decreases
with height. In this circumstance, one may consider integrated forms of the
hydrostatic equation for particular vertical variations of the scale height H
rather than for particular vertical variations of T. For example, (1.3a) and
(1.3b) are valid not for an isothermal layer but for a layer where the ratio T]m
is constant (if vertical variations of g may be neglected). Corresponding to a
constant lapse rate of temperature, one may consider a constant gradient* of
+
scale height, such that H = Ho and fi = aH/az.
The counterpart of (1.6) is
(1.13)
and in such a layer
(1.14)
* Note that by convention the variation of scale height in a linear layer is described
by the vertical gradient 6, which is positive when scale height increases upward.
1.1 Variables Describing Structure and Composition 5
A particularly interesting case, applicable at high enough levels, is that of
diffusive equilibrium, where each gas individually obeys* an equation of the
form(1.12):
8pi/az = -ni,uig (1.15)
Then with the aid of (1.10) the vertical distribution of partial pressure pi and
number density n, for each gas can be computed according to the vertical
distribution of the scale height Hi= kT/pig for that particular gas. The vertical
distribution of the mean molecular mass can be determined by combination
of the results for the individual gases.
Sometimes, especially in connection with standard atmospheres, the molecular-
scale temperature T, is used. This is defined by
T,,,lm, = Tim (1.16)
where m, has the sea-level value 28.966. The molecular-scale temperature is,
of course, equal to the kinetic temperature when the mean molecular weight
has its sea-level value. The equation of state can then be written
.
where R, is the gas constant for (dry) air at sea level, R, = R/m,
1.1.3 VARIATIOONFS g ; GEOPOTENTIASTLA, NDARGDE OPOTENTIAL
The acceleration of gravityg varies with both latitude and altitude. At sea level,
it is about 0.5 per cent higher at the poles than at the equator. Its variation
in the vertical is given approximately (but not exactly, because g includes not
only Newtonian gravitation but also the effect of centripetal accelerations) by
+
g(4 = g(O)/[l (4re)I2 (1.18)
where g(0) is the value at sea level and Y, is the radius of the earth. For example,
the value of g at 100 km is about 97 per cent of its value at sea level.
A vertical coordinate called geopotential is often introduced to absorb the
variability of g. It is defined by
1:
go@ = gdz (1.19)
where @ is the geopotential and go is a constant chosen to make the numerical
value of geopotential similar to the numerical value of the geometric altitude
* This is not quite correct but is sufficiently accurate for our purposes.
