The Dynamic Meteorology of the Stratosphere and Mesosphere

221 Pages·1975·18.382 MB·English

by  James R. Holton (auth.)

THE DYNAMIC METEOROLOGY
OF THE
STRATOSPHERE AND MESOSPHERE
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METEOROLOGICAL MONOGRAPHS
Volume 15 August 1975 Number 37
THE DYNAMIC METEOROLOGY
OF THE
STRATOSPHERE AND MESOSPHERE
James R. Holton
University of Washington
American Meteorological Society
Copyright c 1975 by the American Meteorological Society
Softcover reprint of the hardcover 1st edition 1975
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in
any form or by any means, electronic, mechanical, photo
copying, recording, or otherwise, without the prior written
permission of the publisher.
Library of Congress Catalogue Card No. 75-17141
American Meteorological Society
45 Beacon Street
ISBN 978-1-935704-31-7 (eBook)
DOI 10.1007/978-1-935704-31-7
PREFACE
In this monograph I have attempted to provide a coherent account
of the fundamental dynamical processes which control the general
circulation of the stratosphere and mesosphere. The work is not in
tended to be a comprehensive review of the extensive literature on the
meteorology of the stratosphere and mesosphere. Rather, it is designed
to provide a systematic development of the principles necessary for
the understanding of the dynamics of large-scale motions in the
stratosphere and mesosphere. Thus, the monograph should prove
useful not only as a reference for research workers, but also as a
textbook for advanced courses in the dynamic meteorology of the upper
atmosphere.
Most of this manuscript was prepared during a sabbatical visit to
the Department of Applied Mathematics and Theoretical Physics,
Cambridge University. I have benefited from discussions with a number
of colleagues both in Britain and the United States. In particular, I wish
to acknowledge discussions with Dr. Michael Mcintyre and Dr. Adrian
Simmons. In addition, useful comments on the manuscript were pro
vided by Dr. J. M. Wallace, Dr. R. E. Dickinson and Mr. L. Pfister.
I am especially grateful to Dr. J. D. Mahlman for his perceptive and
thorough critical review of the manuscript.
This work was supported in part by the National Science Founda
tion, under Grant GA-23488.
James R. Holton
December 1974
TABLE OF CONTENTS
PREFACE
Chapter 1: Introduction: The Observational Basis
1.1 The zonally averaged circulation . . . . . . . . . . . . . . . . . . . 3
1.2 The energetics of the stratosphere and mesosphere . . 10
1.3 Extratropical planetary waves and the sudden strato-
spheric warmings............................... 14
1.4 Equatorial stratospheric waves . . . . . . . . . . . . . . . . . . . . . 23
Chapter 2: The Development of Dynamical Models
2.1 The basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Scale analysis: dynamical simplifications . . . . . . . . . . . . 38
2.3 Beta-plane descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4 Linear waves in a motionless basic state . . . . . . . . . . . . 53
2.5 Radiative heating: sources and sinks . . . . . . . . . .. . . . . 75
Chapter 3: Baroclinic Instability in the Stratosphere and Mesosphere
3.1 Necessary conditions for instability: the Charney-Stem
theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 Dynamic stability of the lower stratosphere . . . . . . . . . 91
3.3 Baroclinic instability in the mesosphere . . . . . . . . . . . . . 97
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Chapter 4: Forced Waves and Wave-Zonal Flow Interactions
4.1 Basic properties of linear waves in shear flow . . . . . . . 106
4.2 Extratropical planetary waves . . . . . . . . . . . . . . . . . . . . . 114
4.3 Equatorial stratospheric waves..................... 134
4.4 Wave-zonal flow interaction . . . . . . . . . . . . . . . . . . . . . . . 149
4.5 Atmospheric thermal tides . . . . . . . . . . . . . . . . . . . . . . . . 162
Chapter 5: Numerical Modelling of the General Circulation of the
Stratosphere and Mesosphere
5.1 Two-dimensional models . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.2 Quasi-geostrophic models . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.3 Primitive equation models . . . . . . . . . . . . . . . . . . . . . . . . . 188
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
BibUography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Chapter
1
Introduction:
The Observational Basis
Meteorologists conventionally divide the atmosphere between
0-80 km into three layers based on the vertical gradient of tempera
ture (Fig. 1.1). In order of increasing elevation these are the
troposphere, the stratosphere, and the mesosphere, respectively. In
the troposphere and mesosphere the temperature generally decreases
with height, while the lower stratosphere is nearly isothermal and the
upper stratosphere has a positive temperature gradient with height.
The troposphere and the stratosphere are separated by the
tropopause, a level of temperature minimum which varies in height
from about 15 km at the equator to 9 km at the poles. The
stratosphere and mesosphere are separated by the stratopause, a level
of temperature maximum which occurs near 50 km. The mesosphere
is itself bounded above by the mesopause at about 80 km which is a
level of temperature minimum similar to the tropopause. Thus, the
troposphere and the mesosphere are regions of relatively low static
stability while the stratosphere has relatively high static stability.
Interest in the meteorology of the stratosphere has been
stimulated in the past few years by concerns over possible adverse
effects which a large fleet of supersonic aircraft might have on the
stratospheric environment and hence on the global climate. There has
1
2 CHAPTER 1
been an upsurge in research on various aspects of the meteorology of
the stratosphere. These research efforts have concentrated primarily
on the radiative and photochemical aspects of stratospheric meteorol
ogy. However, it is generally recognized that transport of radiatively
and/or photochemically active substances-ozone, water vapor, and
oxides of nitrogen-by the general circulation provides the basic link
between human activities and the global climate. Thus, nothing
definitive can be said concerning the possible effects of human
activities on the upper atmosphere and/or global climate unless full
account is taken of atmospheric motions and their interactions with
radiative and photochemical processes. Similarly, any definitive
evaluation of the alleged effects of solar cycle variations on weather
and climate will require detailed quantitative models of the coupling
between the upper and lower atmospheres provided by atmospheric
motion systems. The eventual goal of providing reliable predictions of
the possible climatic effects due to human activities or solar
variability can only be realized through the development of numerical
general circulation models which are capable of simulating faithfully
the physical processes occurring in the upper atmosphere and the
coupling between the upper atmosphere and the troposphere.
Clearly such models cannot be developed without first obtaining
a detailed quantitative understanding of all the chemical, physical and
dynamical processes relevant to the meteorology of the upper
atmosphere. Various observational and theoretical aspects of the
chemistry and physics of the upper atmosphere have been reviewed
by Craig (1965) and more recently in the ClAP monographs
(Department of Transportation, 1974). In this review we will not
discuss the distribution or radiative and photochemical properties of
ozone and other trace substances in any detail. Nor will we discuss
the transport of such substances by the general circulation. Rather we
will be concerned primarily with purely dynamical models which seek
to provide understanding of the basic causes of the observed
circulation systems and their variations in space and time. This
emphasis seems justified because only a dynamical model which
correctly represents both the eddy and mean flow components would
be capable of properly describing the transport of trace substances.
Furthermore, the separation of dynamics from the photochemistry
can be justified in the lowest order approximation on the basis of
scale considerations. In the upper stratosphere and mesosphere
where radiative heating by solar absorption in the ozone layer
provides the primary energy source for the mean zonal circulation,
the photochemical time scales are so short that a local equilibrium
occurs and atmospheric motions have very little effect on the ozone
INTRODUCTION: THE OBSERVATIONAL BASIS 3
distribution. In the lower stratosphere, on the other hand, the ozone
distribution is almost entirely determined by the motion field, i.e.,
ozone is advected like a passive tracer (Leovy, 1964a; Blake and
Lindzen, 1973). In either situation the interactive coupling between
the photochemistry and the motions is likely to be a second-order
effect. Thus, it would be prudent to develop a thorough understanding
of the separate photochemical and dynamical processes before attempt
ing to combine them in a global general circulation model simulation.
The plan of this monograph is as follows: In the present chapter
we briefly review the observed characteristics of the primary motion
systems in the stratosphere and mesosphere. In Chapter 2 we develop
the basic equations for dynamical modelling of the upper atmosphere.
We also consider the properties of linear wave perturbations in a
resting atmosphere on a sphere and a simple model for radiative
heating/cooling. In Chapter 3 we discuss the possible role of
baroclinic instability in the stratosphere and mesosphere. In Chapter
4 we consider the properties of vertically propagating forced waves
and the nature of their interactions with the mean zonal flow. Finally,
in Chapter 5 we review the progress in the numerical simulation of
motions in the stratosphere and mesosphere.
1.1 THE ZONALLY AVERAGED CIRCULATION
Basic to all studies of the atmospheric general circulation is the
distinction between the longitudinally averaged (zonal mean) flow and
the deviations from this mean, or eddies. In the troposphere the
deviations of the flow from the zonal mean, which are generated by
internal flow instabilities and topographical and thermal forcing, are
generally strongly nonlinear in character so that only rather idealized
studies are possible with linear theory. In the stratosphere and
mesosphere, on the other hand, the eddies primarily consist of
planetary-scale waves which to a surprising accuracy can be
described in terms of linear wave dynamics. Therefore, the splitting
of the motion into zonal mean and eddy components in the
stratosphere and mesosphere provides a far more powerful tool for
theoretical analysis than is true for motions in the troposphere.
The observed zonal mean structure of the atmosphere for various
seasons can be determined up to the 10 mb level (- 31 km) from
routine radiosonde data. Above that level rocketsondes have been the
primary data source (Webb, 1966) although remote temperature
sounding from satellites is now beginning to provide far better
coverage at higher levels (Barnett et al., 1972).