James I.N. Introduction to Circulating Atmospheres

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Preface

The wind blows where it wills; you hear the sound of it, but you do not know

where it comes from, or where it is going. (John, 3, 8)

In the ancient world, the question of where the wind came from and where it

was going to was one of life's unanswerable puzzles. Indeed, so unpredictable

and unknowable was the wind, that the evangelist used it as an elaborate

pun on the inscrutable purposes of God's Spirit (in the Greek of the New

Testament, the same word means 'wind' and 'spirit'). Meteorology of any

sort must have been a most frustrating study. Hints of regular patterns

emerged, only to vanish on closer inspection. Wise saws about the weather

were wrong as often as they helped. And if you were a farmer, a sailor or a

campaigning soldier, guessing the winds or the weather wrongly could lead

to disaster. Truly, through the weather and the winds, the gods played with

man, teased and tormented him, and confirmed their authority.

And here matters more or less rested until the Newtonian revolution of

the seventeenth century. By then, many different aspects of the natural world

had been reduced to reproducible laws. Kepler showed how the motions of

the planets were governed by strict rules, although he did not quite succeed in

explaining why his laws of planetary motion had the forms they did. Galileo

showed how the motions of simple bodies, such as heavy metal spheres on

inclined planes, or pendulum bobs, were orderly and predictable. Newton

with his three Laws of Motion and single Law of Universal Gravitation

unified all these various studies and showed how the observations of earlier

scientists could be predicted by his set of four laws.

It was not long before the problem of atmospheric motions was addressed

using the new Newtonian mechanics. Halley, in 1687, advanced a theory of

the Trade Winds, which he suggested were caused by the rising of heated

air on the equator sucking in air from higher latitudes. Hadley, in 1720,

xii Preface

advanced much the same ideas, suggesting that there must be poleward flow

aloft over the surface trade winds. Thus the earliest attempts to demystify

the winds and the large scale circulation of the atmosphere began. In the

latter part of the eighteenth century, the motions of a fluid on the Earth

were put on a more rigorous mathematical basis, and with the formulation

of the 'Coriolis force', the crucial role of the Earth's rotation began to be

appreciated. Nevertheless, these attempts were hampered by lack of both

theoretical tools and, especially, of observations.

The dream of Newton's disciples was to describe the atmospheric cir-

culation as a predictable mechanism, an objective to be achieved by the

systematic application of Newton's laws of motion to the air. It is ironic

that this dream appeared to become more of a possibility after the First

World War, just as quantum mechanics and the theory of relativity were

undermining the simple deterministic Newtonian account of the dynamics

of systems in other branches of physics. As aviation developed, the need

for detailed meteorological information, and the capability of gathering, and

more particularly collating, the necessary data, both expanded. With the

development of the Norwegian frontal cyclone model by members of the

Bergen school, and their clear objective of quantifying that model in terms

of Newtonian fluid mechanics, the scene was set for the great flowering of

meteorology in the wake of the Second World War. The stability analyses

of Charney and Eady accounted for the development of cyclones in terms

of fluid instabilities. The development of the computer made numerical

weather prediction possible, based upon the integration of the intractible

nonlinear equations of motion. And as a global network of observing sta-

tions and telecommunications links was established, a truly global view of

the atmospheric circulation began to emerge.

To my mind, in the computer the meteorologist found a most diverting

toy. The effort to develop realistic models, first for short range weather

prediction, and more recently for climate simulation and prediction, took

precedence over attempts to understand the dynamical nature of the large

scale atmospheric circulation. Since the governing equations are complex

and nonlinear, it seemed to many that their numerical solutions would afford

the only feasible approach to understanding their implications; and so many

of the most ingenious brains in the business devoted themselves to refining

numerical schemes and improving the representation of various unresolved

but important processes. The deep physical insights into the nature of

the atmospheric circulation gained by such men as Rossby and Ertel were

all but forgotten by a whole generation of atmospheric scientists. A few

academic meteorologists continued to be drawn to the attempt to reduce the

Preface

xiii

atmosphere to its simplest possible essentials, and out of that effort came

a deeper appreciation of the way in which nonlinearity manifests itself in

the atmosphere. The work of Lorenz and others led to the development of

so-called 'chaos' theory, which has become so fashionable in many fields of

modern science. This revealed that nonlinearity can act to generate great

complexity out of really rather simple equations. The language of chaos now

illuminates our studies of the large scale atmospheric circulation.

The Newtonian dream was severely compromised with the realization that

unpredictability is a fundamental property of such systems as the atmosphere,

and not just a technical limitation. Unpredictability is most obvious in

the weather forecasting problem: two nearly identical approximations to

the atmospheric circulation at a particular moment quickly diverge as the

forecast proceeds. The attempt to carry out long range forecasts by analogy

with the history of similar atmospheric states is clearly doomed. Intimately

related to the limited validity of weather forecasts is the difficulty of identi-

fying discrete 'parcels' of air. As the chaotic motions in the atmosphere

advect any such parcel around, it becomes distorted; long, thin streamers of

material are pulled off it, and eventually it is completely dispersed through

the rest of the atmosphere. In the process, it loses any identity.

After the naive optimism of the Newtonian era, we now realize that

indeed, St John's observation is quite right; where the wind comes from and

where it is going to are, in a sense, profoundly and essentially unknowable.

From the static concept of a precise and definable global circulation, we

now understand the atmosphere as an infinitely varied, evolving system,

with complex structure on all space and timescales. By dint of much

time and spatial averaging, we can arrive at a static view of the global

circulation of the atmosphere which is built up from the combined effects of

smaller subsystems or 'building blocks', in the classic Newtonian reductionist

tradition. But when we look more closely, the same building blocks are

capable of building entirely different edifices. The building itself modifies

the building blocks. We conclude that these simple pictures always have

limited validity and are severely limited when we try to extend them to

different situations. That is partly why predicting the climate of the high

carbon dioxide world that mankind is rapidly creating is so difficult and

controversial. It is also why recent attempts to survey the atmospheric

circulations of the other planets have led to unexpected surprises on every

front.

Much of the earlier part of this book is taken up with a description of the

modern elaboration of the deterministic account of the global atmospheric

circulation. The approach will be based on physical principles, relating the

xiv Preface

thermodynamical processes which drive the circulation to the mechanical

processes which determine the resulting motions of the atmosphere. I have

tried to present both observations of the actual circulation as well as simple

models based on the laws of mechanics and thermodynamics. These models

are approximate and limited, but they do provide a vocabulary, a set of

conceptual models, which enable the researcher to interpret observations of

the real atmosphere on one hand or the results of immensely complex 'global

circulation models' on the other. Towards the end of the book, I will survey

some more recent developments in the field which point to the complexity

of the real circulation, and the limitations of our simple models.

Chapters 1-6 concentrate essentially upon the deterministic view of the

global circulation, developed over the last 50 years or so. The basic physical

laws,

expressed in suitably quantitative language, will be given in Chap-

ter 1. Chapter 2 discusses both observations of the large scale atmosphere

and the weather prediction and global circulation models which between

them provide our modern tools for the study of the global circulation. The

thermodynamic imperative for that circulation is provided by the inhomo-

geneous heating of the atmosphere. This will be addressed in Chapter 3.

The dynamics of the resulting motion is strongly constrained by the Earth's

rotation and other mechanical factors. The atmosphere exhibits considerable

ingenuity in circumventing these constraints in order to transport heat. The

various responses of the atmosphere to differential heating will be outlined

in Chapters 4, 5 and 6.

The remaining chapters focus on some more recent developments in our

understanding of the global circulation. The traditional view of the circu-

lation as a meridional overturning is of course a great oversimplification.

Variations in the zonal direction have been studied more intensively in recent

years,

with an emphasis on the maintainance of the midlatitude storm tracks

and on those processes which generate the long wavelength, semi-permanent

troughs and ridges in the midlatitude westerlies. Zonal asymmetries in the

tropics have assumed greater importance, not least because they seem to offer

some limited degree of predictability of weather regimes at higher latitudes

on the seasonal timescale. The underlying theme in these chapters is the

interaction between different scales of motions in the atmosphere. The end

result is that the large scale structure of the circulation is, to a considerable

extent, organized by smaller scale, transient features, and not the reverse.

These topics form the subject of Chapter 7.

Similar results hold in the time domain. The timescales predicted by the

work of the earlier chapters are all fairly short, not generally exceeding

a few days or, at most, weeks. Yet the atmospheric circulation fluctuates

Preface xv

on much longer periods. 'Low frequency' variability, that is, variability

with timescales of ten days and longer, is considered in Chapter 8. While

the preceding material is of some help in understanding some of the basic

mechanisms for low frequency variability, the modern developments in the

field of chaotic behaviour assume explicit importance.

Routine satellite observations, and greatly improved satellite instrumenta-

tion have led to a considerable upsurge of interest in the stratosphere

and the circulation of the 'middle atmosphere', that is, of the stratosphere

and mesosphere. Such research has gained considerable urgency as the

interactions between ozone chemistry and mass circulations in the middle

atmosphere are seen as central to attempts to understand human influences

on ozone. The appearance of the 'ozone hole' in the southern hemisphere

spring has clearly demonstrated that such human influences are present.

The increasing suspicion that ozone depletions on a more global scale are

beginning means that there is an urgent need to understand the circulation

of the stratosphere. The transport of trace consituents such as ozone and

the various trace chemicals which interact with it again brings into sharp

focus the chaotic and unpredictable nature of the atmospheric circulation.

Chapter 9 is devoted to an introduction to the stratospheric circulation and

its influence on ozone distribution.

Finally, in Chapter 10, we step back from a myopic consideration of the

Earth's atmosphere in isolation. Properly, we may understand the circulation

of the Earth's atmosphere as a particular realization of a great range of

possibilities, some of which we see exemplified in the other planets of the

solar system. The study of the global circulation has perhaps always suffered

from being the study of a single system. Now at least a small core of data is

available for virtually all the bodies with substantial atmospheres in the solar

system. Meteorology can join with the other earth sciences, and embark on

the

comparative

study of the range of possible global circulations.

The level of the exposition is intended to be suitable for advanced under-

graduate and for masters level students. I hope it will also be found useful by

researchers who wish to acquire enough background knowledge of the global

circulation to tackle the original literature confidently. The text is an expan-

sion of courses that I have taught to our MSc and BSc students over the past

few years. Indeed, an important motivation for the text was the need to rec-

ommend suitable reading to accompany these courses. The standard texts on

dynamical meteorology devote only a small proportion of their pages to the

global circulation. Other more general texts are very descriptive and scarcely

enable the student to get to grips with the physical processes underlying the

global circulation at any quantitative level. So this book deliberately sets

xvi Preface

out to address, not the whole of dynamical meteorology, but the application

of dynamical meteorology to the large scale circulation. It is presumed that

the reader will have studied the basics of atmospheric dynamics, though in

order to make the text self-contained and to establish the notation that I will

use,

the most important results are quoted without rigorous derivation in the

opening chapter. The various processes which drive the circulation, such as

absorption and emission of electromagnetic radiation, microphysical cloud

processes and turbulent transports in the atmospheric boundary layer (a

group of processes often miscalled 'atmospheric physics', as if Newton's laws

are not physics!) will not be developed to any great extent; once more, a few

important results will be quoted, and readers requiring more information

will be referred to other texts. What this book will concentrate on is the

transport of heat by large scale atmospheric motions, and the way in which

these transports release more energy to drive the circulation. Transport of

heat inevitably implies transport of other quantities, such as moisture or

momentum. It is the transport of these quantities which form the central

theme of our studies.

Each chapter finishes with a short section of problems. These serve a

number of purposes. One is to encourage the student to develop a quant-

itative, as well as a qualitative, understanding of the subject. I hope the

problems will lead the student to develop the habit of carrying out little

calculations and estimates whenever data and equations occur in proximity.

In this way, an appreciation of the relative importance of different effects and

of the circumstances in which different sorts of balances can occur will be

built up. Another function of

the

problems is to suggest some lines of thought

or to introduce some additional results which have had to be dropped from

the main text. These extensions are mainly fairly straightforward. It is worth

spending time with them; only when they can be tackled confidently does one

truly understand the material of the text. Of course, staring at an insoluble

problem for hours is a depressing experience of limited educational value.

For this reason, I have included outline answers to the problems. Brevity

and clarity do not always go together in such a context, and I hope that

what I have written will at least contain enough hints to help the student

produce a more detailed solution.

The bibliography gives further reading for each chapter, and in some cases

for each section. The sources of many of

data and figures are given there.

However, in the main, the bibliography is deliberately pedagogical in intent;

I have not attempted to make this complete or slavishly sought out first

attributions. Rather, the books and papers which are mentioned are chosen

to be helpful to the student who requires more detail or a fuller explanation

Preface

xvii

of particular topics. One of the results is that there is a preponderance

of references to papers by my own colleagues. This parochial bias is not

meant as a criticism of the work of those who are omitted; rather, it is a

consequence of the huge amount of global circulation related research which

has been published in recent years.

Many people have helped me in the preparation of this book. Some

have helped unknowingly, by their teaching, writing and conversation about

matters relating to my themes. In particular, I would like to record my

gratitude to Dr Raymond Hide, who introduced me to the study of atmo-

spheric circulations, and to Professors Brian Hoskins and Robert Pearce,

who provided a stimulating environment at Reading, where I learned about,

and explored, the Earth's global circulation, with the aid of both data and

simple models. I would like to record my grateful thanks to a host of col-

leagues who generously helped me with advice and who spent considerable

time and effort attempting to satisfy my insatiable appetite for data and

figures. Among them, I would mention Paul Berrisford, James Dodd, Paul

James,

David Jackson, Adrian Matthews, Michiko Masutani, Fay Nortley,

Mark Ringer, Keith Shine, Julia Slingo, and Paul Valdes. Michael Blackburn

deserves special thanks for his patience in helping me to write the computer

programs needed to prepare plots of the ECMWF climatology. Many col-

leagues in other institutes have not only given me permission to reproduce

their diagrams, but have generously supplied original artwork. I would like

to mention X. Cheng, R. Hide, D.A. Johnson,

Lyjak, B. Naujokat, A.

O'Neill, R. A. Madden, A. Scaife, J. M. Wallace, and G.

Williams. Several

of my colleagues have read and commented upon early drafts of various

sections of the text. Among them are M. Collins, M. Juckes, F. Nortley, R.

Pearce and S. Rosier.

A large number of the diagrams in this book have been prepared from

climatologies based on operational meteorological analyses carried out at

the European Centre for Medium Range Weather Forecasts (ECMWF). The

climatologies have been built up over several years as part of a joint project

with the UK Meteorological Office and the University of Reading. I must

acknowledge a debt to all my colleagues who have worked on this project

over the last ten years or so; among them are Paul Berrisford, Huang Hsu,

Michiko Masutani, Sarah Raper, Prashant Sardeshmukh and Glenn White.

Special thanks are due to ECMWF for their interest and patient support for

this diagnostics project and to the UK Meteorological Office who afforded

access to the data.

It is also traditional for authors to thank their long suffering families at

this point, and I am no exception. I owe a tremendous debt to their patience

xviii

Preface

and understanding. I trust their resigned indulgence can now be rewarded

with a positive orgy of gardening, decorating and model making.

But above all, this book owes its existence to my students at Reading.

Over the years their interest in my lectures, and their determined efforts to

learn about the global circulation, have inspired me to refine my material

and write this book. I am also conscious of many able students around

the world who would like to attend universities in the West to learn about

the atmosphere, but for whom raising the necessary finance to travel is

impossible. Perhaps books like this will help them to develop their studies.

While it is all too imperfect and partial, I hope that all these people and

their successors will find my account of the atmospheric circulation helpful.

Ian James

Bracknell

February 1993

Notation

A Wave action density, Eq. (6.32).

a Radius of planet (6.371 x 10

m for Earth).

Specific heat at constant pressure.

Specific heat at constant volume.

Drag coefficient.

Components of group velocity.

Group velocity vector.

Phase speed of external gravity wave

for equivalent depth ho, see Eq. (7.7).

D Horizontal divergence.

3} Form drag, see Eq. (8.15).

Dp/Dt Rate of change following a wave packet, Eq. (6.22).

E Rate of evaporation.

E 'E-vector', Eqs. (7.20) and (7.26).

e Vapour pressure.

Saturated vapour pressure.

e& Saturated vapour pressure at reference

temperature; for water, taken to be 611 Pa at 273 K.

F Friction tendency of the vertical component

of the relative vorticity.

F Eliassen-Palm flux, Eq. (6.68).

/ Coriolis parameter.

/o Coriolis parameter at some reference latitude.

J* Friction force per unit mass.

g Acceleration due to gravity (9.81 ms~

for Earth).

H Pressure scale height, RT/g.

h{p) Ratio of

dQ>/dp

and 6, see Eqs. (1.54) and (5.23).

ho Equivalent depth, see for example Eq. (7.4).

K 1 - Diffusion coefficient.

2 - Kinetic energy per unit mass.

3 - Total wavenumber, (k

)

1/2

Total stationary wavenumber.

xix

xx List

Notation

k Zonal wavenumber.

k Vertical unit vector.

kp Rhines wavenumber,

see Eq.

(10.25).

1 - Characteristic horizontal length scale.

2 - Latent heat of condensation of water vapour.

Rossby radius of deformation, NH/f.

I Meridional wavenumber.

M (t/2 - uft)/2.

m Vertical wavenumber.

N 1 - Brunt-Vaisala frequency.

2-wV.

P Rate of precipitation.

p Pressure

Standard reference pressure (usually taken

100

kPa

for

Earth).

Surface pressure.

1 -

Heat added

per

unit mass

to an air

parcel.

Arbitrary scalar variable.

DO/Dt

due to

heating.

Q Forcing

omega equation,

see

Eqs.

(1.77)

and

(1.78).

q Quasi-geostrophic potential vorticity,

Eq.

(1.75).

Ertel's potential vorticity,

Eq.

(1.79).

Gas

constant (287

kg"

for dry air).

jR* Universal

gas

constant (8314

(kg

mole)"

Gas

constant

for dry air.

Gas

constant

for

water vapour (461.5

kg"

r Humidity mixing ratio.

Saturated humidity mixing ratio.

1 -

Heating rate, dQ/dt.

Flux

solar radiation.

1 -

Static stability parameter,

Eq.

(1.72).

Specific entropy,

Eq.

(3.13).

T Temperature.

t Time.

1 -

Internal energy

per

unit mass.

Characteristic velocity scale.

u Zonal component

wind.

Ageostrophic zonal component

wind.

Geostrophic zonal component

wind.

u Vector velocity

(w,t?,

w).

v Meridional component

wind.

Ageostrophic meridional component

wind.

Geostrophic meridional component

wind.

v Horizontal component

velocity vector

(w,

v,0).

w Vertical component

wind.

W Work

per

unit mass done

by an air

parcel.

Zonal coordinate.

Y Width

Hadley cell

Held-Hou theory,

see Eq.

(4.12).

y Meridional coordinate.

z Height above Earth's surface.

Pseudo-height,

-H

ln(p/p