Invisible in the Storm: The Role of Mathematics in Understanding Weather

344 Pages·2013·11.062 MB·English

by  Ian Roulstone

InvIsIble In the storm

InvIsIble
In the storm
The Role of MaTheMaTics
in UndeRsTanding WeaTheR
Ian Roulstone and John noRbuRy
Princeton University Press

Princeton and oxford
copyright © 2013 by Princeton University Press

Published by Princeton University Press, 41 William street,

Princeton, new Jersey 08540

in the United Kingdom: Princeton University Press, 6 oxford street,

Woodstock, oxfordshire ox20 1tW

press.princeton.edu

all rights reserved

Library of congress cataloging number 2012037453

isBn 978-0-691-15272-1

British Library cataloging-in-Publication data is available

This book has been composed in Minion Pro

Printed on acid-free paper. ∞

Printed in the United states of america

1 3 5 7 9 10 8 6 4 2
Contents
Preface vii

Prelude: New Beginnings 1

one
the fabric of a vision 3

two
from Lore to Laws 47

three
advances and adversity 89

four
When the Wind Blows the Wind 125

Interlude: A Gordian Knot 149

fIve
constraining the Possibilities 153

sIx
the Metamorphosis of Meteorology 187

Color Insert follows page 230
seven
Math Gets the Picture 231

eIght
Predicting in the Presence of chaos 271

Postlude: Beyond the Butterfly 313

Glossary 317

Bibliography 319

Index 323

PrefaCe
to most of us, meteorology and mathematics are a world apart: why
should calculus tell us anything about the formation of snowflakes?
But mathematics has played an ever-growing and crucial role in the de-
velopment of meteorology and weather forecasting over the past two
centuries.
The continuing development of modern computers allows prodigious
amounts of arithmetical calculation to be performed every minute, and
every day forecasters harness this computational power to predict to-
morrow’s weather. But to appreciate the success of modern weather
forecasting, and to figure out why it occasionally goes wrong, we need
to understand how the behavior of the atmosphere and oceans is quanti-
fied in terms of mathematics.
computer operations are couched in mathematical instructions and
follow abstract logical rules to organize the calculations, so it is neces-
sary to describe both the present state and the changes of the earth’s
atmosphere in terms of appropriate mathematical language for imple-
mentation on computers. However, this is an enduring problem for two
important reasons. first, we will always have less than perfect knowl-
edge of the interactions of clouds, rain, and the eddying gusts of wind;
and second, computers can only execute a finite number of calculations
in producing each forecast.
This presents forecasters with an interesting challenge: how to capture
the essentials of the behavior of the atmosphere without being “blown
off-course” by the lack of perfect knowledge. This challenge preoccupied
the pioneers of weather forecasting well before the advent of modern
computers. By the end of the nineteenth century, the basic physical laws
governing the motion of the atmosphere were in place; attention then
turned to finding solutions that predicted the weather.
This book describes the developing role of mathematics in our on-
going quest to comprehend and predict weather and climate. The pur-
suit of meteorology as an exact, quantitative science was precipitated in
the early twentieth century by a relatively small group of mathemati-
cians and physicists from quite disparate backgrounds. Their story is
viii • Preface
fascinating and informative in itself, and their legacy is more than the
foundation of modern weather forecasting—they showed us why the fu-
sion of mathematics and meteorology will always underpin the science
of predicting weather and climate.
But along with the realization that forecasting the next storm was a
difficult problem in science, mathematicians, while probing the mystery
of the stability of the solar system, discovered chaos. The key question
was whether the planets would continue their motion around the sun
forever, or whether a chance collision—for example, with a meteor—
might eventually lead to their future motion changing entirely.
today weather forecasters constantly push at extending the limits to
predictability that the physical laws encapsulate. continually improving
the forecasting procedure provides more reliability in the predictions
and requires bigger computers, ever-better software, and more accurate
observations. Within modern supercomputers, the scale of the number
crunching almost defies comprehension, but mathematics allows us to
see the order amid the detail.
in the first half of the book we describe four key elements in the his-
toric development of weather forecasting: first, how we learned to mea-
sure and describe the atmosphere; second, how we encapsulated this
knowledge in terms of physical laws; third, how we learned to express
the physical laws in terms of mathematics, thereby enabling us to make
predictions; and fourth, how we learned to recognize the devil within
the detail—the phenomenon we call chaos.
The second half of the book then describes the post-1930s modern
approach where the mix of mathematics and machines has enormously
improved our ability to predict future weather and climate. The second
World War and the subsequent expansion of civil and military aviation
drove many new agendas in meteorology and related technologies such
as radar, satellites, and, not least, computers. This technology push fa-
cilitated the breakthrough in 1949 of the first weather forecast calcu-
lated by a computer. But underlying the well-documented development
of this pioneering work lies a little-known story about the role of math-
ematics in the discovery of the key to successful computer calculations.
so we end by describing how math is being, and will continue to be,
exploited by forecasters to separate the predictable from the unpredict-
able. This becomes even more relevant in the context of understanding
and predicting future climate.
Preface • ix
for scientific completeness, tech boxes are used to detail the techni-
cal material in the text. The book is designed so that those who prefer
to skip the content of the tech boxes may do so and still understand the
overall concepts. The glossary following the postlude uses simple lan-
guage to explain the concepts used to design weather-forecasting com-
puter programs.
Acknowledgments
over the many years we have been researching and writing this book,
we have become indebted to many friends, family, and colleagues for
useful discussions and critical feedback. in this regard, we thank sid
clough, Mike cullen, Jonathan deane, dill faulkes, seth Langford, Peter
Lynch, Kate norbury, anders Persson, sebastian reich, Hilary small,
Jean velthuis, and emma Warneford. Particular thanks are due to andy
White for his very careful reading of, and commentary on, the penulti-
mate draft of the manuscript.
We also thank sue Ballard, ross Bannister, stephen Burt, Michael de-
vereux, david dritschel, ernst Hairer, rob Hine, rupert Holmes, steve
Jebson, neil Lonie, dominique Marbouty, John Methven, alan o’neill,
norman Phillips, david richardson, claire roulstone, and Mike White
for their help in providing artwork and illustrations.
We are grateful to the following organizations that provided images,
and in particular we would like to thank staff at the american Meteo-
rological society, the University of dundee, the european centre for
Medium-range Weather forecasts (ecMWf), the Met office and na-
tional Meteorological Library, and the royal society of London, for
valuable help. ian roulstone gratefully acknowledges the support of the
Leverhulme trust, via a fellowship in 2008–9.
We would like to thank vickie Kearn of Princeton University Press
for her patience and constant encouragement, and her many colleagues,
past and present, including Kathleen cioffi, Quinn fusting, dimitri
Karetnikov, Lorraine doneker, anna Pierrehumbert, stefani Wexler,
and Patti Bower, for their help in producing the book.
finally, the love and support of our families was, to say the least, in-
valuable, and we dedicate this book to them.