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

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Overview

Invisible in the Storm is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times?the use of mathematics in weather prediction. Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and ...

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

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Overview

Invisible in the Storm is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times—the use of mathematics in weather prediction. Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and weather stations, Ian Roulstone and John Norbury narrate the groundbreaking evolution of modern forecasting.

The authors begin with Vilhelm Bjerknes, a Norwegian physicist and meteorologist who in 1904 came up with a method now known as numerical weather prediction. Although his proposed calculations could not be implemented without computers, his early attempts, along with those of Lewis Fry Richardson, marked a turning point in atmospheric science. Roulstone and Norbury describe the discovery of chaos theory's butterfly effect, in which tiny variations in initial conditions produce large variations in the long-term behavior of a system—dashing the hopes of perfect predictability for weather patterns. They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability. Millions of variables—known, unknown, and approximate—as well as billions of calculations, are involved in every forecast, producing informative and fascinating modern computer simulations of the Earth system.

Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather.

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Editorial Reviews

Prospect - Philip Ball
[O]ne of the great strengths of the book is the way it picks apart the challenge of making predictions about a chaotic system, showing what improvements we might yet hope for and what factors confound them.
Nature
Mathematicians Ian Roulstone and John Norbury demystify the maths behind meteorology. Trailblazers' work is vividly evoked, from eighteenth-century mathematician Leonhard Euler on hydrostatics to physicist Vilhelm Bjerknes's numerical weather prediction. The pace cranks up with twentieth-century advances such as Jule Gregory Charney's harnessing of the gargantuan ENIAC computer for his work in the 1940s and 1950s on forecasting pressure patterns.
MAA Reviews - James Rodger Fleming
A welcome and authoritative account of the 20th-century contributions of mathematically sophisticated meteorologists such as Vilhelm Berknes (1862—1951), Carl-Gustav Rossby (1898—1957), Jule Charney (1917—1981), and Ed Lorenz (1917—2008). . . . Clearly, this book is informative and inspirational, leaving plenty of room for innovations by future generations of mathematicians and modelers.
European Mathematical Society - Vicente Muñoz
This book gives a deep insight of the mathematics involved in the forecast of weather. . . . The authors have done a brilliant work to collect a huge amount of historical information, as well as mathematical information, but keeping always a level in the explanations that makes the text accessible to undergraduate students in the first years, and even to people not so familiar with mathematics. All in all, this is a very interesting and enjoyable reading.
From the Publisher
Winner of the 2015 Louis J. Battan Author's Award, American Meteorological Society

"Mathematicians Ian Roulstone and John Norbury demystify the maths behind meteorology. Trailblazers' work is vividly evoked, from eighteenth-century mathematician Leonhard Euler on hydrostatics to physicist Vilhelm Bjerknes's numerical weather prediction. The pace cranks up with twentieth-century advances such as Jule Gregory Charney's harnessing of the gargantuan ENIAC computer for his work in the 1940s and 1950s on forecasting pressure patterns."Nature

"[O]ne of the great strengths of the book is the way it picks apart the challenge of making predictions about a chaotic system, showing what improvements we might yet hope for and what factors confound them."—Philip Ball, Prospect

"A welcome and authoritative account of the 20th-century contributions of mathematically sophisticated meteorologists such as Vilhelm Berknes (1862—1951), Carl-Gustav Rossby (1898—1957), Jule Charney (1917—1981), and Ed Lorenz (1917—2008). . . . Clearly, this book is informative and inspirational, leaving plenty of room for innovations by future generations of mathematicians and modelers."—James Rodger Fleming, MAA Reviews

"This book gives a deep insight of the mathematics involved in the forecast of weather. . . . The authors have done a brilliant work to collect a huge amount of historical information, as well as mathematical information, but keeping always a level in the explanations that makes the text accessible to undergraduate students in the first years, and even to people not so familiar with mathematics. All in all, this is a very interesting and enjoyable reading."—Vicente Muñoz, European Mathematical Society

"Shows how much modern weather forecasting depends on mathematics. . . . A superior read."—Alexander Bogolomny, CTK Insights

"Takes readers on a journey, starting with the initial vision of Bjerknes, and then leads them through the early unsuccessful hand-calculated attempts at forecasting the weather mathematically, progressing to the use of early electronic computers which, even though successful, could not produce a timely forecast. It concludes by describing the current methods of Numerical Weather Prediction . . . a book that will appeal to the intelligent 'popular science' enthusiast without disengaging the more theoretically-versed reader."—David-John Gibbs, Weather

"UK mathematicians Roulstone and Norbury provide a lively account of the evolution of numerical weather prediction, focusing on the individuals involved in advancing measurement of atmospheric properties and the implementation of numerical methods to describe and predict atmospheric processes. . . . This unique historical narrative will interest scholars of the history and philosophy of science."Choice

"Roulstone and Norbury do well within the constraints of this species of book. The story they tell is far from exhausted. I hope they write a sequel!"—John P. Boyd, Mathematical Reviews

"[A] fascinating account of science's admirable but ultimately inadequate attempts to get to grips with the natural environment upon which we depend for life itself, but which is equally capable of visiting death and destruction upon us."—Jonathan Gornall, The National

"[T]he authors have done well to create a book that will appeal to the intelligent 'popular science' enthusiast without disengaging the more theoretically-versed reader."—David-John Gibbs, Weather

"Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather."—Nina Shokina, Zentralblatt MATH

"[T]his is a well-written book giving a generally clear and accessible account of how weather forecasts are prepared. The historical detail enlivens the narrative and makes for an enjoyable read. The authors have considerable knowledge and expertise, and the book is scientifically sound. It can be warmly recommended to anyone who wishes to understand, in broad terms, how modern weather forecasts are made and how we may use models of the atmosphere to anticipate changes in the earth's climate."—Peter Lynch, Notices of the AMS

"This very readable book provides an excellent insight into the history of forecasting the weather, with a considerable, but not too challenging, mathematical bent."—Colin J W Czapiewski, Actuary

"Invisible in the Storm: The Role of Mathematics in Understanding Weather explores how mathematics and meteorology come together to improve weather and climate prediction, taking readers on a fascinating journey through the work of trailblazing scientists over the past 100 years."University of Surrey website

"I really enjoyed reading the book and I would recommend it to specialists who want to get an overview of the history of numerical weather prediction. I think it is also well worth reading for anyone who wishes to understand the developments in the science of meteorology that has led to the present level of forecast skill."—Erland Kallen, ECMWF Newsletter

"Roulstone and Norbury have done an outstanding job and provide readers a fine bibliography to continue their education on this fascinating topic."—Robert E. O'malley, Jr., SIAM Review

"Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather."World Book Industry

"[T]his is a well-written book giving a generally clear and accessible account of how weather forecasts are prepared. The historical detail enlivens the narrative and makes for an enjoyable read. The authors have considerable knowledge and expertise, and the book is scientifically sound. It can be warmly recommended to anyone who wishes to understand, in broad terms, how modern weather forecasts are made, and how we may use models of the atmosphere to anticipate changes in the Earth's climate."—Peter Lynch, Irish Math Society Bulletin

"This book is highly readable and gives a bird's eye view of development of meteorology. . . . It is strongly recommended to practitioners of meteorology and those interested in understanding this complex subject."—Ravi S. Nanjundiah, Current Science

"The authors have to be applauded for having succeeded in writing a very entertaining and accessible book. . . . The book must be considered essential reading for anyone interested in the history and mathematics of weather prediction."—Sebastian Reich, Jahresbericht der DMV

"I recommend Invisible in the Storm both to mathematics undergraduates and educators who are interested in applied mathematics, weather forecasting, or both."—Steven Boyce, Mathematics Teacher

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Product Details

  • ISBN-13: 9780691152721
  • Publisher: Princeton University Press
  • Publication date: 2/24/2013
  • Pages: 346
  • Sales rank: 1,000,247
  • Product dimensions: 6.20 (w) x 9.40 (h) x 1.30 (d)

Meet the Author

Ian Roulstone is professor of mathematics at the University of Surrey. John Norbury is a fellow in applied mathematics at Lincoln College, University of Oxford. They are the coeditors of "Large-Scale Atmosphere-Ocean Dynamics".

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Table of 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

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Customer Reviews

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  • Posted April 12, 2013

    more from this reviewer

    Weather has always been one of the most consequential and most u

    Weather has always been one of the most consequential and most unpredictable aspects of our World. The importance of weather on all facets of human life cannot be underestimated. Storms and hurricanes can have a huge impact, and even less dramatic weather patterns (such as droughts) are of enormous significance. It is no surprise that people have been trying to predict weather for as long as there are any records of civilization, and perhaps for much longer. However, aside from some folk wisdom and very rough rules of thumb, until very recently predicting weather has been little more than guesswork. Things started changing towards the end of the nineteenth century, when a combination of better understanding of the laws of thermodynamics, fluid mechanics, and overall weather patters convinced many scientists that weather forecasting is, in principle, within the reach of the scientific method. Implementing that vision has been far from easy though, and that program has had many obstacles that it needed to overcome. 




    “Invisible in the Storm” is the story of the development of modern scientific meteorology. In particular, it tells the story about the importance of mathematics and its use in solving the problem of weather. It turns out that the equations that we use to model the weather are very complicated and complex, and at best we can hope to have very approximate solutions. Early advances in the mathematical weather modeling had to rely more on some shorthand and general principles that could be judiciously applied to some already observed situations. The full exact solution of the weather equations will probably elude us forever, and even approximate solutions are almost impossible to construct. This is partly due to the phenomenon of “chaos” that has in fact first been widely studied and appreciated exactly in the context of the weather. 




    The alternative to the exact solutions was to use the numerical methods in which smooth functions are replaced by their “pixelated” equivalents. Numerical methods reduce the extremely complicated differential equations with somewhat less complicated and manageable sets of algebraic equations. However, even the simplest numerical methods involve thousands of variables and equations, and early attempts to solve those were nothing short of heroic. Furthermore, the solutions of those early numerical attempts were disastrous in terms of their accuracy. Numerical methods only gained traction with the advent of computers, and only within the last couple of decades were we able to make reasonably accurate predictions that go beyond a single day. 




    This is a thoroughly well written and researched book. If you were unfamiliar with the content of mathematical research in meteorology it would be an incredibly valuable resource and an introduction to this subject. The authors clearly understand their subject, both in terms of its content as well as the rich and interesting history. All of the more mathematically advanced topics are covered in separate boxes throughout the main text, and if higher math is not something that you are familiar with you can safely skip those. Nonetheless, you should be fairly well educated and versed in the scientific method in order to fully appreciate this book. 

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