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Invisible in the Storm

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

Copyright Date: 2013
Pages: 346
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  • Book Info
    Invisible in the Storm
    Book Description:

    Invisible in the Stormis 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 Stormexplains the crucial role of mathematics in understanding the ever-changing weather.

    eISBN: 978-1-4008-4622-1
    Subjects: Physics, Mathematics, Environmental Science

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
    (pp. vii-x)
  4. PRELUDE: New Beginnings
    (pp. 1-2)

    By the end of the nineteenth century mankind was using Newton’s laws of motion and gravitation to calculate the times of sunrise and sunset, the phases of the Moon, and the tides. Such data was carefully tabulated in almanacs and diaries, and many working people, from fishermen to farmers, benefitted from this successful application of science. Then, in 1904, a Norwegian scientist published a paper outlining how the problem of weather forecasting could be formulated as a problem in mathematics and physics. His vision became the cornerstone of modern weather prediction, and the agenda he pursued for the next three...

  5. ONE The Fabric of a Vision
    (pp. 3-46)

    Our story begins at the end of the nineteenth century in the twilight years of the theory of the “ether”: a theory of space, time, and matter, which was soon to be superseded by Einstein’s theory of relativity and by the theory of quantum mechanics. A Norwegian scientist made a remarkable discovery while working on the ether theory, a discovery that was to lead to a new beginning in meteorology.

    A pensive, thirty-six-year-old Vilhelm Bjerknes peered through a quarter-pane of his window at a city shrouded by a sky as gray as lead. it was a bitterly cold afternoon in...

  6. TWO From Lore to Laws
    (pp. 47-88)

    In chapter 1 we introduced the weather pixel, our fundamental unit in building a picture of the atmosphere. Next we need rules to advance the pixels so that we can predict the picture for tomorrow. By 1700 Newton’s mathematics was seen to be astonishingly successful at predicting how planets move around the solar system. It would take the next two centuries to extend this mathematics to the movement of the atmosphere. This chapter introduces the basic rules that determine how our weather pixel variables interact with each other to create tomorrow’s weather. More sophisticated rules—such as the circulation theorem—...

  7. THREE Advances and Adversity
    (pp. 89-124)

    Lewis Fry Richardson, one of the most enigmatic of British scientists, was the first person to turn Bjerknes’s general scheme of diagnosis and prognosis into a precise mathematical algorithm. His calculations were done by hand during the First World War, but the prognosis failed because of a subtle problem in the data from which the forecast was started. Bjerknes’s attempts to predict tomorrow’s weather developed in a very different way. Electronic computing was still generations in the future, and Bjerknes himself believed that any direct assault on the equations was impractical; so Bjerknes’s team developed graphical methods based on charts...

  8. FOUR When the Wind Blows the Wind
    (pp. 125-148)

    Each year the winter solstice is predicted and the Sun returns to the same position in the sky. Why does the winter storm not also exactly repeat itself? In terms of gales, wind chill, rain, or snow, winter storms of the middle latitudes are broadly similar but yet ceaselessly varying. The Bergen School’s attempts to understand the origins and classify the similarities of cyclones would never answer the question of precisely when and where next winter’s major storm would strike. With the enormously greater calculational ability of a modern computer, would Richardson’s forecast procedure provide the answer? In this chapter...

  9. INTERLUDE: A Gordian Knot
    (pp. 149-152)

    In the first half of this book we set out a way to describe weather using a computer. We introduced “weather pixels,” which make up a hologram of our planet’s weather. The hologram shows the wind, warmth, cloud, and rain at each fixed location in our atmosphere and at a given time. Then, just as a movie advances a sequence of images, we need to advance our weather pixels in time, and this requires rules to relate each pixel both to its neighbors and to earlier pixels. But if the weather pixels are to follow actual planet Earth weather, as...

  10. FIVE Constraining the Possibilities
    (pp. 153-186)

    The quantitative model envisaged by Bjerknes and created by Richardson is considered a “bottom-up” view of weather. It includes as much detail as possible and focuses on how each local region of air influences and interacts with its neighborhood. By writing down the laws that govern the detailed physics of the forces and winds, the heat and moisture, we can proceed to simulate “weather”—the consequence of these complex interactions. The problem with this reductionism, à la Descartes, is that the many component parts can interact in hugely complicated ways.

    The Bergen School identified the salient features of certain weather...

  11. SIX The Metamorphosis of Meteorology
    (pp. 187-230)

    Rossby had loosened the Gordian knot of nonlinear feedback in the motion of the atmosphere, albeit only for the large-scale jet streams in midlatitudes. Next we describe how work on both sides of the Atlantic began to change ideas about the origins of cyclones with their attendant warm and cold fronts—the features that preoccupy forecasters in many parts of the world.

    Rossby’s explanation of the meanderings of the jet stream was significant not least because the polar front—the battleground between warm tropical air and cooler polar air—had been considered an essential part of the Bergen School’s model...

  12. Color Insert
    (pp. None)
  13. SEVEN Math Gets the Picture
    (pp. 231-270)

    Charney’s 1948 paper “On the Scales of Atmospheric Motion” reveals how hydrostatic and geostrophic balance, together with the conservation of potential temperature and potential vorticity, set us on the road to understanding much about temperate latitude weather. Fifteen years later, Edward Lorenz published a paper under the somewhat innocuous title “Deterministic Nonperiodic Flow,” and concluded that long-range weather forecasting might be forever beyond our capabilities. Would chaos undo all that had been achieved in theoretical meteorology? In this penultimate chapter, we show how the rather different results and conclusions of Charney and Lorenz can be rationalized within a single mathematical...

  14. EIGHT Predicting in the Presence of Chaos
    (pp. 271-312)

    As the twentieth century came to a close, more aspects of weather and climate were being incorporated into computer programs. What is the state of progress with weather forecasting and climate prediction in the twenty-first century? Uncertainty does affect the way that we view the Earth’s moisture-transporting atmosphere, and affects our ability to predict its changing behavior. Since we will never have perfect knowledge of the air and moisture above, we look at how to do better in the presence of the unknown, and how to improve computer representation of weather.

    So we turn to the heart of the matter....

  15. POSTLUDE: Beyond the Butterfly
    (pp. 313-316)

    Astronomy and meteorology have always played important and interactive roles in driving the historical development of physics and mathematics. Astronomy was among the first of the sciences to benefit from advances in mathematics: Newton’s laws of motion and gravitation, supplemented by the conservation laws of energy and angular momentum, enabled the orbits of the planets to be evaluated for many years into the future. By the end of the eighteenth century, confidence in the science was captured by intricate models, such as the orrery, shown in figure Po.1.

    Contrast this with the challenge of creating computer models of weather and...

    (pp. 317-318)
    (pp. 319-322)
  18. INDEX
    (pp. 323-325)