
Does the future hold more extreme weather? Mathematics helps us answer this question.
Mathematicians think about weather and climate in an unusual way. Our everchanging weather can be visualized as a curve meandering through an abstract mathematical space of logically possible weather. Any one point of the curve corresponds to a particular state of the weather. The surprise is that the curve does not wander around randomly  patterns emerge. One part of the pattern may correspond to 'warm and dry' and another part to 'cold and wet'. Predicting changes in the weather for the week ahead involves working out if the curve will drift from one part of the pattern to another. Understanding climate involves working out how the pattern itself will change.

Mathematics helps us identify the predictable and the unpredictable in weather forecasting.
We all know that the weather forecaster can sometimes get it wrong. And yet, most of the time, the forecast for the next day or two is pretty good. To understand the scientific basis of weather forecasting we need to understand the language that defines the problem; and that language is mathematics. The use of mathematics enables us to work out how reliable any one forecast will be—and the level of confidence the forecaster has in the computer output can then be put into context for the benefit of the user.

Mathematics helps us detect climate change.
Climate depends on many factors: the atmosphere, the oceans, the icecaps, land usage, and life in all its forms. Not only are there many interconnections between these systems, the timescales over which changes occur vary enormously: trees can be felled in a few hours or days  changing the character of the local landscape quickly  but carbon stocks in soil vary much more slowly, perhaps over several millennia. To predict future climate we have to account for the short and longtimescale effects, and this can pose subtle problems. Mathematics helps us to quantify how the different timescales of the changes in the components of the Earth system impact on predictions of climate change. Using mathematics, we calculate how cloud patterns change over the next five days, and how the Arctic icesheet changes over the next five years.

In order to forecast the weather for the week ahead we need a better understanding of what the weather's doing today: mathematics helps us to complete the picture.
One of the main sources of information for a new forecast is yesterday's forecast. New generations of satellites gather more, and more accurate, readings, ranging from the sea surface temperature to the state of the stratosphere. Data is exchanged freely around the world among weather bureaus; global weather prediction relies upon this protocol. However, we will never have perfect, complete weather data, and this is why we need mathematical techniques to combine the new information with the old.

Mathematics enables weather forecasters to forecast more than rain or shine: the computer simulations are useful for predicting everything from pollen levels and pollution to flood risk and forest fires.
Mathematics is the language we use to describe the world around us in a way that facilitates predictions of the future. Even though hay fever and floods are very different natural phenomena, predictions of their occurrence can be made using mathematical models. Weather forecasters are actively engaged in combining their predictions with models that help us forecast weatherrelated phenomena.

The quest to understand weather and climate is leading to new breakthroughs in mathematics.
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 evergrowing and crucial role in the development of meteorology and weather forecasting over the past two centuries. Our story explains how mathematics that was originally developed for very different purposes, such as studying the ether or the dynamics of the solar system, is now helping us to understand the dynamics of the atmosphere and oceans, and the changes in our climate. And it is a twoway process: the diversity of phenomena we seek to quantify means we have to describe them using new mathematical ideas that capture the rapid changes, the slow changes, the randomness, and the order, we observe.

The unsung heroes of weather forecasting
An enigmatic Englishman and a founding father of quantum mechanics are among the small group of pioneers that formulated the scientific basis of weather and climate prediction. Weather is a manyfaceted phenomenon, described by mathematics of ferocious complexity. The pioneers had to raise significant intellectual and financial 'venture capital'  often in the face of scepticism and adversity  and they not only succeeded in establishing modern forecasting, they opened up new areas of mathematical research, and this helps us to decide what we can say about the weather 5 days ahead, and about the polar ice sheets in 25 years time.

The weather front: people, politics and power
The creative tension, generated by organisations pursuing broad scientific agendas versus individuals following their own dreams, led to the intellectual breakthroughs necessary for using modern supercomputers in weather and climate prediction. An unpredicted storm in the Black Sea during the Crimean War spurred the French and English governments to set up forecasting services. Both the First and Second World Wars reinforced the importance of meteorology to the armed forces, as exemplified in the DDay landings. So military imperatives spurred the science that led to modern computergenerated forecasts.
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File created: 2/22/2013