Invisible in the Storm: The Role of Mathematics in Understanding Weather
Ian Roulstone and John Norbury
Princeton University Press
The weather on April 10, 1934 was of little note to the three seasoned meteorologists stationed at the Mount Washington Observatory in New Hampshire.
"A perfect day," they wrote in the log book. "Cloudless and calm. Hazy."
The next day began the same way, with a brilliant sunrise, and from their lofty perch in the White Mountains the men could clearly see the Atlantic Ocean, 120 kilometres to the south-east.
But then the observatory's cats - Oompha and her five kittens - abandoned the great outdoors and started to huddle around the observatory's coal stove.
By late afternoon, everything had changed. Clouds, fog and thick ice set in and by nightfall, the isolated building was being buffeted by winds of more than 218kph.
The meteorologists hadn't anticipated the dramatic weather shift - and it was far from over. By 1.21pm the following day, the winds peaked at 372kph - a super hurricane, and the fastest surface winds recorded on Earth, before or since.
Fortunately, the remote hurricane caused no damage or deaths, but off-the-mark forecasters have not always been so fortunate.
Few people in Britain have forgotten or forgiven the TV weatherman Michael Fish, who on October 15, 1987, told the nation: "Earlier on today apparently a woman rang the BBC and said she'd heard that there was a hurricane on the way. Well," he said, "don't worry, there isn't."
But there was. That evening, south-east England and northern France were struck by hurricane-force winds, gusting up to 220kph in some places; 22 people died, millions of trees were felled, electricity supplies failed and numerous vessels were wrecked at sea.
The problem was - and remains - that although meteorology is one of the most intensively studied scientific endeavours of the modern world, supported by technology such as radar, satellites and supercomputers performing countless calculations a second, the efforts of the best minds on the planet to predict the weather are continually thwarted by a factor that refuses to yield to our desire for order: chaos.
This is the somehow heartwarming admission at the core of Invisible in the Storm, a fascinating if challenging new book from Princeton University Press that examines the role of mathematics in forecasting.
The authors, Ian Roulstone and John Norbury, are mathematicians at the UK universities of Surrey and Oxford and at times their attempt to demystify "the crucial role of mathematics in understanding the ever-changing weather" reads like an advanced textbook and succeeds only in baffling the lay reader.
But between the blocks of incomprehensible formulae - considerately fenced off from the general narrative in pens which should absolutely not be strayed into by anyone armed with less than a bachelor's of science degree in applied mathematics - can be found 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.
In part, the story of forecasting they tell is the history of some of the great names of science - the likes of Archimedes, Galileo, Newton, Joule and Kelvin - who "across the centuries laid the foundations, the mathematical laws, upon which modern meteorology would be built".
From the beginning, meteorology has been one strand of humankind's effort to impose order, and the supremacy of the species, upon our environment, but it has never been solely an academic conceit. Life-or-death interest in what tomorrow's weather might hold is as old as mankind's dependence upon crops for survival, an interest only heightened when fishermen and traders began taking to the high seas in pursuit of food and profit, and when aircraft began soaring into the skies.
In 1920, when the cash-strapped Norwegian government moved to shut down the pioneering Bjerknes meteorological institute in Bergen, it changed its mind in the face of a campaign by Norway's west coast fishermen, "who said that weather forecasting was the best thing the state had done for them".
The Bergen school, led by the pioneering Norwegian physicist Vilhelm Bjerknes, became one of the most influential organisations in the development of modern meteorological methods after Bjerknes began to realise that his earlier work on fluid dynamics and thermodynamics could be applied to an understanding of the apparently random machinations of the atmosphere.
From the outset, however, write Roulstone and Norbury, "no one was under any illusion about how difficult it would be to calculate the weather.
"Predicting the winds and the rain, the fine and the dry spells - by working out the variations in air pressure - temperature, and humidity around the entire planet was recognised as a problem of almost immeasurable complexity."
How right they were.
The necessity of being able to predict the weather, and the cost of failing to do so, has never been in doubt, from the time the first seagoing vessel was overwhelmed by an unforeseen storm to the floods and hurricanes that continue to wash away the very foundations of human society around the world.
The means to do so, however, continue to elude. Forecasting for even five days ahead "remains a challenge for the modern weatherman, even with supercomputers that had not been dreamed of in [the 1920s".
The reason, say the authors of this book - in a virtual admission that mathematics can go only so far - is illustrated by playing a simple game of Pooh sticks.
For those unfamiliar with AA Milne's Winnie-the-Pooh, all that is required are three sticks, thrown off the upstream side of a bridge over running water and observed as they emerge on the other. In theory, the stream is a single body of water, moving at a consistent pace, and upon reappearing on the far side of the bridge each stick should emerge in the same position, relative to the other two, that it entered the water.
This, however, as even a bear of very little brain knows, is almost never the case - and this is why accurately forecasting the weather remains impossible even for the biggest brains.
The technical word for this is chaos, first identified by American mathematician, meteorologist and (thereafter) chaos theorist Edward Lorenz. Throughout the 1950s, Lorenz, an assistant professor at MIT's department of meteorology, worked to identify periodic patterns in the weather. His goal, say the authors, was "to show that numerical models based on the predictive laws of physics would always prove to be superior to statistical methods of forecasting based on information about past events". Eventually, computing power began to catch up with Lorenz's vision. Then, in 1961, while re-running a weather prediction, he entered one number in the numerical sequence of data as 0.506 instead of the original 0.506127. This resulted in an entirely different outcome and the discovery of what came to be known as the Butterfly Effect - "a constant reminder of the ghost in the machine of weather and climate prediction".
In 1972, Lorenz, who had sought to impose order upon the atmosphere but instead found antithetical fame as the discoverer of chaos, remarked that a tornado might be caused over Texas by a butterfly flapping its wings over Brazil.
Lorenz's fanciful imagery, say the authors, illustrated the reality that "forecasters would have to live with the fact that very small uncertainties in our data of what the weather is like now can lead to very large errors in the calculations of the forecast a few days ahead".
So is attempting to forecast the weather beyond the next few days a hopeless challenge?
Roulstone and Norbury think so.
They say, "even with the most optimistic assumptions on computer and satellite development over the next two decades, we will not be able to quantify the impact of all the planes, trains, automobiles and buildings - let alone butterflies - on the atmosphere".
Yet all is not lost, provided we put our faith in mathematics. There are "many detailed interactions, and there are degrees of unpredictability. But there are also many stabilising mechanisms and, most importantly for understanding and prediction, there is the maths to quantify the rules."
The challenge, they say, is "to continue to develop, interpret and use this science, technology and mathematics in the most effective way … Just as our quest to determine the behaviour of the solar system produced surprises that led mathematicians to develop qualitative techniques for studying chaotic systems, so we might imagine that our efforts to understand the Earth system will lead to new mathematics and to a deeper appreciation of the world".
But in the meantime, hang on to that umbrella. After all, this year's annual World Pooh Sticks Championships on the River Thames in Oxfordshire had to be cancelled because unanticipated heavy rainfall had rendered the course too dangerous.
Jonathan Gornall is a regular contributor to The National.