WE'VE all watched those vast heaps of cotton wool float across the sky. Lofted and shaped by updrafts of warm air, cumulus clouds mesmerise with their constantly changing shape. Some grow ever taller, while others wither and die before our eyes. All bear witness to the ceaseless roiling of the ocean of air we call the atmosphere.
About 80 years ago, the British mathematician Lewis Fry Richardson was pondering the shapes of such clouds when a startling thought occurred to him: the laws that govern the atmosphere might actually be very simple.
Even at the time, with scientific meteorology still in its infancy, the idea seemed absurd: key equations governing the behaviour of the 5 million billion tonnes of air above us had already been identified - and they were anything but simple.
No one was more aware of this than Richardson, who is recognised as one of the founders of modern weather forecasting. Even now, the world's most powerful computers are pushed to their limits extracting predictions of future weather and climate from the equations he wrestled with using pencil and paper.
Yet Richardson suspected that behind the mathematical complexity of the atmosphere lay a far simpler reality - if only we looked at it the right way.
Now an international team of researchers analysing signals from satellites, aircraft and ground-based stations have found clear evidence that Richardson's intuition was right and that the complexity of the atmosphere could really be an illusion.
The results point to a new view of the atmosphere as a vast collection of cascade-like processes, with large structures the size of continents breaking down to feed ever-smaller ones, right down to zephyrs of air no bigger than a fly.
The implications promise to transform the way we predict everything from tomorrow's local weather to the changing climate of the entire planet. "We may never be able to view the atmosphere and climate in the same way again," says team member Shaun Lovejoy of McGill University in Montreal, Canada. "Rather than seeing them as so complex that only equally complex numerical models can make sense of them, we're seeing a kind of scale-by-scale simplicity."
Richardson had a reputation for having ideas decades ahead of his time. He pioneered the study of fractal geometry - the study of patterns that look the same no matter how much you magnify them - though the word "fractal" had yet to be coined. Look at the honeycomb pattern in a beehive, say, and the hexagonal structure is only visible if you're not too close or too far away. But look at some kinds of plants and you'll see their fronds are made up of ever-smaller versions of the overall leaf. This is known as scale invariance, and is a feature of fractals. Richardson noticed that coastlines have a similar property, their jagged outlines appearing just as jagged as one zooms in to ever-smaller scales.
Attempting to capture this mathematically, Richardson found the same behaviour in simple formulas called power laws, by which one quantity changes according to another raised to some power. Even something as simple as tiling your bathroom wall follows a power law: reduce the length of each square tile by 1/l and you'll need l2 as many tiles. Such laws also reproduce the scale invariance of objects like ferns and coastlines, which retain the same basic form no matter how big the change in scale.
It was while looking for other examples of self-similarity that Richardson came to ponder the skies above: he noticed how the shape of clouds is constantly modified by the invisible whirls and eddies of turbulent air that surround them.
To get some insight into the laws governing turbulent fluids, Richardson performed simple experiments in which he threw bits of parsnip into a lake and watched how they moved apart under the action of the whirls and eddies on the surface. As with coastlines, Richardson found that a scale-invariant power law seemed to apply - an observation that inspired him to poetry: "Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity" - a parody of Jonathan Swift's famous 18th-century doggerel about fleas and the little fleas that bite 'em.
But behind the humour lay Richardson's growing conviction that the atmosphere is just a collection of cascade-like processes, with large structures breaking down to feed ever-smaller ones, creating a fractal-like structure which acted according to power laws.
As with his work on weather forecasting, Richardson could only dream of a time when his ideas could be properly investigated. That time seemed to come in the 1980s, when fractals and scale invariance hit the scientific big time. Simple scaling laws were suddenly claimed to underpin everything from the size and frequency of earthquakes and avalanches to the rise and fall of stock markets. So why didn't anyone put Richardson's idea to the test and search for simple power laws describing the entire atmosphere?
http://www.newscientist.com/article/mg2 ... ctals.html