Is the Atmosphere Simpler Than We Thought?

The “butterfly effect” is being set aside in favor of a multifractal process that will have a major impact on climate models.



It’s a pretty widely-accepted notion that the atmosphere is a ridiculously complex system, and the best we can do with our models is a rough approximation. The more teraflops we throw at the problem, the more granular the results–but even the best models operate at a scale of a hundred or so kilometers; we’re still just seeing a shadow of the atmosphere’s true complexity.

But what if that’s wrong?

The atmospheric complexity idea has a lengthy provenance. Lewis Fry Richardson, the father of numerical analysis of the weather, proposed way back in 1922 that weather could be forecast using difficult math. This insight, and the work that he produced, led directly to the climate and weather models in use today. But Richardson had another insight: perhaps there’s a simpler underlying system at work, something involving what would later be called fractal geometry. (He once wrote: “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity.”) In the 1980s, when we finally had enough computational firepower to test this, the initial results weren’t good, and the idea was more-or-less abandoned.

McGill University physicist Shaun Lovejoy kept coming back to the idea, though, and he and his team found suggestive indications that there was a multifractal process at work. (Standard fractal systems involve a single exponent defining the “fractal dimension” of a system; multifractal systems involve a range of exponents, given the label “singularity exponent.” Seriously.) The available data weren’t clear though, because the readings were muddied by the effects of the very aircraft and instruments used to gather them. So Lovejoy looked up–to satellites. And digging through data from 1,200 consecutive orbits of the Tropical Rainfall Measuring Mission, the team came up with something pretty remarkable: very strong evidence that the atmosphere follows power laws and shows fractal behavior, visible at scales from under 10km to over 20,000km.

Um, okay. Nice, I suppose. But what does that mean?

Put simply, it means that the classic “chaos theory” problem–that small variations and inaccuracies can lead to wildly divergent results, aka “the butterfly effect”–could be set aside, and we’ll be able to create accurate models down to… well, here’s what New Scientist says:


Now Lovejoy’s team is keen to see cascades extend the reach and reliability of current models. While the existing models cannot handle structures much smaller than 100 kilometers across, the cascades may continue down to scales smaller than a millimeter. “Cascades could help fill in that missing factor of 100 million or so,” says Lovejoy.

This will have a major impact on climate models–both for improving their accuracy, and (interestingly) for verification. If a given climate model’s version of the atmosphere doesn’t result in a system that shows power laws and multifractal behavior, then it’s definitely inaccurate. Fortunately (or unfortunately, if you hope that climate science has this whole global warming thing wrong), the climate models currently in use do show power law and fractal results.


[The article in New Scientist gives a decent explanation of the research; the original paper is available (PDF file), as well, although the math involved made me cry.]

This is one of those discoveries that will undoubtedly take years to integrate into existing global circulation models, so we’re not going to have ultra-accurate climate simulations overnight. But this does give a great deal of impetus to the idea that we can, in fact, generate useful insights into the functioning of global systems using simulations. I’m really curious about how well the multifractal concept could be applied to other ultra-complex systems. Psychohistory, anyone?


Working in the Cloud and Sunset at 34,000 Feet, both by Jamais Cascio, Creative Commons licensed