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Complexity and the Mystery of Predicting the Weather

Posted By Lisa Kimball, Thursday, September 08, 2011

Famed physicist Richard Feynman once said, "Anyone who has been in a thunderstorm has enjoyed it, or has been frightened by it, or at least has had some emotion. And in those places in nature where we get an emotion, we find there is generally a corresponding complexity and mystery about it."

August brought a series of significant weather events in the US including an earthquake, hurricane and floods on the East Coast. Whenever this happens, it reignites the conversation about why we aren't better able to predict the course of weather events - their path and their severity - with greater accuracy.

Edward Lorenz used the mathematics of chaos theory to give us the idea that a flap of a butterfly's wings in Brazil could cause a typhoon in Texas because most atmospheric phenomena involved in weather forecasting are non-linear and highly dependent on initial conditions. This "butterfly effect" has captured the public imagination. Although many phenomenon can be predicted based on a thorough understanding of their initial conditions, weather appears to be particularly dynamic and sensitive system because of the number of possible relevant factors.

 

Chaos graph

Lorenz's experiment: the difference between the starting values of these curves is only .000127. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)

 

William Hartston's article, Weather: Catastrophe, Chaos, Complexity and Crisis suggests that a state of chaos may always be closer than we think. He explains that a branch of mathematics developed in the nineties called Crisis Theory predicts that, "complex systems tend naturally to settle not, as you might think, into the most stable state they can reach, but into the most unstable state that does not collapse completely." He cites the example of a pile of dry sand. If you put a shovelful of sand on the ground it will settle into a neat cone. If you pour a small amount of sand on the top, the sand will trickle down in apparently random paths down the side of the mound and then settle again. "The settling points are perfectly balanced, yet inherently unstable... the smallest perturbation of the initial conditions causes major disruption."

"Calm seas, mild breezes and Newton's laws of motion may produce hurricanes, floods and whirlwinds, which then obey their own physical laws as simple as, but quite different from, those we started with."

Cumulus cloud

 

B N Goswami of the Centre for Atmospheric and Oceanic Sciences Indian Institute of Science in Bangalore writes in The Challenge of Weather Prediction that, even if the equations governing the atmospheric motions were known exactly, due to the intrinsic nonlinearity of the system, weather prediction would be limited to about two weeks in advance. Two weeks actually sounds pretty ambitious given our recent stormy experiences!

"Every weather pattern, every cold front is different from all its predecessors. And yet... the Nile doesn't freeze, and London is not subject to the monsoon" (Rosenhead, 1999). Rosenhead, J. Complexity Theory and Management Practice.

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