A lot of people believe that inadequacies in modeling weather and climate are due to the fact that the computers are not yet fast enough to do the complex calculations involved. But it’s not so. Instead a new study says that the current limit of 10 days of reliable forecasts might be pushed to 15 but no further regardless, “with much less scope for improving prediction of small-scale phenomena like thunderstorms.” Although we can predict an increase in hurricanes in 50 years just by snapping our fingers.
The problem is that “The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible.” And if you’re wondering what half-witted venal hack penned those words, it was… the IPCC. (See the Technical Summary of TAR Climate Change 2001: The Scientific Basis, section G2.)
The importance of chaos theory to the study of climate cannot be overstated. Linear algebra and differential calculus have performed miracles in advancing the physical sciences in the last 500 years, and given powerful credibility to Galileo’s credo that “Mathematics is the language in which God has written the universe”. The feeling for half a millennium has been that if we could not fully understand some phenomenon using these techniques (and understanding here necessarily meaning predict and even control them), it was because either our mathematicians had not yet made the imaginative leap to the right equations or we did not have machines capable of crunching the equations once we had them. But since 1961 and Edward Lorenz’s famous discovery that his very crude weather simulation on a computer resembling an abacus depended not on approximate values but on the last decimal point, we’ve known it was not always true.
Some things literally cannot be modeled because the smallest differences in initial conditions produce huge differences in final conditions, as though handicapping a boxing match depended on the milligrams not the kilograms or whether a rocket reached the moon or crashed into the ocean depended on whether there was dust on its windshield. It's regrettable in some ways, because it means we cannot know some things we very much want to know. On the other hand, it tends to militate against a crudely reductionist vision of the universe; as one climate scientist expressed its significance, “Ed put the last nail in the coffin of the Cartesian universe”. But whether we like it or not, it’s still true.
One result is that as we cram more and more resources into predicting weather and climate, the line depicting accuracy does something simple and linear: it bends downward asymptotically to around 15 days. Not 100 years. Not forever. Two weeks. A fortnight.