FUNDAMENTAL SCIENCE IN CLIMATE FORECASTING WITH MODELS

Abstract

Geophysical forecasting is an exceptional topic. There are few, if any, fields where the deep theory and the practice are so diametrically at odds with each other. The solutions to the basic dynamical equations used in weather forecasting are part of our daily weather reports, even though, paradoxically, no one knows how to actually solve those equations. On one hand, fluid dynamics in long-term geophysical forecasting is considered a routine engineering application of Newtonian mechanics, while on the other hand, fluid dynamics also made it onto the list of the unsolved (Clay millennium) problems of mathematics. That list includes profound mathematical problems like the Riemann Hypothesis and the Hodge conjecture and mathematical issues concerning high-energy physics. Fluid dynamics is considered a deep scientific problem! This isn’t just empty theorist’s talk either; money has been put on it. There is a million dollar prize for solving any of those problems. So if you feel like you could use some extra cash, I suggest that you dust off your Navier-Stokes theory and have a go at it. The good news is that you don’t even need to solve the equations. All you need to do for the prize is to prove that solutions exist. You can even restrict yourself to the incompressible case! Easy money. Of course anyone who has seriously tangled with the problem of turbulence knows that fluid dynamics remains a major scientific problem and that lottery tickets might be a better bet than winning this Clay prize. Nonetheless we are still interested in forecasting the future and, in the geophysical fluids case, the long-term future. The classical problem of long-term forecasting or prediction is celestial mechanics, especially the study of the motions of bodies in the solar system. Success with this gave 18” century scientists, such as Laplace, the confidence to suggest that the future could be fully known with Newtonian mechanics and full knowledge of initial conditions. Confidence in the Laplacian vision of forecasting began to fall apart with Poincare’s work on the three-body problem of celestial mechanics at the end of the 19” century. Today we have a whole century of uncertainty behind us: first there was the intrinsic uncertainty of modem physics, then in the latter half of the twentieth century, classical physics proved to be uncertain too with the emergence of what has come to be called the “butterfly effect,” although Lorenz’s original articles cited a flapping seagull rather than a delicate butterfly. But things take time to sink in. As a child, I recall older meteorologists reciting 18” century Laplacian thinking: more accurate data plus bigger computers equals problem solved. Of course everything is different now. The butterfly effect (chaos, or natural variability as many meteorologists also call it) is now widely accepted. Sensitivity to initial conditions has even become a cliche in the movies. But the cliche typically leaves off the second part of the story, wherein the rapid growth of error from those initially erroneous conditions is bounded. That latter part is