Friday, May 09, 2008

Climate Prediction or how the soothsayers wept

For Dante soothsayers and diviners are practitioners of "magic frauds". In Inferno they are condemned to walk backwards because their heads are twisted so ... with tears running down their backs for false predictions

As the BBC reports. This week, about 150 of the world's top climate modellers have converged on Reading for a four day meeting to plan a revolution in climate prediction.

And they have plenty of work to do. So far modellers have failed to narrow the total bands of uncertainties since the first report of the Intergovernmental Panel on Climate Change (IPCC) in 1990.

And Julia Slingo from Reading University admitted it would not get much better until they had supercomputers 1,000 times more powerful than at present.

"We've reached the end of the road of being able to improve models significantly so we can provide the sort of information that policymakers and business require," she told BBC News.

"In terms of computing power, it's proving totally inadequate. With climate models we know how to make them much better to provide much more information at the local level... we know how to do that, but we don't have the computing power to deliver it."

But can bigger and more powerful computers help with predictions, in a word no.

In an interesting chapter entitled Engineers Dreams from his book Infinite in all directions, Freeman Dyson explains the reasons for the failings of Von Neumann and his team for the prediction and control of Hurricanes.

Von Neumann’s dream

“As soon as we have good enough computers we will be able to divide the phenomena of meteorology cleanly into two categories, the stable and the unstable”, The unstable phenomena are those that are which are upset by small disturbances, and the stable phenomena are those that are resilient to small disturbances. All disturbances that are stable we will predict, all processes that are unstable we will control”

Freeman Dyson page 183.

What went wrong? Why was Von Neumann’s dream such a total failure. The dream was based on a fundamental misunderstanding of the nature of fluid motions. It is not true that we can divide cleanly fluid motions into those that are predictable and those that are controllable. Nature as usual is more imaginative then we are. There is a large class of classical dynamic systems, including non-linear electrical circuits as well as fluids, which easily fall into a mode of behavior that is described by the word “chaotic” A chaotic motion is generally neither predictable nor controllable. It is unpredictable because a small disturbance will produce exponentially growing perturbation of the motion .It is uncontrollable because small disturbances lead only to other chaotic motions, and not to any stable and predictive alternative.

A fact also addressed by Vladimir Arnold

"For example, we deduce the formulas for the Riemannian curvature of a group endowed with an invariant Riemannian metric. Applying these formulas to the case of the infinite-dimensional manifold whose geodesics are motions of the ideal fluid, we find that the curvature is negative in many directions. Negativeness of the curvature implies instability of motion along the geodesics (which is well-known in Riemannian geometry of infinite-dimensional manifolds). In the context of the (infinite-dimensional) case of the diffeomorphism group, we conclude that the ideal flow is unstable (in the sense that a small variation of the initial data implies large changes of the particle positions at a later time).Moreover, the curvature formulas allow one to estimate the increment of the exponential deviation of fluid particles with close initial positions and hence to predict the time period when the motion of fluid masses becomes essentially unpredictable.

For instance, in the simplest and utmost idealized model of the earth’s atmosphere (regarded as two-dimensional ideal fluid on a torus surface), the deviations grow by the factor of 10^5 in 2 months. This circumstance ensures that a dynamical weather forecast for such a period is practically impossible (however powerful the computers and however dense the grid of data used for this purpose)"

The modellers continue,...

“One trouble is that as some climate uncertainties are resolved, new uncertainties are uncovered.Some modellers are now warning that feedback mechanisms in the natural environment which either accelerate or mitigate warming may be even more difficult to predict than previously assumed.”

Yes this is also well known the mathematics (Fokker plamk equation) already tell us this. The Kolgomorov backwards equation (kpe) naturally tends towards global cooling in any bi-stable simulation (hot-cold)

Lorenz called it almost intransitive, this is why climate models have biased towards heating(over paramatization).

NICOLIS, G also showed this

Stochastic aspects of climatic transitions additive fluctuations

The Fokker-Planck equation, corresponding to a zero-dimensional climatic model showing bistable behavior, is analyzed. A climatic potential function is introduced, whose variational properties determine the most probable states of the stationary probability distribution. Both the static and the time dependent properties of the fluctuations are monitored by two basic quantities: (1) the climatic potential, U, and (2) the variance of the noise. A sensitivity analysis of U with respect to system parameters, particularly the temperature feedback coefficient, shows a distinction between a regime where present climate dominates and a regime where a deep freeze climate dominates. Conditions of coexistence of these two regimes in terms of the characteristic parameters were also determined. For small variance, the stationary probability distribution is very sharply peaked around the dominant state while the time scale of evolution becomes exceedingly slow. Moreover, an increase in the temperature feedback coefficient tends to favor the deep freeze climate.

Heck and they are telling us to shut the fires down.

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