Climate vs Chaos and Turbulence

Both climate alarmists and skeptics like to suggest deep understanding by expressing that global climate is a non-linear chaotic system and as such is unpredictable (as discussed by Kip Hansen in a recent sequence of posts):

• The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible. (IPCC TAR WG1, Working Group I: The Scientific Basis)
• It is my belief that most climate variability and even climate change could simply be the result of chaos in the climate system. (Roy Spencer)

But to simply say that a chaotic system is unpredictable is not the entire story. It is true that point values in space/time of a chaotic system are unpredictable, due to strong pointwise sensitivity to pointwise perturbations, but mean values of a chaotic system typically are predictable.

It is certainly impossible to predict the daily temperature of a specific city within one degree one year ahead, but meaningful monthly temperatures are routinely reported in tourist guides.

The book Turbulent Incompressible Fluid Flow presents the following analysis of turbulence as prime example of chaos:

1. Point values are unpredictable due to local exponential instability.
2. Mean values are predictable due to cancellation of instability effects.

It may thus well be possible (with a high degree of certainty) to predict that the global mean temperature will be the same 100 years from now, within a degree up or down.

For the Lorenz system, as a key example of a chaotic system, it is impossible to predict in which lobe a trajectory will be long ahead in time, but the total time spent in each lobe is observed to become nearly equal over long time. About the weather in Scandinavia, we know for sure that it will be variable with alternating low and high pressures, with sunshine following rain and vice versa as a result of the dynamics.