 |
| Waterfall as partially predictable chaotic system |
The idea that global climate is a chaotic system and as such cannot be predicted, because of sensitivity to small perturbations, is often presented as an expression of deep insight into mathematical modeling. But it may hide a common misunderstanding of the nature of a chaotic system. The basic example of a chaotic system is turbulent flow. The nature of turbulent flow is to be unpredictable pointwise in space and time (because of sensitivity) while being predictable in a mean-value sense (because of insensitivity).
This is developed in detail in Computational Turbulent Incompressible Flow and Computational Thermodynamics recommended for download. The combination of mean-value predictability and pointwise unpredictability is expressed by the fact that the drag of a car as total resistance to motion through air, is computable/predictable while the pressure at specific points on the car body cannot be computed/predicted. The reason mean-values are predictable is the fluctuating nature of turbulence with high pressure followed by low pressure forming stable mean-values. This is the reason nature can function as a more ot less ordered system even if being a chaotic system, which can be seen as a form of order in chaos.
The Earth climate system can be described as a turbulent thermodynamic ocean-atmosphere system which forms weather local in space and time and global climate as mean-values over space and time. Experience shows that local weather acts as a chaotic system which is unpredictable pointwise in time over more than a week. The question is then to what extent climate as mean-value weather is computable/predictable?
If all the equations (Navier-Stokes equations and more) modeling the Earth system were known, we would be able to compute/predict for example global mean temperature year 2100 or the onset of the next Ice Age, because of the fluctuating nature of turbulent flow. But we do not know all the parameters entering in the equations nor the initial conditions. Therefore such computation/prediction for now is impossible, but not because the system in principle is chaotic, rather because present climate models contains unknowns.
This means that with better climate models it could be possible to predict e.g. the onset of the next Ice Age, or on shorter time scales the Winther weather over Europe depending on jet streams and La Nina and more. Even without climate model we can predict the global mean temperature 2023 to be about the same as 2022.
In short, global ocean-atmosphere weather system is a chaotic system which as global climate is computable/predictable to a certain degree. Work on better climate models is not meaningless.
What is remarkable is the stability of Earth climate without runaway global warming yet with global cooling into repeated Ice Ages,
Inlägg
I was under the impression that the 'arrow of time' arose due to the necessary loss of mass (remember that mass and energy are two sides of the same coin) in all interactions amounting to E/c^2, where E is the energy transferred or converted in that interaction. This applies equally to nuclear, chemical, electrical, etc. interactions. This is best exemplified by the (admittedly weak) EMP caused by a conventional explosion. No nuclear binding energy (it is, after all, a conventional chemical explosion), it is a result strictly of that necessary loss.
SvaraRadera