The quotes are from Tomas Milanovic at:

http://judithcurry.com/2014/05/23/how-simple-is-simple/

Very nice explanation. One of the things that is interesting to me is that chaotic systems are so resistant to improved accuracy of initial conditions; no matter how precisely the initial conditions are described, the system quickly diverges into unpredictability. For fluid flow, the equations themselves are demonstrably wrong, since the fluid is considered a continuum, when in reality it is a huge ensemble of molecules undergoing constant random motion and impacts. Treating it mathematically as a continuum introduces inevitable (tiny) error.

If you introduce a very small random error at each step in the iterative calculations, does the behavior evolve in the same way? I suspect the system may not “stay on the attractor”.

]]>Adding even weak stochasticity to the set of equations might have an essential influence on the outcome from equations of the simple problem being discussed smoothening probably the averages over long enough averaging periods. At some point the results would not show any dependence on initial conditions any more. Some weak stochasticity might leave the Figure 4 above almost unchanged, but reduce essentially variability seen in Figure 5. The shape of the attractor would not change much in that case, but the way different parts of the attractor get populated might be very different.

When we consider the atmosphere or the whole Earth system the effectively stochastic contribution to the behavior is likely to be strong. The total number of variables is extremely large, infinite in continuum idealizations, some factor times the number of molecules or atoms for the discrete case.

What’s left and where from the deterministic chaos in the real Earth system?

The Earth system is chaotic. but not deterministic. Some subsystems or dynamic modes may follow at an useful level equations of some determistically chaotic model. Large scale ocean circulation might be an example, but I don’t think we have much evidence for that.

]]>First: Your insults on others turn totally against yourself. People, who read this site have seen the value and quality of the contribution of SoD to the understanding. He’s not infallible and errs sometimes on details (you observed correctly one such lapse), but your aggressive style guarantees that people react to you exceptionally negatively.

Then on the mistakes of your above comment.

1) The temperature values I gave depend slightly on methods used in determining them, but that’s negligible relative to the size of the difference of about 33C.

2) I have not referred to any fictitious temperature of the surface, only to the real one.

3) My argument does not refer to any changes in the atmosphere, only to the actual present state.

]]>simply ridiculous.

1) The fact that you relate two observations doesn’t mean anyting about the quality of the theorical construct for the expanation of the relationship – let’s drop the fact that both of those figures are, themselves, certainly not observations, but obviously derivations from observations via lots of (right or wrong) theoricaly-based operations.

2) If you drop the crude averaging issues and also the fact that gases absolutely not follow the blackbody law, the difference simply tells you that the surface is (that) hotter than whatever “mean place” which emits the OLR. Which is no surprise… because this “mean place” is precisely not on the surface but well above: it’s obvious in Trenberth’s diagram that 199 W/m² out the 239 W/m² figure are emitted by the atmosphere. That’s a first way of showing that figuring out a -18°C temperature for the surface in whatever fictIous situation is simply nonsense. If those figures make any sense, the difference is a measure of the “atmospheric effect”. But I know that’s not this step that will convice you folks. Whereas I guess next point is much more straightforward when it comes to demonstrating how high you can fly.

3) See below the post I sent yesterday. Is as simple as that: if you remove the atmosphe ability to absorb and emit radiations (and follow all of you explicit or implicit conventions), the surfaces would obviously not emit 239 W/m² but around 318 W/m². It’s just what would be the flux in and out ouf the atmosphere when you remove the surface albedo (assumed to be the same) from the total income solar radiation… Which would correspond to +0,9°C, not -18°C. Yielding around 14°C difference, not 33°C.

If you cannot follow up such a basic reasoning, I’m afraid it’s useless to discuss about so much compex stuff.

]]>Pekka is entitled to regard effort as being equivalent to power, but I think that equating it with work is at least equally valid.

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