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The atmosphere is a highly dynamical system, and exhibits many chaotical features. An operational weather forecasting model tries to model an initial value problem, in fact one of the most famous examples of a chaotic system.

Climate however, is the statistics of the behaviour of the atmosphere over a long period of time. It is not an initial value problem; it is a boundary value problem. Whereas small changes in initial values can imply large changes in behaviour over time, can there be any similar behaviour in climate?

For example, we force a climate model with prescribed atmospheric constituents, coastlines, orbital characteristics, etc. Can a small change in any of those boundary values lead to a climate exbiting a different state? Or, similarly, can, in the context of natural variability only, the climate suddenly switch to a very different state?

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  • $\begingroup$ "small change in [...] boundary values [...] different state" - yes, it can, at least in models. For an atmospheric physicist, this is a rather philosophic question, is not it? $\endgroup$
    – s-m-e
    Apr 15 '14 at 19:41
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    $\begingroup$ @ernestopheles I don't think it's a philosophical question. The question whether the climate system could unpredictably jump to an entirely different state (think of very different ocean circulations) is quite relevant. $\endgroup$
    – gerrit ♦
    Apr 15 '14 at 19:45
  • $\begingroup$ Of cause it is relevant. I am just questioning current understanding and most importantly tools. I think you can come up with a pretty good argument that drastic state changes due to small changes are possible. But I do not see a nice (compelling) way of proofing that at the moment ... $\endgroup$
    – s-m-e
    Apr 15 '14 at 19:49
  • $\begingroup$ Is your question fundamentally, are there "discontinuities" between small changes in the causal variables of climate, and changes in the climate itself? $\endgroup$
    – Tom Au
    Apr 15 '14 at 22:06
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    $\begingroup$ I have a feeling there are two separate questions here: first, "can a small change in system parameters result in a very different equilibrium", and second "Are shifts between multiple equilibria (of the same system) stochastic (e.g. unpredictable, except in a probabilistic sense)". I'm not sure whether it makes sense to have them both in the same question, and it certainly confuses things and makes it harder to answer. $\endgroup$
    – naught101
    Apr 16 '14 at 2:52
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There's quite a bit of evidence to support that at least part of the climate system is chaotic.

According to the IPCC:

The climate system is particularly challenging since it is known that components in the system are inherently chaotic; there are feedbacks that could potentially switch sign, and there are central processes that affect the system in a complicated, non-linear manner. These complex, chaotic, non-linear dynamics are an inherent aspect of the climate system.

There's also evidence to support this from an Iowa State University course:

The climate system is thought to possibly have such multiple states; that is, the climate (or some components of the climate system) could be stable for a period of time and then abruptly, and for no overtly evident reason, change to another stable regime. There is evidence that certain components of the climate system have done this. The circulation in the north Atlantic Ocean is believed to have gone through an abrupt change in which the Gulf Stream, instead of tracking northeastward off the East Coast of the United States and heading toward Scandinavia, at one time switched very abruptly over about fifty years (that's abrupt on geological time scales) to an easterly direction toward the Mediterranean Sea. This caused an abrupt cooling of the climate in Scandinavia.

In summary, almost-intransitivity is an inherent characteristic of the dynamics of the climate system that may, for seemingly small or unknown reasons, launch some component of the climate system into a pattern not previously seen.

Even more information is given in this NASA post.

To sum all of this up: yes, at least some parts of the climate system are chaotic. But is all of it chaotic? I'm not sure, but I really don't think so.

But as to the definition of a chaotic system, yes, climate is chaotic. There are definitely some things in the climate system that when changed minutely can cause everything to shift. We don't understand everything about climate right now, so it may not be truly chaotic. But as of our research right now, it is chaotic.

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  • $\begingroup$ What do you mean that you really don't think it's all chaotic? $\endgroup$
    – naught101
    Apr 19 '14 at 22:27
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    $\begingroup$ @naught101 I might just take that part out, I dunno. I meant that I don't think every variable in it is chaotic (some things when minutely changed might not cause a huge difference). $\endgroup$
    – hichris123 ♦
    Apr 19 '14 at 22:34
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One problem here is the defition of chaos. In the mathematical theory of dynamical systems, a system is chaotic if it contains both dense and periodic points. This is somewhat different from what one thinks chaos means.

Let's say that by chaotic, for continuous-time dynamical systems, we mean sensitive to initial conditions, i.e., that a (general, random) small perturbation of the state modifies the trajectory (future) of the system significantly. This is generally refered to as the butterfly effect.

It's been proved that, for instance, large towns have a microclima, i.e., they change the local weather significantly, and that these changes know to have a significant impact on the wheather in much larger areas. This can be taken as an evidence that the system is sensitive to small perturbations.

(I've taken more the "mathematical chaos" part of the question, the other answer by hichris123 aims more on the evidence of chaotic behaviour itself. I hope it's fine, suggestions are of course welcome.)

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