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Chaos theory and global warming: can climate be predicted?

What the science says...

Select a level... Basic Intermediate

Weather is chaotic but climate is driven by Earth's energy imbalance, which is more predictable.

Climate Myth...

Climate is chaotic and cannot be predicted

'Lorenz (1963), in the landmark paper that founded chaos theory, said that because the climate is a mathematically-chaotic object (a point which the UN's climate panel admits), accurate long-term prediction of the future evolution of the climate is not possible "by any method". At present, climate forecasts even as little as six weeks ahead can be diametrically the opposite of what actually occurs, even if the forecasts are limited to a small region of the planet.' (Christopher Monckton)

One of the defining traits of a chaotic system is 'sensitive dependence to initial conditions'. This means that even very small changes in the state of the system can quickly and radically change the way that the system develops over time. Edward Lorenz's landmark 1963 paper demonstrated this behavior in a simulation of fluid turbulence, and ended hopes for long-term weather forecasting.

However, climate is not weather, and modeling is not forecasting.

Although it is generally not possible to predict a specific future state of a chaotic system (there is no telling what temperature it will be in Oregon on December 21 2012), it is still possible to make statistical claims about the behavior of the system as a whole (it is very likely that Oregon's December 2012 temperatures will be colder than its July 2012 temperatures). There are chaotic components to the climate system, such as El Nino and fluid turbulence, but they all have much less long-term influence than the greenhouse effect.  It's a little like an airplane flying through stormy weather: It may be buffeted around from moment to moment, but it can still move from one airport to another.

Nor do climate models generally produce weather forecasts. Models often run a simulation multiple times with different starting conditions, and the ensemble of results are examined for common properties (one example: Easterling & Wehner 2009). This is, incidentally, a technique used by mathematicians to study the Lorenz functions.

The chaotic nature of turbulence is no real obstacle to climate modeling, and it does not negate the existence or attribution of climate change.

Last updated on 8 September 2010 by chuckbot. View Archives

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Comments 51 to 75 out of 120:

  1. Aside from KR's answer, you might like to look at Realclimate here and here for comments from the people that do the modelling
  2. scaddenp - Agreed; those are well written, certainly better than I can do late on a Friday night. Ed Loretz was truly a genius.
  3. scaddenp @51 & KR @50 Thanks. Those were interesting discussions to read. I believe they confirm, as I was trying to point out, that there is indeed chaotic behaviour in climate models themselves. When one takes long averages of climate model output it does not appear chaotic - by rather reflects the forced response of the system - I agree. That is why climate models have performed well at predicting the forced response to CO2 so far. This success does not discount the possibility that the climate system could "flip" into a totally separate equilibrium, given enough forcing. This is the idea of abrupt climate change, and although the chances of this may be very small - it certainly should not be ruled out as a possibility. This type of chaotic behaviour actually exists throughout a hierarchy of models: Stommel's classic analytical model of the thermohaline circulation is very simple, yet demonstrates mutiple equilibria are possible for the oceanic circulation. People in the field have sometimes questioned whether this behaviour would exist in a complex-model: The new results from the MITgcm team confirm that it does. The MIT experiments use a state-of-the-art fully coupled AO-GCM, including a dynamic-thermodynamic sea-ice model. The model is therefore similar to any AR4 model in terms of the ocean-atmosphere dynamics (it had a simplified representation of the continents though). (The MIT study by Ferreira et al. ) I'm not trying to argue the predictability of the forced response to CO2 - its clear the models are capable of that. I'm suggesting that there are good reasons to carefully consider what uncertainties exist - because we may have underestimate the climate risks associated with our CO2 forcing.
  4. Completely stuffed that post... Trying again. That is an interesting paper Neil. Coincidentally, someone else I think has asked about at RealClimate I have posted the link to this paper. I would say stay tuned.Phil
  5. neil - Agreed, multiple equilibria are very possible. In fact, that was discussed here in the What would a CO2-free atmosphere look like thread. One important point about the dynamics, though - many times a particular equilibrium (a local minima in terms of the N-dimensional state space of the system) can be quite robust, stable through a fair amount of peturbation yet remaining in that region. Small perturbations shift the system a bit, but it tends to return to the local minima. Only upon a very large perturbation can such a system be moved over a ridge to another valley in the state space, another equilibrium, where it again will be stable until a large perturbation shifts valleys again. The thread I referenced shows that for a very simple model - there are three different equilibria for a single value of CO2, but the shift to a different valley of stability regarding CO2 concentrations takes a very large perturbation. I find it very interesting that this has now been shown for more complete models of the climate, although given state space behavior it's not entirely surprising. At the edges of the equilibria are the phase changes - glaciation, melt of the icecaps, severe thermohaline shifts, clathrate release, and so on. Large perturbations to watch out for...
  6. neil - Gah; all that typing and I forgot to include the main point. Given a system with multiple equilibria, a wide variety of initialization points will almost certainly provide a sampling of the equilibria, with various initializations stabilizing to local minima in the state space. That doesn't mean it's easy to move from one equilibrium to another, just that they exist. That said, we look to be heading to an ice-free Arctic, and if we maintain high temperatures for a few millennia we may see significant loss of the Antarctic as well. Florida (and Bangladesh) are not great long term real-estate investments.
  7. Sadly, this skeptic meme has resurfaced at WUWT. The poster in the June 13th item, Dr. Andy Edwards (not a climate scientist, mind you - his background is in AI and chaotic systems) claims climate is unpredictable based on the chaotic behavior of weather. Sigh.
  8. I posted a link back to this discussion on WUWT. It will be interesting to see if there's any response.
  9. The parts of chaos theory that worry me in the context of climate change involve phase shifts and Lorenz' "strange attractors." Heating a teapot full of water from 70 degrees (F) to 211 degrees (F) just means hotter water, but with just a little more heat making it one degree hotter, a phase change occurs and the water starts turning into steam. Strange attractors often occur in non-linear systems where huge numbers of observable data circle around one region of a graph, but then, either due to a slight pertubation or for no apparent cause, the data starts to circle around another portion of the graph. The implications for climate change could be profound, but not readily testable. While temperatures now are generally circle around a mean temperature with a range of about -10 degree (F) to 110 degree (F), these aspects of chaos theory suggest that it is conceivable that the next tiny increment of carbon dioxide in the air could cause a radical shift with mean temperatures and ranges far different up OR down. I'm not suggesting that this is true, but it is one possible explanation for another problem with climate models. Last I heard, we still don't have good models to explain either why the earth has entered ice ages or how it ever gets out of one. Chaos theory suggests that for some very minor reason or no particular reason other than the way the non-linear interactions operate, huge changes in climate could result.
  10. rgriffin42... With regards to chaos theory Tamino has a very good recent post on this explaining that this issue is basically the difference between weather and climate. And on the issue of glacial-interglacial cycles... yes, there are very good and clear explanations on how this happens. Several articles are located here on Skeptical Science. And you can just try googling Milankovitch cycles.
  11. rgriffin42 @59, the same thing concerns climate scientists and interested observers like me. That is what all the discussion of tipping points is about. It is very possible that at a certain rise in temperature, some natural feedback will kick in that is strong enough that will rapidly accelerate the rate of warming. Potential candidates are the the release of methane from clathrates, the release methane from formerly frozen tundra, and the deforestation of the amazon, two of which can individually release more CO2 equivalent of methane than has been released by humans since the industrial revolution. Another suggested tipping point is the possible shut down of the North Atlantic conveyor, with a consequent significant reduction in temperatures in Europe. However, as best understood at the moment, that is not likely for several centuries, at which time it may bring relief to Europe, but will not trigger an ice age. In fact, from geological studies, we know the possibility of a cooling tipping point is remote. If there was such a cooling mechanism, it would place a hard ceiling on global temperatures - but we know global temperatures have been significantly higher than they currently are. Hence the instability you mention may make things get a lot worse a lot faster than we are expecting, it is very likely that they will be our salvation.
  12. Dana69 (on another thread) wrote: "If climate is deterministic in nature you could have reasonable assurance of the outcomes. If more stochastic (governed by the laws of probability) it would be problematic. ... Seems most arguers here land on the deterministic side." Both weather and climate are deterministic. A chaotic system is one that is deterministic, but so sensitive to initial conditions that it is essentially unpredictable beyond a short prediction horizon. STochastic processes are not necessarily a problem either, the field of statistics (the mathematics of stochastic processes) is well developed and we have means of dealing with it. One of them is Monte Carlo simulation, which is the basis for both weather forecasting and climate projection (although used in different ways). "They do not specifically say so, but the reference to Lorenz and the use of “attractor” imply that chaos theory is being invoked here not determinism." If you knew anything about chaotic systems, you would know that they are deterministic. A little bit of knowledge can be a dangerous thing if one is not fully aware of the limits of ones knowledge. I suspect the scientists who wrote that section of the IPCC reports have a very sound grasp of chaos theory and understand very well what it implies for climate projection.
  13. Can I suggest linking to this superb visual metaphor in the article. I'm sure there are other posts where it could also be used effectively.
  14. Strangely, there are not a lot of comments on this topic. LOL

    The little I know on chaos I would like to share. As it was explained to me by ST Ariaratnum, an apparent god in random vibrations. Chaotic systems are analogous to bifurcation problems, like column buckling. As a forcing reaches a critical value, large changes in the system can occur.

    A column buckles when it reaches its critical load. Ariaratnum however prefered to call it the 'alternate equilibrium configuration'. So the column buckles when it reaches a state where it can resist the load by deforming in a different way. At this forcing, this altrenate configuration stores less potential energy (this last sentance I don't remember well).


    [JH] What is the point you are attempting to make?

  15. I could add to my last post ^^^, about modeling column buckling. Its a rather simple problem but is analogous to bigger chaos problems, I think.

    In order to model column buckling you need to do equilibrium in the deformed configuration. That is, the other possible degrees of freedom and their physcal behaviour have to be introduced in to the model. For numerical models, the increment steps and constiuative relations algorithms must be able to handle large changes. 


    [JH] What is the point you are attempting to make?

  16. Razo @64, when it comes to chaos, many people who are slightly informed probably have the lorenz attractor in mind as archetypical of strange attractors:

    With the lorenz attractor, after a given number of steps (successive evaluatons of the formula), it is not even possible to predict which lobe you will be in so that you truly have a bifurcation.  The bifurcation is reversible, however, which makes it quite unlike column buckling.  More importantly, the lonrenz attractor is not the only strange attractor, and not all strange attractors have a multilobe shape.  The rossler attractor, for example, has a single lobe:

    With the rossler attractor, it is not possible to tell well in advance on which side of the "orbit" you will be, but you will generated values will always orbit the same point.  The analogy to bifurcation fails.

    The climate system is even more precictable than a rossler attractor (in one sense).  Specifically, thermodynamics requires the climate system to have a net zero energy exchange between the planet and space over a very short term.  Consequently while it is not possible to predict far in advance exactly how far the planet will diverge from that equilibrium point within limits, it is possible to predict that it will track the equilibrium point very closely (within plus or minus 0.3 C from observations over the holocene).

    There is a possibility, however, of genuine bifurcations.  Melting of ice sheets, release of methane, large scale vegetative die back and other possible consequences of global warming could suddenly shift the equilibrium point.  Such sudden shifts, however, are almost certainly towards a warmer climate.  That is, to the extent that models fail to capture such bifurcations, they underestimate the potential risk from global warming.  It is strange that when pseudo-skeptics plead the chaos of the climate system, they always assume that that chaos is predictable, and will counter the effects of global warming.  We know enough, however, to know the genuine bifurcations are unpredictable, and will make things worse. 

  17. All: Please do not Post any responses to Razo until he makes a specific point about the OP. .

  18. Okay then.

    i offered the phrase 'alternative equilibrium configuration' as a concept to help people understand chaotic systems changimg states. Before I used to have a kind of mythical understanding of bifurcation problems. When it was told to me, it was a real help in understanding. 

    Second I continue the very simple analogy of modelling columns to suggest requirements for a model: the alternative configuration has to be programmed into the model, the numerical algorithm has to be very robust.

    these may seem trivial to some, but I don't think they are. I am not making any statement on the worthiness of existing GCM.


    [TD] This site is not an appropriate place for you to ruminate on topics marginally or totally irrelevant to climate change.  You have responded to moderator requests to specify the relevant point you are trying to make by posting more ruminations and your own admission that you are not addressing the "worthiness of existing GCM."  We will begin to simply delete your posts that are irrelevant to the topic.

  19. I would point out the person that told me this was a person that could read Bell laboratory research on superconductors and say that the same math can apply to solid mechanics and bifurcation, ST Ariaratnam.


    [JH] So what! Name dropping is no substitute for well-reasoned comments that are relevant to the OP, or in response to someone else's on-topic comment

    Per the SkS Comments polciy (which you should read in its entirety):

    The purpose of the discussion threads is to allow notification and correction of errors in the article, and to permit clarification of related points.

    Very few of your posts have met this standard.   

  20. Razo @69, so?  Did the person in question have experience of climate models, and tell you that the same considerations applied to climate models?  Did they explain how the climate was supposed to evade the limits placed by conservation of energy on variability in climate?  If not, your analogy has no relevance to the discussion, and your implied argument from authority is irrelevant.

  21. i will respond still to this question as it is directed to me. You may delete them if you wish.

    TC, its still relevant because the mathematics of physical phenomena  can be very similar between many fields in the physical sciences: electromagnetics, fluid dynamics, thermodynamics...(it's been many years ago now since university). climate models integrate partial differential equations. One can get inspiration from other fields, and many breakthroughs are done this way.

    I don't want to take more room on this post for this, but it's a fundemental point.


    [TD] Good, at least you explained what you claim is relevant.  However, you continued to fail to address how the specifics of climate models that have been explained to you are trumped by the "lessons" of models of entirely different domains.

  22. Razo @71, I am going to disagree with TD.  You have not shown the relevance of your claims.  You are not a researcher into climate models drawing inspiration from another field.  Nor do you show how that inspiration from another field should effect our thinking about climate models.  At best you have pointed out that in another field there are certain problems and that it is possible that the same problems exist for climate models.  As a response to that, pointing out that it is also possible that they do not exist for climate models is an adequate rebutal.

    In this case, however, we can make a stronger rebutal because we know future climate states are constrained by the requirements of conservation of energy, and hence constrained by the forcing history.  As such, it is analogous to a hollow ball containing a 3D triple pendulum running down a u shaped track.  The detailed motion of such a ball will be chaotic, but the mean path and velocity of the ball will be well constrained, and departures from those means will be short term variations only.


    [TD] Tom, I didn't write that Razo showed the relevance of his/her claims, only that he/she at least tried this time.  Better than before.  Nonetheless, Razo's followup post was mere continuation of his/her sermonizing without addressing the specific features of climate models that have been explained to him/her; so I deleted it.

  23. Razo, I should point out that just because weather is chaotic that does not imply that climate (the long term statistical properties of the weather) is similarly chaotic.  It is not difficult to think of other phsyical systems where this is the case, for example a double pendulum in the presence of an electromagnet.

    Sadly expertise in one field is often a recipe for the Dunning-Kruger effect when moving into a different field as it can blind you to the important differences between fields and give undue confidence in ones ability that makes you unable to see your mistakes.  The climate modellers are experts in their field, best to understand first and make assertions afterwards.

  24. I seem to be being critisized for not making any assertion by the moderator and making false assertions by others. So I will try to make an assertion here, to at least be worthy of the criticism. ;-)

    Firstly, my previous post was adding to the definition of chaos. Although I do not know why it would be rebuted, a rebuttal would be on my definition of chaos. I didn't touch the rest of the argument.

    But now I will. It's seems to me that people are confusing randomness and mathematical chaos a little.

    "For certain values of the parameters, the overall movement of the atmospheric air was oscillating unpredictably"

    The key phrase is 'for certain parameters', not 'oscillating unpredictably'.

    "Actually proving that these indices are chaotic is exceedingly difficult, but Tziperman et al. (1994) showed in a simple model how El Niño is likely a seasonally induced chaotic resonance between the ocean and the atmosphere."

    The key phrases here are 'induced chaotic resonance', which I called 'alternative equilibrium configurations', and 'proving that these indices are chaotic is exceedingly difficult'. But then, I'm not sure if the next sentance is correct:

    "Chaotic influences from oceans and volcanoes etc. makes both weather more unpredictable and creates the unpredictable part of the 'wiggles' around the average trend in climate"

    That is, although volcanic eruptions are chaotic in the regular sense or the word and can impact the climate greatly, do they involve indicies that are chaotic at certain values? Also, I don't think the formation of high pressure air masses come about after thier chaotic parameters reach a critical value.

    How chaos could impact climate might be more like this, I think. If one could show that global warmimg is effecting the chaotic indicies that cause ElNino to the degree that it becomes a more frequent and long lasting event, ie, the regular weather, that could impact climate. Or maybe if one could show that the pacific trade winds, that are presently causing a slow down of average global surface temperatures, are an induced chaotic resonance caused by global warming itself.(These are just absolute hypothetical ideas by me, I am not saying this is happening. the point is indicies reaching critical values)

    Regarding Lorenz's chaotic systems of rising warm air, well its on the scale of local weather thats going on all the time. I would guess it is accounted for emperically in the models as required (depending on the purpose of the model: forcasting, climate change, or downscaling etc)


    [JH] This post, sans the first paragraph, is the type of post we are accustomed to seeing on the SkS comment threads. It has a beginning, a middle, and an end.

    FYI, Moderation complaints are also prohibited by the SkS Comments Policy.  

    Please note that posting comments here at SkS is a privilege, not a right.  This privilege can and will be rescinded if the posting individual continues to treat adherence to the Comments Policy as optional, rather than the mandatory condition of participating in this online forum.

    Moderating this site is a tiresome chore, particularly when commentators repeatedly submit offensive or off-topic posts. We really appreciate people's cooperation in abiding by the Comments Policy, which is largely responsible for the quality of this site. 
    Finally, please understand that moderation policies are not open for discussion.  If you find yourself incapable of abiding by these common set of rules that everyone else observes, then a change of venues is in the offing.

    Please take the time to review the policy and ensure future comments are in full compliance with it.  Thanks for your understanding and compliance in this matter.

  25. correction:

    The key phrase is *'for certain values of the parameters'*, not 'oscillating unpredictably'.

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