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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 76 to 100 out of 120:

  1. Razo, as I have pointed out, climate (the long term statistical properties of the weather) is not necessarily chaotic, even though the weather is.  Climate models do not try and predict the behaviour of a chaotic system, but to simulate it. 

    "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."

    El-Nino is a mode of internal climate variability, it is one of the things that gives rise to the spread of runs from a particular climate model, but (at least assymptotically) it doesn't affect the forced response of the climate (estimated by the ensemble mean), which is what we really want to know as a guide for policy.

    You clearly know something about chaotic systems, however your understaning of climate and what climate models aim to do is fundamentally misguided.  Please take some time to find out more about the nature of the problem, as otherwise you are contributing to the noise here, not the signal.

  2. This is just a bunch of heuristic chatter. 

    Lets make it simple.  Forget climate.  Prove mathematically to me that you can predict averages based on the simple Lorenz equations.

    You will be famous.

  3. nickels, lets make it even simpler (a case where the physics is easily visualised).  The movement of a double pendulum is clearly chaotic (as it is deterministic, but the precise path of the pendulum is heavily dependent on the initial conditions).

    now consider placing an electromagnet to one side of the (iron) double pendulum.  As we increase the current through the electromagnet, the position of the pendulum will become increasingly biased to that side.  Now we can't predict the exact path of the pendulum, but we could simulate an ensemble of double pendulums, and apply the same magnetic field to each and take the average position of all of them as an indication of the effect of the elecrtomagnet on the pendulum.

    This is effectively what we are doing with climate models (but with much more simple physics).  The force applied by the electromagnet corresponds to radiative forcing.  The unforced movement of the pendulum corresponds to the unforced climate change (i.e. weather).  The statistical behaviour (average position) of the pendulums corresponds to the forced climate change (which is what we want to estimate).

    So with the double pendulm, its movement is chaotic, but the statistical properties of that movement is deterministic and non-chaotic.

  4. nickels - Chaos is involved in initial value problems such as predicting the weather, and for that reason we cannot determine the precise temperature or precipitation for a region several weeks in the future. 

    Climate is a boundary condition, and we use boundaries to quite accurately predict that summer will average warmer than winter. More precisely, that boundary systems such as climate are thermodynamically trend-stationary (tending to return to a balance of input/output) in their mean values. 

    Armwaving and arguments from incredulity on your part do not represent a disproof. 

  5. nickels - Also see the shifting of Burden of Proof fallacy, directly relevant to your demands in light of demonstrated model skills. 

    The case for models and for predicting climate has already been made and presented in the literature. You have presented exactly zero support for your contrary claims. 

  6. KR to nickels: "You have presented exactly zero support for your contrary claims."

    Also known as "handwaving."

  7. @DM

    I understand your argument, but this is not a proof.  And it does not extrapolate to more complex models.  I'm not saying you are wrong, I am just claiming that this sort of reasoning is not rigorous.  In math we call this 'hand waving'.

  8. @DSL

    Your science is not going to get very far (and hasn't) when you shoot down people that point the issues with your scientific method rather than take them seriously and consider how to address them.

    Best of luck.


  9. nickels, the kind of proof you are asking for us unavailable in many fields, but that does not stop similar results being used in a wide range of others, which is why we have computational fluid dynamics, rather than mathematical fluid dynamics.  There are many problems that you can only solve by simulation, rather than in closed form.  This does not prevent them from being rigorous, many excellent mathematicians (some of them in the same building as me) work on fluid dynamics (and indeed climate modelling).

  10. @DM

    Understood.  And I am certainly not saying climate models are wrong or unuseful or anything of the sort.

    But I refuse to listen to arguement about how 'we can predict averages' without asking for a proof, because the statement is simply not accurate.  That is all.

  11. nickels, do you accept that the statistical properties of the double pendulum in a magnetic field are non-chaotic?

  12. @DM

    I would be happy to read a paper that has some proof along these lines (would actually be interested in literature in this area).

    Even if there isn't a proof, a numerical study with serious attempts at aposteriori error control would be interesting...

  13. nickels, O.K., I am moderately surprised that you are unwilling to accept that the electromagnet will cause the double pendulum to be closer to the electromagnet on average than it would otherwise be, given that it is abundently obvious that this is true (consider the case as the magnetic field becomes very large).  However, at least your position is consistent.

    So, do you accept that we can predict planetary orbits?

  14. @DM

    If there is one thing that my mathematical training has taught me, it is to ignore any statement like 'abudnantly obvious'.  Its a cultural different between mathematicians and climate guys.  Very obvious things turn out to be very wrong all too often.

    And I also am not into 'proof by extrapolation of argument', so I don't want to take the planet bait.  Mathematically it is my understanding that the entire solar system could actually go infiite.

    My literature request is sincere.  Stability of computing averages is actually possible to make a decent mathematical argument towards.  This is part of my mathematical background. 

    Which is why I have to produce literature requests whenever I talk to climate guys....



    [JH] Your response to Dirkan's question about the pendulum is an artful dooge. Dikran also posed a legitimate question to you about planetary orbits. Your repsonse suggests that you are not here to engage in a civil conversation. We have little patience for concern trolling.

  15. nickels,

    Firstly, I notice that you didn't answer my question.  Scientific discussion relies on both parties being interested in seeking the truth, and this in turn requires an honest attempt to give a direct answer to direct questions and an absence of evasion.

    I know plenty of mathematicians (I am married to one), and I don't know any that are so rigid that they would ignore any statement of something that was abundently obvious regarding the real world.  Very obvious things do turn out to be incorrect (actually rather rarely), but that does not mean that it is rational to ignore them.  Proofs turn out to be incorrect occasionally as well.

    "My literature request is sincere."

    my attempts to explain a truth of applied mathematics to you is equally sincere, it would help if you were to give direct answers to my questions.

  16. O.K., so nickels is rather impolite!

    My question regarding planetary orbits was not baiting.  It was an attempt to make a serious point.  I'm sure that most of us are happy with the idea that planetary orbits can be predicted, however we can't write down an equation for the solar system that gives the orbits of the planets, i.e. we can't have proof of their orbits, and we have to solve them numerically.  Does that mean planetary scientists are not rigorous?  No.  Does that mean that we should not accept their predictions of planetary orbits?  No, of course not.

    As Einstein said "" ... as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.".  

  17. We appear to,have 2 nickels running down two different threads with the same arguments, this thread and the one here*.

    nickels @89.

    You tell us elsewhere* that you hold a PhD in Maths. You tell us here that "Mathematically it is my understanding that the entire solar system could actually go infiite." I find these two statements uncongruous, unless you are not being serious. It is akin to an aerodynamics engineer pronouncing that a bumble bee theoretically cannot fly.

    Indeed, apart from demanding/requesting a mathematical proof for the findings of climate models, your posts are entirely vacuous, a situation that is not compatable with your stated background.

    Of course it may be part of your nature that you present an aggressive posture here, but buddy I don't give a dime.

    (By the way, to call the structural calculations of a building's design a "proof" in the mathematical sense is very poor use of the english language.)

  18. nickels, calling people names is not doing you any favours.  It is also likely to result in the mdoerators deleting your post [ah, I see that has already happened], so if you want to make a substantive point, make it politely.  Please read the comments policy and adhere to it.  We get a fair few visitors here who deliberately try and get themselved banned, so they can whine about it elsewhere.  That is not very mature behaviour, so please demonstrate that you are above that sort of thing.


    [RH] Agreed. The only reason nickels is getting deleted is for violations of commenting policy. No problem with him presenting a dissenting position, it just has to be done in a way that conforms with policy.

  19. Dirkran Marsupial @93.

    I was being quite aggressive myself @92. I did catch the comment calling me but a single uncomplimentary name. It was referring me to look at Saari & Xi (1995) - Off to Infinity in Finite Time. Now the Newtonian n-body problem addressed by Saari & Xi (1995) is a fun mathematical construct but its applicability to the solar system (which has managed to remain ib situ for a few billion years without "going infinite") is something the authors fail to mention. They don't mention bumble bees either.

  20. It is a shame that nickels' two posts above will be deleted as they show that he is deliberately trying to get his posts deleted, rather than trying to engage in scientific discussion.  I have no idea why people seem to find that a good use of their time, life is short, much better to spend it on something more productive.

    Note all I have done is to ask questions politely - note the response from nickels.


    [JH] I sincerely believe that climate deniers are awarded a "merit badge" when they relinquish their privilege of posting on SkS comment threads.

  21. nickels, it isn't hostile if you stick to the comments policy and give straight answers to direct questions.

  22. <Snip>


    [PS] Conformance with the  comments policy is not optional. It appears you have not bothered to read it. We delete comments that do not conform whether they are pro or anti on any argument. Got that? Take a deep breath, read the comments policy and continue the debate. Asking questions is not baiting - it is about about establishing a common ground. This site is concerned with scientific truth and is not a high school debating contest.

  23. nickels. For your information, I am a moderator at SkS, but I didn't moderate any of your posts, not one.  I do not moderate any discussion in which I am taking part, and leave it to others, for obvious reasons.

  24. Nickels: Your comments have been deleted because they were not in conformance with 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, off-topic posts or intentionally misleading comments and graphics or simply make things up. 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, as no further warnings shall be given.



    [PS] And lest there be any misunderstanding about what was breached, then we have:

    - No cyberstalking.

    - No moderation complaints

    - No inflammatory tone.

    - No sloganeering.

    The threads are full of skeptics able to discuss the science without violating the commentary policy.

  25.  (snip)


    [PS] Please stop using Skeptical Science to advertize your website. Further attempts will be regarded as spam.

    [RH] Snipped content.

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