I think I need another break!

I think I probably need to take another short break from all of this online nonsense. I’ve recently been commenting on Bishop-Hill and had been quite enjoying it. I’d been accused by other commenters of being patronising and condescending, but that was somewhat intentional. I knew that if I took it seriously, the responses would just wind me up too much. Then, I made the mistake of taking it seriously, and the wheels fell off.

It related to a lengthy discussion about the significance of chaos. It’s clear that our ability to forecast weather events more than a few days in advance is very difficult, if not impossible. This is a consequence of the system being non-linear and, essentially, chaotic. The precise evolution is very sensitive to the initial conditions and since our models can never set the initial conditions with infinite precision, our ability to forecast specific events decreases with increasing time. If you want to know more, you can read the Realclimate post by James Annan and William Connolley, which says,

Although ultimately chaos will kill a weather forecast, this does not necessarily prevent long-term prediction of the climate. By climate, we mean the statistics of weather, averaged over suitable time and perhaps space scales (more on this below). We cannot hope to accurately predict the temperature in Swindon at 9am on the 23rd July 2050, but we can be highly confident that the average temperature in the UK in that year will be substantially higher in July than in January. …… models based on physical principles also reproduce the response to seasonal and spatial changes in radiative forcing fairly well, which is one of the many lines of evidence that supports their use in their prediction of the response to anthropogenic forcing.

This is really all I was trying to point out in the discussion. I was also trying to stress the importance of the boundary conditions. Our climate’s boundary conditions are essentially the albedo, the solar insolation, and the composition of our atmosphere (the greenhouse effect). These boundary conditions broadly set the overall of state of our climate, which is essentially a consequence of energy conservation (these boundary conditions will set the equilibrium temperature at which we are losing as much energy as we gain).

It is possible for internal variability to influence some of these boundary conditions, but we have little evidence to suggest that it can have a significant impact in our current climate state. There’s a suggestion that it can have a small impact that may last a decade or so (see this post) and there is some evidence to suggest that some of our past climate changes were internally forced. However, we don’t expect (at the moment) internal variability to play a significant role (it might, but the evidence for this is weak). So, even though the system is inherently chaotic doesn’t mean that it can simply shift into an entirely new state – the overall state of our climate (the conditions averaged over a suitable time interval) are largely constrained by the boundary conditions.

Well, this discussion didn’t go well. Apparently the boundary conditions are irrelevant in a chaotic system, and why was I so focused on energy conservation anyway (because it’s a fundamental law of physics, maybe). My tolerance – which had already been strained – disappeared when someone (who shall remain nameless) popped along to point out that I was an idiot because it is indeed possible for non-linear dynamical systems without boundary conditions to simply shift into an entirely different state. Well, yes, because it’s a non-linear, dynamical system WITHOUT BOUNDARY CONDITIONS! Telling me I’m an idiot because a system that is not really comparable to our climate can do something our climate probably can’t do, is a remarkably poor rebuttal.

Anyway, I need to finish working through some lecture notes, finish working on a paper (which happens to be on a non-linear, dynamical system – I hope I know what I’m doing) and take a few deep breaths. I think I’m now being moderated on Bishop-Hill as my comments weren’t appearing. I haven’t gone back to check recently, so they may have appeared now. I’m kind of hoping Andrew Montford will ban me. Not so that I can then complain about it, but so that I can stop wasting my time there. I’m well aware that I don’t have much self-control, so Andrew would be doing me a favour if he were to do so.

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136 Responses to I think I need another break!

  1. Pblackmar says:

    Fishing can help relieve the stressj. However, you should be careful as many use fishing as an opportunity to drink which can cause the benefit to time relationship to become slightly chaotic.

  2. Pblackmar,
    Maybe I’ll skip the fishing part 🙂

  3. The best way to squash the “we can’t predict the weather next week accurately, so how can we predict the climate in 50 years’ time?” meme, is to respond with, “we can’t predict whether the next coin toss will be heads or tails, but if we toss it 10,000 times we know with 100% certainty that the distribution will be 50/50.”. That also enables the idea of ‘loading’ the die/coin to be introduced.

    I also like the analogy, “we can’t predict whether the next wave will go further up the beach than the last, but if we take an average of waves over time and along the beach we can calculate the tide’s ebb or flow, its speed and even predict when high tide might occur”. I like it because one can also throw in the suggestion that anthropogenic influences, like a passing ferry, a jet skier, a breakwater or a tidal barrage can produce short or long-term term fluctuations or changes.

    I know it won’t counter dyed-in-the-wool denial, but it might point a passing fence-sitter in the right direction.

  4. Sorry, forgot to close the italics after …might occur”. A time-limited edit function might be useful, attp.

  5. John,
    I definitely wasn’t dealing with fence-sitters. Not sure I’d go quite as far as dyed-in-the-wool denial, but I think I was dealing with “I understand chaos. Noone else understand chaos. Therefore climate models are wrong. Therefore we know nothing.”

  6. John,
    I noticed and fixed it. I don’t think the free WordPress account allows that. Maybe my friendly, and WordPress expert, moderator can advise 🙂

  7. ATTP,

    I’ll do some nitpicking again.

    You refer twice in your comment to the weakness of evidence for strong variability, but in my opinion you do that in sentences that would require stating that there’s significant evidence against strong variability. If you think there’s such evidence then say it, otherwise think again whether what you write is fully logical.

  8. Pekka,

    I’ll do some nitpicking again.

    Thanks.

    You refer twice in your comment to the weakness of evidence for strong variability, but in my opinion you do that in sentences that would require stating that there’s significant evidence against strong variability. If you think there’s such evidence then say it, otherwise think again whether what you write is fully logical.

    I don’t get this. As far as I’m aware there is little evidence to support an argument that internal variability has played a big role in the last century (or, even, millenium) or can play a big in the coming century. I don’t see the problem with saying this, but – right now – I don’t really feel up to another discussion about the meaning of a word like can. You seem to be suggesting that I can’t say that there is little evidence to support a position unless I also state that there is strong evidence against that position. I don’t quite get the logic of this, but really can’t quite face trying to work it out. Since I broadly agree with your position, why not just assume that I should have written it differently and that we’ve agreed that I should have written it differently, and we leave it at that for now?

  9. Attp writes… “I definitely wasn’t dealing with fence-sitters.”

    I’m sure you weren’t: however the thing about fence-sitters is that they don’t comment and are therefore not visible. Perhaps you should ask Mr Montford how many visitors he has compared with how many commenters. Come to that, you probably know that answer for this site. Winning over passers-by is the most constructive thing we can do (after running a successful blog, of course 🙂 ).

  10. Pekka,
    Actually I will push this a little further. The point I was trying to get at was that the argument I was getting on Bishop-Hill was that a chaotic system can shift into a new state by following a different attractor. All I was trying to point out was that even though this may well be true of a chaotic system, our climate is constrained by the boundary conditions and there is little evidence to suggest that these boundary conditions are particularly sensitive to internal variability (at least, in our current state). So, I wrote it that way intentionally to address that point (i.e., just because something is possible doesn’t make it likely). I don’t know if that makes it more logical, but I have a sneaky suspicion that I may be incapable of writing something that you won’t be able to nitpick (although, to be fair, your nitpicking does make me think about what I’m writing but I’m not always sure how to write something that would avoid it).

  11. ATTP,

    The issue is really on the old question on absence of evidence vs. evidence on absence.

    You make statements that certain kind of variability is likely absent. That’s a statement on absence, for that you need evidence on absence. It’s not enough to point to absence of evidence for the opposite claim.

  12. > by James Annan

    …and *cough* 🙂

    From experience, the best way to get banned by the likes of BH, or AW, is to carefully point out the errors in the blog-owners original post. I don’t think either of them read the comments when its just the commentators arguing with each other – they’re both smart enough to know that most of their commentators are worthless.

  13. Pekka,

    You make statements that certain kind of variability is likely absent.

    No, I didn’t. That’s how you interpret what I’m saying : it’s not what I’m saying.

    Firstly, as I was pointing out above, it was really to address the claim that the system being chaotic means that it could simply shift into a new state. I was simply trying to point out that since there is little evidence to suggest that internal variability can strongly influence our boundary conditions, this property of chaotic systems doesn’t seem that relevant (at least, not as a strong argument against climate models). Secondly, that there is little evidence to suggest that internal variability does/will play a big role in the evolution of our current climate is a defensible statement and does not immediately imply that it is likely absent. That is your interpretation of what I said. Maybe you could stop starting discussions in which I end up defending your interpretation of what I said. It’s hard enough defending what I intend to say, without also having to defend what you think I said (I just get confused).

  14. William,
    Indeed, sorry, I did notice that and then forgot.

    I don’t think either of them read the comments when its just the commentators arguing with each other – they’re both smart enough to know that most of their commentators are worthless.

    Yes, the only time I’ve had a comment deleted was when I did that. It appears that I’m now being moderated. Not sure if I am or why, but it could be that I asked AM is he ever wrote a blog post in which he didn’t mock a mainstream climate scientist and in which he didn’t completely dismiss a piece of scientific research with which he disagreed.

  15. JWhite says:

    ATTP,

    Too bad. Though I don’t post much (hardly any actually), I do enjoy the coherent discussion and feel I have learned much. This is especially true since RC is essentially dead these days (barring Gavin’s latest, of course).

    Anyways. Go relax and remember that it’s always beer-oclock someplace.

  16. How the statements are perceived depends on own prior views. If you think that variability that involves state shifts between attractors are inherently unlikely, you may see your formulations as not involving any logical fallacy, but otherwise I do think that they do involve the fallacy. Absence of evidence for such transitions has very little weight for people, who consider it highly possible that such transitions do take place, but think that the empirical data available cannot separate efficiently such events from other variability (forced and unforced).

    When you argue against someone with different views you must formulate the argument in a way that’s perceived correctly from the background of the opponents.

  17. Pekka,

    How the statements are perceived depends on own prior views.

    Yup, that certainly seems to be the case.

    If you think that variability that involves state shifts between attractors are inherently unlikely, you may see your formulations as not involving any logical fallacy, but otherwise I do think that they do involve the fallacy.

    Again, you’re putting words in my mouth. If someone says “climate models are wrong because it’s possible that this could happen and they’re not capturing that” a suitable response would appear to be “okay, but there is little evidence to suggest that that is likely, therefore that seems to be a poor argument against climate models.” I guess one could go further and point out that changing the boundary conditions would typically take a substantial amount of energy and hence making it unlikely. Fine, but I was actually trying to be careful in what I said and you’ve still managed to interpret it in some way that I didn’t actually consider. As I said, maybe I’m incapable of actually writing something that you can’t nitpick, however hard I might try.

    When you argue against someone with different views you must formulate the argument in a way that’s perceived correctly from the background of the opponents.

    Assuming this is actually possible. My view would be that people who are willing to engage in good faith will attempt to clarify or understand what someone else is trying to say. If they’re not willing to do this, there is probably no formulation that would be suitable.

  18. Commenting shortly on the issue itself.

    I think it’s virtually certain that there’s some noticeable multidecadal variability, on variability on time scale of around 60 years we have some evidence, but not as strong as on shorter time scales. We know also that the patterns of ocean circulation vary and that part of that variability has a persistence on decadal or multidecadal level. There’s much evidence also on more persistent variability in the circulation patterns.

    We do not know what all factors have driven these different patterns. Forcings have been involved as are other factors external to oceans and atmosphere, but there may well be quite a lot of internal variability in that.

    Little in that variability is fully regular. It’s very likely, perhaps virtually certain, that effects that can be considered chaotic are involved.

    How much all that variability affects the climate on relevant time scales is an open question, perhaps not very much, perhaps quite significantly. This is really an area on which the science cannot say much at present as far as know.

  19. > It’s not enough to point to absence of evidence for the opposite claim.

    That’s true. For that conclusion to obtain, you need something like bivalence. Either natural variability plays a significant role, or not. Either you’re a realist or you’re not, a dichotomy that only works for realists [about realism].

    But one only needs to claim that we have no evidence of P to say that we have no evidence that P. I fail to see why AT would need to argue for something stronger. He’s not proposing a categorical syllogism here.

    Incidentally, we should note that the absence of a syllogism is no evidence of illogism.

  20. Pekka,

    Little in that variability is fully regular. It’s very likely, perhaps virtually certain, that effects that can be considered chaotic are involved.

    Indeed, would be surprised if the chaotic nature of the system were not playing a role.

    How much all that variability affects the climate on relevant time scales is an open question, perhaps not very much, perhaps quite significantly. This is really an area on which the science cannot say much at present as far as know.

    Really? Say anything with certainty, maybe. On the other hand, there is evidence that we’ve been broadly stable throughout the Holocene. Right? So, that’s at least some evidence that we can have extended periods where we don’t see such large changes to our boundary conditions that we go through an extended (multi-decade, century) period of warming/cooling. I guess that doesn’t mean that it can’t happen, but would seem to suggest that it is possible to go through long periods without a substantial influence due to internal variability. Maybe I’m still making some kind of logical fallacy but I’m sure there is some kind of Bayesian way to approach this that would allow a stronger statement to be made. I just can’t quite think of it at the moment.

  21. I asked AM is he ever wrote a blog post in which he didn’t mock a mainstream climate scientist and in which he didn’t completely dismiss a piece of scientific research with which he disagreed.

    I just wanted to propose that you take lessons from William on how to get banned and get your life back, but it seems you already know how to do so. 🙂

    My advice would be not to try to convince the die hards. They probably already know that they are completely wrong, but they prefer not to say so. Because they like the consequences of climate change. There is nothing you could say that would make them publicly change their minds. Try to see it as a game and communicate with the normal readers (indirectly).

  22. Victor,

    Try to see it as a game and communicate with the normal readers (indirectly)

    That’s kind of what I was doing, and then the wheels fell off. Admittedly, I was being a little flippant and somewhat condescending, so it may not have been a particularly good way to communicate with the lurkers. I thought that might help me to not take it too seriously. It only worked for a while 🙂

  23. I feel that I must repeat the other side of my argument:

    The lack of knowledge on internal variability does not prevent us from knowing more about AGW.

    When we search evidence on the strength of AGW we can use all relevant empirical data directly to answer questions about AGW without answering first questions about internal variability. We can use many different types of evidence for that. One example is the argument of Fred. It tells additional information relevant for estimating TCR. Even if it tells little on what the internal variability may be like at other times, it does tell something on hoe much internal variability may have contributed to recent warming. Perhaps it does not tell anything highly accurate, but it does tell relevant additional information. The same is true for many other approaches used to constrain estimates of TCR.

    Thus my view is that an argument that internal variability could not have influenced significantly warming over past decades – even over the full interval 1950-2010, is very weak. It could have done that based on the limited understanding that we have on internal variability.

    The stronger argument is that the totality of evidence tells that AGW has caused roughly as much warming as the observed warming. Thus the contribution of internal variability is smaller for this particular change in temperatures.

  24. Pekka,

    The stronger argument is that the totality of evidence tells that AGW has caused roughly as much warming as the observed warming. Thus the contribution of internal variability is smaller for this particular change in temperatures.

    Fine.

  25. AT,

    I think the crux of the matter is related to this argument by Dan Hughes at the end of that thread:

    > If the calculated response was not chaotic, ensembles would not be necessary.

    Here was a part of my response at Andrew’s, [a response that] got moderated:

    Any travelling salesman would agree, no doubt. But I’m not a travelling salesman. So an explanation might be nice.

    This kind of claim is too “complex” for my little head, if you catch my (post-modern?) drift.

    The “postmodern” refers to a jab Nullius took the other day at [Andrew]’s, when I was discussing with the Auditor his “MBH98” category. Spence had high praises for Dan’s fu in the thread.

    ***

    The gist of Spence’s argument is that [since] any box that is chaotic inside will be chaotic outside, because divergence propagates. Or at least that’s how I see it. I could post the rest of my moderated comment if you care. It’s related to the fact that the concept [of] chaos is not as clear as Spence presumed. For instance, [Spence’s argument about how chaos spreads chaos everywhere it goes] may require infinite resources.

    Oh, and I’m the one to blame for not mentioning Dr. Connolley. I found the RC article because of this challenge I could not pass up: “Anyone who tries to make the claim that weather is chaotic and climate isn’t doesn’t understand chaos.”

    ***

    Blog communication is mainly an ethological problem.

  26. Willard,
    Feel free to post the rest of your comment if you wish.

    The gist of Spence’s argument is that since any box that is chaotic inside will be chaotic outside, because divergence propagates. Or at least that’s how I see it.

    This was why I tried to use the example of a double pendulum. If you put a double pendulum on a table the motion of the pendulum will be chaotic, but the entire system is not going to spontaneously leap into the air and land on the floor.

  27. A system of morons (neither bosons nor fermions) displays essentially the same behavior.. It is impossible to impose boundary conditions on them, and they may quickly become an entirely new system of boarons. They don’t follow the laws of physics as we currently know them.

  28. > This was why I tried to use the example of a double pendulum. If you put a double pendulum on a table the motion of the pendulum will be chaotic, but the entire system is not going to spontaneously leap into the air and land on the floor.

    I forgot that you said it, AT, so I had to rediscover it in my shower a minute ago by recalling thy Wiki’s gif:

    Source: http://upload.wikimedia.org/wikipedia/commons/4/45/Double-compound-pendulum.gif

    (Via http://en.wikipedia.org/wiki/Double_pendulum)

    I thought of this because my introduction to chaotic systems relate[s] to child’s development:

    How can a learner who does not know what there is to learn manage to learn anyway? This is a more difficult question than it might first appear. The issue is whether one needs to prespecify the learning tasks and the learning goals, whether the agent or its designer has to know what needs to be learned to learn. Evidence from human development gets us out of this quandary by showing that babies can discover both the tasks to be learned and the solution to those tasks through exploration, or nongoal-directed action. In babies, spontaneous movement creates both tasks and opportunities for learning. One demonstration concerns the study of reaching (Corbetta & Thelen, 1996). The week-by-week development of four babies was tracked over a 3-month period as they transitioned from not reaching to reaching. Four very different patterns of development were observed. Some babies in the nonreaching period hardly lifted their arms at all, but sat placidly watching the world. Other babies were more high-strung and active, flailing and flapping and always moving. These different babies had to learn to solve very different problems to learn to reach out and grasp an object. The flailer would have to learn to become less active, to lower his hands, to bring them into midline. The placid baby would have to learn to be more active, to raise her hands, to lift them up from their usual positions on her side. Each baby did learn, finding a solution that began with exploration of the movement space.

    http://onlinelibrary.wiley.com/doi/10.1002/9780470147658.chpsy0106/full

    Philosophers study strange things, nowadays.

  29. John Hartz says:

    ATTP: Your teaching abilities and scientific knowledge could be put to much better use by authoring original articles for publication on Skeptical Scince or other like websites.

  30. anoilman says:

    Logically, if they delete your comments that point out the errors in their article, then you can conclude that they don’t want to admit error, and they don’t want to be held accountable.

    It seems that is what you must do, and they insist you do it else where. Like here.

    I thinking keeping a score card for their bullshit would be real handy.

  31. I like the gif, Willard: ‘chaos constrained within predictable bounds’.

    And now we’re slowly changing those bounds.

  32. entropicman says:

    Against stupidity
    The Gods themselves
    Contend in vain.

    Friedrich Schiller

  33. Here’s a good TL;DR to the “Yes, but Chaos” argument:

    It is the climate’s broadly deterministic response to forcings that are of interest, and all evidence points to such determinism.

    http://scienceblogs.com/illconsidered/2006/03/chaotic-systems-are-not-predictable/

  34. Rachel M says:

    A time-limited edit function might be useful, attp.

    Yes, AndThen is right. This is not possible on WordPress.com. I’ll wait for the right moment and put in a request for you. I’m fighting for something else at the moment though so let me wait for that to be decided.

  35. Willard,
    Good post, thanks.

    Rachel,
    Thanks. I can edit my own comments, so there’s no rush 🙂

  36. Since I’m not a moderator anymore and argue that we need way more editors than we need auditors [1], I could provide editing services on this site.

    http://planet3.org/2014/07/03/10150/

    Send your editing requests to languageisasocialart at that other G spot you like.

  37. Doug Bostrom says:

    Axiom: climate discussions touching on nonlinearity and chaos become chaotic and nonlinear. Something about there being no boundary condition for obtuse, I think.

  38. izen says:

    How can a chaotic process change the volume of the oceans?

    It requires the gain of a lot of energy to melt sufficient ice and expand the total ocean volume to generate the (unprecedented in millennia) change in sea levels.

    chaotic processes may play a role in the variations in time and locality of the melting and expansion. but he shape of that chaos is determined by the boundary conditions, insolation, albedo and the thermal resistivity of the atmosphere.

    The known stability of past sea level in the Holocene, and the rapid changes at terminations may have some bearing on the magnitude of internal climate variations and what happens when boundary conditions do change.

  39. izen,

    chaotic processes may play a role in the variations in time and locality of the melting and expansion. but he shape of that chaos is determined by the boundary conditions, insolation, albedo and the thermal resistivity of the atmosphere.

    I tried saying something like this. It didn’t work. Apparently I’m too focused on the concept of energy conservation.

  40. anoilman says:

    Energy Conservation is just a greeny fad anyways….

  41. jsam says:

    You are not alone. Trolls don’t need facts, just a target. http://skepticalscience.com/learned-from-debating-science-with-trolls.html

  42. izen says:

    @-“….the concept of energy conservation.
    Energy Conservation is just a greeny fad anyways”

    It is not a concept or a greeny fad…
    Because Conservation of Energy, to quote Judge Dredd,
    “It’s the LORE!”
    (grin)

    In politics, if you want to know what’s going on, follow the money.
    In physics, chemistry and reality, follow the energy.

    (Note that money and energy follow opposite versions of the laws, money can be created and destroyed and tends to become more unequally distributed with time.)

  43. Pblackmar says:

    TTP-please tweet this comment you made earlier to Pekka, it was so very accurate and many need to take it to heart “My view would be that people who are willing to engage in good faith will attempt to clarify or understand what someone else is trying to say. If they’re not willing to do this, there is probably no formulation that would be suitable.”

  44. Spence seems to be monitoring this thread:

    Willard’s latest comment is a good example of this – apparently, willard is continuing to try to defend the idea that a linear reduction in error can outstrip exponential error growth […]

    http://www.bishop-hill.net/blog/2014/8/24/gcms-and-public-policy.html?currentPage=6#comment21031927

    I have no idea why he’s putting that idea into my mind. As if it was implied by anything I said or did in that thread. I do hope that Spence will contact James to tell him he (James) does not understand chaos.

    For the moment, let’s analyze Spence’s latest ClimateBall ™ moves:

    Interestingly, willard also links to that article from RealClimate [1] – which I think is an example of exactly the type of argument that willard and ATTP are trying to present. Unfortunately this argument – by analogy of a simple, low dimensional system with Markovian dynamics – is of an exceptional, rather than typical, example of a chaotic system [2], and real (high dimensional, fractal dynamics) systems, which are more common in nature, behave nothing like this [3]. But I think it is quite informative in the sense, this is where willard and ATTP get their claims from [4]. They are impressed by the presentations like the ones at RealClimate [5], because it has technical terms they can sort-of relate to, but they do not have sufficient knowledge [6] to see the arguments are full of holes [7].

    When they present the claims to someone more knowledgeable, who asks the questions they had insufficient knowledge to ask [8], they both get angry [9] because they can’t answer them [10], and resort to the limited options available to them [11]. Shout, swear and search google for an article to quote which doesn’t have any bearing on the current discussion [12]. That has to be better than learning something, right [13]?

    So here’s what Spence does:

    [1] Some mild RC bashing.
    [2] Some special pleading to evade having to confront James.
    [3] Persisting in conflating model and reality.
    [4] More RC bashing.
    [5] More mind probing.
    [6] Persisting in playing the man.
    [7] Arguing by assertion.
    [8] Bragging.
    [9] More mind probing.
    [10] Some gaslighting.
    [11] Still persisting in playing the man.
    [12] Blaming the other for the food fight.
    [13] Playing innocence abused.

    [Op. Cit.]

    As we can see, there’s not one single sentence that does not contain a cheap shot. A whole comment dedicated to attack another commenter and to whine about how difficult it is to learn anything out of these exchanges.

    ***

    To make sure that gaslighting is what’s happening, here’s the comment that never appeared at Andrew’s, except for the last two parts, which were already quoted.

    > People misusing technical terms has no impact on a discussion? How ridiculous!

    Spence claimed that nothing I’ve written “has any impact” in the discussion. All my comments so far undermine Spence’s vapid claim that “chaos” has a specific technical meaning. The only valid conclusion is one Spence himself finds ridiculous.

    Fancy that.

    ***

    > Chaotic systems conform to a number of criteria, and one of those is exponential error growth from initial conditions, which ensures any arbitrarily small error will overwhelm the solution in linear time.

    This seems to refer to the definition (SD, which stands for Sensitivity Dependence):

    http://plato.stanford.edu/entries/chaos/#ChaDetQuaMec

    See section 1.2.5. Defining chaos that way excludes a weaker definition that does not specify any rate of divergence; see (WSD) in the same section. The entry observes that Poincaré’s examples satisfied WSD.

    Anyway. These definitions are incomplete. But even if we patch them, SD is still problematic:

    At best, SD can only hold for the large time limit and this implies that chaos as a phenomenon can only arise in this limit, contrary to what we take to be our best evidence. Furthermore, neither our models nor physical systems run for infinite time, but an infinitely long time is required to verify the presumed exponential divergence of trajectories issuing from infinitesimally close points in state space.

    It is only by turning this into a food fight that Spence managed to prolong that silly thread. He almost succeeded.

    ***

    > The real, interesting debate is that once you realise that the systems are constrained by the same limits of predictability, moving on to determining what those limits of predictability are, which are governed by the time horizon (Lyapunov exponents) and the fractal dynamics.

    The Stanford entry, again:

    But as a practical matter, all finite uncertainties saturate at the diameter of the attractor. This is to say, that the uncertainty reaches some maximum amount of spreading after a finite time and is not well quantified by global measures derived from Lyapunov exponents (e.g., Lorenz 1965). So the folklore—that on-average exponential divergence of trajectories characterizes chaotic dynamics—is misleading for nonlinear models and systems, in particular the ones we want to label as chaotic. Therefore, drawing an inference from the presence of positive global Lyapunov exponents to the existence of on-average exponentially diverging trajectories is invalid. This has implications for defining chaos because exponential growth parametrized by global Lyapunov exponents turn out to not be an appropriate measure. Hence, SD or Chaosλ turn out to be misleading definitions of chaos.

    This is the second time we quote that paragraph. This time, we quoted it in full. With our emphasis.

    ***

    My main point is not that complicated: we can read in the Stanford entry that the notion of chaos Spence keeps hammering has very steep limitations: it is said to be misleading. No wonder Spence tries to dodge that point by pretending it is irrelevant.

    It’s just a flesh wound, I guess.

    The harder Spence will try to claim that whoever does not share his intuitive notion of chaos “does not understand chaos”, the more I will persist in quoting authorities who do not understand chaos according to that criteria. It’s a challenge that’s too good to miss. Spence’s blunder is a keeper.

    The concept of Long-Term Persistence might have application in ClimateBall ™.

  45. This line is particularly revealing

    When they present the claims to someone more knowledgeable

    If only Spence had made that clearer at the beginning, I would have known to sit at his feet and listen with awe and wonder. I suspect, though, that Spence is more knowledgeable than me about Chaos, but not sufficiently so to realise that it isn’t nearly as relevant to this particular issue as he appears to think (energy conservation, radiative physics and all that).

  46. Only in their apprehension of the truth can people be truly free. ‘Twas always thus, and always thus will be.

    (Modified quote from “Dead Poets Society”.)

    Please continue speaking the truth at least at blogs like this. The world desperately needs more places like this. Those who wage war on the truth should not be allowed to win.

  47. Willard,
    I thought I might comment on this, which may actually be from your comment, rather than from others, but I suspect this is the main issue here

    Chaotic systems conform to a number of criteria, and one of those is exponential error growth from initial conditions, which ensures any arbitrarily small error will overwhelm the solution in linear time.

    Whatever strict mathematical definition a chaotic system may have, it really is simply a non-linear system that is extremely sensitive to the initial conditions. Since one can never set the initial conditions with infinite precision, an attempt to model a specific system will end up with model results that are likely to diverge from reality with time. So, if those who are playing “but Chaos” are criticising climate models because the results won’t match reality then, by their own argument, they are setting a requirement that is impossible to meet.

    However, the equations being used are still the correct equations for the system and therefore the result of any model run will be a possible outcome for a system with those initial conditions. Therefore if you run many realisations of the model, each with a slightly different set of initial conditions, the results will tell you something of the possible evolution of such systems. Of course the range of possibilities could be so large as to tell you little, but not necessarily.

    Also, in the case of climate models, the current understanding (amongst modellers at least) is that the average state of a climate model run (i.e., the statistics of weather, averaged over suitable time and perhaps space scales as James and William put it) is more dependent on the boundary conditions than on the initial conditions. Therefore, even though the system is chaotic, if your goal is to understand the average state of the system at some point in the future, climate models are probably fine (they can always be improved, but this outcome is not strongly dependent on the chaotic nature of the system). On the other hand, if your goal is to actually make some kind of specific forecast about the future weather, then climate models can’t do this. In a sense, those playing “but Chaos” are essentially criticising climate models because they can’t do something that they’re not being used to do and that noone is claiming they can actually do.

    Anyway, that’s my understanding. I doubt that those playing “but Chaos” will agree, but that’s no surprise.

  48. KeefeandAmanda,

    Please continue speaking the truth at least at blogs like this.

    Thanks. Doing my best to do so 🙂

  49. AT,

    Someone who starts waving “f of xes” around should be able to back them up. In our case, he’d need to identify the effs, the xes, and their respective domains.

    Anyway.

    I think the most delightful part of all this is that those who insist in “but chaos” should be the ones who’d require predictability the most. After all, the idea of looking inside your box is to be able to see just how much predictability [one can get] out of it. When your focus is on the upper points that reaches [a] double pendulum, the swing trajectories are of little concern. So yet again we see a “but” argument that [ships with both] the requirement and the frustration it provides.

    **”

    Speaking of chaos, here’s a bit of news that matters a bit more to me than all this:

    Elsevier does not have a comparable tradition of involvement in mathematics publishing. Many of the mathematics journals that it publishes have been acquired comparatively recently as it has bought up other, smaller publishers. Furthermore, in recent years it has been involved in various scandals regarding the scientific content, or lack thereof, of its journals. One in particular involved the journal Chaos, Solitons & Fractals, which, at the time the scandal broke in 2008–2009, was one of the highest impact factor mathematics journals that Elsevier published. (Elsevier currently reports the five-year impact factor of this journal at 1.729. For sake of comparison, Advances in Mathematics, also published by Elsevier, is reported as having a five-year impact factor of 1.575.) It turned out that the high impact factor was at least partly the result of the journal publishing many papers full of mutual citations. (See Arnold for more information on this and other troubling examples that show the limitations of bibliometric measures of scholarly quality.) Furthermore, Chaos, Solitons & Fractals published many papers that, in our professional judgement, have little or no scientific merit and should not have been published in any reputable journal.

    http://johncarlosbaez.wordpress.com/2012/02/08/the-cost-of-knowledge/

    Knowledge production is still quite chaotic.

  50. Joshua says:

    Anders –

    reading your 11:19…

    It’s kind of scary because I think I actually kinda sorta maybe understood some of that. The description you gave of the relative function of initial vs. boundary conditions (and their interplay with chaotic interactions) was very instructive for me .So I have a questions.

    The claim is made that the models aren’t “fit for purpose,” but it seems, then, that the question must be answered: How are you defining purpose?

    You say: “On the other hand, if your goal is to actually make some kind of specific forecast about the future weather, then climate models can’t do this.”

    So the question for me becomes where lies the “boundary” between future wifeather and climate? Judith can point to decadal scale and regional forecasting to say “See, not fit for purpose.” Since we don’t have observational data on the century scale (what’s the adjectival form of “century?”) the fit for purpose on a century scale can’t really be determined except as a theoretical conjecture.

    I wonder if there isn’t some theoretical way to describe the boundary between climate and weather. I have seen analogies use (e.g., waves versus tides), but how is the distinction of weather versus climate, or the time period associated with “purpose,” or the distinction as to whether initial or boundary conditions are most applicable, anything other than arbitrary (not in the sense of random, but in the sense of based on subjective criteria)?

    As always, if my question is based on so limited (or incorrect) an understanding that it’s impossible to construct a reasonable answer, just say so. There will be no hurt feelings if that’s the case.

  51. Joshua,

    The claim is made that the models aren’t “fit for purpose,” but it seems, then, that the question must be answered: How are you defining purpose?

    I think that is a valid question. I would certainly argue that if one is going to criticise something for not being fit for purpose one should understand what the purpose is.

    So the question for me becomes where lies the “boundary” between future wifeather and climate? Judith can point to decadal scale and regional forecasting to say “See, not fit for purpose.”

    I’ve certainly seen Judith suggest this. It’s my understanding that most climate modelling has not been focused on decadal scales. Each model may be able to model variability on decadal scales, but given the stochastic nature of this variability, it’s difficult to predict it precisely. Hence, the claim that climate models have failed because they didn’t predict the “pause” seems silly because I don’t think any climate modeller ever expected that the models would be able to precisely predict when such a “pause” would occur, even if they were able to predict such “pauses” should occur.

    I believe that there are now people who are working on making more precise decadal predictions. Personally, I don’t really understand this, as I don’t think we expect changes to be that significant on decadal scales (i.e., do we expect tropical storms to suddenly get more extreme, do we expect rainfall in the UK to suddenly get more extreme?). It seems to me that the important question is how our climate will change over the coming century, not the next decade. Of course, I see nothing wrong with trying to improve decadal predictions as being able to do so will presumably improve climate models. I do think, however, that this is partly a response to claims that climate models have failed because they are currently unable to make accurate decadal predictions, rather than because there is a real need to do so.

  52. JCH says:

    Smith et al out of the met office. You have to define success. They correctly predicted natural variation would offset warming in the early years of their forecast. They predicted 2014 would be a very hot year. It’s not as hot as their prediction, but 2014 is looking hot.

  53. Here’s the Met Office on chaos:

    The pictures below show three different ensemble forecasts in the Lorenz attractor. In each case the starting point for the forecast is known only approximately, represented by the first black circle – we know the starting point is somewhere within this circle, but not exactly where. This is exactly like a weather forecast where we can analyse all the main pressure systems and the temperatures and humidities of the air averaged over large areas, but we cannot know every detail of the current state. From each of these circles of possible initial states in the Lorenz attractor we calculate a whole set of forecasts – an ensemble – of where in the attractor we expect to be after a number of time-steps:

    http://research.metoffice.gov.uk/research/nwp/ensemble/concept.html

    Here’s the illustration:

    Sometimes, you’re lucky and can be confident in weather forecasts, [as seen in the first image]. Sometimes, you’re not: see the other two images.

    Just like Bull Durham said. Sometimes you win. Sometimes you lose. Sometimes it rains.

  54. Steve Bloom says:

    Re the Met Office efforts for the UK, note that it’s an especially hard location for which to do weather forecasting or climate projections.

    Probably the current efforts re U.S. Southwest drying and drought make for a better case study.

  55. David Young says:

    yes Willard, this graphic is also in a recent Palmer and Slingo. However, the real truth here is that depending on initial states, the system is either predictable with reasonable certainty or unpredictable with a spread the full range of the attractor. And this is where our ignorance is profound. Some things are simply not predictable. The attractor can in fact have very high dimension just for Navier-Stokes. The only bound known is proportional to the Reynolds’ number which is usually large, in the case of the atmosphere, its huge. The other problem here is of course that numerically, particularly for the atmosphere, we must make large change to the system to solve it, such as sub grid models, numerical viscosity and “hyper-viscosity” etc. etc. Numerical stability can completely change the behavior of the system as any numerical analyst knows from bitter experience.

    My view as I’ve said many times is that the only hope here is to find simple models that can be constrained by data whose analysis is actually computationally feasible. The One Happy Bird site has a great lecture on the Lorentz system that explains this clearly and with extensive computations. You can do single cell convection with the Navier-Stokes equations and your computational times are huge and you gain little insight. The Lorentz system can be analyzed, the stability of its orbits determined, etc. It’s well worth watching.

  56. DY,

    My view as I’ve said many times is that the only hope here is to find simple models that can be constrained by data whose analysis is actually computationally feasible.

    I think one might call these energy budget models. They’re broadly consistent with paleoclimate but if you want to try and understand how climate change might influence our climate on smaller scales (scales that we might call regional) you – I think – need something more sophisticated, something we might call, what is it now, hmmmm,………, ohhh, yes, Global Climate Models, or General Circulation Models.

  57. DY,
    I’ll add that, here

    However, the real truth here is that depending on initial states, the system is either predictable with reasonable certainty or unpredictable with a spread the full range of the attractor. And this is where our ignorance is profound. Some things are simply not predictable. The attractor can in fact have very high dimension just for Navier-Stokes. The only bound known is proportional to the Reynolds’ number which is usually large, in the case of the atmosphere, its huge. The other problem here is of course that numerically, particularly for the atmosphere, we must make large change to the system to solve it, such as sub grid models, numerical viscosity and “hyper-viscosity” etc. etc. Numerical stability can completely change the behavior of the system as any numerical analyst knows from bitter experience.

    you appear to have said many things, none of which seem to mention the relevance of the boundary conditions which – I think – are quite important. If you continue to ignore the boundary conditions, I think I’m going to have to assume that you don’t really know what you’re talking about.

  58. > However, the real truth here is that depending on initial states, the system is either predictable with reasonable certainty or unpredictable with a spread the full range of the attractor

    At least you take into account an attractor, David, which I believe should constrain a bit the “exponential error growth” that seems to concern Spence so much. I mean, being able to determine an attractor as a ballpark for [the] chaotic function [we study] sounds reasonable enough for our forecasting needs. We find attractors … and then there’s physics.

    By the way, what do you mean by “initial states”? Specifying them should help obtain simpler, more tractable models.

  59. Eli Rabett says:

    The major boundary condition is conservation of energy, which pretty well stomps on the butterflies and sub unit climate sensitivity

  60. Eli,

    The major boundary condition is conservation of energy, which pretty well stomps on the butterflies and sub unit climate sensitivity

    Yes, I’m pretty sure I used that one. In fact I think I may have rather lost my civility tag when I described the reason why I thought it was important as being because it was a f**king fundamental law of physics!

  61. Here’s the website David was alluding to in his last comment:

    http://www.uvm.edu/storylab/2013/03/18/chaos-in-an-atmosphere-hanging-on-a-wall/

    Many thanks!

    As an aside, and because it seems that such gestures matter among the primates that we are, I’m all for simpler models. I’d rather go with no model at all. Except perhaps Gisele Brundchen. Grrr.

  62. To answer Joshua’s question, here’s an old quote fished out by Richard Betts at Andrew’s:

    The climate system is an angry beast and we are poking it with sticks.

    http://www.bishop-hill.net/blog/2014/8/27/more-on-gcms-and-public-policy.html#comment21028684

    Sticks and stones is a tried and true model of us, chaotic humans. But are we chaotic, good, evil, or neutral?

  63. BBD says:

    Willard

    Grrr.

    Everyday sexism penetrates climateballs?

    Whatever next?

  64. BBD and Willard,
    You made me look up Gisele Brundchen. Well, I don’t know what to say (and that’s really because I’m lost for words).

  65. > Everyday sexism penetrates climateballs?

    You’re right, BBD. So I’ll amend my claim to Gisele Brundchen and Amhed Angel:

    http://www.huffingtonpost.com/2013/05/16/ahmed-angel-iraqi-model-is-planet_n_3281604.html

    I’m open to other suggestions. Rachel?

    ***

    Another way to say about the same thing as Eli and AT:

    When you regard the climate as a boundary problem, as Gavin does, then you do indeed see that climate becomes predictable and in that sense nonchaotic. Take this example: I do not know the weather for an exact day in December because of fundamental limitations due to chaos. However, I know that the weather statistics for the December month will show lower temperatures than now.

    […]

    The simulated weather in the climate models is chaotic. Such behaviour has been studied by numerous scholars, from simplified models to full-scale weather models. But the question of whether the weather is chaotic does not imply that the response to a systematic forcing (boundary condition) is chaotic.

    http://www.climatedialogue.org/long-term-persistence-and-trend-significance/#comment-365

    Another one who does not understand chaos according to Spence.

    Make that two, since it starts with a discussion about a quote from Gavin.

  66. Willard,
    Again, you made me look it up and, again, I’m lost for words.

  67. Rachel M says:

    I’m open to other suggestions. Rachel?

    Don’t bring me into this shallow discussion, thanks. But if I must, that model is not my type at all.

    I’ll pick Ray LaMontagne who is not exactly a model but perhaps a good role-model. He also seems nice and sings well and his behaviour is probably better than AT’s was at BH. 😉

  68. Rachel,

    He also seems nice and sings well and his behaviour is probably better than AT’s was at BH’s.

    But I bet he’s never had to argue with people who think that conservation of energy isn’t such a big deal 😉

  69. Oh, and I suspect you’re biased because he has a beard!

  70. Rachel M says:

    But I bet he’s never had to argue with people who think that conservation of energy isn’t such a big deal

    Yes, ok. You’re forgiven.

    Oh, and I suspect you’re biased because he has a beard!

    Never! I would never be so shallow 😉

  71. Eli Rabett says:

    Yeah, well conservation of energy is a law not a theory. There is no reason for it (OK, if your idea of a hot model is Emmy Nother there are equivalent statements)

  72. Another one who doesn’t seem to get chaos:

    Two common questions that I (and many others) often get are “How can you predict anything about the state of the atmosphere 100 years from now when you can’t predict the weather 10 days in advance?” and “How do you know that the climate system isn’t far more complicated than you realize or can possibly model?” I often start my answer in both cases with the title of this post. It may sound like I am being facetious, but I’m not; the fact that summer is warmer than winter is an excellent starting point when addressing both of these questions.

    I don’t think that we have to spend much time on the first question here. We all successfully and continually predict the state of the atmosphere several months in advance whenever we plan our summer or winter vacations. Of course, the seasonal cycle is forced; no one can predict the chaotic day-to-day weather months in advance. More reasonably, we do try to predict whether the temperature averaged over the next summer will be warmer or colder than average in some region, part of the challenge we call seasonal forecasting.

    Analogously, when we talk about predicting the trend in the climate over the next 100 years due to a projected increase in carbon dioxide, we are talking about a forced response, fully analogous to predicting the extent to which summer is different from winter on average. The forcing in this case is through a reduction in the outgoing infrared flux rather than a redistribution of the solar flux, so the details are different. And the time scales are different. And – the biggest difference of all , of course– we have experienced a lot of seasonal cycles and don’t have to rely on theories/models to tell us what the forced response is going to be. But just because we have a lot more observational input into one problem than the other does not change the fact that the two physical problems are very closely analogous. The analogy to seasonal forecasting, whether next summer will be warmer or wetter than average, is the challenge of predicting the decadal-to-multi-decadal internal variability, generated by the oceans, that will modify the emerging forced signal.

    http://www.gfdl.noaa.gov/blog/isaac-held/2011/04/27/9-summer-is-warmer-than-winter/

    Summer is warmer than winter: I like that!

  73. Seems that NG doesn’t get chaos either:

    [T]he one thing everybody has agreed upon, albeit grudgingly, is that no single weather event can be attributed to AGW. But that’s not really true. Weather is chaotic, which means (among other things) that a small perturbation to the atmosphere grows over time, becoming progressively more noticeable and influencing other weather phenomena in a chain of causality so that eventually (in two to three weeks or so) the weather is totally unlike what it would have been without that small perturbation, even though the climate is unaffected.

    http://blog.chron.com/climateabyss/2010/08/did-it-happen-because-of-global-warming/

    How could climate be unaffected by the weathering chaos?

  74. How about the behaviors that don’t necessarily reach the chaotic stage? Nothing precludes this from happening and it is actually quit common in nature. The crash of a cymbal for instance.

    The quasi-periodic set of processes occupy a significant range between the purely periodic and the chaotic. These also follow boundary conditions. Variations of the double pendulum or a swing responding to periodic gusts are other examples that may not necessarily go chaotic.

    Invoking chaos in describing a behavior such as ENSO is like punting on first-down. You basically state that you don’t want to have a chance of winning …. No thanks — if there is a possibility that some quasi-periodic process governs ENSO, then some of us will try to decipher it.

  75. Web,

    The strategy may be to punt and punt and punt and punt and score a touchdown:

    The recently discovered Parrondo’s paradox claims that two losing games can result, under random or periodic alternation of their dynamics, in a winning game: “losing + losing = winning”. In this paper we follow Parrondo’s philosophy of combining different dynamics and we apply it to the case of one-dimensional quadratic maps. We prove that the periodic mixing of two chaotic dynamics originates an ordered dynamics in certain cases. This provides an explicit example (theoretically and numerically tested) of a different Parrondian paradoxical phenomenon: “chaos + chaos = order”.

    http://www.sciencedirect.com/science/article/pii/S0167278904003999

  76. The research that chaoticists such as Tsonis reference includes this work by Osipov [1]. In it they say:

    Very common to destroy chaos, which they conveniently overlook.

    [1]G. V. Osipov, J. Kurths, and C. Zhou, Synchronization in oscillatory networks. Springer, 2007.

  77. David Young says:

    I see the usual appeal to the boundary conditions which of course are taken into account in everything I said. The weather and the climate are initial value problems with time varying forcings which are volume source terms, not boundary conditions. I must assume that anyone who seems to say otherwise doesn’t know what they are talking about. They at the least have a gap in their training in mathematics. Source terms can be the strongest influence on long time behavior, or not, it depends. The boundary value statement is little better than a gloss whose origin is lost in the mists of past “communication” of inaccurate science.

    The truth here is that some things are impossible to predict. An example is asteroid impacts. The N body problem is chaotic and it is impossible to say with certainty if and when we will get hit. On short time scales, it is possible with a reasonable small error bound. On longer time scales, its impossible. One can say “eventually it will happen” which is a statement that is of nil value in decision making. That’s the “boundary value” problem answer or the statistics of the attractor.

  78. DY,

    The weather and the climate are initial value problems with time varying forcings which are volume source terms, not boundary conditions.

    I don’t believe anyone has said they’re not an initial value problem, simply that the statistics of weather, averaged over suitable time and perhaps space scales depends more on the boundary conditions than on the initial conditions.

    That’s the “boundary value” problem answer or the statistics of the attractor.

    Yes, exactly, isn’t that the point?

  79. DY,

    I see the usual appeal to the boundary conditions which of course are taken into account in everything I said.

    I always find it interesting that in some cases when someone doesn’t explicitly mention something, it’s obvious that it was being taken into account and in other cases it’s a dismal failure. Just saying.

  80. I thought I’d add this comment from a post written by Steve Easterbrook.

    For understanding climate, we no longer need to worry about the initial values, we have to worry about the boundary values. These are the conditions that constraint the climate over the long term: the amount of energy received from the sun, the amount of energy radiated back into space from the earth, the amount of energy absorbed or emitted from oceans and land surfaces, and so on. If we get these boundary conditions right, we can simulate the earth’s climate for centuries, no matter what the initial conditions are. The weather itself is a chaotic system, but it operates within boundaries that keep the long term averages stable. Of course, a particularly weird choice of initial conditions will make the model behave strangely for a while, at the start of a simulation. But if the boundary conditions are right, eventually the simulation will settle down into a stable climate. (This effect is well known in chaos theory: the butterfly effect expresses the idea that the system is very sensitive to initial conditions, and attractors are what cause a chaotic system to exhibit a stable pattern over the long term)

  81. As an example of another phenomena that appears chaotic, yet is better characterized as a non-linear quasi-periodic oscillation, consider the sloshing of water within a volume. The sloshing height is routinely modeled as a solution to the Mathieu differential equation [1].

    Here is an Alpha snippet that one can try:
    http://www.wolframalpha.com/input/?i=x%27%27%28t%29%2B%283-2*cos%28t%29%29*x%28t%29%3D0

    Depending on the parameters chosen, the behavior can be tailored from strict periodicity to a progressively more erratic behavior. Yet it can be solved and used for predictions just as a sinusoidal solution of a linear DiffEq can be solved and predicted.

    Now what is intriguing is that some aspects of the ENSO phenomena relates to the sloshing of water in the Pacific ocean. Thus there is a possibility that ENSO can be modeled in the same way and that its erratic nature can be unraveled and decoded.

    Unfortunately, this outcome would make David Young’s brain a splode.

    [1]J. B. Frandsen, “Sloshing motions in excited tanks,” Journal of Computational Physics, vol. 196, no. 1, pp. 53–87, 2004.

  82. David Young says:

    And its all about the structure of the attractor about which almost nothing is known except that it can be very complex and have a wide range of behaviors.

    The fact that climate scientists seem to use “boundary value problem” incorrectly should give one pause. it’s clearly a communication device to make sure people know “the initial values are not important.” Unfortunately, this is clearly false in general as shown by the example Willard showed above. Different sets of initial conditions give rise to different long term behaviors as the Lorentz system shows. Watch the lecture about it. Willard found the site.

  83. DY,

    And its all about the structure of the attractor about which almost nothing is known except that it can be very complex and have a wide range of behaviors.

    No, it’s not all about this. That’s the point.

    Unfortunately, this is clearly false in general as shown by the example Willard showed above. Different sets of initial conditions give rise to different long term behaviors as the Lorentz system shows.

    No, this is not clearly false. What Willard showed was an illustration that a small change in the initial conditions can result in the system evolving into a number of different states. However, that does not invalidate the suggestion that averaged over a suitable time interval and area, our climate is determined more by the boundary conditions than by the initial conditions. It simply shows that small changes in the initial conditions, can produce a wide range of outcomes that are constrained by the possible attractors. For you to be right, you’d need to evolve those systems for a great deal longer and show that the average state can be wildly different for small changes in initial conditions.

    The fact that climate scientists seem to use “boundary value problem” incorrectly should give one pause.

    I’ll make a slightly stronger comment that I’m been thinking about for a while. What got me incredibly frustrated on Bishop-Hill (more frustrated than I should have done) was that I was discussing this with people who seemed absolutely certain that they were right and everyone else was wrong. There appears to be no doubt in their mind that they could be mistaken. You appear to hold the same view.

    For starters, I don’t really understand why anyone would engage in this way. I find it incredibly arrogant. To be fair, you and the others do appear to understand what they’re talking about very well. What they fail to realise – IMO – is that their good understanding of that particular topic does not mean that they suddenly understand the whole issue better than others. Also, this is an incredibly complex issue. The idea that we can simply state that one particular issue completely invalidates, or not, climate modelling seems absurd.

    Here’s my position which comes from my understanding of physics and from reading what others (who are experts in this area) say. It makes sense that the state of our climate (weather averaged over a suitable timescale and area) depends more on the boundary conditions (albedo, TSI, atmosphere) than it does on the initial conditions. This sets the latitudinal temperature gradients which, together with the coriolis effect sets the different climate zones. This determines which areas will be dry, wet, cold, warm. These conditions set the mean temperatures both globally and regionally. Unless the initial conditions can change one of the boundary conditions, it’s hard to see how the overall climate can differ significantly.

    Now, it is possible that something completely unexpected could happen. That in fact there is an initial condition that could produce some kind of outcome that significantly changes our climate, but that seems unlikely, especially as the biggest changes we’re making are continually adding CO2 to our atmosphere. Additionally, it appears that climate models do a reasonable job of representing how our climate responds to changes in forcings. So, even if something unexpected did happen, that doesn’t mean that we should ignore what climate modelling is telling us about how we’ll respond to increasing anthropogenic forcings. The unexpected thing could make things “better”, but they could make things even worse (assuming it were to happen). So, I’m not claiming that what you and others say can’t be true, simply that it seems unlikely that it will be true (or, that even if it is, it’s not obvious why this possibility invalidates what climate models are presenting).

    So, what seems absurd to me is that a small group of internet commentators, who have experience in an area related to climate modelling, have decided that their concerns are absolutely right and that those who actually do climate modelling are wrong. It’s possible that you will be right and, if you are, you can crow about it in 10 or 20 years time. I, however, don’t really see the point in discussing this with people who are so certain of their infallibility that they are willing to completely dismiss the views of actual experts.

  84. David Young says:


    Different sets of initial conditions give rise to different long term behaviors as the Lorentz (sic) system shows.

    The Lorenz system is a very sensitive set of differential equations to initial conditions; and it may not even apply to the climate system.

    Consider the Quasi-Biennial Oscillations (QBO) of the stratospheric winds. This has a very strong period centered at 28 months that appears to wiggle about that point. If there is a continuum between periodic, quasi-periodic, and chaotic, the QBO occupies the region between periodic and quasi-periodic.

    Now if we compare the QBO to ENSO, we find that ENSO has a significant forcing with the same 28 month quasi-period as QBO (it also has a forcing of another period). Yet, in contrast to QBO, ENSO is definitely more quasi-periodic as it obviously has more erratic behavior.

    How are we able to deduce this periodicity in ENSO?
    It’s because the phenomenon behind ENSO is sensitive to boundary conditions of the forcing function. In this case the forcing is a guide or boundary, in the analogous sense that the sides of a bobsled track are boundary guides for the sled’s travel. Whatever forcing is causing the QBO to reveal a 28-month period is also contributing to the ENSO quasi-periodicty.

    However, this is not chaotic behavior and is not as sensitive to initial conditions as it is to boundary conditions. This flavor of boundary conditions guides the behavior and also results in a reversion to the mean and places limits to the excursion of the peaks.

    Do you understand the concept of boundary conditions a little better now?

  85. Weather is essentially a description of the state of the atmosphere at a single moment. It shows directly the chaotic nature of the physics of the atmosphere.

    Climate refers to such averages of the weather variables that all the chaotic features of the atmosphere alone average effectively out, but chaotic features of the dynamics of other components of the Earth system, such as the oceans, may influence significantly climate. While oceans are the most certain additional system to behave chaotically at some level, biosphere and cryosphere might also contribute to that.

    How strongly the chaotic features of the atmosphere affect the climate can be seen by observing weather over periods of time easily available for observation, but we do not possess comparable knowledge on the chaotic dynamics of oceans or other subprocesses of the Earth system that have persistence on time scales longer than a few decades.

    The time scales of atmospheric dynamics are so different from the time scales of the other processes of the Earth system that their chaotic features are probably only weakly coupled. Scientific papers have been written on many of them, but I think that everything that concerns other systems than the atmosphere alone are largely speculative, both when they tell of observing significant effects as Tsonis has done, and when they claim evidence against chaotic effects of such magnitude.

  86. Raff says:

    Anders, I have been flattered on BH to be confused for you Sadly, the reverse (you being confused for me) would not be flattering, sorry 🙂

  87. Eli Rabett says:

    David Young is spouting crap. What is meant by boundary conditions is that there are physical limits constraining variations of the weather. While external forcings (volcanoes, greenhouse gases) can change these limits, without them hell (aka Washington DC) will never freeze over in the summer.

    Pekka also has to admit that huge excursions in ocean dynamics such as he is trying to invoke have not happened for a very, very long time. The Baskerville’s hound is a very hungry beast..

  88. David Young says:

    ATTP, You are basically saying that I may be right, but its arrogant to say so in the face of confused climate science pronouncements. You resort to the false alternative by saying that climate models can’t be completely wrong. OK, that’s not a scientific statement. I of course said no such thing. I do believe it highly unlikely that climate models are very accurate, but that is not a controversial view. I also see similarities to the situation in fluid dynamics where the simulations were for a long time believed to be much more accurate that in fact they are. The favorite fig leaf was that the absolute values might be wrong but the increments between 2 simulations were much more accurate. Sound familiar?

    Like SoD, I find its hard to engage when the argument rapidly descends to the false alternative, the argument from authority, and the diagnosis of psychological characteristics by people who have no idea what they are talking about.

    Rabbit, Aside from the rabbit scatology you invoke, you are just wrong on this. There is a technical definition of a boundary value problem. Some things are boundary value problem and some things are initial value problems. Its a clear distinction. What novice mathematicians and perhaps some climate scientists naively understand by boundary value problem is elliptic boundary value problem which is indeed well posed and computational methods work very well, as in structural analysis. I have always wondered if the terminology was chosen in this field to elicit this false analogy.

    There may be physical limits on climate but you have specified nothing but that they must exist, ex cathedra so to speak. Certainly, the “boundary values” for the climate problem are the top of the atmosphere flux which according to climate scientists is essentially constant and the wall condition at the planetary surface which on scales of interest doesn’t change either. The boundary values are according to climate science orthodoxy for practical purposes fixed. What changes are the constituents of the atmosphere and thus there are volume sources that are defined by ill posed processes such as convection. But the climate problem is an initial value problem with varying volume sources. Boundary values have essentially no effect according to orthodoxy.

  89. David Young says:

    Sorry, I misspoke. Boundary values are constant and thus they don’t really affect any of the incremental changes we are looking for.

  90. DY,

    You are basically saying that I may be right, but its arrogant to say so in the face of confused climate science pronouncements.

    No, David (and this isn’t a complicated concept) I’m saying that it’s arrogant to state that you will definitely be right and that others are definitely wrong.

    You resort to the false alternative by saying that climate models can’t be completely wrong.

    No, I didn’t. Read it again.

    Like SoD, I find its hard to engage when the argument rapidly descends to the false alternative, the argument from authority, and the diagnosis of psychological characteristics by people who have no idea what they are talking about.

    Are you trying to prove my point? Quite how you’ve interpreted my comment as an argument from authority and a psychological diagnosis is beyond me. Are you sure you read it carefully enough? Also, if you’re not happy with what I said in my comment, then maybe think about how you engage in such discussions. How you can criticise how others engage is quite something.

    There may be physical limits on climate but you have specified nothing but that they must exist, ex cathedra so to speak. Certainly, the “boundary values” for the climate problem are the top of the atmosphere flux which according to climate scientists is essentially constant and the wall condition at the planetary surface which on scales of interest doesn’t change either. The boundary values are according to climate science orthodoxy for practical purposes fixed. What changes are the constituents of the atmosphere and thus there are volume sources that are defined by ill posed processes such as convection. But the climate problem is an initial value problem with varying volume sources. Boundary values have essentially no effect according to orthodoxy.

    I have to say, I think Eli’s comment nails it.

  91. Raff,
    I think your ability to remain calm on B-H far outweighs mine, so I’m not sure you should feel flattered 😉

  92. verytallguy says:

    David Young,

    Things are becoming a little heated.

    I’d like to understand if you’re debating science, semantics or politics

    Perhaps you could clarify your position?

    As I understand it you are arguing that the initial conditions of a climate model affect not just the specific realisation but also the statistics of climate predicted by the model over a long term run.

    is that your claim?

    [the other reading of what you’ve written is that some terms eg boundary value / volume source are poorly defined (semantics) or that statistics don’t help policy (politics)]

  93. Andrew Dodds says:

    The biggest problem I have with the Internal Variability hypotheses – by chaos or any other mechanism – is that you’d notice.

    For example, if a random excursion in air temperatures for a couple of years led to a greening of a chunk of a continent, which then led to local climate changes via albedo changes, which then maintained the original excursion, leading to globally detectable changes – that would be an example of internally generated climate change. The point being that internally driven change leaves real, observable footprints. Even if it was based purely on ocean circulation changes and therefore changes in sea surface temperatures, we could find paleo evidence for sea temperature changes.

    As far as I am aware, this evidence has not been found – indeed, those most keen on the internally generated hypothesis such as David Young above seem disinterested in the idea of empirical confirmation..

    My personal guess on this stuff is that if there are distinct stable states for the climate (‘attractors’ if you really want..) they are a fair way apart, as in several degrees, for example –

    – Full Glacial conditions
    – Current conditions (GIA+WAIS+EAIS)
    – Pliocene conditions (EAIS only)
    – Hothouse conditions (no ice)

    And these ‘attractors’ (if they even exist) have very distinct physical profiles. There does not appear to be an equivalent at smaller global temperature scales.

  94. Dan Hughes says:

    http://onlinelibrary.wiley.com/doi/10.1002/2014GL060478/abstract?deniedAccessCustomisedMessage=&userIsAuthenticated=false

    S. Lovejoy, Return periods of global climate fluctuations and the pause, Geophysical Research Letters, Volume 41, Issue 13, pages 4704–4710, 16 July 2014

    From the Abstract:
    Similarly, the “pause” since 1998 (0.28–0.37 K) has a return period of 20–50 years (not so unusual). It is nearly cancelled by the pre-pause warming event (1992–1998, return period 30–40 years); the pause is no more than natural variability. [ bolded not in original ]

    Author’s Draft:
    http://www.physics.mcgill.ca/~gang/eprints/eprintLovejoy/neweprint/Anthropause.GRL.final.13.6.14bbis.pdf

    McGill press release:
    http://www.mcgill.ca/newsroom/channels/news/global-warming-pause-reflects-natural-fluctuation-237538

  95. Dan,
    What’s your point? There’s not really much dispute that natural variability can produce periods where warming is accelerated and periods where it’s slower. I haven’t had a chance to look at your links, but is that all you’re trying to point out, or was there something more?

    Of course, one issue I have with most of these x year cycle ideas is that they seem to often not remove the forced component, which means that the cyclical signal could well be forced, rather than simply natural variability.

  96. Actually, the Lovejoy paper seems to have removed the anthropogenic component when doing the analysis, so – as I understand it – is simply suggesting that there is natural variability superimposed on top of an anthropogenic trend. Seems perfectly reasonable.

  97. Joshua says:

    ATTP –

    Judith linked the article as a continuation of the natural vs. forced warming argument. the pause is no more than natural variability is what Judith highlighted, along with To be fully convincing, GCM-free approaches are needed: we must quantify the natural variability and reject the hypothesis that the warming is no more than a giant century scale fluctuation. ”

    And she added:

    I like Lovejoy’s general approach, but convincingly rejecting a centennial scale giant fluctuation requires more robust paleo proxy reconstructions. Lovejoy identifies a magnitude of the natural fluctuations of ~0.4C, which is the largest such estimate I’ve seen.

    I’m guessing that was Dan’s point – that Judith think’s that the paper aligns with her views about variability. But perhaps he will elaborate?

  98. Joshua,
    Yes, that was the impression I had but the fundamental equation seems to

    T_{globe}(t) = \lambda_{2xCO2,eff}log_2(\rho_{CO2}(t)/\rho_{CO2,pre}) + T_{nat}(t)

    so – as I understand it – the first term on the right-hand side is the expected anthropogenic warming based on increasing CO2 (which I would like to know more about as it should probably really have the overall anthropogenic forcing, not just CO2) and the second term is some natural variability contribution that varies with time. Seems a little simple, but pretty much exactly what one might expect.

  99. BBD says:

    Is this the same Lovejoy that wrote:

    Although current global warming may have a large anthropogenic component, its quantification relies primarily on complex General Circulation Models (GCM’s) assumptions and codes; it is desirable to complement this with empirically based methodologies. Previous attempts to use the recent climate record have concentrated on “fingerprinting” or otherwise comparing the record with GCM outputs. By using CO2 radiative forcings as a linear surrogate for all anthropogenic effects we estimate the total anthropogenic warming and (effective) climate sensitivity finding: ΔT anth = 0.87 ± 0.11 K, λ2xCO2,eff=3.08±0.58K . These are close the IPPC AR5 values ΔT anth = 0.85 ± 0.20 K and λ2xCO2=1.5−4.5K (equilibrium) climate sensitivity and are independent of GCM models, radiative transfer calculations and emission histories. We statistically formulate the hypothesis of warming through natural variability by using centennial scale probabilities of natural fluctuations estimated using scaling, fluctuation analysis on multiproxy data. We take into account two nonclassical statistical features—long range statistical dependencies and “fat tailed” probability distributions (both of which greatly amplify the probability of extremes). Even in the most unfavourable cases, we may reject the natural variability hypothesis at confidence levels >99 %.

  100. Dan Hughes says:

    I sent the link to the paper to Professor Curry and I decide how the views in the paper reflect, or not, my own. Equally important I decide the merits, or not, of the methods and data basis of the report.

    I also sent a link to a much more provocative paper by Lovejoy. She has not cited that one. The GANG at McGill has done lots of mighty fine work, IMO. As has V. Lucarini across the pond.

  101. Dan Hughes says:

    BBD, the same. And that’s the paper to which I referred.

  102. Dan,

    I sent the link to the paper to Professor Curry and I decide how the views in the paper reflect, or not, my own. Equally important I decide the merits, or not, of the methods and data basis of the report.

    Sure, I don’t think anyone was intending to decide your views for you. Maybe, however, you could elaborate if you were willing to do so. In not, that’s also fine.

  103. BBD says:

    And Dr Curry did not mention the second Lovejoy reference you provided? How very strange.

  104. BBD,
    It’s an extension of the same work. The abstract comments on this, and the paper says

    However, the probability of a centennial scale giant fluctuation was estimated as ≤0.1%, a new result that allows a confident rejection of the natural variability hypothesis.

    If I get time, I may write a short post about this. My main issue with the paper is that the forcing appears to be entirely CO2 which suggests to me that it’s likely some of what the paper concludes is the natural variability contribution is partly forced.

  105. TrueSceptic says:

    Just to say, I really don’t see the point of trying to reason with the denizens of Bishop Hill (and the others). They are way past rational discussion.

    Oh, and how about Geronimo’s comment as an example of ultimate irony?

    The grace and tolerance they show in the face of the contempt amd lies being hurled at them by a bunch of scientific wannabes is remarkable.

  106. TrueSceptic,
    Yes, I think I responded to that comment of Geronimo’s by pointing out that some people regard being told that they’re wrong as a form of bullying. I don’t think Geronimo agreed 🙂

  107. Eli,

    I would be very happy to see a clear exposition of, what can be said about the limits of variability related to ocean processes using any well defined theoretical or empirical arguments.

  108. David Young says:

    I need to revise and extend my remarks because there may be common ground here. Climate is influenced by boundary values of flux and by initial values. However, the signal we are looking for is a function of the volume source terms which are very difficult and ill-posed and small compared to the overall energy in the system. This is a classical problem that is going very difficult to compute accurately. So we might call it an initial boundary value problem.

    I do think the question of why one would expect these simulations to be very accurate is unanswered when the errors are acknowledged to be rather large on all scales. The only answer is that the attractor is so strong these errors don’t matter. That’s it seems speculative to me. Paul Williams has shown this is false and its false for the Navier-Stokes equations. Subgrid models do make a big difference that is an order of magnitude bigger than the truncation error and the signal we are looking for. It may be that climate models are like turbulence models postdictive and predictive.

  109. DY,
    I think you need to define what you mean by error. Of course the difference between the result of a single simulation with a single set of initial conditions can/will be very different to reality. That’s why what’s being considered is the average over some time and region. So, what you haven’t addressed (see Andrew Dodds’ question) is whether this average will have a large error (i.e., how will this differ from reality). Noone is claiming that the precise results of a single run will match reality. What’s being suggested is that the average will be a reasonable representation of how anthropogenic forcings will influence our future climate.

    However, the signal we are looking for is a function of the volume source terms which are very difficult and ill-posed and small compared to the overall energy in the system.

    Are you sure? It seems to me that what you’re criticising is the signal that you think is being looked for, rather than the actual signal that is being looked for.

    I do think the question of why one would expect these simulations to be very accurate

    I don’t know why you think anyone thinks they’re very accurate. I suspect that that is a poor term in this context. Again, there is evidence that they can model the influence of external forcings on our climate and hence can be used to determine how anthropogenic forcings will influence the average of our weather over some time and region.

  110. > Paul Williams has shown this is false

    Citation needed. All I found was a presentation where a RAW filter would improve accuracy over some other filter without being more complex. The same presentation is alluded to here:

    http://judithcurry.com/2013/06/24/how-should-we-interpret-an-ensemble-of-models-part-i-weather-models/#comment-336712

    Notice JimD’s response:

    The reason that climate is not an initial value problem, but a boundary value problem, is that climate depends on the forcing, not the initial state. This is the fundamental difference. In a climate context, the boundaries are the forcing, which includes continental configuration, atmospheric composition, solar radiation, orbital characteristics, etc. Keep these the same and climate has a limited range of variation, apart from some sensitivity with the ice-albedo feedback when it gets cold enough (i.e. Ice Ages) or warm enough (loss of sea ice and major continental glaciers like Antarctica and Greenland) where tipping points are seen in paleoclimate. However, you could argue the initial state comes in via a hysteresis effect. That is a characteristic of catastrophe theory, for example, where hysteresis and tipping points are seen. In certain cases, the climate may do one thing in a cooling trend and another in a warming trend, such that for a given forcing there may be two quasi-stable states, depending which way it got there from, but this collapses to one state at a tipping point when the trend continues. This is usually associated with the area of ice albedo regions. The ongoing loss of the Arctic sea ice is one possible such tipping point, where it won’t easily come back even if somehow we reduce CO2 to current levels in the future because the albedo is that much lower leading to a warmer state.

    Or what Eli said.

    Chief mentions Williams quite a lot at Judy’s.

  111. Pingback: The length of the “pause”? | …and Then There's Physics

  112. David Young says:

    Willard, The reference is to a Newton Institute talk from several years ago where Williams showed for the Lorentz system that too large a time step results not just in wrong transient behavior but a different “climate.” The example is quite clear and it fits my experience too. You can easily get on the wrong branch if errors are too large in the initial phases of a simulation. Or worse still, you an get on a spurious branch that never converges to anything at all.

    Jim D’s quote you give I think is just clearly untrue. For the Lorentz system initial conditions do make a difference even to the ultimate climate especially near bifurcation points. But perhaps a more relevant model problem is the Navier-Stokes equations themselves.

    This is very frustrating since I have on a previous thread given references to the refereed literature with proof that there are multiple solutions to the RANS equations and that SMALL DETAILS of the transient numerical method can make LARGE DIFFERENCES to the state arrived at. I also pointed out that people were surprised by these results and by the large errors documented in our other publications. There is another one just accepted that I can send you privately where the common ideas about errors being pretty small are shown to be wrong by an order of magnitude using the best codes and methods.

    So, what I see is just people repeating stuff that sounds reasonable but that is known to be false for subsystems of the climate system. That’s the frustrating part.

    However, Willard, you seem to be an exception and do the home work which I do appreciate. The quote from climate etc. was from a while ago I think before some of our papers came out.

  113. > There is another one just accepted that I can send you privately where the common ideas about errors being pretty small are shown to be wrong by an order of magnitude using the best codes and methods.

    That we can get better tools does not change the nature of our problem, David.
    Whatever the error, the response still lies around an attractor. To understand how a baby can succeed in learning to grasp an object, as I said earlier, that’s enough. My intuition is that there’s a problem in stating that initial conditions are so strong to overthrow boundary conditions. Better code is always welcome, and as far as I’m concerned matters more than theorical questions.

    ***

    You can find my email on my tumblog, or you can send the paper to AT. I’ll take a look. But I need to get serious out of sudden, and I will need to divest from ClimateBall ™ a bit. I’ll be around, but perhaps to throw in some irrelevant but interesting anecdote, just like this one:

    In 1918, after a few years as a student at the University of Berlin, Carnap enrolled as a graduate student at the University of Jena to obtain a Ph.D. in physics. As Carnap explained it to me, his plan was to formalize Einstein’s theory of relativity using notations from Principia Mathematica (although the notation that figures in this anecdote is older, from the “algebra of relations” of Peirce and Schröder). Using the notion of the square of a relation­ – that is the product of a relation[2] with itself – Carnap found that he could write the statement that the relation T, “earlier in time than”, is transitive and dense simply as T=T2. When Carnap went to his professor’s office to discuss his plan (here Carnap imitated the professor’s pompous voice) the professor said,
    “It seems to me that if T=T2, then either T=1 or T=0”. Carnap explained that T was not a symbol for a number but rather for the temporal precedence relation, etc., etc., etc., and at the end the professor said, “It still seems to me that if T=T2, then either T=1 or T=0. Young man, you had better try the philosophy department.”

    http://putnamphil.blogspot.ca/2014/09/an-anecdote-of-carnaps-in-1953-54-my.html

    And then, for Carnap, there was philosophy.

  114. David Young says:

    For completeness a reference showing not only multiple solutions but sensitivity to initial conditions is AIAA Journal, Vol. 52, Issue 8, August 2014, pp. 1686-1698. ” Numerical Evidence of Multiple Solutions for the Reynolds Averaged Navier Stokes Equations.”

  115. DY,

    So, what I see is just people repeating stuff that sounds reasonable but that is known to be false for subsystems of the climate system. That’s the frustrating part.

    And what I see is someone who is arguing against their own strawmen. That’s the frustrating part.

    This is very frustrating since I have on a previous thread given references to the refereed literature with proof that there are multiple solutions to the RANS equations and that SMALL DETAILS of the transient numerical method can make LARGE DIFFERENCES to the state arrived at

    How does this prove that the AVERAGE OF THE WEATHER OVER TIME AND SPACE is chaotic? Please answer this question in straightforward way.

  116. DY,

    For completeness a reference showing not only multiple solutions but sensitivity to initial conditions is AIAA Journal, Vol. 52, Issue 8, August 2014, pp. 1686-1698. ” Numerical Evidence of Multiple Solutions for the Reynolds Averaged Navier Stokes Equations.”

    Again, I don’t think anyone here is stating that the system is not sensitive to initial conditions. Do you at least recognise this? What is being suggested is that the average over time and space is not chaotic. Given that the total energy and the distribution of that energy is set by what I’ll call boundary conditions, this appears reasonable (i.e., we’re unlikely to start getting TCs in the Arctic, the UK will not suddenly become a desert,…). So, again, can you at least try to address the issue being discussed, rather than continually pointing out things that noone disputes, as if it proves we don’t know what we’re talking about.

  117. Andrew Dodds says:

    DY –

    As before, you’d be a lot more convincing if you could tie your synthetic models back to the real world. Your attractors represent distinct, theoretically identifiable states; if you make no effort to identify them then why should I think they even exist?

  118. You don’t even seem to know what a boundary condition is. Albedo and the composition of the atmosphere are not boundary conditions.
    As I said elsewhere, I admire the patience of people like David Young who are prepared to discuss things with those who have no idea of what they are talking about.

    [Paul, FWIW, you’re right that those aren’t really boundary conditions (I may argue the albedo might be, but I don’t really care). That was rather poor of me. For those who are interested (and I’m pretty sure you’re not) the point I was getting at is that there are certain conditions that essentially determine the total energy and the distribution of energy in the system. Even though the system is inherently chaotic, it seems likely that the energy in the system will constrain the state of the climate (the average of the weather over a suitable time and area).

    Given that you seem incapable of making a constructive comment and given that I suspect that I would be incapable of engaging constructively if you tried, I suspect it would be best if you didn’t bother wasting your time commenting here again. To be clear, it would be a waste as I will shortly be adding you email address to the list of those whose comments go directly to spam. You’re of course welcome to continue writing your own posts about me being a hypocrite (illustrating that – rather ironically – you don’t appear to read things before criticising them) and are welcome to complain about censorship on Twitter with all the others who appear to have a similar understanding of physics and the English language.]

  119. Dan Hughes says:

    Google Scholar search for The Exact Phrase, ‘chaotic climate’ yields the text snippets listed below, among many others ( I might have restricted the hits to Since 2010, but I’m not sure. I think ‘chaotic climate variability’ or ‘chaotic climate predictability’ will return like hits. I haven’t filled in the details of the hits; the Google search is easy and quick.

    The range of possibilities for future climate evolution (1, 2, 3) needs to be taken into account when planning climate change mitigation and adaptation strategies. This requires ensembles of multi-decadal simulations to assess both chaotic climate variability and model response uncertainty (4, 5,6, 7, 8, 9). [Literature citations that were superscripts are in ().]

    The predictability of weather and climate forecasts is determined by the projection of uncertainties in both initial conditions and model formulation onto flow-dependent instabilities of the chaotic climate attractor.

    The title of a September 2013 article in Journal of Climate: Separating Forced from Chaotic Climate Variability over the Past Millennium

    A major reason for this is the presence within this chaotic system of discernible periodic cycles varying from very low frequency of a hundred thousand years or so to inter annual variations such as El Niño and the Quasi biennial Oscillation.

    Climate models are not perfect either. Errors evolve in climate simulations as a result of incomplete physical understanding and limited knowledge of past (or future) climate forcing. These errors must be considered along with the uncertainty related to climate chaos, which occurs because of nonlinear interactions in the global climate system. Climate chaos errors can be addressed through repeated runs of a climate model with the same forcing, but different starting conditions. These ensemble simulations can then be used to estimate the magnitude of the uncertainty introduced by a chaotic climate system (2).

    [3] Because the climate system is chaotic, climate predictions must be predictions of distributions. Predictability concerns the degree to which a forecast distribution can differ from the climatological distribution and thus potentially provide information about the future. For systems at equilibrium predictability comes from initializing with a distribution of small perturbations about a specific initial state. As a prediction progresses, the distribution takes on the characteristics of the climatological distribution and predictability is eventually lost when the two distributions cannot be distinguished.

    CHAOTIC BEHAVIOUR OF CLIMATE
    Huard writes: “The natural variability of the climate system is largely chaotic” and thus “unpredictable”. Not only do we endorse this statement, and not only have we presented research results on this issue (Koutsoyiannis 2003, 2006, 2010, Koutsoyiannis et al. 2009, Christofides and Koutsoyiannis 2011), but we have also pointed to this problem in the second paragraph of the conclusions of our paper, the one that begins: “However, we think that the most important question is not whether GCMs can produce credible estimates of future climate, but whether climate is at all predictable in deterministic terms.” It is climate modelers who say or imply otherwise; for example Schmidt (2007, our emphasis):

    Weather is chaotic; imperceptible differences in the initial state of the atmosphere lead to radically different conditions in a week or so. Climate is instead a boundary value problem—a statistical description of the mean state and variability of a system, not an individual path through phase space. Current climate models yield stable and non chaotic climates, which implies that questions regarding the sensitivity of climate to, say, an increase in greenhouse gases are well posed and can be justifiably asked of the models.

    Therefore, again we are not the right recipients of Huard’s warning that climate is chaotic.

    Nevertheless, because the climate is a chaotic system and contains natural variability on all time scales, there is a level of uncertainty that will always exist however much the model uncertainty is reduced.

    Apparently, the climate system in the physical domain is chaotic, but climate in some, but clearly not all, computer domains is not. How does that work?

    A brand new physical principle has been introduced in these discussions as follows:
    The major boundary condition is conservation of energy, which pretty well stomps on the butterflies and sub unit climate sensitivity.

    Conservation of energy is not a boundary condition. The concept of conservation of energy as a mere boundary condition very significantly reduces the universally-accepted fundamental principle to an auxiliary augmentation of ODEs and PDEs. A mathematical illustration of application of this so-called boundary condition in a mathematical model of a physical system would be very useful.

  120. Dan,
    I’m not really following you. None of what you’ve quoted appears to contradict what’s being said.

    Apparently, the climate system in the physical domain is chaotic, but climate in some, but clearly not all, computer domains is not. How does that work?

    You appear to be arguing against your own strawman. Noone is suggesting that the underlying system is not chaotic. The basic point being made is that the average of the weather over a suitable time and area can be regarded as representative of the climate and that this is not chaotic. More completely, the idea is that climate models can tell us something of how our climate (the average of the weather) will evolve under changes in anthropogenic forcings.

    There may well be unexpected consequences and noone’s suggesting that the climate models are perfect (we’re more confident about certain aspects than others) but they can still tell us something of how we our climate will respond to changes in forcings.

    Conservation of energy is not a boundary condition

    But it is a fundamental law of physics. The point being made is that there are certain conditions (which I have in some cases incorrectly called boundary conditions) that set the total energy and the distribution of energy in the system. Unless you can show that the chaotic nature of the system alone can change these conditions, then the energy is essentially determined by these conditions. Since the total energy and the distribution of the energy is likely to determine the overall state of our climate, that the system is chaotic does not mean that we cannot determine how our climate will evolve under changes in forcings (even if we can’t precisely determine the weather).

    Maybe you could try to lay out your issues in more detail and more clearly. As I understand it you’re saying

    • The system is chaotic – I agree.
    • We can’t predict the weather significantly into the future – I agree.
    • Therefore climate models are useless – I disagree.
  121. Dan,
    Also, just in case it wasn’t obvious, noone is suggesting that there isn’t uncertainty associated with the climate model projections, simply that the range of the projections gives us an indication of the possible influence of increasing anthropogenic forcings.

  122. anoilman says:

    Dan, Anders,

    In terms of chaotic systems, I believe the Global warming signal will drown out the previously understood notions of temperature variability. Specifically, the distribution of hot and cold days per year is not just shifting (getting hotter), its widening (getting more variable).
    http://www.giss.nasa.gov/research/briefs/hansen_17/

  123. Dan,
    Actually, maybe you can explain why you included this

    “Weather is chaotic; imperceptible differences in the initial state of the atmosphere lead to radically different conditions in a week or so. Climate is instead a boundary value problem—a statistical description of the mean state and variability of a system, not an individual path through phase space. Current climate models yield stable and non chaotic climates, which implies that questions regarding the sensitivity of climate to, say, an increase in greenhouse gases are well posed and can be justifiably asked of the models.

    as this appears to be pretty much what I’ve been saying. Do you agree with this, or not? If you do, then I fail to understand what we’re arguing about. If you don’t, then it seems there is at least some of the literature that disagrees with you.

  124. DH said:


    Apparently, the climate system in the physical domain is chaotic, but climate in some, but clearly not all, computer domains is not. How does that work?

    Never mistake a lack of sufficient skills or of sufficient effort for your claim that new mathematical patterns which describe a particular climate phenomenon will never emerge. We may yet find the pattern and it is an over-reach to say it doesn’t exist. Chaos seems to be a weaselly rationale for the nay-sayers.

    So prove to me that ENSO or QBO are in fact chaotic, since you referred to those by name.

  125. David Young says:

    I’ll try this one more time since ATTP you seem to be issuing the point. I said that initial conditions can make a big difference to the final state. I cite a carefully done high quality paper from the refereed literature and you say something that is somewhat beside the point. Whether climate is chaotic is another question. The Navier-Stokes equations are sometimes chaotic and sometimes not.

    I further say that the details of the numerics can also make a big difference to the final state and point to the same paper as well as to Paul Williams.

    Since Navier-Stokes is a subsystem of the climate system albeit a lot simpler and easier to study, its hard for me to believe this phenomena is not present in the Navier-Stokes equations or the shallow water equations on a sphere. Why would you suppose otherwise?

  126. David Young says:

    “… missing the point.” Autocorrection strikes again.

  127. DY,
    Okay, I’ll try one more time again too (we can both be condescending). I agree with you. I’m not claiming that the final state is not dependent on the initial conditions. I’m suggesting that the overall energy in the system and the distribution of that energy is set by conditions that are not sensitive to the initial conditions. For example, the TSI is clearly not, the albedo is probably not unless small changes in the initial conditions can substantially change the ice cover, and we’re the dominant driver of changes to our atmosphere.

    Give this, the suggestion that is made (by many, not just me) is that even though climate models may well be sensitive to initial conditions, they can still be used (by averaging over a suitable time and area and by considering simulation ensembles) to investigate how changes in anthropogenic forcings may influence our future climate (again an average of weather).

    You say,

    I cite a carefully done high quality paper from the refereed literature and you say something that is somewhat beside the point.

    and yet it seems to me that have completely failed to address whether or not climate models can investigate how our climate will evolve in the presence of changes in anthropogenic forcings. If all you want to do is keep repeating the same thing (initial conditions, initial conditions,…) I’ve got the point, but you have still haven’t addressed the broader issue. Paul Matthews might be impressed by your patience, but I’m not convinced I’ve seen any, and I’m losing mine.

    I’ll even address the paper you highlighted. The abstract says,

    In this paper, evidence is presented for the existence of multiple solutions of Reynolds-averaged Navier–Stokes equations with the one-equation Spalart–Allmaras and two-equation Wilcox k-ω turbulence models on fixed grids in three dimensions and how they were obtained is described/

    This, unless I’m mistaken, is an extremely high-resolution 3-D simulation trying to model turbulence. Not surprising that the results are very sensitive to initial conditions. Climate models are not trying to do this. Noone’s claiming that they’re accurately capturing the small scale structures. The only suggestion is that they have skill at capturing the global properties (and some regional properties) of the system and can be used to investigate how we will evolve in the presence of changes in anthropogenic forcings.

    Let me summarise your position.

    • Very sensitive to initial conditions.
    • Climate models useless.

    Here’s mine

    • With suitable averaging and the use of ensembles, climate models can be used to investigate how we will respond to changes in anthropogenic forcings.
    • They’re not perfect, there is still uncertainty.

    Here’s my challenge. Can you at least address the broader point? I suspect that you can’t but I really can’t face you pointing our another paper on turbulence that’s meant to illustrate something significant about climate models when, in fact, what it really illustrates is that modelling turbulence is extremely difficult.

  128. DY,
    And I’ll add that by using this terminology

    The boundary values are according to climate science orthodoxy for practical purposes fixed.

    Boundary values have essentially no effect according to orthodoxy.

    you’ve presented – to me at least – the impression that really all you are is a denier (and if you don’t like the term, tough) who’s using complicated terminology and experience in a related area, to justify your denial. If I’m wrong, feel free to convince me and I’ll apologise.

  129. DY,
    Initial conditions make little difference if the specific climate phenomenon is guided by periodic forcings.

    Look at the Quasi-Biennial Oscillations for evidence.
    Look at ENSO for evidence.
    Look at Milankovitch ice-age cycles for evidence.

    even look at seasons or daily cycles, for goodness sake!

    Any initial conditions are swamped as the phenomenon locks into the forcing groove as a boundary condition.

    So your chaos argument is weak tea, and it is just a matter of time before patterns such as ENSO and QBO and even Milankovitch are fully decoded. We are making progress towards that end at the Azimuth Forum. http://azimuth.mathforge.org/

  130. Google Scholar has this hit for “chaotic climate boundary condition”:

    > The Earth’s atmosphere is generally considered to be an example of a chaotic system that is sensitively dependent on initial conditions. It is shown here that certain regions of the atmosphere are an exception. Wind patterns and rainfall in certain regions of the tropics are so strongly determined by the temperature of the underlying sea surface that they do not show sensitive dependence on the initial conditions of the atmosphere. Therefore, it should be possible to predict the large-scale tropical circulation and rainfall for as long as the ocean temperature can be predicted. If changes in tropical Pacific sea-surface temperature are quite large, even the extratropical circulation over some regions, especially over the Pacific–North American sector, is predictable.

    http://m.sciencemag.org/content/282/5389/728.short

    For ” chaotic climate”, the first hit is Broecker’s Scientific American 1995 article.

  131. In case BBD wonders, yes, SHRL97 is in that list:

    > We investigate the roles of climate forcings and chaos (unforced variability) in climate change via ensembles of climate simulations in which we add forcings one by one. The experiments suggest that most interannual climate variability in the period 1979–1996 at middle and high latitudes is chaotic. But observed SST anomalies, which themselves are partly forced and partly chaotic, account for much of the climate variability at low latitudes and a small portion of the variability at high latitudes. Both a natural radiative forcing (volcanic aerosols) and an anthropogenic forcing (ozone depletion) leave clear signatures in the simulated climate change that are identified in observations. Pinatubo aerosols warm the stratosphere and cool the surface globally, causing a tendency for regional surface cooling. Ozone depletion cools the lower stratosphere, troposphere and surface, steepening the temperature lapse rate in the troposphere. Solar irradiance effects are small, but our model is inadequate to fully explore this forcing. Well-mixed anthropogenic greenhouse gases cause a large surface wanning that, over the 17 years, approximately offsets cooling by the other three mechanisms. Thus the net calculated effect of all measured radiative forcings is approximately zero surface temperature trend and zero heat storage in the ocean for the period 1979–1996. Finally, in addition to the four measured radiative forcings, we add an initial (1979) disequilibrium forcing of +0.65 W/m2. This forcing yields a global surface warming of about 0.2°C over 1979–1996, close to observations, and measurable heat storage in the ocean. We argue that the results represent evidence of a planetary radiative imbalance of at least 0.5° W/m2; this disequilibrium presumably represents unrealized wanning due to changes of atmospheric composition prior to 1979. One implication of the disequilibrium forcing is an expectation of new record global temperatures in the next few years. The best opportunity for observational confirmation of the disequilibrium is measurement of ocean temperatures adequate to define heat storage.

    http://onlinelibrary.wiley.com/doi/10.1029/97JD01495/abstract

  132. Eli Rabett says:

    David Young

    Sorry, I misspoke. Boundary values are constant and thus they don’t really affect any of the incremental changes we are looking for.

    Boundaries change, talk to the Ukraine.

  133. jsam says:

    If the climate is unmodellably chaotic then why is summer always warmer than winter?

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