Nature Physics Insight – Complexity

by Judith Curry

In many large ensembles, the property of the system as a whole cannot be understood from studying the individual entities alone. The past decade has seen important progress in our fundamental understanding of what such seemingly disparate ‘complex systems’ have in common; some of these advances are surveyed here.

Nature Physics – Insights has a special issue on Complexity (h/t David Hagen).  The papers are publicly available until Jan 31.  From the table of contents:

  • Editorial: Complexity, by Andreas Trabesinger
  • Commentary:  The Network Takeover, by Albert Laszlo-Barabasi
  • Between Order and Chaos, by James Crutchfield
  • Communities, Modules, and Large-scale Structures in Networks, M.E.J. Newman
  • Modeling Dynamical Processes in Complex Socio-Technical Systems, by Alessandro Vespignani
  • Networks Formed From Independent Networks, by Jianxi Gao et al.

I’ve selected the [article complexity network takeover]  by Albert Laszlo Barabasi to highlight here:

Reductionism, as a paradigm, is expired, and complexity, as a field, is tired. Data-based mathematical models of complex systems are offering a fresh perspective, rapidly developing into a new discipline: network science.

Reports of the death of reductionism are greatly exaggerated. It is so ingrained in our thinking that if one day some magical force should make us all forget it, we would promptly have to reinvent it. The real worry is not with reductionism, which, as a paradigm and tool, is rather useful. It is necessary, but no longer sufficient.

[A]n increasing number of the big questions of contemporary science are rooted in the same problem: we hit the limits of reductionism. No need to mount a defence of it. Instead, we need to tackle the real question in front of us: complexity.

[D]ecades of research on complexity were driven by big, sweeping theoretical ideas, inspired by toy models and differential equations that ultimately failed to deliver. Think synergetics and its slave modes; think chaos theory, ultimately telling us more about unpredictability than how to predict nonlinear systems; think self-organized criticality, a sweeping collection of scaling ideas squeezed into a sand pile; think fractals, hailed once as the source of all answers to the problems of pattern formation. We learned a lot, but achieved little: our tools failed to keep up with the shifting challenges that complex systems pose.

Yet something has changed in the past few years. The driving force behind this change can be condensed into a single word: data. As scientists sift through these mountains of data, we are witnessing an increasing awareness that if we are to tackle complexity, the tools to do so are being born right now, in front of our eyes. The field that benefited most from this data windfall is often called network theory, and it is fundamentally reshaping our approach to complexity.

Born at the twilight of the twentieth century, network theory aims to understand the origins and characteristics of networks that hold together the components in various complex systems. By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, it led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour.

With its deep empirical basis and its host of analytical and algorithmic tools, today network theory is indispensible in the study of complex systems. [Q]uestion by question and system by system, network science has hijacked complexity research. Reductionism deconstructed complex systems, bringing us a theory of individual nodes and links. Network theory is painstakingly reassembling them, helping us to see the whole again. One thing is increasingly clear: no theory of the cell, of social media or of the Internet can ignore the profound network effects that their interconnectedness cause. Therefore, if we are ever to have a theory of complexity, it will sit on the shoulders of network theory.

JC comment:  On a previous post, I presented the complexity challenge facing climate science in the following way:

Complexity and a systems approach is becoming a necessary way of understanding natural systems. A complex system exhibits behavior not obvious from the properties of its individual components, whereby larger scales of organization influence smaller ones and structure at all scales is influenced by feedback loops among the structures.  Complex systems are studied using information theory and computer simulation models.  The epistemology of computer simulations of complex systems is a new and active area research among scientists, philosophers, and the artificial intelligence community. How to reason about the complex climate system and its computer simulations  is not simple or obvious.

The tools we are currently using seem inadequate to understand the complex climate system.  We have massive amounts of data (particularly global satellite data sets) that are being put to little use in understanding the climate system or in evaluating models.  Ever increasing degrees of freedom in climate models has surpassed our ability to understand how to reason about and draw inferences from climate model output.  New insights are needed, and network theory may be one such source of new insights.

201 responses to “Nature Physics Insight – Complexity

  1. “Decades of research on complexity were driven by big, sweeping theoretical ideas, inspired by toy models and differential equations that ultimately failed to deliver.” :-)

    This sounds very interesting, especially the welcome focus on “deep empirical basis”.

    Will try to read more about it. You can always tell a true enthusiast when he/she has a pop at any previous ideas (chaos, fractals, self-organised criticality), so will approach it with a mix of hope and scepticism.

    • This stuff on network theory is pretty interesting. I have some analysis on the web for things like link connectivity, scholarly citations, TCP/IP statistics, etc. I look at the data via dispersion analysis and do think the math behind it can help with climate science uncertainty analysis. Most of the climate data scientists collect shows dispersion — droplet size, wind speed, wave height,etc. The connection to artificial networks is tenuous, but properties such as dispersed growth rates are common to all sorts of stochastic behaviors.

      • That is very interesting, webbie. We will all rush over and take a look. After, we first check in to bobbie the Idiot Tractor’s blog. We have been waiting a long time for his next big revelation.

    • “Big, sweeping theoretical ideas . . . that ultimately failed to deliver” actually delivered exactly what they were designed to deliver.

      The atomic bomb explosion that ended WWII confirmed the importance of theoretical physics [E = mc2] to world leaders.

      The USA started the Apollo program to overtake the USSR lead in space in 1960, and someone organized the successful effort to destroy the USA’s lead in theoretical physics.

      It worked beautifully!

      Awaken to reality.

      With deep regrets,
      Oliver K. Manuel
      Former Principal
      Investigator APOLLO

      • I am grateful to Professor Curry for this topic.

        I witnessed the destruction of our space program with “Big, sweeping theoretical ideas” like superheavy element fission in meteorites, the neon alphabet game [Ne-A, Ne-B, Ne-C, etc], interstellar diamonds in meteorites, etc., ad infinitum.

        Those “big sweeping” and alluring concepts, generously funded from Washington, DC, successfully blocked consideration of irrefutable experimental evidence since 1975 that our elements were made locally in the same nuclear furnace that sustains life and heats planet Earth today.

        CSPAN News recorded this same plan still in operation on January 7, 1998: NASA Administrator Dr. Dan Golden belatedly released xenon isotopes data from the Galileo probe of Jupiter – data that confirmed local element synthesis.

        Intriguingly, the USSR/Russian NAS published every paper I submitted there on local element synthesis; the USA NAS actively hid or ignored these.

      • Toy models and differential equations for government scientists, TV reality shows and gladiator sports for other adults, video games for kids, and drugs for teens.

        These are a few of the distractions used to keep the public unaware of reality.

        For a quick check on reality, try to imagine a scenario by which the public takes back control of our government.

        I can’t imagine one either.

      • Here are a few of the “big, sweeping theoretical ideas” from major research institutions that were used after 1974 to distract attention away from evidence that our elements were made locally in the same nuclear furnace that sustains life and heats planet Earth today:

        1. Extinct superheavy element in the Allende meteorite (U Chicago)
        2. Nearby supernova explosion (Harvard, U Oklahoma)
        3. FUN isotopic anomalies in meteorites (Caltech, U Chicago)
        4. Ne-A, B, C, D, E, etc in meteorites (Lunar Science Institute, U Bern, U Chicago)
        5. Interstellar grains in meteorites (Rice, U Chicago, Washington U)

  2. Self organized criticality – Ah, Frank Lemke!

  3. There has to be some concept of a system response time that is valid here. IMO, craploads of data will only help so much in the face of things changing on very long time scales. I mean, they will help some…

  4. Many of us have been complaining that taking a system as complex as climate and running a linear relationship through it (2*CO2 = 3C, or whatever) is sooo 18th Century.

    If some new science which can take an empirical look at complexity comes along, it sounds a lot better than the ‘toy models’ we have now.

    The downside may be that it’s also likely to leave some of us palm-faced trying to get to grips with it!

    • The public has wrestled with this before.
      When evolutionary science was young, many very well educated people made conclusions that seemed scientific at the time that resulted in the social mania (and disaster) that was eugenics.

      • ceteris non paribus

        Right.

        Eugenics is how we know that Darwin was completely wrong about evolution.

        Same with climate science – as soon as you say anything that seems scientific at the time, you can be confident that it’s actually wrong, and will result in a social mania and disaster.

      • ceteris,
        Are you working to miss the point or is it possibly an accident. I will be clear:
        Eugenics was based on a *mis*understanding of evolution, but was extremely popular with progressive and intellectuals of the time.
        The implosion of eugenics was not a disproof of evolution.
        The implosion of AGW is not a disproof of climate science.
        I hope that helps.

      • I gotta agree with the frustrated impotent warmist troll on this one. Let them equate skepticism of CAGC, with a belief in Creationism. Eugenics has nothing to do with climate science. That was another place, another time, different people.

      • Don,
        History does repeat itself. Eugenics was led by a coalition of the most progressive and intellectual elites of the day.
        Sort of like AGW. I respect your view, but I respectfully disagree: History does repeat, and past is prologue.
        And, ceteris’ take on the lesson of eugenics is so backwards as to boggle the mind.

      • hunter,

        History does not repeat itself. Each moment of history is unique, and what’s past is past. People do repeat similar patterns of behavior that other people in the past have repeated, and so on. Different people, different times, different slices of history.

        Progressives of today, have their own sins and inadequacies to answer for. They are not responsible for the behavior or the particular beliefs of of the progressives in the past. I doubt that you could find 5 of them, who believe in Eugenics. We can’t hang Eugenics around progressive’s necks any more than they can hang Creatonism around ours. But you are free to do as they do, and try that tactic anyway. It is not a meaningful argument.

      • Don,
        I appreciate your taking the time to explain why you disagree with my points on history.
        While I disagree with you that history does not repeat, I do agree with you that the sins of the past should not be hung on people of today. That was not the point I was attempting to make, and if it seems I was, I was possibly not being sufficiently clear.
        My point is that each age carries challenges and that in broad outline people, being genetically and often culturally predisposed to certain reactions and views will take similar stands. Eugenics was most assuredly then. AGW, from my perspective, is now. If you were to read a critique of eugenics written during that social mania, you would be amazed at some of the similarities in how eugenics believers approached eugenics and how AGW believers approach AGW. The opinion leaders of eugenics were the intellectual leaders of the day: past presidents of major universities, Nobel prize laureates, progressive intellectuals, etc. Sound familiar?
        And the tactics they chose to push the eugenics agenda- scientific consensus, political power, sweeping laws- all have a familiar ring with today’s social mania.
        In no way am I implying AGW believers are responsible for eugenics. They have enough to answer for today.
        Is that any more clear?

      • hunter,

        Yeah, I guess. By the same token you could compare modern day climate scientists, with the priests who ran the Aztec temple business. It’s deja vu, all over again. But people and the level of accumulated social and scientific progress, between Aztec times and modern times, are not comparable. It is a meaningless comparison. Eugenics and AGW are not similar. AGW has some plausible scientific basis, and it is not inherently evil. You could not get 5 modern day so-called “progressives”, to believe in Eugenics. Even “progressives” can learn, from the most egregious past mistakes.

        Another point, the “progressives”, who were around in the early 20th century, were basically good people, despite some mistakes made out of ignorance. Most of them would be conservatives today.

        i just think that a more fertile argument to use on the modern day “progressive” AGW alarmists is that they are greenie socialist pinheaded ideologues. Can I get an Amen! brother, hunter

      • Eugenics, like CAGW, was a perverse extension of uncontroversial science.

        By dismissing Eugenics, as we should, we don’t dismiss Darwin.

        By dismissing warmism, as we should, we don’t dismiss the good science that preceded the establishment of climate “science”, just the bad science that followed it.

      • Tom FP,
        You summed up my point very well. Thanks..

      • ceteris non paribus


        By dismissing warmism, as we should, we don’t dismiss the good science that preceded the establishment of climate “science”, just the bad science that followed it.

        You guys apparently think that your historical opinions give you the ability to determine good science from bad.

        I find it telling that you are able to make these determinations without resorting to a single measurement.

        Look – the science of eugenics was actually sound. Farmers still use it all the time to, for example, breed better dairy cows.

        The fact that “human” eugenics is morally repugnant has exactly nothing to do with its scientific validity.

      • ceteris,
        Perhaps you would be able to discuss eugenics better if you knew something about it.
        Eugenics was far more than cattle breeding applied to humans.
        It was in fact demonstrated to be flat out wrong AND morally repugnant.
        AGW is far more than applying climate science.
        It is proving to be flat out wrong and morally repugnant.
        But you seem to have moved past your complete misunderstanding of the point about eugenics irt evolution, so progress is possible.

      • ceteris non paribus


        It was in fact demonstrated to be flat out wrong…

        Really? Do tell.

        You apparently learned everything you know from the US school system.

        Google “Dor Yeshorim”. Self imposed eugenics – practiced by some of the people who should, historically, be most frightened by it.

  5. As bad as reductionism may be to model climate, that as Philip Stott observes, “is the most complex, coupled, nonlinear, chaotic system known,” it is a nonstarter when scientists fascilitate the abandonment of basic principles of statistical significance by the feckless and superstitious ideologues with a political agenda who are on the government’s payroll.

  6. I’ve just deleted half the comments, which have no conceivable relevance to the topic of the thread. At least in the beginning of the thread, pls try to keep the comments relevant to the topic. Thx.

    • Tallbloke has taken the same attitude for a while now, and scientific facts are able too be seen from the noise.

      Probably time you think about your ability to lead the pack, and keep those mongrels behind in order.

      • markus –

        Fair point, although Judith often negates the need for such disciplining action by saying “this is a technical post and comments will be moderated for relevance“.

        That usually is enough to keep us mangy dogs on the leash – perhaps she forgot today and had to descend with the big stick?

        But did you see how everybody jumped into line without a whimper?

        Fantastic! :)

      • As one of the snipees, I’ve been desperately trying to say something relevent to network theory ever since, despite being mathematically challenged!

    • cui bono

      I’m shocked. Shocked I say!

      I thought you were far too civilised and well-mannered to fall foul of Judith’s extremely indulgent moderating.

      You must have been most vexed indeed!

      P.S. I spend a goodly portion of my time here keeping my fingers crossed that my fundamental innumeracy remains an embarrassing secret.
      Shush!

      • Anteros,

        Oh, I wasn’t rude, just o/t. As for the maths, let’s just keep it to ourselves!

      • A – you will be even more shocked that it was I who committed the original sin. I guess passing references to it are probably OK now as we are much deeper athread.

    • Thanks for:

      1) non-paywalled links

      2) squashing the trolls

      The previous thread “no missing heat ?” became very interesting when these things happened. Chaos resulting from non-linear interaction of multiple factors all with unknown thresholds seems to me to be where its at

  7. randomengineer

    Dr Curry

    There was a recent interview with Donald E Knuth (the father of algorithm analysis) wherein he wasn’t optimistic regarding the ability of programming to leap the multi-processor hurdle.This reads like a similar effort.

    Given that he wrote a paper with denizen Vaughan Pratt (he’s also from Stanford) you may want to see if you can page/email Prof Pratt and get him to weigh in on this topic.

  8. Sorry Dr. Curry! You must go to a lot of trouble finding all these nuggets for the blog – we shouldn’t instantly go off on tangents. :-(

    To assuage, do you know of any attempts to apply this to climate research as yet? I couldn’t find a reference to climate in the papers.

    I liked this bit: “The idea was that a new, ‘higher’ level is built out of properties that emerge from a relatively ‘lower’ level’s behaviour. He was particularly interested to emphasize that the new level had a new ‘physics’ not present at lower levels.” (from J. P. Crutchfield paper).

    This seems spot on. Simple linear relationships may not hold in a complex system. The world is not a table-top gas experiment, and the whole panoply of variables make climate something beyond simple feedbacks. If they can handle complexity with (relatively) simple maths, that’s got to be good.

  9. A search of the academic literature for “network theory” and “climate” returns a series of 4 articles by these folks, here is the most current. References to Tsonis etc. etc.:

    Donges, J.F.a b , Schultz, H.C.H.a c , Marwan, N.a , Zou, Y.a , Kurths, J.a b
    Investigating the topology of interacting networks – Theory and application to coupled climate subnetworks
    (2011) European Physical Journal B, pp. 1-17. Article in Press. Cited 2 times.

    AFFILIATIONS: Potsdam Institute for Climate Impact Research, 12 03, Potsdam, 14412, Germany;
    Department of Physics, Humboldt University of Berlin, Newtonstr. 15, Berlin, 12489, Germany;
    Department of Physics, Free University Berlin, Arnimallee 14, Berlin, 14195, Germany

    ABSTRACT: Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. Specifically, the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

    ISSN: 14346028
    DOI: 10.1140/epjb/e2011-10795-8
    LANGUAGE OF ORIGINAL DOCUMENT: English
    ABBREVIATED SOURCE TITLE: Eur. Phys. J. B

    • Thanks Bill. It sounds promising. Any paper that says it’s a ‘first step’ sounds hype-free.

  10. This may be off topic so feel free to delete.
    When I read the article the words that popped into my mind were: my brain. I have frequently said that I have to “sleep on and idea” to get a sense of that idea. To me, this is analogous to complexity network takeover. While I am awake, my mind is focused upon acquiring and evaluating what comes through my senses: sight, hearing, touch, etc. Each sense is an independent source of data with its individual algorithm unique to me. The process of acquisition seems to relegate to the background thoughts of connectivity and in particular, weighing the strength of the signal. When I sleep on it, many of the conscious barriers I erect to acquire and categorize information are now subjugated to the process of integration, being better able to see the whole. Not every morning do I awaken with an aha moment, but when one does come along, I can trace the origins and again be in a more selective data acquisition mode.

    • RiHo08 –

      I don’t think your comment is off topic at all. It seems very apt.
      I’m reminded of the circumstances in which parallel processing was first conceptualised – many people were looking at the differences between early computer structures and our own cognitive processes.

      Cui bono mentions upthread about the need/space for a new science to deal with the complexity of chaotic systems….

      I’ll just mention one thing that I take from your appropriate description of some of the processes involved in integrating information in human beings. It is essentially a messy, disorganised, impressionistic, non-numerical process – even though we start with ‘data’.

    • Good post RiHo08. Climate science badly needs a fresh approach to the study of the already very large volume of weather observations available and the rational thinking processes of current scientific method are too linear to be of much use in developing appropriate hypotheses and theories.

    • The most current thinking of neuroscientists confirm what your perceptions

    • Right brain – left brain?

  11. Nature is not a closed system anymore than Christianity is. The later is in fact very open to the use of scientific approach concerning things that can be quantified about the former. It is nevertheless a truism that “a hypothesis that cannot be falsified by empirical observations, is not science.” That certainly goes for global warming. AGW theory is just that: a theory. Those who cannot poke holes in the AGW hypothesis as it has been presented by the UN-IPCC cannot be real scientists by definition because that is the job of a scientist.

  12. Network theory also seems to be used to re-analyse paleoclimate changes:

    http://arxiv.org/pdf/0907.3368.pdf

    From the conclusion: “…we have used our approach to investigate a marine climate proxy record representing the climate variability over Africa during the last 4.5 Ma. The different measures highlighted various transitions in the recurrence structure and, hence, in the dynamics of the studied climate system. By applying the recurrence approach and complex network measures, we were able to identify more subtle transitions than those that were previously reported from using linear approaches,”

    Wonder what it would say about the Hockey Stick?

  13. Dyslexia prevents many of the trees to be seen, but the forest sure looks beautiful from up here.

    No good looking at trees in the wrong forest, as Michael Mann has done.

    My heart does feel for those lost in the forest of Greenhouse.

    The climatic system on Earth cools the rays from the Sun, it must be so, a refrigerator. The principal is now known and cannot be broken, it is a Law in the making.

    Greenhouse system or Refrigeration system – Time to pick one gents, before it is chosen for you.

    Markus Fitzhenry.
    .

  14. A simpler form of this, neural networks, has been applied to climate questions (just google “neural networks” climate or look at this paper by Knutti) and it works, problem is that neural nets have no conscience, they tell you what, but not why, the principle benefit of reductionism

    • ceteris non paribus

      Re the benefits of reductionism:
      The quoted piece says (rather poetically):

      Reductionism, as a paradigm, is expired, and complexity, as a field, is tired.

      But then reductionism conveniently sneaks in by the back door…

      By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, it led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour.

      Oops.

    • Eli said, “They tell you what but not why.” That is what is frustrating about chaos theory also. That is why I am think a type of convergence reductionism is needed. You may never know all the whys, but should be able to understand more of the whys. Tunnel vision reductionism is the problem in chaotic systems. Some parts of noisy data appear to agree with an assumed cause others don’t. Often the ones that don’t agree, have the information. That is the problem with linear no threshold modeling. That is the problem with climate science.

      • Capt. dallas

        I think that commentators and scientists would often be better off using real life anecdotal material rather than the unreliable modeldotal stuff they often come up with that is based on dubious or incomplete data.
        tonyb

    • Chief Hydrologist

      Knutti is usually sensible – unlike some. But this link doesn’t work?

  15. This is very simple. Look at the actual data. Every time it gets warm, it next gets cool. Every time it gets cool, it next gets warm. When the oceans are warm and the Arctic is open it snows and cools the earth. When the oceans are cool and the Arctic is frozen it snows less and ice retreats and that warms the earth.
    The complex climate theory and models do not do this and they are wrong. The other climate drivers are complex, but Arctic Sea Ice controls the set point of the thermostat of earth and it is simple.

  16. “Reductionism deconstructed complex systems, bringing us a theory of individual nodes and links. Network theory is painstakingly reassembling them, helping us to see the whole again. One thing is increasingly clear: no theory of the cell, of social media or of the Internet can ignore the profound network effects that their interconnectedness cause. Therefore, if we are ever to have a theory of complexity, it will sit on the shoulders of network theory.”

    I cannot take seriously someone who compares our theory of the cell to our theory of social media. Our theory of the cell is profound. Our theory of social media is nonexistent. You can prove the latter point for yourself. Just ask yourself what phenomenon of social media can be explained and predicted by our theory of social media?

    Having compared our theory of the cell to nothing, he then points to the interconnectedness found in both and jumps to the totally unrelated claim that our theory of complexity will rest on network theory.

    Maybe he meant “communist cell” rather than cell. Then his comparison between our theory of the communist cell, which is nonexistent, and our theory of social media, also nonexistent, is a tautology.

    This is not an auspicious beginning.

    • The day they named Social Sciences as such, was the day a pollution crept into pure science, and that filth has been growing since.

      • The day when natural philosophy decided to set itself up as an alternative to religion [and call itself 'science'] was a day when pollution crept into pure thinking.

      • Careful there: I used the fetid and… Bazinga!

      • ceteris non paribus


        The day when natural philosophy decided to set itself up as an alternative to religion [and call itself 'science'] was a day when pollution crept into pure thinking.

        Ah yes – the good old days of pure logical religion…

  17. One of the points missed is that the interrogation system one uses, biases the outcome one can observe.
    It is back to the ‘if your only tool is a hammer, then everything is a nail’. Referees ‘like’ hammers and nails, as they have a very good understanding of how hammers and nails work. Coming along with a screwdriver always meets resistance.
    In many fields, the inertia in the grant awarding process is such that novelty is frowned on, as they want to know that the investigation will work, before the investigation has been done.

  18. Has climate science lost sight of the forest by looking at the trees (rings)?

    With the IPCC’s bold lead of 0.20 C/decade, why has UAH global temperature only followed by rising 0.07C/decade in the last decade since Jan. 2001?

    It appears that missing / miss adjusted components in climate models and misstuning have skewed the system to give decadal trends that are off by ~290%.

    It is time to address the full interacting complex network of ALL the physics, especially clouds, solar and cosmic interactions!

  19. “AFFILIATIONS: Potsdam Institute for Climate Impact Research, 12 03, Potsdam, 14412, Germany;
    Department of Physics, Humboldt University of Berlin, Newtonstr. 15, Berlin, 12489, Germany;
    Department of Physics, Free University Berlin, Arnimallee 14, Berlin, 14195, Germany”

    Thanks. I was just about to ask what university would pay someone to produce this stuff. No doubt each of the authors has shown considerable achievement in their studies of Heidegger.

  20. If you are hunting down articles on network theory, be warned that there’s a sociological thing called ‘actor-network theory’ which seems to be about debates and strategies. Ironically, the first instance of it I came across was about Michael Mann and his defence of the hockey stick in congress!

  21. Surely the challenge of complexity is to understand exactly the parameters which are the major drivers of the system state – in this case climate.

    Rather than building layer upon layer of imperfect model based on simplistic equations, surely the computers should be used the other way around – feed in *all* the available data and get the computer to figure which parameters are the major drivers.

    Let the computers try to make predictions based on real live data.

    Willis Essenbach demonstrated that current models are not much more complex than a simple equation.

    http://wattsupwiththat.com/2011/05/14/life-is-like-a-black-box-of-chocolates/

    • All Essenbach demonstrates is the blindingly obvious that you can approximate the temperature response of climate models with a simple equation. We already knew that surely, climate scientists have been telling us that for decades: temperature change = forcing x climate sensitivity anyone?

      No idea why such an obvious fact needed to be written in so much text with the tint that something new had been “discovered”. But I guess it might have something to do with the venue…

      But then it gets more bizarre because after making this “discovery” he uses it to base an argument that he doesn’t believe it. Of course I suspect he didn’t really realize he did that:

      “Me, I find the idea of a linear connection between inputs and output in a complex, multiply interconnected, chaotic system like the climate to be a risible fantasy. It is not true of any other complex system that I know of. Why would climate be so simply and mechanistically predictable when other comparable systems are not?”

      He’s actually acting incredulous about the very result he “discovered”. Climate models are “complex, multiply interconnected, chaotic” systems. And they exhibit the behavior he doesn’t think such systems can…

      • lolwot,
        That “risible fantasy” comment by Willis also caught my eye.
        I can actually believe that all that “chaos” map to random functions which leads to a straightforward transfer function.

        There is a math research area called Random Matrix Theory, whereby large matrices with arbitrary elements reduce to eigenvalue solutions that have a distribution corresponding to semi-circle PDF. The issue is explaining why the solutions are predictable independent of the input. Terence Tau is currently working on this subject at his popular math blog.

        The generic answer is simplicity can drop out of complexity if you know the tricks. As an example, the trick I used on modeling the “missing heat” of the climate system basically reduces multiple rates of diffusion and path lengths into a simple stochastic formulation. The bottom line is that this may work good enough to provide the insight we need, without having to generate a complex model.

        Many of the authors mentioned in the post, such as Crutchfield and Newman, come from the Murray Gell-Mann school of complexity, who have a goal to replace complexity with simplicity whenever possible.

      • Willis – Eschenbach btw – can surely defend his point of view, but isn’t Willis’s point more to comment that he has a hard time believing the models represent reality, and this is a piece of his evidence?

  22. I would like to repeat my recommendation of a book that I think is more pertinent to the debate: Modern Thermodynamics by Dilip Kondepudi and Ilya Prigogine, and especially chapters 18 and 19. The systems that they present, mathematical and chemical, are low dimensional, but the same phenomena (traveling waves, standing waves, spiral waves and others ) are readily observable in the climate, over multiple time scales. There are more complete presentations of dynamical systems, but that one addresses in particular thermodynamic systems far from equilbrium, hence it pertinence to the climate and theories of CO2-enhanced future warming.

    Dr Curry wrote: The tools we are currently using seem inadequate to understand the complex climate system. We have massive amounts of data (particularly global satellite data sets) that are being put to little use in understanding the climate system or in evaluating models. Ever increasing degrees of freedom in climate models has surpassed our ability to understand how to reason about and draw inferences from climate model output.

    I would recommend not the study of complexity theories, but more time spent collecting and analyzing data, and more time spent developing all sorts of dynamical and statistical models until we have some that are accurate. Just the idea that the climate system might be in an attracting set instead of equilibrium, steady-state, or one of the other simplifications has hardly had time to sink in for people doing the modeling and analysis (I include, for example, the excellent work “Principles of Planetary Climate” by Raymond T. Pierrehumbert wherein nearly all the mathematical physics is based on equilbrium approximations.) Or so it seems to me.

    Obviously, Dr. Curry’s recommendation is well-grounded in scholarship and experience, but it looks to me as though what is really needed is just more time carrying out the traditional approaches.

    • Excerpt of what MattStat wrote:
      “more time spent collecting and analyzing data”

      Agree. Data exploration (absolutely not to be confused with culturally-demanded statistical inference based on patently untenable assumptions) needs to be improved by orders of magnitude. Sensible judgement is NOT founded on untenable assumptions, no matter what “convention” says; historians are going to have a field day
      writing about the philosophical breakdown (culturally-demanded paradoxical misinterpretation of statistical inference based on patently untenable assumptions) of logical reasoning in the present era. Efficient Rehab Step # 1 for journal editors: Abolish the p-value from publications. Rehab Step # 1 for stats educators: Develop a massive flood of examples of paradoxical misinterpretation arising from allowing cultural prescription (culturally-demanded p-values) to take precedence over absolute philosophical logic. This issue needs to be confronted head-on before it derails society & civilization. There appear to be very few with the perception needed to diagnose the fundamental roots of the problem. Immersion in the social mesh of ivory tower group-think appears to be blinding the majority of academic insiders, presenting a formidable obstacle to the minority with more lucid perception. Regards

  23. My research group at OSTI has done some network analysis. They found a topological transition in co-author networks that occurs when a scientific community adopts a new theory. The topology of consensus, a central feature of science. It is useful stuff.

    But Barabasi is over the top and always has been. There aren’t that many networks in nature and treating other relational systems as networks need not work. So I consider network theory research a bit of a fad, even though I do it.

    • Network theory also includes anything to do with gridded models, which are important in scientific computing for FEA, fluid dynamics, etc.

      Then you have all the inferencing network models, such as local computing, generic inferencing, hidden Markov models, Petri nets, etc. Even something like the FFT is a network using elements of dynamic programming for efficiency.

      Network theory may be so comprehensive as to be meaningless. As some computer scientists are fond of saying: “every problem space is a graph, and the solution is a search of that graph”.

  24. “Reductionism deconstructed complex systems, bringing us a theory of individual nodes and links. Network theory is painstakingly reassembling them, helping us to see the whole again.”

    Eg climate models. Putting all those reconstructed complex systems together into one model to see the global sum of their behavior. Seems like climate science has been well ahead of the ball on this one.

    • Chief Hydrologist

      ‘AOS models are members of the broader class of deterministic chaotic dynamical systems, which provides several expectations about their properties (Fig. 1). In the context of weather prediction, the generic property of sensitive dependence is well understood (4, 5). For a particular model, small differences in initial state (indistinguishable within the sampling uncertainty for atmospheric measurements) amplify with time at an exponential rate until saturating at a magnitude comparable to the range of intrinsic variability. Model differences are another source of sensitive dependence. Thus, a deterministic weather forecast cannot be accurate after a period of a few weeks, and the time interval for skillful modern forecasts is only somewhat shorter than the estimate for this theoretical limit. In the context of equilibrium climate dynamics, there is another generic property that is also relevant for AOS, namely structural instability (6). Small changes in model formulation, either its equation set or parameter values, induce significant differences in the long-time distribution functions for the dependent variables (i.e., the phase-space attractor). The character of the changes can be either metrical (e.g., different means or variances) or topological (different attractor shapes). ‘ http://www.pnas.org/content/104/21/8709.full

      Try to keep up numbnut.

      • stop trying to pretend you are replying with anything relevant

      • Chief Hydrologist

        Stop pretending you understand what it means or have looked at the PNAS paper.

        ‘McWilliams held a Research Fellowship in Geophysical Fluid Dynamics at Harvard from 1971-1974 and afterwards worked in the Oceanography Section at NCAR where he became a Senior Scientist in 1980. In 1994, while still retaining part-time appointment at NCAR, he began his work at UCLA where he became the Louis B. Slichter Professor of Earth Sciences in the Department of Atmospheric and Oceanic Sciences and the Institute for Geophysics and Planetary Physics. In 2002, McWilliams was elected to the National Academy of Sciences. Today, he continues his career in academia at UCLA.

        James C. McWilliams primarily does research in computational modeling of the Earth’s oceans and atmospheres. McWilliams has written numerous papers from 1972 to the present[4], attempting to construct accurate models to describe the Earth’s fluid reservoirs. One of McWilliam’s most influential papers was a paper written in 1990 titled “Isopycnal mixing in ocean circulation models”, in which together with Peter R. Gent they proposed a subgrid-scale form of mesoscale eddy mixing on isopyncal surfaces for use in non-eddy resolving ocean circulation models[5].

        McWilliams has contributed greatly to the development of accurate models of the Earth’s atmosphere and ocean, and his subjects of interest are maintenance of the general circulations; climate dynamics; geostrophically and cyclostrophically balanced (or slow manifold) dynamics in rotating, stratified fluids; vortex dynamics; planetary boundary layers; planetary-scale thermohaline convection; coherent structures of turbulent flows in geophysical and astrophysical regimes; magnetohydrodynamics; numerical methods; and statistical estimation theory.

        More recently, he has helped develop a three-dimensional simulation model of the U.S. West Coast that incorporates physical oceanographic, biogeochemical, and sediment transport aspects of the coastal circulation. This model is being used to interpret coastal phenomena, diagnose historical variability in relation to observational data, and assess future possibilities.’

        Relevant? God you are a twit.

      • The true believers not only deeply believe in AGW, they think everything about AGW is the bestest ever.
        The one thing that even informed defenders of AGW have admitted is that AGW promoters have not been using well maintained data bases or well documented techniques. Dr. Curry has been quoted saying so so in this very thread.
        “Dr Curry wrote: The tools we are currently using seem inadequate to understand the complex climate system. We have massive amounts of data (particularly global satellite data sets) that are being put to little use in understanding the climate system or in evaluating models. Ever increasing degrees of freedom in climate models has surpassed our ability to understand how to reason about and draw inferences from climate model output.”

      • Chief, why don’t you take a timeout and read the blog rules.

        Insulting others does nothing for your scientific reputation.

      • bob,
        Chief and others who critique or otherwise diagree with the consensus get insulted much more often. I think someone who uses their real name should receive much more leway than some of the anonymous talking point repeaters who attack him.
        But that is only my opinion. Our hostess is the final arbiter on this.
        As for me, I am just pelased to see Chief posting here again.

      • Really, Hunter,
        Just because you claim others do it makes it all right for Chief to insult lolwot?
        I realize you have to defend the Chief because you are quick with the insults as well with all the “true AGW believers” rants.

        This is Judy’s blog, but she is light on the moderation and if I want to express my views that this blog would be better with more science and less insults, then I am going to try and make that point.

        If someone can’t make a point without an insult, then I am not going to value that person’s input at all.

      • I didn’t even get what CH’s “point” was anyway. See his original reply he just quotes a load of text from some random paper I have no idea why because it doesn’t even seem to relate to my point. I am not completely dumb so I wonder how many other people actually understood what his vague point was.

        His only commentary was “try to keep up numbnut”

        Is he just posting long vague scrawl to cover up the fact he doesn’t have an actual response? Lets see if this is part of a recurring theme..

      • lolwot said, “Seems like climate science has been well ahead of the ball on this one.”
        CH responded
        lolwot said, “I didn’t even get what CH’s “point” was anyway. See his original reply he just quotes a load of text from some random paper I have no idea why because it doesn’t even seem to relate to my point. I am not completely dumb so I wonder how many other people actually understood what his vague point was.

        His only commentary was “try to keep up numbnut”

        Is he just posting long vague scrawl to cover up the fact he doesn’t have an actual response? Lets see if this is part of a recurring theme.”

        Ever thought that a subject might be outside of your area expertise a touch? I know I have. I have some of the craziest theories, generally though, I at least have an inkling what I am talking about. May not communicated it all that well, but real world thermo, testing of flow rates, maximizing efficiencies and reducing indoor air pollution was my thing. That involved controlling non-linear dynamic systems, simple ones admittedly, but interesting ones with potential to break things and people if not properly adjusted. Chief was letting you know that “..climate science has been ahead of the ball on this one.” was gullibly naive, in his quaint Aussie way.

      • Chief Hydrologist

        Numbnut made some twee remark on models. I quoted something else on models – something quite obvious to anyone familiar with the partial differential equations used in fluid dynamics – in relation to climate models and complexity – and from a major figure in the field. So entirely on topic, linked to, peer reviewed, published in the Proceedings of the National Academy of Sciences and quoted in context.

        The comment from numbnut was that I should stop pretending to cite anything relevant. The title of the paper reads – ‘Irreducible imprecision in atmospheric and oceanic simulations’ and is from someone with impressive credentials in the field – which numbnut might have realised with a quick google – but which I subsequently copied him in on.

        ‘AOS models are members of the broader class of deterministic chaotic dynamical systems, which provides several expectations about their properties (Fig. 1).’ Professor James McWilliams. This has implications in terms of ‘irreducible imprecision’ in the result of models.

        ‘Sensitive dependence and structural instability are humbling twin properties for chaotic dynamical systems, indicating limits about which kinds of questions are theoretically answerable. They echo other famous limitations on scientist’s expectations, namely the undecidability of some propositions within axiomatic mathematical systems (Gödel’s theorem) and the uncomputability of some algorithms due to excessive size of the calculation.’

        I suppose numbnut and Bob Drone fail to understand that either. Numbnut is a serial pest with nothing to offer but ill informed snarks in support of a tribal consensus. He says he is smart – but frankly I think he is the cyber village idiot. Now it is a random paper with no relevance to climate models.

        And Bob drones in with puerile homilies about insults, it not being about the science and not valuing me. These characters have scant regard for any science that doesn’t suit the terms of their psychological disorder. You need to remember tha it is not about open mindedness in the least. I could care less what they think of me – I suppose.

      • Chief, just a block quote and an insult is all you gots.

        Maybe some analysis on the effects of the identified irreducible imprecision of models and their application to weather and climate models would be welcome.

        But if you are just trying to say that since weather models can not predict weather more that a couple weeks or so into the future, then how can climate models predict climate changes over decades, then you are just spouting giberish just like your arguments on infared not heating the oceans surface.

        If you are saying that models are imprecise, well thanks for that comment Mr Obvious.

      • Chief Hydrologist

        I don’t know Bob – why don’t you try reading the rest of the paper – although it is a bit of a stretch for close minded warmists like you who really just want the convenient take away propaganda version.

        For others ‘irreducible imprecision’ is based on the idea of emergent properties in the deterministic chaotic system that is the AOS. Make small changes in inputs and there are large changes in the solution. There is a solution space that can only be understood by systematically exploring model families – but this is something that has not been done and the ‘solution’ is determined on the basis of the ‘plausibility’ of the solution after the fact. There are in fact many solutions within the range of plausible inputs – they pick the one they think is right and send it it the IPCC where it is graphed along with other ‘plausible’ solutions.

        Climate models are a scal of Madoff proportions – or at least using a tool in the wrong way for propaganda purposes. But most of us knew that already – but you and numbnut seem to think it is something I made up to fool sceptics. That is why I quoted the ‘science’. You should try it sometime – you might earn some credibility.

      • bob,
        lolwot is a big boy, and he does not hesitate in sharing the insults.
        Are you his catcher in the rye or something?
        I find these little detours into manners at this stage difficult to distinguish from a complete waste of time.

  25. Chaos theory has indeed taught us more about unpredictability than about how to predict nonlinear systems. That is it’s basic point, that such systems can be intrinsically unpredictable. But this is not a fault, as Barabasi suggests. The fault is that science refuses to embrace the message. The science of unpredictability is still waiting to happen, including in climate science, where it is sorely needed.

    • Some aspects in climate science are what I have referred to in print as “predictably unpredictable”.

      In other words, if you can characterize the disorder, you can take advantage of the information. That is part of information theory.

    • Bob said the Chief should take a time out. I don’t know Bob, the Chief is Australian and colorful. He adds a bit of charm to the blog. TWIT may be Australian for Technically Worthless Ideological Theory. Now if he had called someone a Drango, that may be insulting. “What do you think this is? Bush week? could be taken the wrong way.

      • Chief Hydrologist

        Capt’n my Capt’n,

        No – twit has the usual meaning – ‘the kind of person that makes a retarded chimp look smart.’ There are 67 other meanings in Urban Dictionary none of which are complimentary and a few of which involve bicycle seat sniffing. I don’t necessarily have a problem with people who sniff bicycle seats. Whatever happens between a twit and a consenting bicycle is none of my business. I do object to the despicable, lycra wearing, leg humping, pissant liberal, social democrats who ride bicycles. You see I have some past experience with numbnut. Used to be you could have a nice lunch, a cigar and a port and roll over poor bastards on bicycles in your Bentley. A sort of urban fox hunt. I am going to call it characterising the disorderly with thanks to Webby for the neat euphemism.

        I see you have some grasp of the vernacular. But the word is drongo – which might easily apply to numbnut and his cohorts. It is a little confusing. Remember that a total bastard was a friend but someone totally despicable was only a bit of a bastard? In contrast – a drongo is someone who is up themself and a total drongo is someone who is so far up themself they couldn’t find the dunny with a flashlight. Numbnut is a total drongo – to characterise the disorderly – and he doesn’t really expect a serious discussion of the ‘science’. It is about close mindedness after all – closing ranks – taking pot shots at the enemy – repeating ad nauseum a litany of nonsensical conceits in narrative form. Models are a prime example. Every modeller knows that if the input is changed ever so little – a totally different answer is arrived at. It is not a topic that is raised, however, in polite numbnut company and numbnut is too dumb to find out for himself. The former is what I call emergent behaviour –but let’s call it instead non-linearity. Just like the broad range of natural variability of climate emerges from small initial changes propagating through the complex system – emergent behaviour.

        I am not even a sceptic. For God’s sake – small changes in greenhouse gases could propagate through the system causing untold and rapid changes to climate. It goes with the theory of abrupt and non-linear climate change. This is what they have been saying at Woods Hole for many years.

        The warmist drongos have got just about everything wrong, they are a laughing stock, they have succeeded in nothing, nada, zilch and blame it on dumb white men. So they come here expecting to hold the moral and scientific upper hand but it just a joke. They don’t know squat and don’t want to know anything that undermines the sense of themselves as the torch bearers for a benighted humanity.

  26. Chief Hydrologist

    Hi David,

    I was struggling to think of a system that might have the data to map emergent climate features. The simple network model of Tsonis comes to mind – using atmospheric and oceanic indices. It relies on autocorrelation as a property of complex systems at phase shifts. ARGO data might be worth looking at with pattern visualisation techniques.

    But you are right – before solving problems of emergent behaviour one first must recognise that there is a problem.

    Cheers
    Robert I Ellison

    • Pattern visualization. There are common patterns in nonlinear systems. The perfectly symmetrical peak of the 1997/8 El Nino event and a rogue wave for example. There are also the “w” wiggles that are more subtle. There really should be more done with chaotic pattern recognition.

      A common factor, BTW is doubling and fractional harmonics of peak-peak values. Averaging and smoothing data destroys most of the information that can be gained from pattern recognition. Raw data is cool!

    • David Mumford has a recent book out called Pattern Theory, which serves as a cookbook of methods to use in deconstructing stochastic behaviors in nature and elsewhere.

      I use bits and pieces from the book. For example, Mumford has a good explanation of the Ornstein-Uhlenbeck random walk process, which can be used to model temperature excursions.

  27. We consider many methods to group or summarize data in model development. Fundamentally, the processes used to compile the data to be used in making a model is really only important to the model developer. To all others, what is important is whether the model has been demonstrated that it is able to predict or simulate specific final outcomes within an acceptable margin of error.

    There is no “magic method” to develop complex models and simulating the future weather over the long term requires extremely complex models that will employ various methods of summarizing data. The methods used to develop GCMs are important to the developers. Knowing that a GCM is reliable when being used for implementation of government policy is important to everyone else.

    When discussion comes to climate models, shouldn’t the developers of each model state what specific attributes the model has been proven to be able to predict, over what time period, within what margin of error?

    How has it become reasonable to implement government policy based upon models where this information is not known. How is it reasonable to rely upon a GCM’s to predict future conditions within a margin or error over the long term when the same model can not accurately predict the same criteria over the near term?

    The method of building the model is not important to users, accurate outputs are important.

  28. The opposite view to this is that climate is a very damped system that mostly responds to its forcing with other non-equilibrium variations damping out quickly. This seems to be what the data and models tell us is a better paradigm.

    • Chief Hydrologist

      Jim,

      I respectfully submit that you are totally clueless.

      ‘Most of the studies and debates on potential climate change have focused on the ongoing buildup of industrial greenhouse gases in the atmosphere and a gradual increase in global temperatures. But recent and rapidly advancing evidence demonstrates that Earth’s climate repeatedly has shifted dramatically and in time spans as short as a decade. And abrupt climate change may be more likely in the future.’ http://www.whoi.edu/page.do?pid=12455

      ‘Researchers first became intrigued by abrupt climate change when they discovered striking evidence of large, abrupt, and widespread changes preserved in paleoclimatic archives. Interpretation of such proxy records of climate—for example, using tree rings to judge occurrence of droughts or gas bubbles in ice cores to study the atmosphere at the time the bubbles were trapped—is a well-established science that has grown much in recent years. This chapter summarizes techniques for studying paleoclimate and highlights research results. The chapter concludes with examples of modern climate change and techniques for observing it. Modern climate records include abrupt changes that are smaller and briefer than in paleoclimate records but show that abrupt climate change is not restricted to the distant past.’ http://www.nap.edu/openbook.php?record_id=10136&page=R1

      Although I do think there is cause to constrian the growth in carbon emissions – that argument has been lost because of fools with one-dimensional brains.

      Robert I Ellison
      Chief Hydrologist

      • You can refer to wild oscillations that we haven’t seen in the last millennium, with instead subtle solar signals being reflected in surface temperature observations. Where is the chaos you speak of? Is it the two tenths of a degree PDO that concerns you so much? This is not to say there are no tipping points, but those are not spontaneous and will come from forcing changes.

      • Chief Hydrologist

        I don’t know Jim – why don’t you try reading the information at the Woods Hole Oceanographic Institute and the National Academy of Sciences before being a complete dunderhead.

      • You are going to have to explain why abrupt climate change negates the possibility of gradual climate change. I am missing this particular point or its relevance to what is happening now which is very gradual and predictable based on forcing changes occurring now.

      • Chief Hydrologist

        No Jim you re going to have to read Chapter 2 of the NAP document at least – have a look at this – http://isccp.giss.nasa.gov/zFD/an9090_SWup_toa.gif – and then explain how anything is gradual and predictable.

      • The biggest signal there is Pinatubo, and we know how transient those effects were. If the forcing goes up by 5 W/m2 in this century, do you not expect to see a detectable effect given that the LIA forcing was only -0.5 W/m2 and that was detectable as a half degree cooling?

      • The chief is conflating chaos with extreme events, what the chief likes to refer to as “dragon-kings” which is a term coined by Didier Sornette to describe Taleb’s Black Swans in a more quantitative fasjion. I have Sornette’s book on critical phenomena, and he spends more time on characterizing statistical disorder than modeling chaos, that’s for certain.

      • Chief Hydrologist

        ‘We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of self-organization that are not apparent otherwise from the distribution of their smaller siblings. We present a generic phase diagram to explain the generation of dragon-kings and document their presence in six different examples (distribution of city sizes, distribution of acoustic emissions associated with material failure, distribution of velocity increments in hydrodynamic turbulence, distribution of financial drawdowns, distribution of the energies of epileptic seizures in humans and in model animals, distribution of the earthquake energies). We emphasize the importance of understanding dragon-kings as being often associated with a neighborhood of what can be called equivalently a phase transition, a bifurcation, a catastrophe (in the sense of Rene Thom), or a tipping point. The presence of a phase transition is crucial to learn how to diagnose in advance the symptoms associated with a coming dragon-king. Several examples of predictions using the derived log-periodic power law method are discussed, including material failure predictions and the forecasts of the end of financial bubbles.’ http://arxiv.org/abs/0907.4290

        Black swans are something different – an unanticiapted occurence (the discovery of black swans) rather than an extreme event associated with a chaotic bifurcation.

        Here is a couple of other references.

        http://arxiv.org/pdf/1007.1376v4.pdf

        http://www.pnas.org/content/105/38/14308

        Neither of you get that chaos (or complexity) theory is a theory of emergent behaviour in complex and dynamic system rather rather than simply indicating a state of disorder of some sort.

      • Some of you lot are really insolent, Bob Ellison is a known as a noble man where I live, and deserves due respect.

        He knows more than the lot of us put together, about oceans.

      • Pinatubo is merely the largest volcano to blow during the highly instrumented era. It was by no means the biggest.

      • Markus – while I’m sure Chief is deserving of respect, he’s been insulting people a lot and I for one wish he’d stop. I wish WHT would stop insulting people. Both these guys have a lot to add to the debate. I tend not to complain about insults from people who don’t seem to add much to the debate (might apply to me but I try to keep away from insults).

        Anyway regarding the threads of the past few days and with particular respect to Fred Moolten, Pekka Pirila, Max Manacker, WHT and Chief, I do think there is valuable information being exchanged however heated the rhetoric – to wit:

        1) Disagreement about the solar forcing. As I said before I know nothing about this, having not looked into it. Fred says it increased since the LIA and peaked mid 20th century and is now declining. Max and (I believe) Chief also disagree, claiming strong recent solar forcing. I believe this has something to do with spectral differences vs. TSI and other things I can only guess at. While I suspect the differences could be discussed in more detail, I will hazard a guess that the simultaneous uncertainty about aerosol forcings will render this issue hard to make progress on.

        2) The argument between WHT and Chief, regarding whether maximum entropy-type methods can be used to characterize chaotic systems, strikes me as useful.

        3) On the previous thread, Girma brought up the 2005 Knight et al paper with Michael Mann as a coauthor, which used models to calibrate and simulate a prediction of the Atlantic Multidecadal Oscillation (AMO – I always thought the M was Meridional, but I guess that doesn’t make physical sense) and thermohaline circulation (THC). In response to Max’s commentary about that on the previous thread, I read the paper and think the following apply:
        a) The AMO can cause the global temperature anomaly to fluctuate by about 0.1 degrees.
        b) It’s been in a positive phase recently contributing possibly 0.1 C to the 0.6 C late 20th-century warming (yay, TCR down, was this in Gillette)
        c) The (negative?) phase of the AMO in coming decades will have a cooling effect superimposed on other trends – lowering any AGW warming trend.
        d) If c) is combined with an AGW-induced weakening of THC, the slowdown may be greater.

        The conclusions of the Kinght/Mann et al paper seem to be headed in the other direction from the Santer et al paper and its 17-year threshold. We haven’t even mentioned the PDO, and if ocean oscillations and solar forcings (and aerosol forcings?) remain on the cooling end of things, it seems possible that a long flat temperature trend could result, even in the face of significant CO2 forcing. (And I still think positive feedbacks are overestimated).

        More civil discussion would be welcome.

      • Bill c – fair summation. What I would point out is I believe all of those factors have been included in the Smith et al prediction of continuing temperature rise through 2014, which looks to be in fairly good shape since ground zero, the place to which the skeptic team immediately skates for refreshment, for the flattening is HadCrutchIII, which is a dead series.

      • JCH – Link or citation? I’ve only recently started keeping a list. Thx.

      • I don’t think Smith et al is available online.

        There is a discussion of it here.

        James Annan recently posted an article in which he expressed a belief the Smith prediction may be in trouble, but shortly after that he posted about HadCrutIV, the death of HadCrutchIII. So I don’t know what he would say now.

        I found this update the other day when somebody was implying the cowards had not updated.

        The other relevant paper, if you don’t already have it, is Keenlyside et al.

      • Bill c, also, I must besiege you with my graph updating the Tsonis-Swanson climate shift! The lavender trend is my primitive “cowboy” attempt at predicting the future trend. I don’t doubt there can be climate shifts, I just sort of doubt one happened just in time to pull our butts out of a very unpopular political fire.

        You are an excellent addition to comment section.

      • JCH – thanks for the compliment. I have got compliments from Joshua, Fred and yourself. I even got an “I agree” from WHT. Must resolve in the future to be much meaner.

        I can probably get to the Smith paper.

        As far as the TS climate shift, all I can say is it’s probably weaker than the authors would like, b/c such is the nature of provocative studies. It certainly can’t be true (?) that the shift alone, and solar and cloud forcing alone, and both together, are all responsible for saving our butts.

        Nevertheless I will make you a counter prediction – that the apparent rate of warming as measured by the “major indices”, will continue to be less than the 1980-2000 (ish) rate of 0.15C/decade.

        Until 2020 at least.

      • billc –

        I look to your comments on the debate to get the best handle on an unbiased perspective – the scientific aspects of the debate in particular because in those areas I am completely reliant on parsing the opinions of others.

        Of all the commenters here, you seem to me to be the most inclined to question and reason as opposed to bang a drum.

      • JCH & Bill,

        Smith et al. 2007 is available here. I don’t think the Smith et al. prediction should be viewed in terms of right/wrong, hit/miss. As the update points out, these kinds of decadal predictions are experimental. The point at the moment is to determine to what extent they can be useful.

        It could turn out that the prediction is pretty much correct but for different reasons than Smith et al. were suggesting. It could turn out that their prediction misses the target but for reasons that couldn’t be foreseen. One example is given in the original paper where they state that all bets are off if there is a Pinatubo-type eruption. Something they didn’t mention is the possibility of an extreme solar minimum, such as the one we recently experienced. Looking at their Figure 4 it appears their forecast included rising TSI from a minimum around 2008, to a maximum in 2012. In reality the minimum was deeper than expected and lasted for nearly two years longer.

        Of course this illustrates a problem with the idea of decadal predictions in general. Without the ability to predict what’s going to happen with the Sun or explosive volcanic activity to any satisfactory degree decadal temperature predictions can only ever be prefaced with a collection of if statements: ‘if nothing weird happens with the Sun.’ ‘If there are no Pinatubo-type eruptions’. The trouble is it doesn’t appear that these two potential factors carry probabilities small enough to ignore.

      • Paul S – I certainly agree that model predictions cannot anticipate and have to be adjusted for what in the context of climate modeling are random, exogenous perturbations. Likewise if we have an inability to predict TSI, which is a separate system, later corrections to that must be reapplied to the climate models to correct them.

      • billc: We haven’t even mentioned the PDO, and if ocean oscillations and solar forcings (and aerosol forcings?) remain on the cooling end of things, it seems possible that a long flat temperature trend could result, even in the face of significant CO2 forcing.

        Concise modest summary of a few lines of research. Good post.

        If solar forcing has been underestimated up til now, and if the solar output continues to decline, we could be in for even worse than you describe. And if the effect of increased CO2 is to increase the rate of surface warming and transport of water to the upper troposphere and other cloud forming mechanisms, leading to increased afternoon cloud cover in places/times like the summer tropics and summer American midwest, the cooling could be even more intense.

        “The terrible ifs accumulate.”

        “[The case is so uncertain that it is absolutely urgent that we act now to avoid the end of civilization]” — that’s a modest paraphrase of some urgent calls to action. Unfortunately, we can’t tell whether we should urgently act to avoid future warming, or whether we should urgently act to avoid future cooling.

      • billc: I certainly agree that model predictions cannot anticipate and have to be adjusted

        I agree.

        As the future unfolds, each model will have to be rerun in light of observed events like volcanic eruptions, better or updated measures of aerosols, changing insolation, and so on. I think the upcoming 2 decades will provide a stringent weeding out of inadequate models, but each model should not be judged solely on what it has predicted now, but on the full series of recalculated predictions conditional (or contingent) on the observed sequence of changed forcings. From the model testing point of view, recomputing the predictions is necessary, and it should be clearly distinguished from (1) re-estimating the parameters and (2) (ad hoc) adjustments to the models.

      • markus: Bob Ellison is a known as a noble man where I live, and deserves due respect.

        I have no quarrel with that. Bob Ellison should be respected.

        However, this is a forum for discussion, and some of his posts deserve derision and disgust. This forum is about expressions of ideas and, sometimes, links to evidence. Nobody’s intrinsic human worth, accumulated experience, or many scholarly degrees counts for anything except as it leads to debatable and (hopefully) decidable propositions.

        Except, of course, for our host Dr. Curry who daily deserves our gratitude for introducing us to new papers, and permitting us to read and post comments.

        Like Bob Ellison, I am a noble man where I live, and I deserve due respect. My comments, by contrast, are fair game for anyone.

      • Matt – “From the model testing point of view, recomputing the predictions is necessary, and it should be clearly distinguished from (1) re-estimating the parameters and (2) (ad hoc) adjustments to the models.”

        Absolutely.

      • JCH: I found this update the other day when somebody was implying the cowards had not updated.

        Thanks for the link. I downloaded the pdf.

  29. re•duc•tion•ism
    noun
    1. The practice of analyzing and describing a complex phenomenon, esp. a mental, social, or biological phenomenon, in terms of phenomena that are held to represent a simpler or more fundamental level, esp. when this is said to provide a sufficient explanation

    Reductionism can either mean (a) an approach to understanding the nature of complex things by reducing them to the interactions of their parts, or to simpler or more fundamental things or (b) a philosophical position that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents

    [Wiki]

    In the case of climatology, would this include:

    – fixation on human GHGs, specifically CO2, to “provide a sufficient explanation” of our planet’s climate?
    – kidding ourselves into thinking we can meaningfully model our climate by successfully ”reducing it to the interactions of its parts”?
    – fooling ourselves even further into believing that we can actually predict our future climate 100 years ahead with the tiny bit of knowledge that we actually have?

    If that is the case, I’d say we need to move away from reductionism.

    A further thing we need to move away from IMO (which has been noted on other threads) is the IPCC “consensus” process, which exacerbates the problem by blocking out dissenting views and scientific findings that do not support the IPCC paradigm that most of the recent warming has been caused by human GHG emissions and that this represents a serious threat.

    Max

    • ” (a)an approach to understanding the nature of complex things by reducing them to the interactions of their parts, or to simpler or more fundamental things or.”

      Arrhenius practiced it, and got that part wrong. Because he didn’t get this part right.

      (b) a philosophical position that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents.

      Why would a God, give man a greenhouse, when he needed refrigerator for protection from the enhancement of the Suns rays?

  30. Each culture, and each generation within each culture, continues to try and resolve the problems associated with living in an indeterminate universe.

    Some can accept this fact and happily say “I don’t know”, while others continue to cast yarrow sticks, read entrails or create complex models that fail time and again to “predict” the future.

  31. Everyone should be permitted to dream.

    However, noticing something about networks as in the following:

    “By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, it led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour.”

    is not the way scientists dream. Scientists dream about network systems by explaining that they have used a network system to successfully explain and predict some interesting phenomena in nature. Their dream is about the future applications that this success might bring in its train. Science always begins and ends with explanation and prediction as the goal. Once someone has shown that a network system can do what well confirmed physical theories have always done, explain and predict, then I will be interested in the system and the theorist’s dreams. But if there is no explanation and prediction then there is no science. Theorists of network systems must begin with explanation and prediction even in their dreams.

    • Like this Theo?

      The troposphere is the condenser, the tropopause is the separation device and the stratosphere is the fridge cabinet of outgoing heat, cooling incoming rays, as they warm to the gravitational pressure of the atmosphere, after preceding through the thermostat of the mesopause, and then onto the thermostat of the tropopause, before again heating closer as pressure increases at the Earths surface, until thermodynamics of the enhanced potential energy completes the system back to the separation device of the troposphere.

      I predict no warming by greenhouse, but certainty of cooling by refridgeration.

  32. In biology we call them emergent properties.

    There’s a group in Germany that explores climate data. A recent thesis from that group includes network exploration:

    Bergner, A. (2011). Synchronization in complex systems with multiple time scales.

    http://opus.kobv.de/ubp/volltexte/2011/5340/pdf/bergner_diss.pdf

    • Paul Vaughan: Synchronization in complex systems with multiple time scales.

      That topic has been studied a lot in neurophysiology. You can get a lot of titles from the proceedings of the SIAM conferences on applications of dynamical systems.

  33. People like trenberth, hansen did not know thermodynamics and radiations mess things up that bring chaos to climatology and harmed integrity of sciences.

  34. I don’t see any complexity in finding hole in AGW.

    a) Global Mean temperature (GMT) => http://bit.ly/zISeEo
    For the period from 1880 to 1940, GMT increased by about 0.35.
    For the period from 1940 to 2000, GMT increased by about nearly the same 0.35.

    b) Human CO2 emission => http://bit.ly/wD1SZj
    For the period from 1880 to 1940, CO2 emission increased by about 150 G-ton.
    For the period from 1940 to 2000, CO2 emission increased by about 840 G-ton.

    How come the increase in CO2 emission by 460% has not caused any change in the GMT?

    • “How come the increase in CO2 emission by 460% has not caused any change in the GMT?”

      A. Because there is no greenhouse.

      Score: 100%

      • markus

        There may “be a greenhouse”.

        But there is no empirical evidence that it is a major factor.

        Max

      • How is it a greenhouse when its hotter on the outside?

      • Moreover, how does physics , model greenhouses, when its hotter on the outside, or, do we not consider the mesosphere?

        Do we really consider the mesosphere separate from the climatic systems of Earth?

        As Pauline Hanson would say, Please Explain?

  35. Judith,

    I think the idea of a network theory would give us the better knowledge base.
    Every individual thinks differently and may see insights that the author/discoverer may not have known or understood.
    I have had to cover many fields which were very much limited by parameters that enclosed that field from expanding.
    Many areas of science have errors generated from being enclosed or from short sighted scientists who NEVER want their areas of study to change.

    The drawback is everyone wants to be acknowledged or first to come up with insight. This is very hard with so many fields of study involved to actually work together and not fight each other.

  36. Tomas Milanovic

    Judith

    Fully agree with the the diagnostic of inadequacy of reductionism when we face highly non linear, possibly non ergodic out of equilibrium systems.
    I partly disagree with the statement of Barabasi that establishes a (fundamental ?) difference between non linear dynamics what many call now “chaos theory” and “network theory”.
    Even if I already partly did it on some previous threads, I would like to illustrate the reductionism inadequacy for those of readers who are not necessarily familiar with the technical, mathematical apparatus of chaos.

    – The Feigenbaum constant.
    It has been proven that the transition to chaos by period doubling is governed by the Feigenbaum constant.
    This constant is independent of the precise (reduced) mechanism of the process being considered – actually one can mathematically prove that it only depends on the presence of a quadratic extremum which may appear in many very different processes.
    This is an example of “order” in “chaos” which couldn’t be found by any reductionist method.
    So there is an infinity of very different and chaotic non linear systems but they will all transit to chaos with the same Feigenbaum constant if they do so by period doubling.

    – The topology of attractors
    The attractors are invariant subsets of the phase space (space of dynamical states) where the chaotic systems live. Their dimension is vastly inferior to the dimension of the phase space itself. Their topology e.g dimension, form and boundaries (fractal or not) depends on the coupling between the dynamical variables.
    A reductionist approach typically neglects couplings (or considers that the system is linear) and is therefore fully unable to describe or even discover the attractors and their topology. In practice it means that a reductionist approach of a chaotic system would let the system live in states which are in reality forbidden because they are not on the attractor.

    – Coupled map lattices

    This paper finds a major and beautiful result for a specific case of spatio temporal chaos (http://amath.colorado.edu/faculty/juanga/Papers/PhysicaD.pdf).
    Technically it could be called indiferently “network theory” or “chaos theory” what shows that the Barabasi’s distinction is largely artificial.
    The paper considers a lattice of coupled oscillators and shows that the transition to coherent behaviour depends on the product of a parameter depending only on the uncoupled dynamics of each oscillator (this is what the reductionist approach would exclusively consider) AND a parameter depending on the network structure.
    This kind of systems cannot be studied by neglecting the whole or considering that all of the “whole” is contained in the properties of its elements.
    In other words the reductionism utterly fails on this system and can’t explain an apparition of synchronisation.
    This paper needs a good level of mathematical training and I would like to point out for the too fast readers that the authors show that the ergodicity hypothesis results in an incoherent state of the system.

    The same type of problem is studied in http://matisse.ucsd.edu/~hwa/pub/ks2d.pdf.
    This rather technical paper deals with spatio-temporal chaos via interaction between small scales and large scales. It is precisely because of this interaction that turbulence is still not understood and it is arguably one of the top most difficult unsolved problems in physics.
    It is this scale interaction/coupling which clearly shows that reductionism doesn’t work on this kind of complex chaotic systems.

    Also, among others, Chief Hydrologist is right when he keeps repeating that this kind of complexity exhibits qualitatively very different behaviours for some critical values of couplings.
    Some could compare that to phase changes what is a rather fitting analogy. Somebody on the thread mentionned “damping” stating that “damping” was some magics which prevents chaotic systems to be chaotic.
    This is obviously very uninformed because “damping” (or energy dissipation) is precisely a necessary condition to have chaos.
    So “damping” has nothing to do with the problem of predictability.

    On a more anecdotical scale Webhub wrote :

    I can actually believe that all that “chaos” map to random functions which leads to a straightforward transfer function.

    There is a math research area called Random Matrix Theory, whereby large matrices with arbitrary elements reduce to eigenvalue solutions that have a distribution corresponding to semi-circle PDF. The issue is explaining why the solutions are predictable independent of the input. Terence Tau is currently working on this subject

    First it is Terry Tao. Btw he wrote a marvelous paper about why Navier Stokes is so difficult. A must read.
    Second believing that “chaos” equals “randomness” shows a, mostly subconscious, postulate of ergodicity. One cannot stress enough that ergodicity is not a given!
    And if a system is not ergodic (there are enough examples which show that many are not) then there is no invariant pdf in the phase space.
    It is not because we are used to popular examples of chaotic systems which are ergodic (f.ex Lorenz chaos, rigid spheres e.g statistical thermodynamics etc) that ALL chaotic systems are necessarily ergodic.

    • Tomas,

      Mathematical training…like averaging?
      Turning a planet into a cylinder and ignoring any and all outside factors?

    • Second believing that “chaos” equals “randomness” shows a, mostly subconscious, postulate of ergodicity. One cannot stress enough that ergodicity is not a given!

      Fine. So you will stall in your progress, but I will keep moving on, and so will all the other applied mathematicians, physicists, and engineers who take a pragmatic view of things and embrace stochastic methods as a way to reduce complexity.

      As they say, it’s your loss :)

      • Is it really sensible to define a “pragmatic view” as one that cordially invites paradoxical misinterpretation?

      • Tomas Milanovic

        Well who says that I should stall?
        However as I know this subject I prefer to ask myself whether there are reasons for ergodicity instead of postulating there is and racing on a false trail.
        This makes the difference between informed and uninformed opinion.
        In the meantime serious scientists (like those in the quoted papers) ask the right questions and bring some answers. They are of course only partial answers but I always prefer partial and right to complete but wrong.
        In my estimation it will take about 50 years minimum to get a correct theory of the climate and this is absolutely not equivalent to say that we will be able to predict the climate in 50 years.

        Sometimes I am under the impression that people talking about “stochastic methods” in chaotic systems have no clue what they are talking about, or to express it more diplomatically, would benefit of some additional study of ergodic properties of dynamical systems.

      • Tomas –

        “In my estimation it will take about 50 years minimum to get a correct theory of the climate and this is absolutely not equivalent to say that we will be able to predict the climate in 50 years.”

        You’re way ahead of me on the math, but that’s one of the most sensible things I’ve seen written on climate.

        Whizzbang, and +10!

      • ceteris non paribus


        In my estimation it will take about 50 years minimum to get a correct theory of the climate…

        50 years minimum?

        Do I have any takers at 1,137 years + / – 102?

        Sometimes I am under the impression that people talking about “theories of climate” have no clue what they are talking about, or to express it more diplomatically, would benefit from some additional study.

      • ceteris non paribus


        You’re way ahead of me on the math, but that’s one of the most sensible things I’ve seen written on climate.
        Whizzbang, and +10!

        Shorter:
        I have no idea whether or not you are correct – but I like the warm feeling I get from your words!

    • “In particular, while the time series of the state of any one of the systems may appear chaotic, on averaging, the temporally chaotic variations cancel, and a coherent periodic oscillation of the globally averaged state is revealed.”

      http://amath.colorado.edu/faculty/juanga/Papers/PhysicaD.pdf

      They’re not talking about time-averaging. Now if we could just get everyone thinking about hydrology in absolutes (since hydrology is not a function of anomalies), we might be able to synchronize rediscovery of day & year dominance. A subset of the terrestrial climate problem may be cycloperiodic semi-annual phase variance as an alternative to frequency-splitting as a means of driving amplitude cycles. Such patterns are undetectable in observational data via conventional unwindowed FFT, but they’re easily detected with variable-grain-&-extent wavelets.

  37. Chief Hydrologist | January 26, 2012 at 3:53 am | ( the Reply option seems to have ended up there )

    . . . chaos (or complexity) theory is a theory of emergent behaviour in complex and dynamic system rather than simply indicating a state of disorder of some sort.

    [ I removed one 'rather' ]

    I think the statement needs modifiers before ‘complex and dynamic system’ and instead should read ‘some non-linear complex and dynamic system’. And, additionally, ‘complex’, not being well defined, introduces some fuzziness. The original Lorenz system of three simple and non-linear ODEs with constant parameters would not be considered complex, in my opinion.

    Complexity, whatever that is, and non-linearity neither separately nor combined as descriptors of a system ensure chaotic response. Non-linearity is necessary, but not at all sufficient: the original Lorenz system does not exhibit chaotic response for all values of the parameters. I think ‘complexity’ originally referred to the calculated complex chaotic response, not to the simple system of ODEs.

    I guess complexity can be estimated in at least two different ways: (1) by the number of important interactions between physical phenomena and processes, and (2) by the number of important physical phenomena for a single important process. A whole bunch of simple and well-understood interactions can lead to some sense of complexity. And some single phenomena are also complex in some sense: these usually involve multi-scale and/or multi-phase phenomena. Not all physical phenomena and processes are important relative to some system response functions.

    Note that many systems characterized by either, or both, of (1) and (2), and non-linearity, do not exhibit chaotic response.

    • Dan, I can think of a 3), the relative magnitudes of important phenomena. Many non-linear dynamic systems “appear” chaotic when assumed negligible functions become significant relative to a more dominate function. Rounding error or precision for example.

      Murphy’s law of controls – the more precise the desire the more unstable the performance.

    • I have never understood including chaos as part of complexity theory. Unless it is just because chaotic oscillations look complex. The logistic equation is arguably the world’s simplest nonlinear equation, but it is chaotic for most values of it’s one constant above 3.52 (if I remember correctly).

      I see nothing emergent about chaos, but then I do not understand that concept. Never have. Is it mathematical, epistemic or psychological?

      • David Wojick: I see nothing emergent about chaos, but then I do not understand that concept. Never have. Is it mathematical, epistemic or psychological?

        There is in fact not a single all-encompassing precise definition, but a lot of “characteristics” that emerge in the study of non-linear dynamic systems. For example, there are systems of equations whose solutions are perfectly periodic, but for which the periods change non-continuously across a boundary in the parameter space. There are dynamical systems where a particular limit of the “transfer matrix” (in linear systems, there is no need to put the phrase “transfer matrix” in quotes) has large eigenvalues of opposite signs, so that the solution produces oscillations that, over short interval, look explosive (this produces the “sensitve dependence on initial conditions) so that these models can reproduce the statistical characteristics of turbulent flow. There are dynamical systems whose trajectories (that is, the solutions of the differential equations) stay within a small subset of the state space, but never repeat, so they are not periodic, but sort of almost periodic (these are the “strange attractors”, also the “topology” that Chief Hydrologist has written about; the dimension of the subspace within which the solutions all lie may not even be integral.) They only thing that they have in common is that they produce trajectories that look random, yet are generated by a deterministic system. Personally, I think we’d be better off had no one thought to name them “chaos”, but it’s just a name for a large collection of stuff that can be demonstrated with computed solutions to nonlinear differential equations, and that have applications in laboratory and other science: chemical oscillations, oscillations of neural networks, heartbeat, and so on.

        That’s my view now. If I come across a good definition of chaos that includes all the characteristics, I’ll pass it along. Meanwhile, I agree that there is nothing “emergent” about chaos. It’s just that you can’t solve the equations analytically, so the understanding emerges from studying lots of computed solutions — that is, graphs.

  38. http://www.pnas.org/content/97/1/28.full

    could be useful. In fact, I don’t see discussion of Laughlin anywhere in the climate debate, even as what he says is enormously relevant.

    or, what about this?

    http://www.sciencemag.org/content/334/6062/1512.abstract

    Though, I think reading through the second one would probably result in several ‘head asplosions’ in the reductionist climate community, willard the blogger, and others.

    • from the first link:

      “But the schemes for approximating are not first-principles deductions but are rather art [sic] (are?) keyed to experiment, and thus tend to be the least reliable precisely when reliability is most needed, i.e., when experimental information is scarce, the physical behavior has no precedent, and the key questions have not yet been identified.”

      I like.

  39. Two observations:

    –Cornell Creative Machines Lab has constructed, and made freely available, a kind of meta-model package, “Eureqa”, which purports to build its patterns and rules and equations from the raw data, no prompting required. Maybe this is the way it will have to go.

    — IRTWT, and the article at the end actually pleads with physicists not to turn up their noses at a derivative field and then miss out on all the goodies that get showered on those who claim it! Almost funny …

    • However, raw data can only generate statistical laws. Scientific explanations require new concepts, typically hidden variable mechanisms with invisible things like atoms, molecules, photons, etc.

      • Have a closer look. Given observations on a jointed pendulum, Eureqa generated Newton’s Laws of Motion.

        Relationships between events and the boundary conditions are real in themselves. Even QM is mostly fitted observation descriptions.

    • Thanks for the link to Eureqa. That is the most amazingly simple, yet useful, pieces of software that I have seen in years. I consider it a de-complexifer because it can find more concise solutions than what you may have in mind. And a simpler solution with an equally good fit is often the most parsimonious explanation.

  40. The Earth’s climate over the eons has maintained some very different, roughly quasi-equilibrium states for very long time scales. Where are the empirical data, or continuous equation mathematical models, that conclusively demonstrate that evolution between these states was in fact the outcome of chaotic climate and not the completely deterministic response of the systems?

    Or put a different way, is the focus of chaos and climate solely the result of the presently rough status of climate models and calculations with them?

    • According to the current definition, chaos is deterministic. That doesn’t mean it is easy to solve, just that given enough information, you should be able to solve the trajectory of the system.

      The converse to that is statistical or stochastic.
      What separates the two is in the eye of the beholder. A chamber full of heated gas is not considered chaos in action, but it is a good example of statistical physics. But if one adds materials with certain properties, it can become chaotic.

      If one knows when to transition, you can save lots of time doing analysis.
      YMMV.

      • Chaos is completely deterministic. It is a property of a class of nonlinear equations, originally discovered by Poincare around 1910. But due to extreme sensitivity to initial conditions one cannot solve the trajectory of a specific case without an infinite amount of information. This is because infinitesimal differences produce different trajectories.

      • DW;
        Exactly. As I said elsewhere, Lorenz demonstrated that you NEVER get to round your numbers for initial conditions, much less truncate, if you want deterministic solutions. So infinite accuracy and precision are necessary once some complexity threshold is reached. Climate certainly is past that point.

  41. Effectively, reductionism is gone from science and it is still maintained by a small group of people as particle physicists (not all).

    However, I am sceptic about network science. I have a copy of Linked, the book, and I was disappointed because I did not find anything really new and fundamental that I did not know before from traditional branches of science.

    For instance, graph theory is rather well-known in chemistry and yes it gives some interesting applications, but it is not giving a new and revolutionary paradigm about our way to study chemical systems.

    I am rather surprised when the SIR model of epidemiology is sometimes considered an important advance done by network theory, when it was developed over a chemical kinetic basis, as Lokta-Volterra and other models.

    In my opinion, the reason which complexity science has advanced very little are two: (i) it is complex! and (ii) many people has tried to study complexity, from an incorrect perspective, without the adequate tools.

    As brilliantly stated by Jean Marie Lehn, complexity is given by the MI2 paradigm

    MI2 = Multiplicity Interaction Integration

    It seems that some some people has recently discovered the importance of links between nodes when studying the whole.

    Well, chemistry has recognized the importance of links (bonds) between nodes (atoms) since ancient times. Maybe by this reason network theory has very little impact in this field.

    • Juan Ramón González (@juanrga) | January 26, 2012 at 3:09 pm | wrote:

      “[...] graph theory is rather well-known in chemistry and yes it gives some interesting applications, but it is not giving a new and revolutionary paradigm about our way to study chemical systems.

      I am rather surprised when the SIR model of epidemiology is sometimes considered an important advance done by network theory [...]

      [...] chemistry has recognized the importance of links (bonds) between nodes (atoms) since ancient times. Maybe by this reason network theory has very little impact in this field.”

      Thank you for sharing cross-disciplinary perspective. Recombination creates the diversity (& hence bet-hedging) needed for survival. We’re collectively not even remotely near exhausting the potential of cross-disciplinary awareness-recombination.


      Juan Ramón González (@juanrga) | January 26, 2012 at 3:09 pm | wrote:

      “[...] many people has tried to study complexity, from an incorrect perspective, without the adequate tools.”

      Agree.

      I can suggest for them careful study of Figure 6 on p.12 as a starting point for improved conception:

      Lilly, J.M.; & Olhede, S.C. (2009). Higher-order properties of analytic wavelets. IEEE Transactions on Signal Processing 57(1), 146-160.

      http://www.jmlilly.net/papers/lilly09-itsp-cp.pdf

  42. Chief Hydrologist

    Hi Everybody,

    Bob Ellison was my dad. I appreciate the vote of confidence but styling myself after Cecil (he spent four years in clown school – I’ll thank you not to refer to Princeton like that) Terwilliger – the noble boat has sailed without me. At this tide in the affairs of men I will be as rude as I care to because we have all missed the boat on rational environmental, social and economic progress.

    Complex and dynamic are necessary properties of deterministic chaotic system. Lorenz’s partial differential equations show the bifurcated solution topology of a deterministic chaotic system so they are by definition a complex and dynamic system. It is a functional classification rather than categorical.

    Atmospheric and oceanic simulations use the same form of PDE’s to represent fluid flow. So they too are members of the broad class of deterministic chaotic systems. As James McWilliams says – this raises certain expectations about the behaviour of climate models. Irreducible imprecision as a result of sensitive dependence on initial conditions and model structural instability. Small differences in input variables (within the measurement error for atmospheric variables) and non-unique choices for boundary conditions result in non-linear metrical or topological changes in the solution.

    Being an Australian hydrologist I spent decades happily searching for an explanation of what we call flood dominated and drought dominated regimes. Average rainfall is four to six times higher in flood dominated than in drought dominated regimes – and these regimes last for 20 to 40 years. A shift in the mid 1940’s to a flood dominated regime, a shift in the late 1970’s to a drought dominated regime and a shift back to a flood regime following 1998. It turned out to be related to changes in the frequency and intensity of ENSO events – changes in the volume and frequency of cold water upwelling in the north and south east Pacific. It took me decades? Doh!

    It seems related to solar UV intensity interacting with ozone above the polar vortices – something that influences pressure fields and therefore climate in both the north and south. Solar UV changes much more than TSI as the magnetosphere evolves – itself the result of deterministic chaotic interactions in a many body field.

    The problem of drought and flood dominated regimes in north eastern Australia tangentially involve global surface temperatures and biology. Upwelling cold water changes the ocean and atmosphere energy dynamic and brings nutrients to the surface causing booms and busts in biological activity. The latter provides another line of evidence for these regime shifts and the shifts are fundamental in certain biological climate feedbacks. There are well documented associated changes in wind, oceans currents, surface temperature and cloud – shifting the energy dynamic of the planet.

    So if I say I am anticipating flooding rains for north east Australia over the next decade or three as a result of quite ordinary chaotic climate shifts – there are implications for global temperature as well.

    If you are looking for evidence of contemporary chaotic spatio-temporal climate shifts – look at fisheries and hydrological regimes – and Claus Wolter’s multi-variate ENSO index that is about to be axed by NOAA – as well as the surface temperature record. Multiple lines of evidence.

    There seems much confusion about chaos theory. Like in climate models, it provides an expectation about certain behaviours. These include an increase in auto-correlation preceding abrupt and noisy bifurcation. Noisy bifurcation is more colourfully known as ‘dragon-kings’ and include the 1976/77 and 1998/2001 Pacific climate shifts – shifts that are exceedingly well documented in ocean dynamics, hydrology and biology. Do try to keep up. Or more politely – as Tomas might more politely put it – spatio-temporal chaos theory is the emergent paradigm in climate science.

    Robert I Ellison
    Chief Hydrologist

    • Chief said, “It seems related to solar UV intensity interacting with ozone above the polar vortices – something that influences pressure fields and therefore climate in both the north and south.”

      That is were I am stuck. Seems like a thermomagnetic or thermoelectric chemistry issue. The Antarctic data is pretty poor, but the MERRA energy budget attempt had what appeared to be geomagnetic flux induced instrumentation error or maybe the real deal. Interesting, but complicated. Quite possibly a red herring, but would make sense if CO2 was involved since the Antarctic CO2 concentration is so stable relative to the Arctic.

      • Chief Hydrologist

        Capt’n my Capt’n

        There you go getting stuck in reductionism again – truly a pervasive and powerful mindset.

        The climate system transcends traditional boundaries. Why would we need to say that – it is a truism? Perhaps in environmental science we are used to thinking in terms of problems being so big and multi-dimensional that the only sensible approach is to use the snyergistics of multi-disciplinary teams. A simple network of 5 to 7 nodes (people) in which concepts evolve – sometimes in startlingly new ways and with sublime results. The deterministic chaotic topology of scientific creativity in a network (team) environment – which is just a beautiful thing when it works.

        The idea starts off with ultraviolet interacting with ozone. Ozone warms and cools intensifying – or not – atmospheric dynamics in the polar vortices pushing – or not – storms into higher latitudes. Try – http://www.bbc.co.uk/news/science-environment-15199065 – but there are a couple of recent papers by Lockwood et al.

        The intensifying vortices send cold polar water in Ekmann spirals along the western coasts of North and South America where they reinforce or not the upwelling of frigid and nutrient rich bottom water. In the north – on a multi-decadal scale in the Pacific Decadal Oscillation. To the south on an inter-annular scale in the El Niño – Southern Oscillation. Different feedbacks and therefore different dynamics but it all emerges as one planetary scale phenomenon in the central Pacific. The rest as they say is climate history. So we have astrophysics merging into biology and back again. A chain of causality like the dragon Ouroborous eating it’s own tail.

        I identify with that worm – because sometimes it feels like I am chasing my own tail.

        Robert I Ellison
        Chief Hydrologist

      • Getting stuck in reductionism again? Possibly. What I was looking at was a way to determine what magnitude of impact the CO2 addition would have on conductivity, mainly in the polar regions. That is were I became stuck with a low sink temperature in the range of -89 to -95C, the tropopause and Antarctic minimums. The tropopause makes excursions to -90 to -95 on occasion. So I was just trying to figure out if this is a real limit imposed by some combination of magnetic, conductive or gravitational forces. If it is real, there are some interesting consequences.

        The Antarctic should benefit from the atmospheric effect after all, and a possible limit of the atmospheric effect is a entertaining notion. As I said real? dunno, but maybe worth pursuing at least for a short while.

        Not a solution by any means, just a step.

      • cap’n –

        Thought you might like this:

        Laypeople have long known that bacon can cure innumerable ailments: depression, unwanted thinness, tastelessness of lentil. And new research suggests that the cured meat has medical applications that have nothing to do with the heart and stomach. It seems that bacon — used in a very unusual way — is one of the best cures out there for a bloody nose.

        We know what you’re thinking: the cure must involve bacon fumes. Surely, the delectable smell of bacon sizzling its way to crispness in the frying pan must be so miraculous that it can dry up nasal hemorrhages as surely as it stops diets!

        Nope, unfortunately not. The real cure doesn’t even involve cooked bacon. Instead, to cure a nosebleed using bacon, you actually have to stick a piece of bacon up the bloody nostril. It turns out raw “cured salt pork” (read: basically bacon) is as effective a nasal tampon as we have. It works especially well for treating certain conditions that lead to chronic nosebleeds.

        http://www.huffingtonpost.com/2012/01/25/bacon-nosebleed_n_1231092.html

      • John Costigane

        Chief,

        Thanks for the BBC link dealing with solar UV and its suggested effect on jetstream position over the UK in winter, offering the possibility of alarmist free forecasting: superb.

      • Joshua, “It turns out raw “cured salt pork” (read: basically bacon) is as effective a nasal tampon as we have.”

        The Power of Bacon! I have a concoction, cornmeal, bacon and cheddar cheese, that promotes domestic tranquility. There is something Zen about bacon cheddar corn muffins.

        Unfortunately, bacon increases your risk of cancer by 33% +/-10% with constant exposure.

    • Chief Hydrologist: At this tide in the affairs of men I will be as rude as I care to because we have all missed the boat on rational environmental, social and economic progress.

      thanks for the warning. I’ll skip your junk from now on.

      • Now MattStat, Chief and Web both have things to offer. Just think of it as a dysfunctional family business or a Taiwanese government session :)

      • Chief Hydrologist

        Yeah – I will miss the depth of knowledge and sparkling intellect.

      • Capt. Dallas: Now MattStat, Chief and Web both have things to offer. Just think of it as a dysfunctional family business or a Taiwanese government session :)

        There is no point to reading 20 sentences that are stupid on purpose just to get to one that might be worth reading.

      • thanks for the warning. I’ll skip your junk from now on.

        Kudos.

        It’s a shame that chief allows his confusion between being a poet and writing colorful insults and/or political diatribes to detract from his contributions to the scientific debate.

        I don’t have an alternative to adding scientifically irrelevant comments. He does, and it’s a shame that he doesn’t stick to making scientifically useful contributions.

      • Mirror, Mirror, on the wall. Who’s the most scientifically useful of them all?
        ===================

    • Chief Hydrologist

      I have 2 long posts right here with nary an insult and barely a poetic turn (unless you count the worm Ourobous as a metaphor for causality on complex and not linear paths) – but treat serious issus consistent with the topic of the thread and with references to evidence in physical systems – rather than the purely mathematical or, God help us, the purely narrative.

      Joshua has an agenda – he thinks I should leave the politics and insults to him.

  43. Chief Hydrologist

    A hand is five,
    another is five.
    So what’s the answer,
    you add five plus five?
    ……a butterfly.

  44. bill c

    You state up-thread (January 26, 1012 at 9:22 am) that I am of the opinion that recent solar forcing has been strong.

    That is not exactly correct. Let me be a bit more specific.

    Reconstructions of solar irradiance (as a measure of solar activity) go back to the early 17th century.

    http://www1.ncdc.noaa.gov/pub/data/paleo/climate_forcing/solar_variability/lean2000_irradiance.txt

    These data show a rapid decrease during the early 17th century reaching a low, which lasted 30 years (Maunder Minimum) in the late 17th century. Around 1700 solar activity recovered sharply until the late 18th century when it again declined to a low point (Dalton Maximum). In the early 19th century it again increased sharply, leveling off and decreasing slightly starting in the mid 19th century. Since the end of the 19th century it rose rapidly, reaching its highest level of several thousand years by the late 20th century. Since then it has leveled off and started to decline. The steepest rate of increase was from around 1900 to around 1980.

    The Dalton, Maunder and earlier Spörer Minima all correlate well with periods of lower-than-average global temperature (Wiki). In fact, solar activity correlates well with global temperature over most of the record. This is all the more pertinent since the record goes back well before there were any significant GHG emissions.

    Another measure of solar activity is the Wolf Number, which measures the number of sunspots on the surface of the sun. This increased by almost 70% from Solar Cycles 10-14 (1858-1902) to Solar Cycles 19-23 (1955-2008).

    Several solar studies (which I cited earlier) have attributed around one-half of the observed past warming to the unusually high level of 20th century solar activity.

    Changes in direct solar irradiance alone are not large enough to have caused these temperature changes. While other mechanisms have been proposed, these have not been corroborated. The Svensmark et al. hypothesis of a cosmic ray / cloud connection has been tested successfully in a simple laboratory experiment. Recent larger-scale work under controlled conditions at CERN has validated the hypothesis of cosmic ray cloud nucleation in the presence of aerosols and additional work is ongoing to attempt to quantify this effect.

    This brings up your statement ”uncertainty about aerosol forcing will render this issue hard to make progress on”, which is all the more pertinent when considering the possible solar / cloud connection.

    So, in summary, I have concluded based on the studies out there that solar activity reached a high of several thousand years around 1980-1990 and has again begun declining since then.

    Max

  45. Yes, there is “much confusion about chaos theory.” I can see many people here saying that chaos is deterministic. Never heard about non-deterministic chaos folks? A well-known Nobel winner has a best-seller book about it…

    In non-deterministic chaos, systems are unpredictable even if you know the initial state with infinite precision.

    • Good point, The Earth’s Climate appears to be deterministically chaotic with two main attractors, glacial and interglacial. Land use and CO2 may shift the system to one main attractor, interglacial? Land use does appear to have changed the duration of extreme climate events. So climate may be shifted to non-deterministic, albeit, within a smaller probability cloud.

      • Capt.,

        We have such a magical planet that scientists do not include a single drop of water loss.
        Motion is just what they do to work but not included in planetary study.

        Just temperature data please! All other factors should be ignored.

  46. Tomas Milanovic

    To answer those who are asking for a definition of chaotic systems or even wonder if there is a definition.
    There is nothing fuzzy or vague about this – chaotic systems can be crisply and clearly defined with one phrase :
    Chaotic systems are those whose dynamics have at least one positive Lyapounov coefficient.

    What are the Lyapounov coefficients?
    Let us take a finite dimensional phase space, f.ex 3D like the well known Lorenz system.
    Imagine a very small ball in this space. As every point of the space uniquely defines the dynamical state of the system, the points in the ball represent a set of initial states which are very close to each other.
    Now look at what happens to the ball when the system evolves in time.
    If at some later time the ball is still a ball or even contracted itself then you deal with perfectly deterministic predictable dynamics, possibly going towards a single point in the phase space (equilibrium).
    But you can also observe that the ball transformed in an elipsoid.
    If you take the largest axis of the ellipsoid, then the ball expanded in that direction.
    Initially very similar states drifted to quite different states along this direction (in the phase space).
    The Lyapounov coefficients are a measure of how fast initially infinitely close states diverge from each other in time and the largest one defines the big axis of the ellipsoid.
    Everything else is then a corollary of this simple definition.

    The system is still deterministic because there are (not necessarily complex) equations that perfectly and uniquely define its dynamics.
    But it is no more predictable because if you start with 2 states infinitely near, they will follow completely different orbits and finish in completely different states. This is the fundamental property of a chaotic system. While the dynamical laws may be quite simple (like D.Hughes rightly says about the Lorenz system) the orbits become extremely complex.
    Arrived at this stage it becomes clear that there is nothing that allows to predict an orbit of the system regardless the accuracy of the knowledge of the initial conditions. A simple rounding (or computer accuracy) will have for consequence that the computed orbit will be as far from the real orbit as one wishes after a certain time.

    That’s why what is left is to study what happens to the orbit when it wanders through the phase space for a very long time – rigorously the time must be infinite.
    And by following the orbit for a long time there slowly appears a generally fractal invariant set called attractor which contains all dynamical states that are allowed for the system.
    Chaos theory is a set of tools and mathematical techniques that study the attractors of chaotic systems.
    Even though it still doesn’t allow to predict the future behaviour of the system because it is intrinsically unpredictable, it allows at least to predict the set of states which are allowed and which are forbidden.

    A step farther one can find attempts to find invariant probability distributions which would say what is the probability of the system to find itself in this or that region of the attractor.
    This sometimes works and sometimes doesn’t and depends critically on the existence or non existence of the ergodicity property of the system.

    When one talks about complexity, network theory or chaos theory then it relates to different techniques to explore the same thing – the topology and the properties of attractors.
    Of course I have constructed the above example with a finite low dimensional phase space where it is easy to “visualise” what’s happening and understand what chaos theory is actually about.
    The phase space of spatio-temporal chaos (e.g weather, climate, fluid dynamics etc) is an infinite dimensional Hilbert space where “points” are fields (functions) and the complexity of the topology of the attractors is increased n times.

    • Tomas, thanks very much for your illuminating comments on this thread

      • Tomas is an attractor in the chaos of climate discourse.
        ================

      • Chief Hydrologist

        Tomas,

        You are a beacon of clarity.

        Cheers

      • Chief;
        Indeed.
        But having just read some of the preceding comments, I had a strange dyslexic moment in which I read you calling Tomas a “bacon of clarity”. “Roger?” I thought …
        But no, just a light.
        ;)

    • Thomas Milanovic: There is nothing fuzzy or vague about this – chaotic systems can be crisply and clearly defined with one phrase :
      Chaotic systems are those whose dynamics have at least one positive Lyapounov coefficient.

      That is one potential definition, but in practice the term covers other cases.

      • Tomas Milanovic

        To be very accurate this is a necessary condition both in practice and in theory.
        It is also a sufficient condition in practice (because there is always energy dissipation) but in theory I would have to add that the allowable region of dynamical states must be bounded.
        I could of course give many other definitions but none would be shorter and clearer.

      • Thomas Milanovic: It is also a sufficient condition in practice (because there is always energy dissipation) but in theory I would have to add that the allowable region of dynamical states must be bounded.

        That clarifies why you did not require any negative eigenvalues (that is, you implicitly excluded explosive systems), whereas I wrote that there have to be at least one pair of opposite signs.

        However, I think that the word is used more sloppily than you would like.

    • “The phase space of spatio-temporal chaos (e.g weather, climate, fluid dynamics etc) is an infinite dimensional Hilbert space…”

      Precisely, those are examples of LPS (Large Poincaré systems), which are described outside a Hilbert space. The chaos in those systems is non-deterministic and irreducible to trajectory dynamics.

      The deterministic (unitary) laws of deterministic chaos only arise as approximation.

  47. If we truly believe climate is complex, then we will have to admit its future states are unpredictable. The boundaries of climate are easily established based on millennia of geological evidence, though all of this assumes the earth exists as a permanent feature of the universe.

    OTOH, can anyone point me to an experiment demonstrating increasing the CO2 content of a gas exposed to light has raised the temperature of anything?

    • A warmist recently jibed that the current fad amongst sceptics is to say that it’s all too, too, complex and there’s no hope of predicting or understanding anything. As opposed, he implied, to the much more constructive and positive approach of CO2 determinism.

      But he resisted the deterministic analysis process called “Follow the Money” which purports to parsimoniously explain warmist research and activism.

      ;)

  48. Championnat europe foot 2012

    Excellent recipe, i tried it recently and all my family loved it

  49. Reductionism, as a paradigm, is expired, and complexity, as a field, is tired. Data-based mathematical models of complex systems are offering a fresh perspective, rapidly developing into a new discipline: network science.

  50. Dr. Curry,
    You are getting some strange links and posts from “servicro-plumbing.com”. Be careful.

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