Climate repeats as fractals, say researchers

Posted: March 16, 2016 by oldbrew in climate, research
Frost fractals [image credit: Schnobby - Wikipedia]

Frost fractals [image credit: Schnobby – Wikipedia] has turned up some research with a new way of looking at natural climate variations here.

Climate variations analyzed 5 million years back in time
The key phrase is…

Even though we do not know the climate variations in detail so far back…

But details matter. The media release is below.


Climate variations analyzed 5 million years back in time

When we talk about climate change today, we have to look at what the climate was previously like in order to recognise the natural variations and to be able to distinguish them from the human-induced changes. Researchers from the Niels Bohr Institute have analysed the natural climate variations over the last 12,000 years, during which we have had a warm interglacial period and they have looked back 5 million years to see the major features of the Earth’s climate. The research shows that not only is the weather chaotic, but the Earth’s climate is chaotic and can be difficult to predict. The results are published in the scientific journal, Nature Communications.

The Earth’s climate system is characterised by complex interactions between the atmosphere, oceans, ice sheets, landmasses and the biosphere (parts of the world with plant and animal life). Astronomical factors also play a role in relation to the great changes like the shift between ice ages, which typically lasts about 100,000 years and interglacial periods, which typically last about 10-12,000 years.

Climate repeats as fractals

“You can look at the climate as fractals, that is, patterns or structures that repeat in smaller and smaller versions indefinitely. If you are talking about 100-year storms, are there then 100 years between them? – Or do you suddenly find that there are three such storms over a short timespan? If you are talking about very hot summers, do they happen every tenth year or every fifth year? How large are the normal variations? – We have now investigated this,” explains Peter Ditlevsen, Associate Professor of Climate Physics at the Niels Bohr Institute at the University of Copenhagen. The research was done in collaboration with Zhi-Gang Shao from South China University, Guangzhou in Kina.

The study concludes:
“In fact, we see that the ice age climate is what we call ‘multifractal’, which is a characteristic that you see in very chaotic systems, while the interglacial climate is ‘monofractal’. This means that the ratio between the extremes in the climate over different time periods behaves like the ratio between the more normal ratios of different timescales,” explains Peter Ditlevsen.

This new characteristic of the climate will make it easier for climate researchers to differentiate between natural and human-induced climate changes, because it can be expected that the human-induced climate changes will not behave in the same way as the natural fluctuations.

View full text original: Climate variations analyzed 5 million years back in time |

Paper: Contrasting scaling properties of interglacial and glacial climates — Zhi-Gang Shao & Peter D. Ditlevsen

  1. peterazlac says:

    An interesting paper until we get to the obligatory nod to AGW:

    “We have to go very far back into the geological history of the Earth to find a climate that is as warm as what we are heading towards.”

    This needs amending to pick any one of three options: the Phonetician Warm Period, the Roman Warm Period or the MWP!

  2. oldbrew says:

    ‘a climate that is as warm as what we are heading towards’

    They must be clairvoyants as well as climate researchers – or, they are selecting stock phrases from their ‘How to Survive in Climate Research’ guide book 😉

  3. One of the features of 1/f type noise is that it is fractal in nature – that is to say, if you look at a small section of the temperature, you can often see the same features as you see over e.g. 100 years. That is why e.g. I can be so certain that most of the changes we saw over the last 100 years are natural.

  4. Paul Vaughan says:

    We see the usual FALSE spatiotemporal assumptions built into the interpretations.

    Once again:
    Climate is NOT a time-only phenomenon.

    I read a ridiculous statement a few days ago. The suggestion was that since landmasses don’t move appreciably at human-life-timescale, land-sea distribution must be irrelevant to multidecadal climate.

    That’s fundamentally wrong.

    Each time-input has MANY possible aggregate outputs due to constraining geometry & flow topology. (It’s not 1:1; it’s many:1.)

    Thus the constraints are AGGREGATE constraints, which means you can’t predict temporal events events in deep ignorance of initial spatial form & flow (should be hardly surprising, but sketchy, shady characters (a dime a dozen in the climate discussion) pretend and project otherwise, arousing suspicion in the process…)

    People are simply NOT being sensible about this at ANY climate discussion venue (alarmist, skeptic, or whatever) that I’m aware of. I have to deliberately restrain the level of anger it causes me. When people appear so determined to be obtuse rather than realistic, of course it arouses suspicion …but could it be that people are just conceptualizing FUNDAMENTALLY WRONG (a case of ignorance)? I suppose it’s possible, but how could be people be SO obtuse??? It just doesn’t make any sense….

    Application of time-series methods …on what??? On SPATIOTEMPORAL series. All of these are spatially aliased by flow topology and many are also aggregated spatially …and yet people pretend they can be interpreted as purely-time series. It’s total BS.

    There’s a lot of turbulence in the flow, so the relations are many:1 and the constraints are in the spatiotemporal LIMITS …which should neither be confused nor conflated with strings of temporal events in one place or collections of events at different locations at one time that are sensitively dependent on initial spatiotemporal form & flow conditions. People talk about chaos in the TIME-ONLY sense. That’s 100% f****d up!!! because it IGNORES THE GEOMETRY. For ****’s sake people!

    I want to say again that I’m actually very angry at how obtuse shady & sketchy climate discussion agents are about this. It just completely razes trust. The people running those “skeptical” american climate blogs are 100% untrustworthy. I regard them as I would a sketchy shady criminal. Underhanded & corrupt. That’s a slithering snake stalking to bite in the dark.

    Let’s get the fundamentals right before trying to interpret folks. It’s necessary to understand WHAT’s being interpreted. The sampling assumptions are NOT met!!!!

    [ :

  5. Walt O'Brien says:

    Tallbloke, had you thought to apply principles of projective analysis to the weather paradigm yet using the findings of the two Nobel Prize winning (2003) econometrists in the arena of ARCH-based futures forecasting? 70+ years of data are open to the public on file at the NOAA website. The dastardly digital doodahs at IBM have acres of Crays at our beck & call to crunch the numbers if we can sort out the needed elements relating to the “causation wheel chart” input required: it would require about 10 trillion Riemannian reference frame Lorentz transform point-to-point causative simultaneities to be conducted to generate an empirically-determined semantic model of Earth’s weather patterns covering the principal 10 mile thick layer of atmosphere to a resolution of one mile by one mile of Earth’s surface layer grid.

    Anyone up for developing an unsolicited proposal to DERA or the US Department of Defense to devise a predictive weather tool using Tallbloke’s work to date and IBM’s toys? I have visions of royalty & lease right payments not sugar plums dancing in my head.

  6. tallbloke says:

    Walt, Sounds fun, but I don’t have the time to commit.

  7. tallbloke says:

    Paul: The suggestion was that since landmasses don’t move appreciably at human-life-timescale, land-sea distribution must be irrelevant to multidecadal climate.

    Crazy. These people don’t seems to appreciate the interaction of Moon and Earth. e.g. lunar tidal cycles changing flows around the complex topology of the Earth’s coasts on longer timescales.

  8. Paul Vaughan says:

    And even more simply: the solar cycle length differintegral.

    Moon for tides, sure — but sun drives flow.

    So in summary: NO I do not think ozone determines Earth’s land-sea distribution.

  9. Walt O'Brien says:

    Understood. We all only live just so long unfortunately. I chose to defer to you as you and your peers here had done the lion’s share of the work toward setting up the research framework to be used. Theoretically your group have done the most lucid research of anyone yet toward a workable solution which in the realm of CFD ought very well be doable.

    I will keep you posted. Many thanks once again for all your hard work.

  10. tallbloke says:

    Walt, I’m fully committed to the EU referendum campaign until July. After that, I hope to have some innovative science time. Meantime, keep the ideas flowing a post here about them. Hopefully you’ll pick up some feedback and ideas.

  11. oldbrew says:

    1989 paper: Fractal analysis of long-range paleoclimatic data

    Abstract says: ‘R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing δO18 ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 106 years. Given this temperature curves based on fractal parameters of long-term δO18 data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.’
    [bold added]

  12. oldbrew says:

    ‘it can be expected that the human-induced climate changes will not behave in the same way as the natural fluctuations’

    Eh? Sounds like science-free assertion.

  13. catweazle666 says:

    I thought the fractal nature of climate/weather had been settled by inter alia Benoit Mandelbrot and Edward Lorenz around half a century ago, self-similarity and all that good stuff.

    I have even seen reference to it in works on economics, usually as ‘self-affinity’.

    Perhaps more so-called scientists need to read James Gleick’s excellent work ‘Chaos’.

  14. Michele says:

    On the roads…

  15. Walt O'Brien says:

    oldbrew says:

    March 17, 2016 at 7:53 pm

    1989 paper: Fractal analysis of long-range paleoclimatic data

    Thanks very much for the link, oldbrew. To date however the extent of those who have spent time and money on the issue of empirically-metricated complex field-like simultaneous fluid phenomena projections have been futures traders, computational fluid dynamicists, astrophysicists like Prof. Rachel Ronen and Prof. Lee Smolin at Perimeter Institute, magnetohydrodynamicists concerned with molten metal’s magnetic behaviour like Prof. Branover at the MHD Institute in Riga, digital seismologists, military submarine sonar systems designers and operators, and most interestingly, semantic logician by the names of Givant and Tarski whose all-important truth validation criteria as applies to such complexities’ metamathematics make determination of what temperature, barometric pressure, cloud cover, precipitation, direction and strength of wind at any given point on th eplanet at any given time in the future a possibility.

    Tallbloke has indicated that after July he may beinterested in spending a bit of time on this so I shall be throwing my time at prepping the needed reference doc’s. I already have several dozens of pertinent reference papers so I shall put those in order then post them here between now and then.

    There is no rush, after all. In my view the method proposed but for the calculation mechanism which of course requires a data-defined (not a priori-defined) semantic algorithm to serve as the kernel for the needed algorithm could have been completed in 1922 or so by Russell and Whitehead based on my overview of Givant and Tarski on the topic of the 4th volume of their work Principia Mathematica.

    Fractals are but 1/10 of the solution though. It is how to deal with extracting forecasts for weather events in time on defined points on the globe through drawing pre-algebraic lines of causation between millions of interconnected complex weather events which of course is a semantic construct and which inturn is what Tarski and Givant hammered out in 1999 in their work on proof validation criteria for complex physical phenomena.

  16. Paul Vaughan says:

    Temporal chaos and spatiotemporal chaos differ fundamentally.

  17. Paul Vaughan says:

    Spatiotemporal chaos accounts for only 20% of the variance. On the Pareto Principle it’s not worth the effort. On the Pareto Principle, 80% (sun-climate 101) was the endpoint of exploration. My interest is drifting elsewhere at an accelerating pace. This may be the end of my climate exploration I’m realizing. The funding and free time for detail wasn’t there — at all — during the window of my interest. And now my interests are moving on. (I should say they have (past tense) moved on.) I’ll probably keep a watch on things for quite awhile to come, but it’s starting to sink in that recent revelations (hale/phi) marked an endpoint for me. Once there’s that much clarity, there’s no craving left. My interest is shifting to the rise of China. That’s what I read about now. Not climate anymore. Climate discussion is same old same old repeats and failure to acknowledge truth. It reminds me of the west: stagnation. But like I say I’ll keep a watch on the climate discussion. My prediction: It will become more and more and more corrupt over time, not less. Unfortunately it’s a form of poison due to infiltrated dark agency. The Talkshop at least has been an oasis in the desert, but v4 did NOT get retracted. That’s a cultural problem. It will be solved not with predictions, but rather with imagination.

  18. Walt O'Brien says:

    Paul Vaughan says:

    March 18, 2016 at 6:16 am

    “Spatiotemporal chaos accounts for only 20% of the variance. On the Pareto Principle it’s not worth the effort. On the Pareto Principle, 80% (sun-climate 101) was the endpoint of exploration. My interest is drifting elsewhere at an accelerating pace. This may be the end of my climate exploration I’m realizing.”

    It is exhausting, is it not? No one can think you ill for saying good-bye to the entire social construct accompanying what ought very well to be a straightforward “let the data write the theory” bit of scientific analysis w/proofing based on empirical and bench lab-level duplication of projected results.

    I shall remember your observation respecting the spatiotemporal. There is no other choice available as with the semantic framework needed to get the job done the key variables must of necessity be time-independent altogether: the problem is analog not linear in nature, after all. Think of sand caused to dance on a drumhead caused by a sound generator 30 feet away putting out an audio signal tuned to the resonant frequency of the drum itself, is the Dr. Science kiddies’ TV show to describe the problem at hand.

    As stated earlier, I should have most of the guts of what is to be proposed up and posted here by the end of July.

  19. tom0mason says:

    So climate past is like a fractal – oh!
    “History never repeats itself but it rhymes,” said Mark Twain, a man who had an enlightened and profound understanding of science and scientists. I feel he would have had much to say about all these periodic changes that are now apparently chaotically accelerating.


  20. A. Ames says:


    Fractals and Hurst-Kolmogorov stochastic dynamics are the domain
    of Demetris Koutsoyiannis, who has done some very interesting work.

  21. oldbrew says:

    Abrupt climate fluctuations during the ice age

    “We can see that the climate during an ice age has much greater fluctuations than the climate during an interglacial period. There has been speculation that the reason could be astronomical variations, but we can now rule this out as the large fluctuations during the ice age behave in the same ‘fractal’ way as the other natural fluctuations across the globe,” [said] Peter Ditlevsen.

    So because ice ages are much longer than interglacial periods the climate fluctuations are greater, but the proportions are the same relative to the overall period (= fractal self-similarity).

  22. Paul Vaughan says:

    Ditlevsen is factually incorrect in that statement OB.

    It’s an angering statement because of the apparently deliberate way in which it attempts manipulation of frail minds ignorant of the fundamental differences between temporal & spatiotemporal chaos.

    Again: Spatiotemporal chaos differs fundamentally from temporal chaos. Same applies to H-K & Koutsoyiannis. Fundamental misinterpretations abound (and persist).

    Like Walt says, they’re engineering a social construction. That’s part of why my focus has shifted to that area. I don’t (yet) have much background in that area, but from what I’m now reading I understand that those who get praised in that realm are those who IMAGINE. The game goes something like imagining all different ways of looking at things (by class, by gender, by nation, by economics, by geopolitics, by whatever) to COMPLICATE narratives in such ways that they inspire a driving desire for change (especially in the powerful elite). (Messing up temperature records is just a really simple way to do this.)

    I’m convinced that the climate scare is a western energy security strategy based in deliberate deception. So then given that I’m a westerner (genetically at least), why would I not decide to get behind such deception? That is a question I will leave unanswered (at least for now).

    Walt wrote:

    “No one can think you ill for saying good-bye to the entire social construct accompanying what ought very well to be a straightforward “let the data write the theory” bit of scientific analysis w/proofing based on empirical and bench lab-level duplication of projected results.”

    Philosophical clarification:

    The aim of exploration is not to predict. When I explore a mountain trail network, it is NOT because I wish to predict something. It is rather primarily to stay healthy from the exercise of knowing nature and secondarily to discover (but not to predict).

    You can simplify your computational objectives by orders of magnitude by limiting your predictions to the classes of statistics that are limited in aggregate.

    This is NOT what the skeptical community wants of course. They want every last detail of the spatiotemporal chaos predicted. They may socially construct desire for that all they want in support of left-leaning politics (that’s what it does), but their social constructions will not change nature as she’s observed. They can keep harassing all they like. She won’t change. They may however manage to chase realistic observers away from the discussion with their harassment, which is what I allege is their whole intention (in support of the climate scare — and camouflaged otherwise).

    I’m not leaving the climate discussion. I’m just announcing that on the Pareto Principle the exploration is finished and the task remaining is to understand the cultural dimension (another part of nature encountered along the trail).

    Ever heard of the term “creative tension”?… (hehe…)
    [ :

    I’ll keep an eye on your contributions Walt, volunteering strategic commentary as feasible.

    Here’s a terse graphical summary of the stats systematically limited in aggregate:

    That’s like saying:
    I went up this trail. It goes to a waterfall.
    I went up that other trail. It went to a lake.
    And there’s a trail that connects the 2.

    It’s conclusive. The cultural question arousing deep suspicion is: Why are there so many vocal skeptics who want to redefine the end-goal of exploration to be prediction?? (creepy as h*ll!) I suspect a single domineering donor (supporting a handful of activist discussion dark agents) concerned with social construction supporting (yes, supporting, not opposing) the climate scare (and camouflaged otherwise).


    Exploration is not science. I come here with exploration asking the question: Why do skeptics who CLAIM devotion to science IGNORE basic insights of exploration and instead base their social constructions on IMAGINED (AND FALSE) geometric & spatiotemporal assumptions???

    I’m here to help correct the community where it has gone seriously wrong. I observe resistance to this generous help. That’s cultural. It’s not logical.

    Why do people insist that political optics are somehow enhanced by talking about how to achieve “scientific” prediction based on FALSE assumptions??? It makes no sense!! One of the interesting things for me recently has been realizing that while righties like to hate lefties for all their social construction psycho-babble, they do the exact same thing!! It made me feel naive. I hate feeling naive. Lesson learned…

    Good fun…

    Can’t wait to see these predictions based on false assumptions. (Note that I’ve generously summarized the false assumptions graphically for the community’s benefit — see link above.)

    So far as I can tell there’s some kind of top-down dictation that proven-false (geometric & spatiotemporal) assumptions about enso MUST form the basis of prediction-discussion framing. It’s creepy (domineering biased wealthy donor at the american climate skeptic blogs maybe?) That’s why I’m reading up on social construction and the role of the imagination in social movement steering. I realize that I’m in conflict with someone’s imagination (presumably someone elite). I didn’t mean to ruin the liberal party by coming along with exploratory observation that proved domineering imagination wrong. All I did was explore and observe and then say, “Hey, you guys are trying to model but you’re making FALSE geometric & spatiotemporal assumptions. Here I’ve graphically summarized all you need to know to correct your imagination!”

    Just sayin’: I suggest doing the bad-assumption corrections BEFORE trying to model.

    …But it’s totally obvious that somebody-influential’s imagination about good optics somehow depends on bad-assumptions.

    Not sure what can be done about that but I’m exploring the possibilities…


  23. oldmanK says:

    In “Abrupt climate fluctuations during the ice age” oldbrew said “So because ice ages are much longer than interglacial periods the climate fluctuations are greater”. More likely ice ages are longer because its a condition in which a planet ‘character’ can get stuck. I think evidence from other sources indicates that fluctuations of conditions are wilder in interglacials. For example the fossils in rock in a mountain top is the result of interglacial events.

    PV said: “The aim of exploration is not to predict. When I explore a mountain trail network, it is NOT because I wish to predict something. It is rather primarily to stay healthy from the exercise of knowing nature and secondarily to discover (but not to predict).” The real explorer takes to the mountain trail because the mountain is undeniably there, and with it a mountain of questions about it. Levi Strauss argued that because its there man fears it and is urged to unravel its mysteries, to discover and to find an explanation for it. (making a god out of it is one common way of getting very lost).

  24. Paul Vaughan says:

    Just imagine how constrained social construction would be if imaginations were limited by observation. Too inconvenient even for right-wingers if we’re honest and realistic. Easier to harass truth-speakers out of the picture, right? Never mind trying that slippery slope without an ice-axe…

  25. Paul Vaughan says:

    Perhaps the american pundits have convinced the (easily-duped) donors that if they limit the construction framework to be compatible with exploratory observations there isn’t enough (imagination-wise) to work with to win the political war in america.

    If that’s what’s going on, that’s such obvious BS and they’ve got the wool completely over the donor’s eyes while both insulting and underestimating the capacity of the people.

    It’s remarkable how much more sensible the international climate skeptic community is on the sun-climate file than the dark-agency-infested american community. Politics in their nation is spinning out of control.

  26. Paul Vaughan says:

    You know, the more I think about it the more I’m convinced that at least a few of the key people running that joint MUST be (infiltrated) LEFT-wingers because they rely SO heavily on imagination (their whole sun climate narrative is strategically based on a few proven-false geometric & spatiotemporal assumptions).

    California dreaming… Internationally we don’t see the same pattern of corruption in climate skepticism.

    I think I owe non-american right-wingers an apology for painting them with that brush.

    Whatever’s going on with america’s politics is spinning out of control and I do apologize for targeting right-wingers everywhere with a scolding that should probably be directed at some left-wing infiltrators who hijacked a website that aims to look right-wing on the surface …but this is confusing american politics (which has strong regional flavors that are hard to understand not knowing the regional contexts firsthand). How did they get so politically corrupt? Maybe not worth thinking about — probably sensible to just step back from all that chaos and focus on being sensible without expecting any trustworthy signals worth following out of that spinning mess.

    Internationally I think right-wingers are making sense: The sun runs terrestrial climate. That’s what I’m hearing from the international climate skeptic community. Loud, clear, sensible, no BS.

    And I do offer my apologies for conflating unrelated groups. My bad.

    What I’m left wondering: When are more sensible people going to grab the reigns in America?
    What I’m sure of: The rest of us should have a plan B….

  27. oldbrew says:

    oldmanK says: ‘More likely ice ages are longer because its a condition in which a planet ‘character’ can get stuck.’

    Yes, it seems that having a lot of ice is a more durable state for Earth than not having so much (like now). The impression I got from the authors was they thought that if the ice age was (say) 10 times as long as the interglacial, some of its ‘behaviours’ might also be 10 times longer, or at least longer, than the interglacial equivalents.

    Quote: ‘This means that the ratio between the extremes in the climate over different time periods behaves like the ratio between the more normal ratios of different timescales’

    But maybe they meant something else.

  28. oldmanK says:

    I’m not at all sure what is meant by the statement. Or what they are comparing with.

    The picture above shows frost fractals(?). What I would rather call ice crystals, which leads to a comparison. Take steel. Fine grained has more crystals and is more homogeneous in character, while coarse grained has less but more variability. So the more fractals the more stable. However using that as a comparison for the weather–???

    Weather is an end-result of combinations of dictating events. Example. The African Sahara changed radically from say 6k years ago, and from evidence, the change was sudden. That change was long-lived. What was the driver of that change?

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