Climate variations analyzed 5 million years back in time show repeating fractal patterns

From the UNIVERSITY OF COPENHAGEN – NIELS BOHR INSTITUTE

Peter Ditlevsen's calculations show that you can view the climate as fractals, that is, patterns or structures that repeat in smaller and smaller versions indefinitely. The formula is: Fq(s)~sHq .(Credit: Maria Lemming)

Peter Ditlevsen’s calculations show that you can view the climate as fractals, that is, patterns or structures that repeat in smaller and smaller versions indefinitely. The formula is: Fq(s)~sHq .(Credit: Maria Lemming)

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 researchers studied: Temperature measurements over the last 150 years. Ice core data from Greenland from the interglacial period 12,000 years ago, for the ice age 120,000 years ago, ice core data from Antarctica, which goes back 800,000 years, as well as data from ocean sediment cores going back 5 million years.

“We only have about 150 years of direct measurements of temperature, so if, for example, we want to estimate how great of variations that can be expected over 100 years, we look at the temperature record for that period, but it cannot tell us what we can expect for the temperature record over 1000 years. But if we can determine the relationship between the variations in a given period, then we can make an estimate. These kinds of estimates are of great importance for safety assessments for structures and buildings that need to hold up well for a very long time, or for structures where severe weather could pose a security risk, such as drilling platforms or nuclear power plants. We have now studied this by analysing both direct and indirect measurements back in time,” explains Peter Ditlevsen.

The research shows that the natural variations over a given period of time depends on the length of this period in the very particular way that is characteristic for fractals. This knowledge tells us something about how big we should expect the 1000-year storm to be in relation to the 100-year storm and how big the 100-year storm is expected to be in relation to the 10-year storm. They have further discovered that there is a difference in the fractal behaviour in the ice age climate and in the current warm interglacial climate.

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 fluctuation during the ice age behave in the same ‘fractal’ way as the other natural fluctuations across the globe,” Peter Ditlevsen.

The astronomical factors that affect the Earth’s climate are that the other planets in the solar system pull on the Earth because of their gravity. This affects the Earth’s orbit around the sun, which varies from being almost circular to being more elliptical and this affects solar radiation on Earth. The gravity of the other planets also affects the Earth’s rotation on its axis. The Earth’s axis fluctuates between having a tilt of 22 degrees and 24 degrees and when the tilt is 24 degrees, there is a larger difference between summer and winter and this has an influence on the violent shifts in climate between ice ages and interglacial periods.

The abrupt climate changes during the ice age could be triggered by several mechanisms that have affected the powerful ocean current, the Gulf Stream, which transports warm water from the equator north to the Atlantic, where it is cooled and sinks down into the cold ocean water under the ice to the bottom and is pushed back to the south. This water pump can be put out of action or weakened by changes in the freshwater pressure, the ice sheet breaking up or shifting sea ice and this results in the increasing climatic variability.

Natural and human-induced climate changes

The climate during the warm interglacial periods is more stable than the climate of ice age climate.

“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.

“The differences we find between the two climate states also suggest that if we shift the system too much, we could enter a different system, which could lead to greater fluctuations. 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. Even though we do not know the climate variations in detail so far back, we know that there were abrupt climate shifts in the warm climate back then,” points out Peter Ditlevsen.

###

UPDATE: The article is Open Access at Nature Communications
http://www.nature.com/ncomms/2016/160316/ncomms10951/full/ncomms10951.html

h/t to Doug Huffman

174 thoughts on “Climate variations analyzed 5 million years back in time show repeating fractal patterns

  1. >”This new characteristic of the climate will make it easier for climate researchers to differentiate between natural and human-induced climate changes”

    What a novel concept. I can’t see it catching on, except to explain why temperatures aren’t cooperating with someone’s model.

      • Is this not eintirely circular? Did Edward Norton Lorenz not discover chaos theory through the study of meterology and weather models?

      • Well, yes, but then again we’re talking about climate here, not weather. See the paper linked to by Belousov. Part of the whole problem here seems to be that the AGW climatologists seem to have forgotten, or never known, about this. As the paper says, the popular assumption is that climactic behavior primarily responds to forcing inputs, neglecting the inherent nature of the system itself.

    • Well it is well known that things like coast lines show randomly chaotic structure at a wide range of size scales, as in an 8×10 picture looks to have a certain “roughness” regardless of whether the scale is in Mm or mm.

      That in itself is not sufficient to call such structures “fractals”.

      Climate is ‘fractal’ just like global warming is ‘logarithmic’ and severe weather is growing ‘exponentially’.

      Weasel words with very specific normal scientific meanings, but used colloquially as a substitute for bovine scat.

      Fractals have a very specific complex mathematical equation, with the real and imaginary parts of complex numbers interpreted as movement on orthogonal axes. So they are totally deterministic. You define the starting point, and you have defined the entirety of the pictorial image. There’s nothing chaotic about fractals.

      G

      • As I read the article I kept waiting to see how he applied his logic to determine the equation for the fractal pattern he discovered but – Nothing. Thus as you wrote above “Weasel words with very specific normal scientific meanings, but used colloquially as a substitute for bovine scat.”

      • Isn’t all calculated math, including recursive processes, deterministic in the sense that picking a set of input variables and choosing the mathematical precision, will give the same results but that if the precision is changed then a deterministic result will result, but will not be predictable from the calculation by the same process with another precision. That turns out to be what chaotic behavior is. Also, it should be possible to have a chosen mathematical recursive process with a random change in, say, the precision at each step of the calculation so that the mathematical process no longer gives a deterministic result as long as the random process is not deterministic itself.

      • Fractals …are totally deterministic … There’s nothing chaotic about fractals.
        Chaotic functions are also totally deterministic.

      • Edward Lorenz said

        “Chaos: When the present determines the future, but the approximate present does not approximately determine the future.”

  2. “easier for climate researchers” ….. to see what they want to see ?
    To excuse their mistakes ?

  3. 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. Even though we do not know the climate variations in detail so far back, we know that there were abrupt climate shifts in the warm climate back then,” points out Peter Ditlevsen. Is this referring to the Holocene Optimum, which was warmer, or the last inter-glacial which was warmer?

    • I must confess vacillating regarding a third option I originally typed. I wondered if I was being unfair, but in further consideration of the first line I quoted, with its inherent vision of inexorable doom, I must submit as a possibility; the era of unicorns and faeries.

    • skeohane: A modest comment: You talk about the Holocene Optimum. You should talk about Holocene Maximum. Optimum refers to e.g. the best or most advantageous of a set of various external conditions for the survival or well-being of a certain population. Like the optimum condition for growing bananas is a warm and suitably moist climate and optimum conditions for a polar bear means cold climate and lots of ice.

      • The optimum conditions for Polar Bears require a lot cold and a lot of ice and snow.
        Otherwise they lose the competitive advantage they have over their close cousins, Brown Bears.
        Replace ice and snow with forest and Polar Bears become recessive genes in the Brown Bear population.

      • If I’m not mistaken, polar bears are a sub species of brown bears that evolved to occupy the Arctic areas due to glacial periods. Maybe they would not not exist without the ice age earth is experiencing.

        Do we really need the ice age? Probably not.

      • Semantics, from what I have read over the last 55 years, i have only seen ‘Holocene Optimum’ which was understood as the time of maximum temperatures in this inter-glacial.

    • The MWP, Roman and every other back to the Holocene — “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.” ?? Heading towards on his computer.

  4. If you could get stronger and stronger microscopes…looking first at molecules, then atoms, then subatomic particles and so on and so on…as you focused more and more deeply, unveiling each new layer, each more infinitesimal than the previous, eventually you would look into the eyepiece and see the back of your own head.

  5. This press release did not provide the article name, so I located it:
    https://dl.dropboxusercontent.com/u/75831381/Ditlevsen%20fractal%20climate.pdf

    Also the Supplemental Information:
    https://dl.dropboxusercontent.com/u/75831381/Ditlevsen%20fractal%20climate%20Supplemental%20Information.pdf

    Not easy reading, but the authors did a ton of work in looking at climate variations and oscillations across 5 orders of temporal magnitude (months to 5 million years). They use Hurst exponents to compare glacials and interglacials, concluding that the two regimes have different characteristic fractal behaviors.

    A useful guide to the power of natural forces in driving climate–and a powerful rejoinder to the CAGW crowd.

    • Yes so many universities are so BAD at issuing press releases, it’s mind boggling. Only about 10% link to the paper the PR is about, the rest make you go fish for it. if they worked for a company, these uni PR folks would lose their jobs for being so incomplete.

      • Maybe they don’t really want people to read the actual study. Because, you know, those people will just try to find errors in the paper.

  6. “The climate during the warm interglacial periods is more stable than the climate of ice age climate.”

    So, if the weather / climate is getting more unstable / severe as alarmists claim, it follows we must be entering the next phase of glaciation / end of the interglacial (i.e. it’s getting colder, not warmer).

    What a conundrum for the warmists / alarmists !

    • You point out an amusing logical inconsistency. That won’t do. Warmunists do not like being consistent. There is (Fyfe, Mann) and is not (Karl, Mears) a pause. The science is settled until CSIRO climate research cuts (settled science does not need further research). unsettled the scientists who then unsettled the science to save their jobs and grants. Paleoclimate varves can be used right side up or upside down. Global warming means less snow until more snow is caused by global warming…
      Like the Queen told Alice in Through the Looking Glass, warmunists practice believing 6 impossible things before breakfast.

  7. Thanks that they don’t refer to models
    But i like this: The climate during the warm interglacial periods is more stable than the climate of ice age climate.

    • Svend are you living in an igloo on Greenland, or izzat another Svend who digs glaciers ??

      G

  8. “the shift between ice ages, which typically lasts about 100,000 years and interglacial periods, which typically last about 10-12,000 years.”

    Let’s see. it’s been ~ 11,000 years since the end of the last glaciation & the weather / climate is supposedly getting less stable – Man , these guys are making a good case for us entering the next glaciation. Not doing much to get people worried about burning up

  9. I wonder just what temperature proxies Ditlevsen is using to state that todays climate is warmer than historic times. Using crop growing seasons as a proxy, Greenland was warmer in the Midieval Warm than currently, as it is not possible to farm barley in Greenland, or raise cattle, which the Norse did.

  10. Milankovitch Cycle varves have been found in Precambrian rocks. Weather may be chaotic but on at least some scales, climate is cyclic.

    • A complex system may become chaotic by going through “bifurcations” (the right term; not “tipping point” as used in climatology) under more by having a periodic component splittig into (sub)harmonics, when a parameter changes slightly over time. The climate system is multiperiodic, with cycles ranging from one day, one year, 11 years, 60 years, 180 years, ~1000 years…up to 100 000 years (the Milankovitch cycles you mentionned) and probably longer. If you make a spectral analysis of temperature proxies (Vostok ice cores i.e.) you discover that these periodicities do not appear as spikes (corresponding to an exact period) but as peaks distributed around a given period:a sign that the system is pseudo-periodic; it is chaotic. Inded, when you have an extremely large number of different periodicities the response of the system beomes extremely senitive to initial coditions and values of the parameters; in other words it becom difficult to extrapolate on more or less long term. This is why nobody can exactly predict when the next transition to an ice age will start. In a nutsell, you are wrong when claiming the climate ischanges periodically. Climate is also chaotic in nature.

      • Milankovitch Cycles are of differing periodicities, one of which is about 100,000 years. The cycles combine to produce glacial episodes that occur now in about 100,000 year periods, with shorter interglacials, the length and other characteristics of which vary. Earlier in the Pleistocene, the 41,000 year cycle was more dominant.

        Climate is also cyclic on longer time frames, and responds to various causes in a non-chaotic way. For instance, distinguished Snowball Earth expert geologist Paul Hoffman has suggested a cosmic explanation for the 1.5 billion year gap in global glaciations between the Paleoproterozoic Huronian and Neoproterozoic Sturtian events.

      • Of course I know there at least three Milankovitch significant cycles and how they are related to earth orbital characterisitcs. I learned also something about how the solar system “wobbles” around the milky way with much longer periods of time. But you need to sum up everything with the right phases and realize that the periodicities are not “sharp” ones: no spikes in the Power Spectrum but some distributions around several peak values: the (pseudo-)periodicities about which we were talking about). If you look at time series oftemperature proxies, you find a clear chaotic signature. => the system is not predictable. One way to detect a chaotic signature is simply by putting the data on a phase plan. I did for the Vostok Data: You can easily identify two” strange attractors”: a “temperate” period and a “glacial” period around wich the system oscillates around trajectories “loosier” than for the “temperate” attractor. You can also see that the system remains for longer time around the “glacial” attractor and that the present temperature has been exceeded by a few degrees in the past. This graph defines the “confinment box” of the system: whatever happens, you will never increase the temperature by more than a couple of degrees, even if the CO2 concentration becomes 10 times larger than 400 ppm, as happened in the past. This is just the end of the IPCC fantasy !!!!! For convenience, I give again the link to the phase plan of the Vostok data (and the embedding dimension and time lack used) here:
        https://dl.dropboxusercontent.com/u/56918808/Phase%20plan%20Vostok.docx
        Sorry for having to repeat this; I don’t want to appear as a troll

  11. “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. ”

    So we can conclude-
    1-that the climate “we are heading towards” has occurred at least once before on Earth (without human influence)
    2-that the climate we are in NOW is not as warm as the climate “we are headed towards” AND that we do NOT have to go very far back in the geological history of the Earth to find a climate that is as warm as where we are NOW (and any “warm” prior to 1880 cannot be human CO2 related at all)

    “because it can be expected that the human-induced climate changes will not behave in the same way as the natural fluctuations.”

    Thoughts-

    So, then, if climate changes today and moving forward behave in the exact same way as they have in the past, then they cannot possibly be “human-induced climate changes”!!! (Or these scientists will have to admit that their expectations regarding human induced climate changes were WRONG)

    Since both carbon and Co2 are naturally existing/occurring things, why would more of them cause changes that were UNnatural? Define “natural fluctuations”. Are they static or small….ALL the time? Constantly predictable and stable? If so…then what caused the “abrupt climate shifts in the warm climate back then”??? It sure couldn’t have been increasing CO2!!

    If they were not constant, and CO2 fluctuates within a greater range naturally-which is what caused the “abrupt climate shifts in the warm climate back then”-surely today’s fluctuation could be natural.

    So…it appears that he is saying that “naturally occurring rises/fluctuations in CO2” would cause climate changes that are DIFFERENT -would not behave in the same way- as human caused CO2 rises/fluctuations right? (cover his butt either way right?) BUT if that is true, then -how do they get away with “predicting” anything at all? Since human CO2 is a modern and “unnatural” state that has never occurred before, AND it will cause changes that are different from all other “natural” changes….we cannot possibly know WHAT it will do! It might cause the reverse to happen…or nothing at all to happen…but it cannot possibly behave in the same way as…so all predictions to this point have been mere conjecture and are false because how “natural “CO2 behaves in a lab will be different than how HUMAN CO2 in the atmosphere behaves.

    I love it when scientists actually undermine other aspects of “science” with their studies and conclusions! I also love it when they cross talk themselves into several corners by contradicting themselves.

    • They seem very certain about “the climate that we are heading towards”.
      Evidence? (Not opinion, model results or guesswork.)

    • From the article: “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. ”

      Yeah, we have to go clear back to the 1930’s to find a climate warmer than it is today.

  12. The statistical implications are enormous. 100 years of climate science statistics down the drain.

    “Dynamical systems in nature exhibit self-similar fractal space-time fluctuations
    on all scales indicating long-range correlations and therefore the statistical
    normal distribution with implicit assumption of independence, fixed mean and
    standard deviation cannot be used for description and quantification of fractal
    data sets.”
    http://arxiv.org/ftp/arxiv/papers/1002/1002.3230.pdf

    • Fred
      You are right. In nonlinear chaotic systems with signature fractal pattern, the mean is meaningless! That is what Ed Lorenz showed with DNF63. It does have huge implications which have an above average chance of being ignored.

    • Lets shout that out a again bit louder

      therefore the statistical normal distribution with implicit assumption of independence, fixed mean and
      standard deviation cannot be used for description and quantification of fractal data sets.

      • Yeap!!! This is a mathematical PROOF, indeed. And this MUST BE the message to be spread for stopping that IPCC scrap and waste of time + money. Also linear analysis (by regression, moving average or other smoothing techniques, etc.) on time series with a chaotic/fractal signature does not make any sense: the result depends on your initial moment and the length of the time window considered. Exactly what puzzles mainstream climatologists, no? Even the concept of “forcing” and the one of “anomalies” make no sense. Those are really basic methodological mistakes that undermine all the “mainstream” analysis of climate science (?). but this is another story.

  13. So if climate behaves like a fractal, then there are sudden drastic changes with only tiny changes to inputs (contributors). This seems reasonable. It isn’t random at all – if its fractal-like then it has strong patterns. This also seems reasonable.

    The questions remain what drives the sudden changes. It seems reasonable that out of hundreds of influences only a few contributors, each possibly make up of several influences (so a group would be several influences that together change one important input so acting as a single contributor on whole) actually drive the patterns.

    If what I speculated is true, then almost CERTAINLY CO2 cannot be a contributor – it can be no more than an influence – otherwise we would have seen a drastic change in climate, and we haven’t – only gradual changes.

    I keep finding myself going back to the Little Ice Age and asking why so strong and why then and why not now?

    Either sunlight changed (intensity or maybe intensity of certain frequencies) or Atmosphere changed (aerosols, particles, clouds), or perhaps something less obvious such as wind or water currents.

    If wind and/or water currents change in fractal-like patterns over time, it would mean man would have almost no impact to future climate shifts – it will happen despite any changes we make. All we could do is raise average temperatures a few degrees during the next ice age – a good thing I think.

    • If its chaotic it doesn’t even need minor changes to head off in a new direction, it can do that all by itself.

      I think that is what a lot of people find hard to grasp, that a totally deterministic system can end up behaving as if it were totally random, within certain limits, just on account of non linearity and time delayed feednback.

    • Robert, your comment:

      “… then almost CERTAINLY CO2 cannot be a contributor – it can be no more than an influence – otherwise we would have seen a drastic change in climate, and we haven’t – only gradual changes.”

      reminded me of a post on WUWT some time ago (2012 – wow how time flys!) by Dr. Brown aka rgb@duke that touched on this. https://wattsupwiththat.com/2012/01/09/strange-new-attractors-strong-evidence-against-both-positive-feedback-and-catastrophe/

      In that post Dr. Brown made the following observation:

      “In an open system in a locally stable phase, the oscillations (fluctuations) couple to the dissipation so that more fluctuation makes more dissipation — negative feedback. If this is not true, the locally stable phase is not stable.

      This is a strong argument against catastrophe! The point is that given that CO_2 is making only small, slow, local shifts of the attractors compared to the large shifts of the system between the attractors, if there was a point where the system was likely to fall over to a much warmer stable point — the “catastrophe” threatened by the warmists — it almost certainly would have already done it, as the phase oscillations over the last ten thousand years have on numerous occasions made it as warm as it is right now.

      The fact that this has not happened is actually enormously strong evidence against both positive feedback and catastrophe. Yes, anthropogenic CO_2 may have shifted all the attractor temperatures a bit higher, it may have made small rearrangements of the attractors, but there is no evidence that suggests that it is probably going to suddenly create at new attractor far outside of the normal range of variation already visible in the climate record. Is it impossible? Of course not. But it is not probable.”

      I think you (and others) would find the post interesting. It certainly relates to this thread.

  14. In a fractal, extreme events are much more common that we would predict from a coin toss or roll of the dice. As a result, when we try and apply every day observations to climate we are misled into thinking things are abnormal or extreme.

    In a coin toss it makes no difference if the last toss was heads or tails. The chance of heads or tails remains the same. However, in climate if yesterday was warm, today is more likely to be warm as well. If last year was warm, this year is more likely to be warm as well.

    This makes it much more likely that temperature will swing to extremes due to natural variability than what we normally expect from chance. Thus we are misled by experience to assume that something other than chance must be the cause.

    • A good start on a very complex issue, if that weren’t enough you need at least a third dimension for time so the gears will mesh.

      • ;-) I understood this very well. My answer was trying to boost the discussion on the structure of this mind map. Trying to get a “consensus” on it.
        Btw: this is also humor of course….

    • I am a businessman, not a scientist. I do have extensive experience in flowcharting for business systems development and mind mapping for route cause analysis. I do have a general understanding of what you are doing with your chart. My not being technically proficient that is probably a good thing. I can offer you the following:

      I would describe your effort as more of a flow chart.
      Shapes & sizes have meaning in a flow chart, yours seem more dependent on the amount of text or text size.
      Perhaps a legend for the different connectors?
      Sometimes several page connectors to subprocesses can be less confusing than trying to fit everything one one page. Also allows more detail to be shown. Keep only the most basic and influential information on the main page.
      Avoid connectors crossing over other connectors and processes (boxes). Organize processes on your chart to avoid this. It will also make it easier to understand.

      I will leave the science to those more capable.

      • Many thanks for your presentation tips. This figure is just a “rough” tentative to summarize the information flowing around the AGW debate on a single PowerPoint sheet.. Indeed each “concept” on this mind map is itself a very complicated chart. More sophisticated software (i;e. Pajek, Gephi or even Decison Explorer) allow more accurate 3D representations and analysis of the structure of a complex system (connectivity, clusters, (in)direct feedback loops, drivers and outcomes, influencing power, etc.). But I just wanted to share here a kind of “helicopter view” of the Climate system, and get some validation / infirmation of its structure by people supposed to follow this debate from very close.. But not so many want to play the game, so far, apparently..

  15. ” 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 ” …..Ummmmmmm…700 years ago it was hotter than today ! ( MWP )..I hardly call that a long time since the Earth’s climate has been changing for 4.5 BILLION years !

  16. watch specially the marginal and relatively unconnected “anthropogenic” box…. And some warmists think they can drive this system by promoting carbon taxes and other market mechanism. Also: how significant is (anthropic) CO2 in this global picture? and how far can it influence the key drivers: cosmic rays and planetary gravity & electromagnetic forces. Watch also the central position of heat and mass transfer between ocean and atmosphere….essntially unknown. “The (climatic) science is NOT settled”

  17. Fractals are a mathematical property of recursive systems. They do not have to be generated by classical mathematical chaos, a subset of recursive systems where Xsubt=f(Xsubt-1). (Strictly, any nonlinear dynamic system is chaotic. Nonlinear = feedback means recursive. Dynamic = lagged feedback.) The Mandelbrot set is a famous example of a fractal recursive but nonchaotic system. Every Mandelbrot set generator always produces the same set no matter the space starting point or degree of resolution.
    AR3 correctly said climate is chaotic. (Proof: water vapor feedback is not instantaneous.) So the fractal property of climate was theoretically inherent. Gets to the boundary conditions versus initial conditions argument about climate model envelopes. Perhaps this new work statistically teased climate fractal dimension out of the temperature records and paleoclimate proxies. Lets study the paper and have some mathematicians and statisticians weigh in.

    • Everything in nature happens as soon as it physically can happen: then something else happens.

      Nothing in Nature waits for something else to happen first. Nothing, even is aware that it is waiting for something else to happen; how could it know.

      (c) defines how fast the next thing to happen can happen.

      G

    • How about an engineer, please see comment at 1224 pm, below.
      As I read the paper, they use data from a specified period to estimate parameters for a longer period as quoted below. Standard practice in estimating future occurrences with probability distributions, i.e. flood peaks in rivers.

  18. Now wait a dog gone minute. Are these people saying, in a published paper, that there are other factors that drive the climate besides CO2? Shazzam Andy! One wonders how this one slipped through the net.

    Now, just because they see fractal behavior does not tell us that there has never been impacts or other major events in the 4.5 billion year history of earth climate. I would also point out that there may be many factors impacting climate that we have not even thought of — not even suspected.

  19. So they confirm what the IPCC wrote in the Third Assessment report (TAR) that,

    “In climate research and modeling, we should recognize that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”

    This means every single penny spent on the IPCC and all other attempts at prediction are a completely futile and delusional waste of money. The TAR comment does not say the science is settled, however it does say the science at least as far as prediction is concerned, cannot be settled.

  20. From the authors ” But if we can determine the relationship between the variations in a given period, then we can make an estimate. These kinds of estimates are of great importance for safety assessments for structures and buildings that need to hold up well for a very long time, or for structures where severe weather could pose a security risk, such as drilling platforms or nuclear power plants. We have now studied this by analysing both direct and indirect measurements back in time,” explains Peter Ditlevsen.
    So they take a shorter period, say the 100 yr behavior, as a model for longer periods. This technique is not new. Hydrologists and engineers, have been using shorter periods of precipitation and runoff peaks to calibrate a probability distribution (log-normal, Log-Pearson III, etc.) and extending it to longer periods. This is how bridges, floodplains, conveyance channels, etc. have been designed for well over a century.
    Calibrate a model to a shorter period of data then extend the model to estimate occurrences over longer periods. Standard practice, whether your estimate is a skew coefficient for a probability distribution or a Hurst coefficient or fractal parameters in your model.
    Consult any hydrology or hydraulic engineering text book.

    • The predictbility horizon of a dynamical (chaotic) system is quite short. Fore climate it is much less than the century taken as time horizon for IPCC projections
      Techniqueallow to quantify this tie horizon (i.e. anaysis of visibiliy)

  21. ” if we shift the system too much, we could enter a different system, which could lead to greater fluctuations. 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. …”

    The Obligatory Nod to the “Consensus”. Feh. Still, interesting work. Step by step, inch by inch… catchee monkee?

    • That’s a bald faced lie as even the most cursory glance at glaciation cycle charts show. We are toward the end of a quite warm spell with glaciation pushed back a long way.

      And the most cursory glance at those charts show the plunging cold and frigidity that is coming, no matter how many government employees, alternative energy peddlers, and environmental wackos try to say otherwise.

      ” if we shift the system too much, we could enter a different system, which could lead to greater fluctuations. 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.”

      You don’t need a link or a guru you can check that story by simply looking at the approximate place we are now in glacial history. We’re in that region of time that from now to – oh even a couple of thousand years from now – there’s going to be a VERY serious plunge into the cold,

      and everyone is going to wish what green house gas effect protagonists said was true: that by using fire, you can make the sky get hot.

      No, you can’t. And it’s going to be katie bar the door the first time the planetary temperature starts showing any seriously determined urge to fall very far.

      All this AGW crap is exactly that: manufactured alarm. Warmth has never threatened biodiversity on the planet; but glaciation wipes out entire sectors of the globe.

    • pdtillman: You cited the two most important falsely premised phrases in that stealth AGW paper, “as warm as we are heading towards,” and:

      … if we shift the system too much, we could enter a different system…

      Setting a foundation for yet another tired rendition of the Precautionary Fallacy, an aria in five words and seven notes:

      “Do this — just in case.”

      (to the tune of “B-I-N-G-O” … oh, you know the one…. from first grade music class: “There was a farmer, had a dog, and Bingo was his name-O. B-I-N-G-O! B-I-N-G-O! B-I-N-G-O! and Bingo was his name-O!” (remember to shout on the “O” like you did when you were 6 and then, leave off the first letter and just ((clap)) once in its place … then the first two letters… and HEY it’s sort of like truncated data adjustment! And almost a fun as a “nature trick.”).

      Yup. The fractal hand waving was, apparently, not a palm tree (or, rather, not a cluster of broccoli, heh) only a beautiful mirage, luring sincere, math-loving, science realists into the desert of AGW — AGAIN!!

      Aaarrrrrrrgh!

      I was really, really, interested in that theory. And now, I don’t even WANT to go read the paper. I’m willing (as a non-math major) to tackle it, but at that level of the difficulty, I need to have more confidence that I am not going to end up wasting hours (yes, likely hourS) of my time!

      Okay. Someone else read the paper and summarize it for us– okay?

      Thanking you in advance… I will be watching for a WUWT article to appear by YOU.

      :)

  22. l feel its an error just to view the ice age as extreme climate change, because in their own way its the interglacial periods are the extreme climate events.
    Because when you look at the last millions years. Don’t the interglacial periods look just like the current temperature spike that has got the AGW crowd into panic mode.

  23. The idea of fractal patterns in weather and climate is not new. Here’s a quote from a 2007 book:

    Spatially extended dynamical systems in nature exhibit fractal geometry to the spatial pattern and support dynamical processes in all time scales, for example, the fractal geometry to the global cloud cover pattern is associated with fluctuations of meteorological parameters on all time scales from seconds to years. The temporal fluctuations exhibit structure over multiple orders of temporal magnitude in the same way that fractal forms exhibit details over several orders of spatial magnitude. Chaotic Climate Dynamics By A. Selvam

    Is it profound or merely pseudo-profound bullcrap? This reminds me of the way the Information Studies folks twisted themselves into pretzels trying to apply Shannon’s Law to the social sciences.

    • If you could come closer to analyzing the work discused here, and try to understand the methodological steps used, and from there draw some interesting conclusions by yourself, may be you would contribute to uplift the level of this discussion

      • Well, please comment on the following links (two working documents made by myself) as a starting point: 1- just a mind map for a tentative structure of the climate system (because if you don’t understand the structure, forget about the dynamics of a complex system). Do you agree with this structure, the “concepts” (the right term in complex system analysis) included and their many links (actually delayed feedback loops)?: https://dl.dropboxusercontent.com/u/56918808/meta-model%20climate.pptx; 2- and another file giving you the phase plane representation of the Vostok data and some bullit style comments by myself: https://dl.dropboxusercontent.com/u/56918808/Phase%20plan%20Vostok.docx

      • Your first diagram is less useful than you might suppose. If you try to take into account all of the possible variables, you end up with an intractable problem. You are forced into reductionism. In the time I have followed WUWT I think I have seen theories that try to explain the climate based on each of the variables in your diagram. That’s a lot of theories. :-) Nobody has found the secret sauce yet and the alarmists take that as proof that it must be CO2. I was trying to figure out which logical fallacy that is and I stumbled on ludic fallacy. The use of computer models to bolster CAGW is a ludic fallacy. :-)

        Your second document passes the smell test. We bang back and forth between glacials and interglacials. Those sure look like attractors to me.

        My beef about fractals and chaos is that I can think of no case where they have been successfully used to make predictions.

      • Thanks for having taken the time to look at those two documents. The first one is just a mind map trying to summarize different hypotheses, potential links from a broad spectrum of scientific papers (some peer reviewed, some from the “grey literature” indeed). This is not a model (one more as you said): it is a condensed way to report a literature survey for discussion purpose. But for that you need to have some affinity for visual thinking, of course. Regarding the second document:it is just an easy way to spot a chaotic signature in time series. Indeed, as you mentionned, the future behaviour of systems exhibiting a chaotic signature is difficult to predict. but some significant progress have been made (in other disciplines than AGW, but the methodology is generic): one promizing track consists in crunching sets of (chaotic) time series with neuronal algorithms and find:the most optimum possible neuronal network. The link between the two approaches (mind mapping the hypotheses from the literature + optimizing neuronal networks) becomes then obvious: how different are those two figures. A step forward in understanding the structure of the complex system before even thinking of describing its dynamics and make forecastings. This make sense , no? Regarding predictability of chaotic time series, another quite interesting track is to look at visibility graphs. Are you familiar with that?

      • Henri Masson says:
        March 17, 2016 at 8:12 am

        … Regarding predictability of chaotic time series, another quite interesting track is to look at visibility graphs. Are you familiar with that?

        Visibility graphs are another one of those things about which I’m on the fence. For instance, we could use them to calculate tool-paths. On the other hand, we’ve been calculating tool-paths without needing them for a long time. The question is whether they actually convey any benefit. I should have been born in Missouri. :-)

    • “…the way the Information Studies folks twisted themselves into pretzels trying to apply Shannon’s Law to the social sciences.

      But Shannon’s laws is intuitively obvious. It shows that nothing can be communicated at all to people who cannot even handle one bit at a time…

      …I’ll get my coat.

      • But Shannon’s laws is intuitively obvious.

        WHAT???

        It shows that nothing can be communicated at all to people who cannot even handle one bit at a time…

        True enough. Actually, it’s worse. There’s a corollary to Murphy’s law that says that incorrect information is always transmitted on a clear channel.

    • Henri Masson says:
      March 17, 2016 at 12:35 pm

      … about visibility graphs: did you spot this paper …

      Here’s the understatement of the century.

      The methods used here have small shortcomings, for example, a good qualitative understanding of the system studied is needed for a correct interpretation of the results.

      I note that the paper cites Henry Mintzberg. He is a serious critic of this kind of thing. He has written extensively that analytical techniques are no substitute for actual managerial expertise.

      In 2004 he published a book entitled Managers Not MBAs (Mintzberg 2004) which outlines what he believes to be wrong with management education today. Mintzberg claims that prestigious graduate management schools like Harvard Business School and the Wharton Business School at the University of Pennsylvania are obsessed with numbers and that their overzealous attempts to make management a science are damaging the discipline of management. wiki

      • “a good qualitative understanding of the system studied is needed for a correct interpretation of the results”.
        Well, this is actually what I try to do by bringing to discussion the tentative “meta-model” recalled hereunder. This “meta-model” is nothing more than an attempt to bring together, on a single mind map, (almost?) all the statements & hypotheses I found by reviewing the (peer reviewed or not) literature on the subject, indeed with a broader set of key words than what is usually done in climatology. I expected from the distinguished participants to this blog discussion some focused remarks, suggestion or critics on the structure of this model, its components and links between them. “un coup d’épée dans l’eau” we say in French :-(

        https://dl.dropboxusercontent.com/u/56918808/meta-model%20climate.pptx

        Please note I want to focus only on the possible overall structure of this “meta-model”. Each component (“concept”) is obviously by itself a rather complex model. But we need to start somewhere; and I proposed a top bottom approach, which allows to get some kind of “helicopter view” of the climate system as a whole….and allows also to put each “component (i;e. anthropogenic global warming) at its right place, with its right “structural” driving force on the other components. …A sound starting point, no?

  24. To add a further point to my first post.
    l feel that the current warm period should not be viewed as the normal stable climate. lt only seems stable because its the only climate we have experienced, l think its better to view both the ice age and the warm periods as extreme climate change. lts only because during the warm period we are having just the one extreme is why it appears stable.

    • Glaciation send interglaciation are the two attractors in the current chaotic climate system.

      • Paul
        l think both ice age and the warm periods are both examples of extreme changes in the weather over the longer term. As l see it the warm periods are caused by a increase in a chaotic weather system. By which l mean there is a great deal of change to the weather patterns over much of the globe. Which spreads warmth across much of the globe. But during an ice age it goes the other way. There is a decrease of chaotic weather in the system. Leading to a lot less changes in the weather patterns and so increasing the amount of blocking in the weather. Which reduces the amount of warming that can spread across the globe, and increases the build up of cold where the the more static weather patterns allows this to happen.

      • dbstealy
        What makes me think that changes in weather are the cause of climate change rather then a result of it.
        ls the fact that the ice age became such a extreme event in certain parts of the NH. Had the weather patterns been just as chaotic during the ice age as they are now, Then yes they would be some cooling but not the extreme cooling like what happened in North America. There would be far too much movement in the global air masses for that to have happened.
        No! this type of extreme event need very static weather patterns over many years to build up that level of cold and then push it as far south as the USA..

      • taxed,

        I’m not arguing that you’re wrong. I don’t know.

        But I do know that the climate/weather conditions over the past century have not been “chaotic”. In fact, the past century has been the most benign climate in the entire geologic record.

        Extreme weather events have been steadily declining, and the 0.7ºC wiggle in global temperatures — over more than a century — is as small a change as anything oberved previously. Just prior to the current Holocene, for example, temperatures fluctuated by tens of whole degrees, within only a decade or two. We have been much more fortunate recently.

      • “But I do know that the climate/weather conditions over the past century have not been “chaotic”. ” You misunderstand the term. A (http://www.businessdictionary.com/definition/chaotic-system.html) “chaotic system” is one that is extremely dependent on initial conditions and in which small changes can cascade into large results. Chaotic systems tend to be inherently unpredictable since even small errors in the model can and will result in large divergence from reality over time.

        Two well-known chaotic systems are weather and orbital dynamics. Two bodies in an otherwise unpopulated universe are predictable. Three or more are not, not even theoretically. A few years ago, some astronomers built a very high-precision computer “orrery” or model of the solar system. Two separate runs, otherwise identical but differing by only a single bit in the position of one planet, resulted after a few million years with Pluto completely on the other side of the Sun and differences in the positions of the other planets.

        Likewise, weather famously exhibits the “butterfly effect”. If you think about it, you can predict the weather a day in advance by taking temperature, humidity, and pressure readings about every 10 miles or so (I forget the exact numbers) for about a 100 mile radius. If you want to go out 2 days, you need readings every 5 miles for 200 miles around, and so on. If you go out more than 2 weeks you need to know the conditions for every square inch on Earth, and past 3 weeks you need to start knowing the states on the other planets.

        This is why, for instance, the National Hurricane Center shows a projected hurricane track as a funnel, widening out as it projects further into the future. There is simply not enough information, nor can there be, to more accurately predict its path. Literally, if you projected, by computer simulation, the track out for a week, a difference between the model and reality in the starting conditions equivalent to one flap of a butterfly’s wings would result in a noticable difference at the end.

        One interesting characteristic of chaotic systems is that they often exhibit what are called attractors: areas of behavior that the system tends to stay close to, even if the exact location is unknowable. (The exact definition is rather mathematical). For instance, planets in the solar system tend to stay in their elliptical orbits. Hurricanes tend to stay in their tracks. However, a system can have multiple attractors and flip unpredictably between them after some stable period.

        So: the fact that the climate has stayed calm for some period is nice, but relatively meaningless in the long run. I suspect, based on the characteristics of the bast million years, that the current climate system has two stable attractors: one being warm, the other involving glaciers. Unless we know a lot more about the “state space” of the climate than we do, we have no idea what characteristics it may show just before it moves from one attractor to the other.

      • dbstealey
        A further point l feel l should have added.
        The key thing about the weather blocking during the ice age is where it formed. lt was near enough to the Arctic circle to draw the polar air southwards.

      • Paul of Alexandria,

        I don’t disagree with anything you wrote. But it isn’t what I replied to.

        I just wondered whether different weather causes the flips, or the flips cause different weather.

      • Sorry, I got carried away. Depends on what you mean by “weather”, I suppose. Climate is more or less the average weather over some period, so the weather for a given period can be called the “state”, or part of the state, of the chaotic climate system.

        See, for instance, the images at http://www.bing.com/images/search?q=chaotic+attractor&view=detailv2&qpvt=chaotic+attractor&id=BA4FF3AE499B18F4F2BECCFE5FCD49646205E3F7&selectedIndex=17&ccid=UwnRlo8A&simid=608019734833595424&thid=OIP.M5309d1968f0037035506dfbf7a6fc1a1o0, in the center of the page. These are (simulated) outputs that you would see on an oscilloscope from a particular chaotic circuit. The two axes represent the “state space” of this system Note that the line circles the two areas that it never enters, switching occasionally between the two. The two areas orbited are the attractors. While the line crosses itself, it can never repeat two consecutive points, if it did it would repeat and not be chaotic.

        The weather, then is similar. “Calm and warm” is one small area on the plane (really in a space with many more dimensions than two). The climate may pass through this area going any which way, orbiting either attractor or being in the process of switching. In the context of, say, WBWilson’s graph above, a particular patch of nice weather may be a peak in a glacial period, a valley in a warm period, or the middle of a crossover. You really can’t say except in hindsight, unless you have a much better model of the whole system than we do now.

    • Taxed, you should probably correct your terminology. We’re still in an ice age, currently in an interglacial period, and patiently awaiting the next glacial.

  25. From the article: “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.”

    I take it they have found no “human-induced climate changes” in their data.

  26. Boris Pavlovich Belousov was a Soviet chemist who in the 1950’s discovered a chaotically oscillating reaction involving bromine and acid. After Belousov’s death it would become known as the Belousov-Zhabotinsky (BZ) reaction or oscillator.

    https://en.m.wikipedia.org/wiki/Belousov–Zhabotinsky_reaction

    However Belousov’s own attempts to publish his findings in international scientific journals ran into a brick wall. Editors and reviews were simply unwilling to believe what Belousov had observed. After more than a decade Belousov published the work in an obscure non peer reviewed journal. He passed on his notes to a student Zhabotinsky, left science and eventually committed suicide. Zhabotinsky eventually managed to gain recognition for the phenomenon.

    How many of you have ever heard of the BZ reaction? That’s what I thought. It remains an inconvenience swept under the carpet, as do chaotic-nonlinear phenomena generally, as evidenced by comments here such as those by george e smith. The physics community still rigorously averts its gaze from nonlinear-chaotic phenomena trying to shoehorn everything into rigid linear models – climate science is a foremost example of this. Ed Lorenz’ astonishing finding in 1963 about deterministic nonlinear flow should have revolutionised science, like the BZ reaction. But it didn’t.

    George – were you one of the reviewers of any of the Belousov manuscripts?

    • Belousov. You might be surprised. I know very well the Belousov-Zhabotinsky reaction since I am a chemist. Moreover, living in Belgium, we have had the chance of having a Nobel Prize winner for precisely studying these oscillating reactions: Pr Ilya Prigogyne. Most scientists in Belgium know about them. I use these oscillating reactions to impress the public and the students during some demos attempting to show the beauty of science.

  27. The crux of the current climate change hysteria hinges on the irresponsible speculation that humans can change their behavior enough to nullify not only the climate effects they are causing but to also mitigate the natural variation that is taking the climate in a direction that is harmful to human habitation and the biosphere.

    The work of Murray Salby shows that the long term trend is due far more to natural causes than to human causes. Should humanity cease to exist in an instant, that would only move the natural trend line by less than 100 years. But if not a single human were alive, that is to say, if humanity sacrificed itself to save the earth, what deity did we offer ourselves to? Gaia?

  28. “The Gulf Stream, which transports warm water from the equator north to the Atlantic, where it is cooled and sinks down into the cold ocean water under the ice to the bottom and is pushed back to the south. This water pump can be put out of action or weakened by changes in the freshwater pressure, the ice sheet breaking up or shifting sea ice and this results in the increasing climatic variability.”

    The Gulf Stream might also be disrupted by geological changes. For instance a continuation of the volcanic activity from the Virgin Islands to Venezuela could one day block the doorway to the heat pump which drives the Gulf Stream. Might just change the complexion of the entire climate system. Life as we know it is tenuous.

  29. “We can see that the climate during an ice age has much greater fluctuations than the climate during an interglacial period. (…)
    The climate during the warm interglacial periods is more stable than the climate of ice age climate.

    Yet they claim

    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.
    “The differences we find between the two climate states also suggest that if we shift the system too much, we could enter a different system, which could lead to greater fluctuations.

    So they claim that a natural warmer climate is more stable but a human induced climate should have more fluctuations! Why would human induced climate change be different? Are laws of physics suddenly changing too? So either a warmer climate is more stable regardless of the reason of the warming or… well, more fluctuations in climate suggest that contrary to the consensus, the reality is climate is not warming, but cooling, which circulation changes do suggest.

  30. Stunning work. Whatever warms me now, warms the day. Whatever warms the day warms the season. Whatever warms the season warms the year. Whatever warms the year warms the decade. And so on.

    I think the 800,000 year reconstruction http://www.climate.unibe.ch/~stocker/papers/schilt09qsr0.pdf shows a cyclic pattern of net evaporative discharge/cloudy trend that happens rather quickly, followed by a long term net recharge/cloudless trend that happens slowly and jaggedly. This reminds me of the relatively second of time of ENSO noise pattern and oscillations, but on a millennial cyclic trend up and down. The oceanic volume and the difference between how quickly oceans evaporate heat, and how slowly they gain heat is likely the physics behind what drives this unbalanced process that then drives the ice ages and warm periods.

    What warms and cools us now, did so over millennials of time. Ergo properly demonstrated in a repeating fractal pattern

    • Pamela
      l feel its not just about the amount of cloud cover, but also how much of this cloud cover moves southwards where it has a greater cooling effect on the climate.

      • The clouds mitigate how much solar insulation is available at the ocean surface. Direct cooling because of cloud cover is not the issue here. It’s solar energy recharge of the oceans, which is diminished with cloud cover, especially in the equatorial band. Cloud cover in the equatorial band means that evaporation is in action, along with release of heat. Cloud cover in that band is a sign of a warming trend, not a cooling trend. Dry and and clear skies is a sign of a cooling trend. To wit, during La Nina, clouds clear and evaporative heat energy is kept at bay, which leaves us in the cold. However, while we are cold, the oceans are getting recharged.

  31. “We only have about 150 years of direct measurements of temperature, so if, for example, we want to estimate how great of variations that can be expected over 100 years, we look at the temperature record for that period,

    BS. With 150 years of direct measurements, you can make estimate of 30-50 years. You need 3-5 cycles in your data to make any estimate at all.

    • You also need 150 years of quality data that is also complete.
      Data that is limited to pretty much north America and Europe does not tell you much about what is happening for the entire world. Even if all the data had been of high quality.

  32. “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 fluctuation during the ice age behave in the same ‘fractal’ way as the other natural fluctuations across the globe,” Peter Ditlevsen.

    Oh good, what a relief. Astronomical variations result in 10s to 100s of watts/m^2 variation in insolation yet apparently they have a smaller effect than the fractal nature of fluctuations. C02 has an effect of a mere watt or two, so there must be no measurable effect of C02 at all.

    Peter

    • My hunch is that it takes longer and in a see-saw pattern, to recharge what was lost to evaporative discharge, and that evaporative discharge is a rapid one-rise process once it gets underway. Place that ENSO process on a long term ocean heat recharge/discharge unequal imbalance, likely because of ocean volume, and you have a fractal.

    • What gets me is that they don’t even understand that “interglacial” is part of the ice age. The correct term would have been “glacial period”, not “ice age”. Can’t say I respect their science much.

      • Never imagined that this is may be just a translation problem they faced and not a “scientific background” one? Everybody is not a “native” english speaking person and has may be been educated in another language. Please be patient with people trying to communicate with you in your language. or do you want to switch to German, French, italian, Spanish, Dutch, Danish, Swedish, etc. and rely on Google translations?

      • Henri, I didn’t see any evidence of that in reading the text. Usually it’s pretty obvious if a poor translation is in effect. Can you show otherwise?

  33. Researchers from the Niels Bohr Institute have analysed the natural climate variations over the last 12,000 years

    Not likely, since we don’t really have accurate climate record of even the last 100 years. Anything older than that is pretty much fantasy.

  34. Mush.

    [quote]We have to go very far back into the geological history of the Earth to find a climate that is [u]as warm as what we are heading towards[/u].[/quote]

    And please send us more money.

  35. Mush.

    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.

  36. From Wikipedia: …in 1724 Daniel Gabriel Fahrenheit produced a temperature scale which now (slightly adjusted) bears his name. He could do this because he manufactured thermometers, using mercury (which has a high coefficient of expansion) for the first time and the quality of his production could provide a finer scale and greater reproducibility, leading to its general adoption. In 1742 Anders Celsius proposed a scale with zero at the boiling point and 100 degrees at the freezing point of water,[8] though the scale which now bears his name has them the other way around.

    So why don’t we have any records of air and water temperature until 1850?

  37. At first glance it seemed to make sense because fractal design is all around us in nature – but shouldn’t meteorologists be able to see weather the same way then? Call me a skeptic…..

    • #4timesayear : just go back to some introductory text to Chaos, i;e. James Gleick, “Chaos, the amazing science of thee unpredictable”(Vintage Books, 1998). Or go through some more recent and more mathematical ones you can find on Google or Amazon. if needed, I can help you in your search, as several other commenters on this blog can do also.

    • They are two different things, although related mathematically. “Chaotic” refers to the sensitivity of a system to initial conditions. “Fractal” basically refers to the self-similarity of a system at different scales.

  38. This is a bit of gratuitous nonsense.

    “… 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. …”

    The Earth is pegging an average ~6C colder now than it was just 15 million years ago, and is currently averaging about 4.5C to 5C cooler than just 5 MYA. Plus we’re at the end of an interglacial phase, and for the last 4k years have been steadily dropping on a trend toward the next glacial cycle.

    Do these people at Niels Bohr Institute, or “Nature Communications”, even reality check the theory and claims against the climate record we actually have before publishing thus stuff?

    Let’s have that again: “… 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. …”

    BUNK

  39. “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”

    A thousand years counts as “very far back”?

  40. One small thing i caught in the discussion is: “generalized Hurst exponent of H~0.7 is significantly different
    from the trivial value H~0.5. The glacial climate state has a distinctly more fractal characteristics, with a much larger generalized Hurst exponent H~1.2”

    The Hurst exponent is typically derived from the Fractal Dimension D where 1<= D <= 2 using D = 2 – H. In which case 0 <= H <= 1, with H = 0.5 being uncorrelated white noise. Not sure where they got that from as there is no citation, but AFAIK it's wrong from the generalized Hurst Exponent.

  41. An observation. If I want to prove man made global warming I start with the industrial revolution, circa early 1800s, and I ignore any temperature records from late 1700s, or any data about inter-glacial periods. Of course the temperature increases for awhile. It is all very natural. But if we are at the end of an inter-glacial, as has been suggested, the long term trend is down, not up.

    Or am I missing something?

    Arthur? Anyone?

    Is my conclusion right?

  42. Hmm. Thinking about climate as a chaotic system, re my long-winded previous posts, what would the state space of the system consist of? I can think of ocean and atmospheric temperatures, with the solar flux and cosmic radiation being system inputs. What else do you need to say “this is the climate”?

      • The Ox axis is the temperature at instant “t” while the Oy axis gives temperature at time “t + tau”. It is a visual way to check the “predictability window” of a system. For a purely deterministic system, the points fall on one well defined curve. For random data, they fillt he whole plan. For a dynamical (chaotic) system, the points are on trajectories around two or more “strange attractors” Finding the best value of “tau” is a little bit tricky. One way to do it is to find the first minimum in the mutual information graph (mutual information vs “distance” between points in the time series)

      • Thank you. Did you happen to read the Nicolis paper cited by Belousov below?
        Thinking about it, this would explain the “snowball Earth” of some 650 years ago and the warm stretch for the dinosaurs. Something, probably continental drift, pushed the attractors far enough apart that switching between the two became very unlikely.

      • Nicolis and other colleagues from the Prigogine team were my professors of Physical Chemistry at the University of Brussels ;-)
        As I said earlier somewhere in this discussion, if you use a phase plan (built according to the Takens theorem) you can “visualize” the position of the two attractors and analyze the trajectories over time around them. Hurst exponents or Lyapounov exponents (more tricky to compute) are a way to describe these trajectories. The exact moment of switching from one attractor to another is driven by the nature of the system (no need for an external forcing) and is unpredictable. What can be predicted is the statisitical distribution of time intervals between switches. This has been found by a climatologist: the Edward Lorenz of the “butterfly effect”.

  43. The author is making huge guesses and speculating with a very limited amount of research and understanding of these “fractal patterns” and earth’s climate systems. Not impressed.

  44. This important descriptive study by Ditlevsen gives useful new detail to the known fractality of climate on all timescales.

    Comments that “fractals are deterministic” miss the point. Fractals are diagnostic of underlying nonlinear-chaotic dynamics.

    In climate the most important implication of this is that climate changes BY ITSELF. The habit of looking for a discreet “forcing” for every wiggle of a climate curve is profoundly wrong, useless and misleading.

    This was expressed better than I can in the following paper:

    Nonlinear dynamic systems in the geosciences

    G. Nicolis1 and C. Nicolis2

    1Université Libre de Bruxelles
    2Institut Royal Météorologique de Belgique

    Abstract

    Geophysical phenomena are often characterized by complex, random-looking deviations of the relevant variables from their average values. Typical examples of such aperiodicity are the intermittent succession of Quaternary glaciations as revealed by the oxygen isotope record of deep-sea cores of the last 106 years or the pronounced spatial disorder characterizing geologic materials. A major task of the geoscientist is to reconstitute from this type of record the principal mechanisms responsible for the observed behavior. Traditional approaches attribute the complexity encountered in the record of a natural variable to external uncontrollable factors and to poorly known parameters whose presence tends to blur fundamental underlying regularities. Here, we consider that complexity might be an intrinsic property generated by the nonlinear character of the system’s dynamics. We review bifurcations, chaos, and fractals, three important mechanisms leading to complex behavior in nonlinear dynamic systems, and stress the role of the theory of nonlinear dynamic systems as a major tool of interdisciplinary research in the geosciences. The general ideas are illustrated on the dynamics of Quaternary glaciations and the dynamics of tracer transport in a sediment.

    Get the paper:

    http://www.kgs.ku.edu/Publications/Bulletins/233/Nicolis/

    • ‘Comments that “fractals are deterministic” miss the point. Fractals are diagnostic of underlying nonlinear-chaotic dynamics.’

      It should also be noted that chaotic systems are also deterministic.

    • Of course, to complicate the matter there are external forcing inputs, which may or may not also be considered random, including changes in the Sun’s output, the particular galactic environment that we’re passing through at the moment, cosmic ray levels, and continental drift.

    • Paul of Alexandria

      It should also be noted that chaotic systems are also deterministic.

      Yes but … when chaotic system are sensitive to initial conditions down to the quantum level then deterministic means not deterministic. It’s analogous to Pierre Laplace’s conjecture that if we knew the location and properties of all the particles in the universe, we could predict the future. What practical use is that?

      Thanks for your endorsement of the paper, I haven’t read it fully yet, I’ll try to do so (maybe skipping the maths).

      • Ultimately, all chaotic systems are sensitive to that level; the question is: how far out can you go before the divergence between model and reality becomes too much? Weather is also chaotic, and we can go out a good week before things start to diverge too much.

        While a good model of the climate won’t let us predict with accuracy too far, it would let us determine what the important characteristics are, where the attractors are, and what kind of excursion is most likely to result in an attractor shift.

      • Paul

        Out of interest – is it known to what spatial scale chaotic systems are sensitive?
        Does it go down to the atomic scale – or even smaller (e.g. quantum)?
        Either in theory or experiment.

      • I really don’t know. I think that it depends on the particular system and the time scale involved. For instance, see https://en.wikipedia.org/wiki/Stability_of_the_Solar_System
        “In 1989, Jacques Laskar of the Bureau des Longitudes in Paris published the results of his numerical integration of the Solar System over 200 million years. These were not the full equations of motion, but rather averaged equations along the lines of those used by Laplace. Laskar’s work showed that the Earth’s orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years’ time.”

        Also http://hockeyschtick.blogspot.com/2013/09/chaos-theory-explains-weather-climate.html
        Lorentz’s original investigations lead him to say that the molecular motion in the atmosphere keeps weather predictions to less than 3 weeks,

        The various chaotic electrical circuits are effected by electrical and thermal noise, so I would think that they could definitely be sensitive to quantum effects.

        It would be fascinating to figure it out.

  45. The author says at the end we are entering a new period of warmth that might be unpredictable because we could be going from one regime to another. So far this hasn’t been proved and that is very important but it must be accepted that this is an accurate statement that unknowns to some extent are hugely endemic to this field. Is it not contradictory to say “it is settled” then? What is settled? Nothing.

    It is not settled if this is unprcedented temperatures. It is not even known what is a temperature of the earth. I have several blogs on all these topics pointing out the many unknowns and many false predictions of this “science” which fails repeatedly to meet any predictions.

    https://logiclogiclogic.wordpress.com/category/climate-change/

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