Statistical study of past temperature records suggest possible undetected natural climate forcing cycles

Godfrey Dack writes in with this:

Everyone will be familiar with the difficulty of listening to a conversation held with a friend in a crowded room with many other conversations going on at the same time. So it is with many fields of scientific investigation where it is difficult to tease a particular trend out from masses of data. In the first case, we could call the friend’s conversation ‘The Signal’, and the background conversations ‘The Noise’.

In looking at climate data, trends (the signal) can be graphically represented by a (generally) smooth curve, usually flanked by a range of experimentally predicted or actually measured values (the noise). Joining up every point on a graph of such data would give a jagged line which could be thought of as a combination of many alternating functions over a wide range of frequencies.

If you tuned an old-fashioned analogue radio away from any station the hiss you would hear would be termed ‘White Noise’ whose frequency distribution would be random but whose intensity would be equal over all frequencies like the spectrum of pure white light. Another type of noise encountered in nature shows a random distribution of frequencies but each frequency octave carries the same amount of energy and, because energy of a wave is inversely proportional to the frequency, to make all ‘octave containers’ have the same energy, low frequency octaves carry a greater proportion of the overall energy and because, in light, low frequencies are at the red end of the spectrum this noise is called ‘Pink Noise’. Pink noise phenomena occur a lot in nature and can be the result of some low frequency (i.e. long time-period) disturbance.

In a recently published paper with the snappy title – ‘Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode ‘ (paywalled) the authors claim to have discovered pink noise energy signatures, on time scales over many decades, appearing in historical climate proxy data both before, and after The Industrial Revolution. The authors looked at two large data sets: monthly average surface temperatures from 1901 – 2012, and radiological ice-core measurements dating back many thousands of years.

The ‘pink-noise’ aspect of the analysis suggests that there may be some aspect of climate variation due to a naturally produced slow varying function which may be acting together with anthropogenic factors in a resonant fashion rather like an adult pushing a child on a swing just at the right moment can rapidly increase the amplitude of the swing.

The authors make no attempt to identify the origin of the suspected natural component, be it solar, astronomical or as yet of an unsuspected nature, however, if such natural forcing does exist on top of man-made forcing, it may exaggerate the significance of anthropomorphic factors in climate change.

Figure 1. Spatial distribution of the shortest timescale (in years) at which pink-noise behavior appears in the GISS data set. This transition takes place on multidecadal timescales nearly everywhere. The red color denotes locations that do not show pink-noise characteristics on timescales up to 65 yr (half of the total length of the data set), with the most prominent feature being in the tropical eastern Pacific. White regions show locations where continuous data are absent.

 

Figure 2 Spatial distribution of the values of d ( τ ) represented by one-point correlation maps and an EOF analysis using the GISS monthly averaged surface temperature from 1901 to 2012. Centered in the eastern Pacific at 120 ′ W , 20 ′ N , we calculate the correlation between the d ( τ ) at this position and that at any other position (a). The spatial distribution of the correlation is nearly identical to the dipole mode called the PDO [1]. The newly constructed index (red), the normalized value of d ( τ ) | 12 0 ′ W , 2 0 ′ N − d ( τ ) | 18 0 ′ E , 4 0 ′ N , is compared with the traditional normalized PDO index (blue), which shows an excellent match. A similar one-point correlation map is constructed based on the geographic position at 50 ′ W , 38 ′ N and is shown in (b). This map is very similar to the SST pattern in the negative state of the NAO [19], as shown by the correlation between d ( τ ) | 50 ′ W , 38 ′ N − d ( τ ) | 40 ′ W , 50 ′ N (red) and the normalized NAO index (blue). The EOF analysis is applied to the values of d ( τ ) , with the leading mode explaining 21% of the total variance, as shown in (c), along with the PC. This mode connects the major PDO region in the eastern Pacific to the Southern Ocean through a continuous same-sign region, as distinguished from the other areas. The time series of the principle component of the mode is analyzed using MFTWDFA (d). At lower frequencies, the variability of d ( τ ) parallels pink noise (red dashed line, β = 1 ), with a crossover time of ≈ 15     yr . Reuse & Permissions Figure 3 Figure 3 The initial (a),(c) and final (b),(d) timescales exhibiting pink-noise dynamics in the paleoclimate data across the globe [20], where (a) and (b) [(c) and (d)] show the analysis for the complete data set (after removing data from 1850 to present), to enable us to distinguish between natural climate variability and anthropogenic forcing. There are no discernible differences between (a),(b) and (c),(d), implying that pink-noise dynamics are an internal characteristic of Earth’s climate system

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89 thoughts on “Statistical study of past temperature records suggest possible undetected natural climate forcing cycles

  1. From the article: “The authors make no attempt to identify the origin of the suspected natural component, be it solar, astronomical or as yet of an unsuspected nature, however, if such natural forcing does exist on top of man-made forcing,”

    Well, I would have to say that that natural forcing definitely exists because humans have only been on the Earth a relatively short time, and the climate was doing its thing long before humans came along.

    Questioning whether natural forcing exists seems a little ridiculous to me.

    • This paper is important because it notes that the temperature data exhibits a pink noise signature.

      In pink noise, low frequencies predominate. In any time scale there will be such low frequencies that the signal will seem to have a long term trend.

      The actual scientists among the alarmists do not deny natural variation, they do claim that they can discern the human signal as distinct from the natural variation.

      What we do see is that, among many other statistical abuses, scientists assume that averaging reduces error. They take measurements with twenty percent error bars and claim to produce calculated results accurate to one percent. You can’t get away with that with pink noise.

      • Excellent observations.

        There are many sins committed by applying the normal distribution and assumptions of IID data to distributions that are neither.

      • Measuring one thing many times with the same instrument and averaging the results reduces error.

        Measuring many things once with many different instruments and averaging the results produces nothing of any use whatsoever.

      • Another point is that averaging only works if you can average at least one full cycle of your noise.
        They are averaging over a period of months to years, yet we know of a number of cycles with frequencies decades long, and suspect the existence of cycles centuries to millenia long.

        If you can’t define the noise, there is no way you can eliminate the noise.

        • Engineering trained signal analysts had already determined around fifty years ago that you need around a 360 year period for one full cycle. They were firmly told a the time to go back to your grease monkeying and leave science to us.

        • If you examine the figures in their paper (figures are not paywalled), you’ll see their Fig 2 is the anthropogenic analysis (using PCA, I might add) of less than a century. Their Fig. 4 is an analysis of paleo-reconstructions going back over 100,000 years.

          They somehow then come up with a proposed hypothesis:
          “We hypothesize that this pink-noise multidecadal spatial mode may resonate with externally driven greenhouse gas forcing, driving large-scale climate processes.”

          This supposed “resonance” is from one (modern era) CO2 forcing impulse. There is no doubt there are long term climatic process on the scale of centuries to millenia to glacial age time scales which have substantial energy balance forcings as the climate dynamically responds. That they think they can impose a century long impulse on these and call it “resonance” is doubtful.

          Analogy:
          From an examination of the tip of the elephant’s trunk, we reconconstructed the whole beast.

          Impossible.

      • “You can’t get away with that with pink noise.” At least not until you know the characteristics of the noise and your measurements exceed them. With the noise increasing about 3dB per octave as the period gets longer it makes it a bit hard to separate a signal from the noise.

      • Averaging to improve error is also not universal it only works on things that have a smooth continuous distribution. You can not use the process on things that have quantized values, or stange distributions like cauchy distributions.

        If you want a bit of a laugh read articles messing around with lorentz attractors and chaos theory with global average temperature data. The background here is a lorentz distribution is usually called a Cauchy distribution. You can not use values derived from a distribution that is forbidden in what you are supposedly trying to study.

        One of the more interesting questions that never seems to get asked in Climate Science because we have to be 97% certain is what is the expected distribution. It is interesting because if you assume CO2 is the driver you have a Quantum process sitting over Classical feedback processes. Quantum distributions and Quantum chaos are very different to there classical counterparts. In a real science field it would actually be interesting to see what could be determined but it will never be studied because of the politics behind Climate science.

      • All these results with precision of 0.01K is nonsense anyway. And if climatologists think they can measure that precise – they need to take a course in metrology. You can’t do better than systematic uncertainty. You can reduce random error, but it will still be added to the systematic error. And systematic error is what? Half a degree?

      • Very good point Bob. The main statistical abuse is fitting a straight line to everything and then pushing the assumption that this will continue into the future as the most likely outcome.

        however, if such natural forcing does exist on top of man-made forcing, it may exaggerate the significance of anthropomorphic factors in climate change.

        One small step in the long walk back. It has taken 30 years to build the hype, it will probalby take another 30 to get back to proper science.

    • Something caused the WUWT website to crash and Anthony had to disable the new commenting software in order to get the website back on line.

      • Something (or someone) wiped-out the commenting interface design which caused the server to stop serving pages. To get the resource back online, WordPress technicians and Anthony had to revert back to some standard interface.

        My conjecture is it was a malicious attack (more sophisticated than a temporary Denial of Service attack) against WUWTs successful and widely read articles. My suspicion is his post on “Google is Evil, this video proves it” triggered some tech-savvy snowflakes into a noble cause corruption attack on his WordPress configuration.

        • Thank the Lord for backups. Sounds like they had to revert to their last one to get up and running. I sympathize… I just had to drop my computer back 7 days after installing what was supposed to be a fully debugged version of a program.

  2. On a spherical planet with a 70% liquid surface, a gaseous atmosphere, a spinning on its axis, orbited by a moon with tidal effects, the pair of them orbiting a star in conjunction with a set of other planets, near and farm, large, very large and small not to mention all that ‘zodiacal dust and asteroids etc and there is evidence of multifrequency and competely natural phenomena in the atmosphere?

    Who’da thunk it?

    Well, not the climate experts apparently.

    • “Who’da thunk it?”

      Quite a lot of people actually. But they are all mistaken.

      Nobody has ever shown a relationship with sun cycles, the moon, the planets or “zodiacal dust and asteroids” and the surface temperature record. It’s exactly the 70% liquid surface and a host of temperature-driven emergent phenomena that shield the atmosphere from this kind of cosmic influences. Willis Eschenbach has shown this time and again.

      • Really – the astronomical cycles over scales up to thousands of years make no difference to our climate? I’m shocked I tell you.

        • Lance, the Milankovich cycles are undoubtedly real.

          However, I can’t name another “cycle” which affects surface climate. Or, as the Polar Bear said just above,

          Nobody has ever shown a relationship with sun cycles, the moon, the planets or “zodiacal dust and asteroids” and the surface temperature record.

          w.

          • The Pacific and Atlantic multidecadal oceanic oscillations are cyclical. ENSO is sub-decadal, hence more of a weather event, but its own cycles of greater or less frequency affect climate.

            The ~11-year solar cycle affects many meteorological phenomena, as do the sun’s longer cycles. Just one of numerous papers finding solar cycle effects on the atmosphere:

            Solar cycle effects on Indian summer monsoon dynamics

            https://www.sciencedirect.com/science/article/pii/S1364682614001370

            Bond cycles appear to be the continuation into interglacials of Dansgaard-Oeschger cycles in glacial intervals.

          • Warm and cool fluctuations during the Holocene Climatic Optimum have been attributed to Bond cycles, as have those after it, ie the Egyptian, Minoan, Roman, Medieval and Modern Warm Periods, and intervening cool periods, such as the Little Ice Age, Dark Ages and Greek Dark Ages SPs.

          • Bond cycles have recently been recalibrated to ~1000 years from Bond’s original estimate of ~1500 years:

            A re-examination of evidence for the North Atlantic “1500-year cycle” at Site 609

            https://www.sciencedirect.com/science/article/pii/S0277379112003095

            Ice-rafting evidence for a “1500-year cycle” sparked considerable debate on millennial-scale climate change and the role of solar variability. Here, we reinterpret the last 70,000 years of the subpolar North Atlantic record, focusing on classic DSDP Site 609, in the context of newly available raw data, the latest radiocarbon calibration (Marine09) and ice core chronology (GICC05), and a wider range of statistical methodologies. A ∼1500-year oscillation is primarily limited to the short glacial Stage 4, the age of which is derived solely from an ice flow model (ss09sea), subject to uncertainty, and offset most from the original chronology. Results from the most well-dated, younger interval suggest that the original 1500 ± 500 year cycle may actually be an admixture of the ∼1000 and ∼2000 cycles that are observed within the Holocene at multiple locations. In Holocene sections these variations are coherent with 14C and 10Be estimates of solar variability. Our new results suggest that the “1500-year cycle” may be a transient phenomenon whose origin could be due, for example, to ice sheet boundary conditions for the interval in which it is observed. We therefore question whether it is necessary to invoke such exotic explanations as heterodyne frequencies or combination tones to explain a phenomenon of such fleeting occurrence that is potentially an artifact of arithmetic averaging.

          • The above paper has been cited 24 times, including in this study published last month:

            Meltwater and seasonality influence on Subpolar Gyre circulation during the Holocene

            https://www.sciencedirect.com/science/article/pii/S0031018218300579

            And in this 2016 book:

            Evidence-Based Climate Science (Second Edition)

            Data Opposing CO2 Emissions as the Primary Source of Global Warming

            Chapter 16 – The Sun’s Role in Climate

            https://www.sciencedirect.com/science/article/pii/B9780128045886000161

          • The Milankovich cycles are at best trivialized by those who are aware of them. The most telling example of this is from the Wikipedia article on the subject:

            The relative increase in solar irradiation at closest approach to the Sun (perihelion) compared to the irradiation at the furthest distance (aphelion) is slightly larger than four times the eccentricity. For Earth’s current orbital eccentricity, incoming solar radiation varies by about 6.8%, while the distance from the Sun currently varies by only 3.4% (5.1 million km). Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its most eccentric, the amount of solar radiation at perihelion will be about 23% more than at aphelion. However, the Earth’s eccentricity is always so small that the variation in solar irradiation is a minor factor in seasonal climate variation, compared to axial tilt and even compared to the relative ease of heating the larger land masses of the northern hemisphere.

            In fact, when the Earth’s orbital eccentricity is at its greatest (0.0697 versus today’s 0.0167), the variation of insolation ranges from -143 W/m^2 to + 160 W/m^2 every year, as opposed to the +/- 88 W/m^2 we see today. A swing of 305 W/m^2 isn’t trivial compared to today’s swing of 176 W/m^2. It dwarfs the ~3 W/m^2 extra we get from CO2. How is this “a minor factor” in climate variation?

      • The fact that there are so many variables makes it impossible to separate out each one’s contribution to the variation. Some may be codependent. No statistical test can replace a real life experiment. I do propose one minor real life experiment. I would like a long term study done on pyrgeometers pointed to the sky from the same surface spot every night to detect any back downward IR. The cloud cover should be noted on each night so as to tease out that variable.

        • How would that tease out the incoming from the atmosphere from its own emissions and the incoming from all of the radiators outside of it, directly, as well as the incoming that is absorbed and re-emitted? Go out at night. Look up. See stars shining from their own light emission and the planets shining from both reflected sunlight and their own thermal emissions. Recall that astronomy sensed from EM waves is impossible if the extraterrestrial objects didn’t reflect light or emit it. Also don’t forget that the theoretical black body emission is a limit and that it has assumptions and conditions embedded in its logic.

          • You are right, perhaps it is hopeless to try to measure back radiation. NASA seems to think they can. However their energy budget figures dont make sense in that they have set up numbers that dont account for upward radiation to correspond to the back radiation ,seeing that CO2 and clouds radiate isotropically.

      • Actually there is some Russian research regarding Zodiacal dust (Ermakov et al 2008) apart from sun cycles and Milakovich cycles but just because ‘nobody has ever shown a relationship’ does not mean that is not a prospective area to research. Unfortunately the carbon obsessed research-political complex is madly spending all its money elsewhere which is probably a good reason as to why nobody has been successful. I doubt if the effects are some nice easy to find, dominant frequency component but rather an physical interaction between different elements. Maybe its a bit like why astrology never came up with the concept of space-time. It just seems more prospective to me than carbon obsessed self loathing.

      • ‘Blair Polaire’ obviously you have not looked at the Fourier Amplitude Spectrum for the Earth’s temperature. As the temperature level determines the rate of change of the CO2 concentration, the weekly CO2 data from Mauna Loa can be used as a proxy for the weekly temperature level. Fourier analysis of the annual rate of change of CO2 derived from the Mauna Loa weekly CO2 series shows maxima that correspond to the synodic and draconic periods of the Moon, the synodic periods of Mars and Venus and the sideral period of the Earth. Other maxima may relate to the interaction of the orbital periods of the Moon and the planets of the Solar System. See: https://www.climateauditor.com

  3. The author has the relationship between the Scientific view of “Signal” and “Noise” exactly correct. Geologists, especially those adapted to utilize Sequence Stratigraphy, think of the “Noise” as a natural variation of sea level from 50 meters higher to 100 meters lower than current level. Therefore, where is the “Signal”? Where is the dramatic change in sea level that shows a fundamental change in natural sea level variation sufficient to constitute a “Signal”? Doesn’t exist.

  4. Think of the Earth as a sphere covered with a thin skin of water and air.

    Some folks investigated what happens to a sphere when it’s excited by a simple signal. The behaviour is very complicated but the resulting signal waveforms closely resemble those observed in the climate. link

    Since some geophysical processes take place on time scales ranging up to centuries and millennia, it is entirely unsurprising to observe “pink noise energy signatures, on time scales over many decades”.

  5. Are climate alarmists trying to blame the failure of their computer models on “pink noise” without making any “attempt to identify the origin of the suspected natural component”?

    And how I they know that “it may exaggerate the significance of anthropomorphic factors in climate change”? Isn’t it just as likely that the forces oppose or mute each other, especially when the waves aren’t synced to each other?

    • Are climate alarmists trying to blame the failure of their computer models on “pink noise” without making any “attempt to identify the origin of the suspected natural component”?

      I don’t think so. It’s pretty important that they acknowledge that the data looks like pink noise. Most human progress has resulted from people observing that something happens without immediately being able to explain why.

  6. So, in summation, climate does what it does, humans are not causing it and can not stop it. Where is my check?

  7. I have not read the (paywalled) paper, so it is not clear to me how the authors can get the spatial resolution in their results shown in Figure 1. Spatial variation is exhibited between remote regions of the oceans where, at least to my understanding, actual data would be extremely sparse when we look back 100+ years.

  8. “Teasing a signal out of noise”. It is an unfortunate selection of terms. I understand there can be legitimacy in such an exercise, but climate scientists have been “teasing” Armageddon that hasn’t happened yet out of noise in their desperate search for the smoking gun that Maurice Strong told them to find now for 40 years now. Innundation of the West-Side Hwy in NYC has been postponed from 2000 to 2100. All manner of death spirals proved to be slower to materialize but they are are collecting in piles to destroy us all in 2100, unless we cough up $100 trillion in “protection” and surrender our civilization to a progressive troika.

  9. I obviously have not read the article with any determined focus yet, but my first impression, on a skim, is …
    NOT “pink noise”, but green noise.

    The pushing-the-child-on-a-swing analogy seems like a future open door for somebody to cite this as supporting the tipping point idea, where humans can push things over a catastrophic edge. Yeah, climate change is largely natural, but humans can kick start a dominoes effect, the fearmongers will say, and here’s scientific proof.

    • Resonance can be constructive, or destructive, depending on phase angle.

      Whether the child is pushed so as to increase the amplitude of the swing’s travel is entirely unknown in the putative analog of climate.

  10. OT but interesting…

    “President Trump was enraged this past year when he found out his predecessor was knowingly funding a terrorist organization. The organization was so bad they had a ‘pay to slay’ program in which they would give money to the family of the murderer—the more gruesome and high profile the kill, the more money the murderer’s family would receive. Sick.

    President Trump was rightfully appalled by this terrorist organization—even more upset when he found out the U.S. was a financial contributor of theirs.

    ~ Allan Reynolds”

    U.S. STOPS FUNDING PALESTINIAN TERRORISM
    https://freedomnewsreport.com/2018/09/17/u-s-stops-funding-palestinian-terrorism/

    The War on Terror has deep financial roots and Pres. Donald J. Trump just bulldozed them by cutting off money to Palestine.

    Left-leaning headlines are once again trying to take the America First president to task by claiming the policy move takes money from hospitals and refugees. Nothing could be further from the truth.

    In fact, the Palestinian Authority has a long-standing relationship with radical Islamic extremists that commit atrocities. If these terrorists die or are incarcerated during their jihad against innocent women, children and civilian men, they and their families are robustly rewarded through a so-called “Martyrs Fund.”
    Palestinian Authority’s ‘Pay to Slay’ Program

    According to recent reports by the watchdog Jerusalem Post, the Palestinian Authority paid out more than $347 million to convicted terrorists and their families during 2017.

    The anti-Jewish organization has created an incentive-based system for Palestinians to wage violence against Israelis. The average Palestinian reportedly takes home about $580 monthly. But if someone is killed or incarcerated while bringing harming to a Jewish person, they are given a much higher monthly income.
    If a Muslim lives in Israel while committing a bad act, the Palestinian Authority funnels nearly four times their average monthly income. Should a terrorist be jailed for 3-5 years, they can expect a check of upwards of $2,900 monthly.

    Included in the money-for-murder is an incentive of $145 if they live in the Jewish state. The pay scale is further incentivized by terrorists receiving higher bonuses if they are married and have children. If the crime is particularly heinous, additional rewards are reportedly doled out.

    [end of excerpt]

  11. Yet more heretical scientists wasting time on a settled science. We already know everything perfectly, and now we must act without hesitation if we want save Gaia from a certain doom.

  12. I can’t really be very rigorous about this, but…

    Pink noise is what you would expect to find with any deep analysis of a complex data-set. What would have been surprising is if the climate had a white noise signature. Intuitively this might be because it is easier increase low frequencies or reduce high frequencies than the reverse, each of which would shift the spectrum towards pink. So failing to find white noise in this case is evidence (for me at least) that there is no significant human contribution.

    Also, it is a common property of pink noise data-sets that they are especially prone to trend reversals as in Simpson’s paradox, so finding a different slope for part of the data is exactly as expected.

    • Beez,
      Might the apparent pink noise be an artifact of the multiple averaging of the raw diurnal temperature data? That is, the daily, monthly, and annual averaging act like a low-pass filter, attenuating the higher frequencies.

      • It’s quite possible. One way to think of pink noise is as an artefact of representing effectively continuous data with effectively discrete numbers. You always have to attenuate frequencies at some level to do it, and that process is what produces pink noise in your output. That’s why you will always find it if you look (an analyse) closely enough.

        You get white or brown noise when your sampling is biased or selective, essentially. If humans were interfering with the system in only a portion of the series, then intuitively one should expect the data to become less pink closer to the present.

        • Steve wrote:
          “pink noise is everywhere. nothing strange nothing special.”

          Steve – pink noise IS everywhere:

          Global warming hysteria is pink noise.

          Climate change hysteria is pink noise.

          Green energy advocacy is pink noise.

          Whenever leftists. Marxists, greens, progressives, or other fellow-travellers speak that is pink noise. It is everywhere, and it is nothing special – it is destructive idiocy – it is nonsense.

  13. At the very least it indicates the settled science story is BS.

    That is one of the key pillars CAGW. They shut the debate down and focus on the next war to bulldoze through.

    I suggest all should engage and discuss the concepts raised, it is in that mode that evolution is enabled of the mainstream position.

    We could also be wrong about what is happening and it is in the domain of science that this will be solved not the overthrow of the economic engine.
    One of the most powerful points in the debate is the realization that if you were to truly want to reduce gross CO2 emissions, then wind farms, solar panels and the destruction of capitalism are not the way to achieve that.

    Remember science changes one funeral at a time. Medicine even more so.

  14. So basically what most of us skeptics have been saying for years. When noise variables act in concert, their effects can be compounded, and this is exactly what happened between 1975-2000.

    • Yes all the noise as they call it from natural factors was in a strong warm mode up to year 2005. Then it started to transition and now all natural factors are pretty much in a cold mode.

      This means AGW will be coming to a definite close , and it has already. AGW will no longer be able to hi jack global warming natural factors.

      This year being a marked transitional year, and I expect several years with no global warming, actually global cooling as we move forward.

      AMO/PDO now shifting to a cold mode , geological activity on the increase, overall sea surface oceanic temperatures cooling, with global snow /cloud coverage will be on the increase.

  15. I am trying to understand that global graphic that is included – if I get it correctly, the dark reddish colored areas are places which indicate the presence of long term cycles. That dark red region in the pacific appears to correspond with the Humboldt Current, which is associated with the La Nina/El Nino phenomena, and the PDO. (If I understand this correctly)

  16. An interesting post. However, I would take exception to the following:

    “The ‘pink-noise’ aspect of the analysis suggests that there may be some aspect of climate variation due to a naturally produced slow varying function which may be acting together with anthropogenic factors in a resonant fashion rather like an adult pushing a child on a swing just at the right moment can rapidly increase the amplitude of the swing.”

    In order for this to be true, some part of the climate system would have to have three things:

    1) Negligible friction

    2) Momentum

    3) Persistent unchanging low-frequency cycles

    All three of these are present in say a child’s swing. There is very little friction. The swinging child has momentum. And the reason we have pendulum clocks is because the cycle doesn’t change.

    If any of these three were absent, you’d have a very hard time pushing a child on a swing as described.

    I kept waiting for the authors to demonstrate the existence of any of these … the problems are:

    1) Natural phenomena are highly damped, and generally run at the edge of turbulence. Both of these guarantee high friction.

    2) Thermal swings generally do NOT have long-term momentum. As Newton observed, moving objects tend to keep moving … but on the other hand, warm objects tend to cool.

    3) Although the structure of the data can be well represented by pink noise, meaning lots of low frequency and equal energy in all octaves, this does NOT mean that the low-frequency cycles are unchanging.

    So the natural system is missing all three of the essential elements necessary for the child-on-a-swing behavior.

    Their abstract closes by saying:

    We hypothesize that this pink-noise multidecadal spatial mode may resonate with externally driven greenhouse gas forcing, driving large-scale climate processes.

    Yes, and I hypothesize that I may resonate with external factors to win the lottery … however, since they seem to be lacking any actual evidence to back up their “resonant” hypotheses, or even a single example of it actually occurring, I’ll put their hypothesis right up there with my chances of winning the lottery.

    They’ve shown that natural climate datasets can be understood as “pink” noise … true, but where is the evidence that this leads to the type of “resonant”, child-on-a-swing behavior necessary for their hypothesis to be true?

    Regards to all,

    w.

    • Willis:

      I think the article suggests a hypothesis based on the data. Other work needs to be shown that the mechanism. My guess is the oceans, which is a huge store of energy differentials, but it’s just a guess.

      Here’s a huge low frequency component – the glacial cycles. The data here suggests strongly that there are components between 60 year periods and 24k year periods.

      I think the problem here is the epistemological problem of: “prove they exist” or “prove they don’t exist”.

      The null hypothesis, when attempting any other hypothesis (such as C02 causes warming), must be to assume cycles between 60 and 24k years exist. Especially when there’s indirect evidence such as this.

      regards,

      Peter

    • I have to agree. Pink noise doesn’t indicate the presence of a low frequency oscillator. It is more a function of our representation of data than of the data itself. So it is more a function of the fact that we use logarithmic concepts like “octave” to represent data, because that’s how our minds see data.

      • Pink noise doesn’t indicate the presence of a low frequency oscillator.

        It suggests the presence. No, it doesn’t prove it. See Figure 2(d). We have not data for what goes off the right hand of the graph. But the data suggests that it keeps going along the trend line.

        We literally have no data to prove yes or no. (Well not quite true. There is some 4k history of data that suggests some energy at 400 and 1000 year cycles. But not enough data to prove it, only sugges t it)

        But the null hypothesis, if you are going to suggest any root cause for temperature changes MUST assume the pink noise is there. And then your signal needs to ride above that assumed baseline in order to be statistically relevant.

        Paper here that shows how this is done for ENSO:

        http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf

        Nobody including anyone theorizing about temperature oscillations has data that goes off the right hand side of Figure 2(d). So EVERYONE is speculating. Including the Warmists.

        best regards,

        Peter

    • Willis,
      You are confusing what the authors stated in the paper and what Mr Dack wrote when
      describing the paper. The authors themselves state for example:

      In data from the past 80 000 yr, we also find a timescale of approximately 1470 yr (Fig. 4), the signal often ascribed to Dansgaard-Oeschger (DO) events [34]. We hypothesize the possibility of a stochastic resonance process due to the presence of pink noise on multidecadal timescales as follows. Nozaki and Yamamoto [35] showed that for noise with 1=fβ , 0 ≤ β ≤ 2, the noise intensity for which resonance takes place is minimized when β ≈ 1 for relax- ation oscillator dynamical systems, and DO events exhibit relaxation oscillation behavior [36,37]. Thus, the resonance efficiency is maximal for β ≈ 1, and in all of these proxies DO events are preceded by pink noise on multidecadal to centennial timescales

      which ascribes a physical mechanism for the resonant behaviour and shows how it might occur. They do not use the analogy of a child’s swing which is how Mr Dack summarises the above paragraph.

  17. I attempted a similar evaluation years ago but I failed to do what Willis has been doing – show what’s happening geographically.

    This article does so. Impressive. Good derivation of the tau coefficient curve.

    Note the strong implication that there are frequency components too low to measure because we don’t have a long enough data record – and those components will be larger than the oscillations we can see.

  18. willis Eschenbach has posted here why he thinks the authors are out to lunch with this study. I agree with Willis. However there is even a more fundamental reason why this study is flawed.

    For those not familiar with EOF it means Empirical Orthogonal Functions. Just like a powerful toy that may hurt a child, climatescientists do NOT have the necessary expertise in using advanced statistical tests properly. More often than not the dangerous toy harms the child. So it is with climate scientists and EOF’s.

    1) There was a paper published in the Journal of Climate Dec 2009 called “Empirical Orthogonal Functions: The Medium is the Message”
    https://journals.ametsoc.org/doi/full/10.1175/2009JCLI3062.1
    In that paper (there were 2 Canadians of which I am proud to say were the lead authors) they cautioned against the very thing that climate scientists do in their “paper(s)”. To understand this you have to understand just what Empirical Orthogonal Functions are. They are a fancy way of pairing values with data points (geographical in nature) so that the values represent something else ( in this case variances).
    They said ” Thus, EOF analysis expresses the (discretely sampled) field x as the superposition of N mutually orthogonal spatial patterns modulated by N mutually uncorrelated time series. The spatial patterns and time series occur in matched pairs, which are generally referred to as EOF modes.
    We note the following points:
    The EOF expansion can be interpreted geometrically as a change of coordinates in 𝗥N through an orthogonal rotation to a basis in which 𝗖 is diagonal. This emphasizes that the EOF expansion is nothing more than another way of describing the time series x in terms of a new basis set in which this description is particularly simple (from the perspective of the distribution of variance).”
    But there are mathematical constraints that you have to meet in your data for this to be a valid approach.
    They go on to say this about
    ” EOFs and dynamical modes
    The most natural system in which the statistical modes produced by EOF analysis might be expected to have clear individual dynamical significance is one governed by linear dynamics for which the notion of “dynamical modes” as eigenvectors of the linear dynamical operator is straightforward. In fact, North (1984) demonstrated that the correspondence between EOFs and dynamical modes holds only in a very specialized class of linear dynamical systems that are expected to be the exception rather than the rule in the (linearized) dynamics of real geophysical flows.”
    “As a first statement about the connection between EOFs and dynamical modes, we can say immediately that the two sets of vectors will not correspond in the case that the linear operator 𝗔 is nonnormal”
    Further they say
    “Nonnormality of the dynamical matrix is the generic case for the linearized dynamics of geophysical systems, particularly in the presence of shear or coupling between systems with very different time scales (e.g., Farrell and Ioannou 1996; Kleeman 2008). It follows that we can say, as a general rule, that EOFs and dynamical modes will not coincide.
    This argument does not rule out the possibility that EOFs correspond to dynamical modes in the special case that the linearized dynamics are governed by a normal operator. In this case, it can be shown (appendix A) that the EOFs will only correspond to the dynamical eigenvectors of 𝗔 if the noise has no spatial structure: that is, if it is spatially uncorrelated. If the driving noise is spatially correlated, then its structure will be imprinted on the covariance matrix of the damped, driven system so that the EOFs of x mix the structure of the noise with the structure of the linearized dynamics. In this case again, the EOFs and dynamical modes will not correspond.”
    The only way that a climate scientist could argue that the noise has no spatial structure is that if the full noise was global warming and nothing else. Indeed that is what climate scientists are alwayss trying to say.. They attribute all variance that isnt caused by ENSO or the PDO to the variance caused by global warming caused by CO2. That would be okay if true, but that cannot be the case for 2 reasons. A) There are many causes for SST (the number one being the sun). B) Climate scientists have not proved any case for global warming caused by CO2. They simply assume it.
    Furthermore the statisticians say
    “The correspondence between EOFs and dynamical modes is even less clear in the case of systems governed by nonlinear dynamics, in which the concept of the dynamical mode must be generalized to the more abstract notion of dynamically invariant subspaces (which the system will not leave once having entered). Such subspaces will not in general even be planar, in contrast to the case of subspaces spanned by EOFs or linear dynamical modes. For such systems the EOFs will be of course determined by—but on an individual basis cannot be expected to bear any simple relationship to—the dynamics. ”
    Is anybody going to argue that SST is simply a linear system?
    The next quote from their study DEMOLISHES ALL GENERAL CIRCULATION CLIMATE MODELS
    “4. EOFs and kinematic degrees of freedom
    We have seen that EOFs will not generally be of individual dynamical significance. Because statistical properties of a system are descriptions of variability and thus inherently kinematic, we might ask if individual EOF modes will be simply related to natural kinematic descriptors of variability. That this cannot be expected to be the case in general will be illustrated by the example of a simple model of a fluctuating jet in zonal-mean zonal wind, for which the EOF problem is analytically solvable.
    In both observations and atmospheric GCMs, the leading EOF of extratropical zonal-mean zonal wind is a dipole with a central zero-crossing at approximately the mean latitude of the eddy-driven jet (e.g., Hartmann and Lo 1998; Codron 2005; Fyfe and Lorenz 2005; Eichelberger and Hartmann 2007). To address the kinematic significance of this EOF mode, we consider a jet in zonal-mean zonal wind with Gaussian profile and fluctuating in strength and position:
    where x is a meridional coordinate. In this model, the jet strength U(t) and position xc(t) are the natural kinematic variables of the jet—what we will call the kinematic degrees of freedom. For convenience, we will assume that fluctuations in U(t) and xc(t) are independent and Gaussian. Based on observations of the extratropical zonal-mean eddy-driven jet (in either hemisphere), we will assume that both of l = std(U)/mean(U) and h = std(xc)/σ0 are ≪1. With these assumptions, the covariance matrix of u(x, t) can be computed analytically and expanded as a Taylor series in the small parameters l, h [details of these computations are presented in Monahan and Fyfe (2006)]. From these expansions the leading EOFs can be determined in terms of the normalized basis vectors f1(x), f2(x), and f3(x) (Fig. 4), corresponding respectively to a monopole, a dipole, and a tripole. By symmetry, the dipole is orthogonal to the monopole and tripole, but the monopole and tripole themselves are not mutually orthogonal (and therefore cannot simultaneously be EOFs).
    In the case of pure fluctuations in jet strength, the only EOF with nonzero variance is the monopole. For fluctuations in position alone, the leading two EOFs are the dipole and the tripole, respectively. When the jet fluctuates in both strength and position, if fluctuations in position are relatively large compared to those of strength (as is the case in observations) then the leading EOF is the dipole f1(x). The leading PC time series is given by (to leading order in the small parameter h)
    That is, while the dipole pattern arises because of the presence of fluctuations in position, the fluctuations in jet strength also project upon it and are therefore mixed into the associated PC time series. The first EOF mode bundles together both kinematic degrees of freedom and cannot be uniquely associated with position fluctuations. Furthermore, the spatial pattern of the second EOF is a monopole/tripole hybrid where the degree of hybridization is determined by the quantity
    When δ ≪ 1, e2 is a monopole and when δ ≫ 1 it is a tripole: in between, it is a linear combination of the two. The monopole comes in from strength fluctuations and the tripole from position fluctuations, but because these are not orthogonal they cannot both simultaneously be EOFs. Spatial structures that are EOFs in the case of fluctuations in a single kinematic degree of freedom on its own will not necessarily be EOFs in the presence of multiple fluctuating degrees of freedom as a consequence of the requirement that the EOFs be mutually orthogonal. Not surprisingly, the time series associated with the second EOF, α2(t), also mixes together variability in both strength and position.
    The observed extratropical eddy-driven jet fluctuates in strength, position, and width (with the first and third of these correlated as a consequence of momentum conservation). The above arguments can be generalized to include fluctuations in jet width (Monahan and Fyfe 2006), to relax the assumptions of Gaussian jet profile and kinematic parameter probability distributions (Monahan and Fyfe 2009), and to consider the geopotential EOFs associated with the fluctuating jet (Monahan and Fyfe 2008). The central conclusion remains unchanged: despite the fact that they directly reflect the kinematics of variability, the defining constraints on EOFs (orthogonal straight-line axes with uncorrelated time series) prevent them in general from being in simple one-to-one correspondence with kinematic descriptors of the field.”
    HAVE YOU HAD ENOUGH? MOST OF YOU WILL HAVE STOPPED READING THIS BY NOW. However there is more.
    Dont forget that the sample mean variances have to be all Gaussian for the climate scientist’s method to work correctly. The statisticians say
    ” Another field in which non-Gaussianity is manifest through statistical dependence of EOF modes is tropical Pacific sea surface temperature, as was discussed in Monahan and Dai (2004). Maps of the leading EOF patters of SST as computed from the Hadley Centre Sea Ice and SST dataset (Rayner et al. 2003) are presented in Fig. 7. Also presented are maps of the estimated standard deviation and skewness fields; the latter corresponds to the normalized third-order moment (measuring the asymmetry of a probability distribution around its mean)
    skew(@) = eigenvector ((a- eigenvector a)/ std(a))
    and vanishes if the distribution is Gaussian. Nonzero values of this statistic are therefore a measure of non-Gaussianity. The skewness field illustrated in Fig. 7 indicates that the SST probability density tilts toward positive anomalies in the eastern equatorial Pacific and toward negative anomalies in a horseshoe-shaped band from the central subtropical South Pacific through the western equatorial Pacific back up to the northern subtropics. The leading SST EOF, which carries the most variance, bears a strong resemblance to the standard deviation field. Also notable is the similarity between e2 and the skewness field, the reason for which becomes evident through an inspection of a scatterplot of α1 with α2 (Fig. 8). From this plot it is evident that strong positive and negative anomalies of α1 (corresponding respectively to El Niño and La Niña events) are both associated with strong positive anomalies of α2. In other words, the second EOF mode makes a positive contribution to the SST field during both extreme phases of ENSO, so on average the strongest positive SST anomalies during El Niño are located farther east than the strongest negative SST anomalies during La Niña. This asymmetry in the SST field between the opposing phases of ENSO is then manifest in the skewness field. Again we see a relationship between non-Gaussianity of the field and statistical dependence of the EOF modes.”

    So in summary EOFs work only in a very limited subset of statistical data. Whenever nonlinearity rears its ugly head EOF’s fall flat. Any climate scientist that uses EOFs to study his data is committing junk sclence.

    • However there is even a more fundamental reason why this study is flawed.

      The study is not flawed if you take the study to mean “there’s a noise floor above which anyone suggesting a cause for change in temperature must prove is bigger than that noise floor”.

      The Null Hypothesis shows the asymmetric nature of the epistemological question “how do we know what we know”. All this paper is doing (and what I believe Anthony is taking it to means) is there’s yet another threshold the warmists must cross before disproving the Null Hypothesis.

      I’ve not seen where EOF suggests a noise floor that is bigger than it should be in the presence of non-linearities. The null hypothesis approach of scientific epistemology would assume that the non linearities increase the noise floor, making the job harder for anyone who is suggesting causality in recent temperature changes have a recent cause, and aren’t just part of (for example) some 400 year cycle.

      Let’s go back to what our esteemed host is saying here: “suggests” longer cycles with big amplitudes. Meaning anyone who is assuming C02 is causing temperature increases must pass a signal-noise test who’s minimum noise floor is set by EOF. Perhaps this is still not be enough noise floor to account for non-linearities, but I can practically guarantee EOF itself makes the noise floor big enough that the C02 warmist hypothesis can’t pass a null hypothesis test.

      Here’s a detailed paper that shows how a noise floor was established to prove that ENSO signal rises above the noise floor:

      http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf

      best regards,

      Peter

      • You are correct in that the authors are really not saying very much. I read into it too much of what they were really trying to say. I will have to be more careful when criticizing. However

        “The ‘pink-noise’ aspect of the analysis suggests that there may be some aspect of climate variation due to a naturally produced slow varying function which may be acting together with anthropogenic factors in a resonant fashion rather like an adult pushing a child on a swing just at the right moment can rapidly increase the amplitude of the swing.”

        Well using EOF’s is certainly not going to tease that out.

        “We study the statistical characteristics of the decadal
        and multidecadal variability of Earth’s climate by analyzing
        the Goddard Institute for Space Studies (GISS) monthly
        averaged surface temperature data from 1901 to 2012.”

        Any researcher using that tampered with data set should think again.

        So I question how can we really trust what pink noise they found?

  19. Low frequencies are due to the clustering of volcanic eruptions, land and sub-marine (with no long term data on the later), but generally do not have fixed periodicity.

  20. “When the jet fluctuates in both strength and position, if fluctuations in position are relatively large compared to those of strength (as is the case in observations) then the leading EOF is the dipole f1(x).”

    There was a typo in the original work. The above f1(x) should have said f2(x).

  21. You can’t identify human impact on “climate” (whatever that is), even less “global climate,” until you have identified and fully accounted for every natural driver. They, the “global warming” charlatans never did this, because they didn’t want to! At the very root of their pseudo-scientific “models” lies the assumption that all global warming is man-made.

    If instead you recognize and take into account just the major natural oscillations we know of, e.g., from the work discussed here (there are also many other similar papers, e.g., [1-6]) due to ocean cycles, solar cycles (they are connected), Svensmark’s effect [7], solar shift to UV in times of high activity, &c., it turns out that just about all 20th century warming has a natural explanation, and in consequence the alleged human impact dwindles to zero.

    [1] https://doi.org/10.1007/s11434-010-4204-2
    [2] https://doi.org/10.1134/S1028334X17120212
    [3] https://doi.org/10.1360/972013-1089
    [4] https://doi.org/10.1016/j.gloplacha.2013.02.011
    [5] https://doi.org/10.1007/s00024-016-1287-y
    [6] https://doi.org/10.1016/j.newast.2016.08.020
    [7] https://doi.org/10.1038/s41467-017-02082-2

  22. Earth’s climate is not amenable to ANY statistical analysis, since it is totally* driven by changing amounts of SO2 aerosols in the atmosphere, primarily from random volcanic eruptions, but since circa 1850, also by anthropogenic SO2 emissions from the burning of fossil fuels resulting from the Industrial Revolution .

    *Since it is impossible to measure total solar irradiance from the Earth’s surface via proxy measurements, there is no evidence that it has ever changed within historical times.

    So far, satellite measurements, above the atmosphere, have only shown changes too small to be discernible in the climatic record.

    • Burl,
      You may be right.

      However, I suspect that there are factors additional to your ‘amount of CO2 aerosols’

      Solar irradiance; other shielding effects besides aerosols; land cover [some anthropogenically caused, some not]and albedo; Milankovitch cycles; vulcanism; ocean currents; which themselves are probably affected largely by the position of continents; albedo of the oceans, with plankton blooms etc.; tectonics and mountain orogeny.

      Some I was able to recall late at night; I am sure other factors will affect weather and temperature and climate, to lesser or greater degrees.

      auto

  23. It is ridiculous to even entertain the thought that non existent AGW, which has hi jacked all natural variability which was in a warming mode from the end of the Little Ice Age to 2005 had any climatic impact on the global temperature rise.

    My point will be proven now – over the next few years as global temperatures continue to fall in response to all natural climatic factors now transitioned to a cold mode.

    If there is any validity to AGW , the global temperatures should continue to rise now-next few years, but they will not because AGW does not exist.

    What controls the climate are the magnetic field strengths of both the sun and earth. When in sync as they are now(both weakening) the earth should grow colder.

    In response to weakening magnetic fields the following occurs:

    EUV light decreases – results in an weaker but more expansive polar vortex. Greater snow coverage.

    UV light decreases – results in overall sea surface oceanic temperatures decrease.

    Increase in GALACTIC COSMIC RAYS- results in changes to the global electrical circuit, cloud coverage , explosive major volcanic activity.

    In other words during periods of very weak long duration magnetic field events the earths cools due to a decrease in overall oceanic sea surface temperatures and a slightly higher albedo due to an increase in global cloud/snow coverage and explosive volcanic activity.

    Thus far all overall global temperature trends for the past year or two have been down and I expect this trend to continue.

  24. Godfrey Dack writes in with this:
    “The ‘pink-noise’ aspect of the analysis suggests that there may be some aspect of climate variation due to a naturally produced slow varying function which may be acting together with anthropogenic factors in a resonant fashion rather like an adult pushing a child on a swing just at the right moment can rapidly increase the amplitude of the swing”
    Are Telluric currents (Earth Currents) the pink noise???
    https://www.nap.edu/read/898/chapter/18

  25. Bruce Leybourne: Earth as a Stellar Transformer — Climate Change Revealed | EU2015
    I see the Hoops he talks about as how high and low pressure systems work.

  26. Emminent meteorologists from the meteorological departments around the world presented a manual on climate change as back as 1966 [WMO, 1966]. In this document they proposed several methods to separate trend from natural variations; and understanding the cyclic nature of natural variation. I used these techniques in around 1975 onwards as one of the author is my boss [late Shri. K. N. Rao].

    Global average temperature anomaly follow the 60-year cycle. The data of 1880 to 2010 presented a trend of 0.6 oC/Century and Sine curve varying between -0.3 and + 0.3 oC. The American Academy of Sciences and British Academy of Sciences combinely broughtout a report inwhich they presented a graph with global mean annual temperature anomaly with 10-, 30- & 60-year moving average curves [I presented the 10 year moving average for dates of onset over Kerala Coast in 1975-77]. At 60-year moving average eliminated natural cyclic part and showed the trend.

    Here the 0.6 oC is the trend associated with all kinds of human interferences including global warming with manipulated/adjusted data series. IPCC said more than 50% is greenhouse effect part inwhich global warming is a part. If we take 50% as global warming, then the trend is 0.3 oC/Century. By correcting the met network factor for urban and rural, this will be around 0.15 oC/Century. With Climate Sensitivity factor coming down with CO2 increase as radiative forcing is not dynamic but static, even by 1000 years the global warming component is far less than 1.0 oC which is far less than seasonal and annual temperature range [> 5 oC]. Scientists must give importance to natural variability in rainfall to understand the disaster proneness of a given area for appropriate planning/action.

    Dr. S. Jeevananda Reddy

  27. climate system [as defined by IPCC], more particularly orography and general circulation pattern.

    If the data follow a cyclic pattern, raising arm of the Sine curve present a different story compared to falling arm. For example for the above mentioned 60-year cycle in temperature, the raising arm presents + 0.6 oC for 30-years and the falling arm presents – 0.6 oC per 30-years. Indian Southwest Monsoon [June to September, 78.0% of annual rainfall] raising arm presented around + 300 mm and falling arm by around – 300 mm. However, over different parts of the country the rainfall patterns are different. For example, Western Ghhats controls the major part of rainfall on leeward side [dry semi-arid zone] and windward side [sub-humid]. Also, general circulation pattern in different seasons are quite different. In Andhra Pradesh met sub-divisions, annual rainfall presents 132 year cycle. The southwest monsoon rainfall presents 56-year cycle. Though northeast monsoon rainfall also presents 56-year cycle but in opposite phase. The cyclonic activity in Bay of Bengal follow the northeast monsoon pattern. In agroclimatic analysis the cyclic nature clearly reflects in floods and drought conditions.

    Dr. S. Jeevananda Reddy

  28. “Pink” noise is characterized by a monotonically decaying signal power density proportional to the inverse of frequency (1/f). Unlike that of any oscillatory system, including natural climate, it is utterly devoid of any spectral lines or peaks produced by periodic or irregular “modes.” Like many wannabe “climate scientists,” the authors baldly invoke advanced signal-analysis concepts without comprehending their basic implications.

  29. It’s a strange spectacle. The climate research community are struggling uncomfortably with whether to allow themselves to believe that the climate is “capable” of changing by itself without human help.

    This amounts to denial of ice ages, and denial of the entire discipline of geology. A small price to pay apparently for self-righteous climate orthodoxy.

  30. Ah. The magic stuff that is anthropogenic CO2 pushes, pulls, tugs, and shoves the intrinsic variables of planet Earth. Just like the magic solar stuff. Tiny catalysts that are trotted out as the true giants of the system, depending on which one you are a fan of. Reminds me of the magic substance humans have that is said to be the reason one needs an adjustment to one’s backbone.

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