De Vries cycle links warming rate peaks to solar system frequencies

Posted: October 22, 2012 by tallbloke in solar system dynamics

Back in 2009, Anthony Watts and Basil Copeland did a study of the HADcruT3 temperature series and found some periodicities in the rate of warming of Earth’s surface. They created a model which achieved a reasonably good match:

Shown in Figure 6, the sinusoidal fit results in periods of 20.68, 9.22, 15.07 and 54.56 years, in that order of significance.  These periodicities fall within the ranges of the spectra obtained using MTM spectrum analysis, and yield a sinusoidal model with an R2 of 0.60.

Model from Watts-Copeland study of HADcruT using HP filtering

I didn’t realise the significance of the periods they found at the time, but now we are a bit further down the road of understanding solar system dynamics, it is starting to make more sense.

A very significant, high amplitude, sharp peak is evident in the spectrographic analysis of many temperature and solar proxies at around 205 years. This is known as the De Vries cycle (The page has been deleted at Wikipedia), commonly given as 200 or 210 years. It doesn’t seem to relate in any simple way to planetary frequencies, and this has been a puzzle. However, there have been some attempts to find combinations which fit the period.

Looking at the frequencies Anthony and Basil found, I realised there may be some connections with the De Vries cycle which will help us understand the links between the variables.

One of the peaks near the solar cycle length we found when Bart made a MEM spectral analysis of sunspot numbers matches the half period of the Jupiter-Saturn conjunction cycle – 9.93 years.

9.93 years multiplied by Anthony and Basil’s 20.68 year frequency gives 205.35 years; close to De Vries cycle length.

205.35 years divided by their 9.22 year frequency gives 22.27 years – close to the solar-magnetic Hale cycle length.

205.35 years divided by their 15.07 year frequency gives 13.62 years – close to a quarter (54.48/4=13.64) of their 54.56 year frequency.

54.56 years is close to five times the average solar cycle length (5×10.94=54.72 years), over the period of the HADcruT record they used.

Roy Martin found a solar pattern repeating at 55.15 years over a longer term, giving an average cycle length of 11.03 years. This is very close to the Venus-Earth-Jupiter cycle of 11.07 years.

But there’s more.

Anthony and Basil found that the frequencies also relate to Lunar periods.

because the bidecadal signal is harmonic, and readily discernible in the time domain representation of Figure 2 and Figure 6, we believe that a better attribution is the beat cycle explanation proposed by Bell [16], i.e. a cycle representing the combined influence of the 22 year double sunspot cycle and the 18.6 year lunar nodal cycle.

As for the decadal signal of 9.22 years, this is too short to be likely attributable to the 11 year solar cycle, but is very close to half the 18.6 year lunar nodal cycle, and thus may well be attributable to the lunar nodal cycle. 

It’s also worth noting that they found a harmonic period period at 4.74 years in the spectrum of the temperature dataset, offset twice this period with Their 9.22 year period and we are  near a quarter of the Lunar nodal cycle.

So how else might the Moon fit into the Luni-Solar picture? One very obvious fact is that the V-E-J average solar cycle length of 11.07 Earth orbits multiplied by the Lunar nodal cycle of 18.61 Earth orbits gives 206.01 – De Vries again! This means there will be beat periods around 27.3 and 58.3 years according to Ray Tomes (private communication). 27.3 years is half of  Anthony and Basil’s 54.56 year period.

Solar cycle 24 has been a damp squib compared to preceding solar cycle 23. We haven’t seen such low activity levels solar cycle 6 reached its peak in 1806 – 206 years ago. The De Vries cycle seems likely to be a solar system wide period linked to the frequencies of planetary motion interactions, affecting both the Sun and Earth-Moon system.

  1. Ray Tomes says:

    No no no! Rog, you cannot multiply years by years and get years. Nor divide them.

    [Reply] Thanks Ray I’ll need to think about what you’ve told me via email some more.

  2. Wayne Job says:

    Sine waves within sine waves ad infinitum, ever adding and subtracting, cycles within cycles, a never ending chaos with harmonic nodes. Thus it always was and shall ever be. Harmonics rule the entire universe from the infinite to the finite, tying all the pieces together in the face of a century of wrong science is a task of mammoth proportions. Well done Roger

  3. tallbloke says:

    Hmm, well Ray says I have it all wrong, and he’s a very clever bloke. But all is not lost, I think there is something fundamental in the relationship of the frequencies of the orbital periods which will save the day. The ratio of the Lunar Nodal Cycle and the Solar cycle is close to phi. and as I discovered while we were looking at Keplers work, there is a strong phi relationship between the planetary orbits too, giving us the Fibonacci series. I came up with this simple formula:

    During the time it takes for Jupiter to complete 2/3 of an orbit, Venus will go past Earth five times, as Earth makes eight orbits, while Venus makes thirteen, and Mercury will pass Venus twenty one times, as it completes thirty four orbits of the Sun.

    2,3,5,8,13,21,34. These numbers are in a familiar series, the Fibonacci sequence.


    This shows that the orbital distances of these planets (and hence by Kepler’s laws their orbital periods), are not what they are by random chance, but form part of the patterns of resonance.

    Now I need the help of clever people to work out how the numbers I’ve outlined in this post relate, even though as Ray rightly says, years multiplied by years do not give a result in years.

  4. Otter says:

    What reason was given for deleting the DeVries article from wikipedia?

  5. @ Ray

    “you cannot multiply years by years and get years”

    dimensionless ?
    Interesting statement Ray !
    It’s a repeating numbers….It is similar to the rotation

  6. tallbloke says:

    What reason was given for deleting the DeVries article from wikipedia?

    Dunno. I’m sure I remember it having it’s own page. Now it get a single line on the solar variation page under the heading ‘hypothesized cycles’.

  7. Tim Cullen says:

    2,3,5,8,13,21,34. These numbers are in a familiar series, the Fibonacci sequence.
    Now I need the help of clever people to work out how the numbers I’ve outlined in this post relate

    Peirce and Agassiz where clever people….

    It is well known that the arrangement of the leaves in plants may be expressed by very simple series of fractions, all of which are gradual approximations to, or the natural means between 1/2 or 1/3, which two fractions are themselves the maximum and the minimum divergence between two single successive leaves. The normal series of fractions which expresses the various combinations most frequently observed among the leaves of plants is as follows: 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, 13/34, 21/55, etc. Now upon comparing this arrangement of the leaves in plants with the revolutions of the members of our solar system, Peirce has discovered the most perfect identity between the fundamental laws which regulate both. 1

    Ed. E. Lurie, Belknap Press, Cambridge, 1962:127;

    Wikipedia provides the following definition:

    In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem (from Ancient Greek phýllon “leaf” and táxis “arrangement”).
    Phyllotactic spirals form a distinctive class of patterns in nature.

    And John N. Harris put it together in 2007:

    The essential question to be investigated here is whether Benjamin Peirce was correct concerning the phyllotactic structure of the Solar System. I suggest that the answer is undoubtedly yes, but nevertheless there is a difference between the approaches adopted by Peirce and myself. Both utilized Time (mean sidereal periods of revolution) rather than mean heliocentric Distances, but my also own included the successive intermediate synodic periods (i.e., lap times) between adjacent planets. It was this step that earlier — as described in Part II of Spira Solaris Archytas-Mirabilis — resulted in the determination of the underlying constant of linearity for the Solar System, which for successive periods (synodic lap cycles included) turned out to be the ubiquitous constant Phi = 1.6180339887949 and for planet-to-planet increases the square of this value, i.e, Phi 2 = 2.6180339887949 (see Part II). This produced in turn to a number of similar Phi-based planetary frameworks including a variant that owed its origin to the use of mean orbital velocities and complex inverse velocity relationships that linked the superior and inferior planets (again, see Part II and Part III for details).

    Even so, comparisons between the Phi-Series planetary frameworks and the present Solar System were fraught with difficulty, not least of all because of three apparent anomalies: 1) the location of Earth in a synodic (i.e., intermediate) position between Venus and Mars; 2) the well-known “gap” between Mars and Jupiter, and 3), an “abnormal” location for Neptune, which produced an atypical synodic lap time for its inner neighbor, Uranus. Some may find the suggestion that Earth is occupying a synodic location uncomfortable, but at least the newly announced Dwarf planet status of Ceres accounts for the Mars-Jupiter gap reasonably enough, though Ceres remains but one asteroid among thousands in this region.

    But in any event it is the location of Neptune that provides the key to Benjamin Peirce’s far-reaching understanding of the matter. This I failed to comprehend when I first added the latter’s material to Part VI owing to a basic difference in methodology. The inner starting point adopted by myself was perhaps always likely to produce the Pheidian Framework, but might not necessarily shed light on the final phyllotactic aspect. Starting from the opposite end, however, onecommences with the latter, and with the larger fibonacci fractions applied by Peirce, one also moves with increasing accuracy towards the constant of linearity, Phi. Thus starting from this direction was (in retrospect) always likely to be more productive. In one sense, however, Peirce’s approach may have appeared almost too simplistic with divisions involving periods of revolution expressed in days and the unexpected constant duplication of his divisors. The reason behind this latter occurrence is more complex than one might suspect since it is intimately related to intermediate synodic periods between adjacent pairs of planets. However, since the latter are simply obtained from the general synodic formula (the product of the two periods of revolution divided by their difference; see Part II), one can readily test the paired divisors applied Peirce from this particular viewpoint. Thus in Table 1 below the fibonacci fractions employed by Peirce are applied firstly to the mean period of revolution of Neptune (given here as 164.62423 years, i.e., Peirce’s 60,129 days divided by365.25 days). Thereafter the divisions continue sequentially from the previous result, i.e., division by 1 again, by1/2, 1/2, then 2/3, 2/3, etc., down to the final divisor 21/34 to obtain the mean sidereal period of Mercury. Further division could, of course, follow with another division by 21/34 and the application of the next divisor (34/55), etc., as far as one might wish.

    For purposes of comparison modern values for the mean sidereal periods and the calculated synodic periods for the planets are given in the Sol.System column. A second comparison lists the ratios for each step followed by the average values obtained from each column. As can be seen, the latter are close to fibonacci ratios of 21/13 and 55/34 with resulting pheidian approximations of 1.61665353 and 1.61737532 respectively despite the variance in the individual ratios.

    The entire John N. Harris article is at:

  8. tallbloke says:

    Thanks Tim, interesting. I was unaware of the square of phi. So:

    0.6180339887949… is the reciprocal of
    1.6180339887949… which is the square root of
    2.6180339887949… which as the divisor of
    1.6180339887949… gets you back to
    0.6180339887949… which differs from it’s reciprocal by unity….

    Hmmmmmmmm. Interesting!

  9. oldbrew says:

    Seven de Vries cycles = 1 Dansgaard-Oeschger event, according to the paper at footnote 32 here:

    Title of paper: Possible solar origin of the 1,470-year glacial climate cycle demonstrated in a coupled model

  10. Gray says:

    Having given some thought as to how the planets arrive at these positions it might be useful to assess the process backwards. Obviously the planet rotations and solar distances conform to the Fibonacci Series. I would theorise that this has happened through a process of collision, Solar activity and a general process of orbital sweeping.

    If you imagine a car race in which through a design fault or maybe just for fun a figure of eight track is used with a crossover point at the midpoint. The cars of various sizes and speeds set off and circle the track. In the early stages the crossroads is a source of carnage as cars collide and are removed from the race. After a while the cars that are left collide less frequently until eventually they begin to conform to a pattern where they miss each other for longer periods. Those travelling at ratios whereby they miss by a small distance but inch closer together ultimately collide. Those travelling at the Fibonacci Ratios keep missing. Over four billion years, forgetting the wear and tear on engines and petrol costs, the drivers end up performing a sort of dance whereby they will never(?) collide.

    Ok it’s a lousy analogy but if you throw in blasts from the Sun that can bump planets into different orbits, collisions which end up with small planets being gobbled by larger planets and the gravitational effects between the solar system bodies it can be seen how perhaps the planets arrived at these specific ratios.

    This process is ongoing thus the Sun trades energy with the planets when the planets arrive in their closest Fibonacci positions and it is the Parker Spiral reaching out to the planets that is capable of modifying the positions and orbits of the planets to achieve this. In many ways the process is a duplicate cosmological version of Darwin’s theory.


  11. Bruckner8 says:

    What will happen when the Sun becomes a Red Giant? Or does this theory only apply to the miniscule amount of time we’re observing now?

  12. Gray says:

    Bruckner8 says:

    I’m assuming you are referring to my comment. I’ve given no consideration to that. This particular microbe has an event horizon spanning no more than thirty years even if my doctor is wrong.

  13. Tim Cullen says:

    Gray says: October 22, 2012 at 4:18 pm
    This process is ongoing thus the Sun trades energy with the planets when the planets arrive in their closest Fibonacci positions and it is the Parker Spiral reaching out to the planets that is capable of modifying the positions and orbits of the planets to achieve this. In many ways the process is a duplicate cosmological version of Darwin’s theory.

    Cycles of “Catastrophic Extinction” seems to fit the Solar System… the Earth’s geology… the Earth’s fossil record… and the Earth’s climate history [as best we can tell].

    My personal perspective is that the “Parker Spiral” should really be called the “Parker Propeller” because it propels the planets around the Sun… not so much a figure-of-eight destruction derby… more a game of pinball… with the “Parker Propeller” acting as the “flippers” and the planets acting as the “buffers”… which probably makes Venus the last “ball” released into the Solar System “pinball” machine 🙂

    PS: I definitely wouldn’t give Darwin any credit… quite the reverse… he observed [and understood] the evidence supporting “Catastrophic Extinction” but chose to ignore it!

    It required little geological practice to interpret the marvellous story which this scene at once unfolded; though I confess I was at first so much astonished that I could scarcely believe the plainest evidence. I saw the spot where a cluster of fine trees once waved their branches on the shores of the Atlantic, when that ocean (now driven back 700 miles) came to the foot of the Andes. I saw that they had sprung from a volcanic soil which had been raised above the level of the sea, and that subsequently this dry land, with its upright trees, had been let down into the depths of the ocean. In these depths, the formerly dry land was covered by sedimentary beds, and these again by enormous streams of submarine lava — one such mass attaining the thickness of a thousand feet; and these deluges of molten stone and aqueous deposits five times alternately had been spread out. The ocean which received such thick masses, must have been profoundly deep; but again the subterranean forces exerted themselves, and I now beheld the bed of that ocean, forming a chain of mountains more than seven thousand feet in height. Nor had those antagonistic forces been dormant, which are always at work wearing down the surface of the land; the great piles of strata had been intersected by many wide valleys, and the trees now changed into silex, were exposed projecting from the volcanic soil, now changed into rock, whence formerly, in a green and budding state, they had raised their lofty heads. Now, all is utterly irreclaimable and desert; even the lichen cannot adhere to the stony casts of former trees. Vast, and scarcely comprehensible as such changes must ever appear, yet they have all occurred within a period, recent when compared with the history of the Cordillera; and the Cordillera itself is absolutely modern as compared with many of the fossiliferous strata of Europe and America.

    Chapter XV: Passage of the Cordillera
    The Voyage of the Beagle (1839) by Charles Darwin

  14. Henry Pool says:

    I analysed ca. 650000 maximum temperature recordings and came to this curve:
    The blue curve is actual speed of warming/cooling measured. Maximum temperatures (energy-in) started dropping in 1995. Earth energy out (global mean) is lagging a bit but we can agree that that lag time is now over
    (e.g.from 2002,

    Follow the blue curve of trhe best sine wave fit: where else must it go, but fall further down – a logical conclusion that is simply inescapable.
    So YES, we do have a change in “climate regime” and my prediction is that we will now fall a further 8x 0.035 = 0.3 degrees C by 2020, globally, at least.

    Before they started with this carbon dioxide nonsense they did look in the direction of the planets, rightly or wrongly, to explain an apparent 100 year weather cycle, if you study the height of the flooding of the Nile over time. See here.

    Click to access arnold_theory_order.pdf

    To quote from the above paper:
    A Weather Cycle as observed in the Nile Flood cycle, Max rain followed by Min rain, appears discernible with maximums at 1750, 1860, 1950 and minimums at 1670, 1800, 1900 and a minimum at 1990 predicted.
    (The 1990 turned out to be 1995 when cooling started!)

    So, indeed one would expect more condensation (bigger flooding) during and at the end of a cooling period and minimum flooding during and at the end of a warm period. This is because when water vapor cools (more), it condensates (more) to water (i.e. more rain/snow). At the same time you would also have more clouds, naturally, so to speak.

    Now put my sine wave next to those dates?
    1995 end of warming – minimum Nile flooding
    1950 end of cooling – maximum Nile flooding
    1900 end of warming – minimum Nile flooding

    Not too bad, heh?

    The wetter weather is also the reason why some places still benefit, (i.e. “warming”) like Norway and the USA east coast.
    I am amazed that I am the only one who has figured it out. I think that even Moses was aware of it (remember 7×7 yr + 1 jubilee year?), so the Egyptians must have known about this ages ago.

  15. Bruckner8 says:

    I remember when I “discovered” this “special value” before I knew it had a name. I was in England when the exchange rate for USD was 1 USD = 0.6 GBP. The reciprocal of that is 1 GBP = 1.67 USD. When the rate was 1USD = 0.61 GBP, the reciprocal was 1.63, so I thought “hmm, I wonder where this converges; where a value of x exists such that (1/x) = (1+x)? That’s just solving the quadratic equation:

    x^2 + x -1 = 0
    x = {0.6180339887949…, -1.6180339887949…}

  16. tallbloke says:

    Bruckner8, nice story. But is it going to help me out of my dilemma with years squared?
    I also had a similar issue with a discovery that the reciprocal of jupiter’s orbital period gives a figure which works out to be the average rotation speed of the Sun!

    I’m sure there’s something going on here, more than simple coincidences with ‘numerology’. But what is it?

    Henry: Welcome.
    Starter for 10: how did you determine your sine wave to be the ‘best fit’ to the blue curve? It looks to be a lousy fit from here. 😉

  17. Henry Pool says:

    data in degrees C or K per annum (versus time) are: 0.036 from 1974 (38 yrs), 0.029 from 1980 (32 yrs), 0.014 from 1990 (22 years) and -0.016 from 2000 (12 years)

    this is the summation result of all those 650000 data on maxima,
    I /we have to live with it
    (actually we are living with it)

    all fits (linear, binominal/ nat log/) show high correlation (r2= 0.998), zero root of the binominal with highest correlation is at +17 (1995)

    I went for the sine wave:

    because it is one that makes most sense and shows the lowest (current) cooling rate….
    I wonder why you think the fit is lousy?

  18. tallbloke says:

    @Henry, because I could see the blue line wiggling either side of the red one. 😉

    Thanks for backing up your study with some numbers.

    So, I mentioned on WUWT that a single sine wave doesn’t really do it for me. Have you taken a look at the study of warming rates Anthony and Basil did in 2009?

  19. Henry Pool says:

    tallbloke says
    Henry, because I could see the blue line wiggling either side of the red one
    henry says
    yes, but the average of the blue is right on target onto the red?

    I have a problem with most data before 1950:
    In the old days they used a simple method to establish the mean: take the max and the min for the day and divide by 2. I am asking you how you can compare those results with current results where measurements are taken every second and recorded and a mean is automatically calculated for the day?
    Better to keep looking at maxima only, as it clearly gave me a good solid result?..
    As to why the (global) mean is the wrong parameter to look at: see one of the comments I made on my blog, here
    I wonder why you guys keep looking at the wrong parameter?

  20. tallbloke says:

    Well, not really, the slope of the red curve is steeper than the slope of the blue curve all the way by the look of it.

    You may well be right about the historical data, but if you want to do studies on long term stuff, you have to work around the inaccuracies of older data. Less dangerous than making long extrapolations from a short record in my opinion.

  21. Roger Andrews says:


    In the February 2011 “Cycles Analysis Approach to Predicting Solar Activity” post Tim Channon identified solar periods of 11.09 and 11.51 years. I’m going to assume that Tim was a few weeks
    off in his estimates – nobody’s perfect after all – and that the periods are actually 10.99 and 11.61 years. When we superimpose two sine waves with these periods this is what we see:

    There’s the 210-year cycle. You didn’t have to worry about square years after all. (Although I wish we had them. We’d get a lot more done.)


  22. Henry Pool says:

    Tallbloke says
    Well, not really, the slope of the red curve is steeper than the slope of the blue curve
    Henry says
    as I asked you: do any other fit ?
    and yes, with high correlation (>0.95) you may take it some years forward and backwards>

  23. tallbloke says:

    Henry, I don’t know. Presumably a red curve which is a bit less steep?

    I’m not meaning to be dismissive, I’m really busy with developing my own model. You asked, and I answered. I hope you find the time to read Anthony and Basils empirical findings and how they made a model to fit them. I think that will inform you of some complexities worth considering. I agree it’s good to keep things as simple as possible, but you can go too far with a good thing. Also, if you find time, have a look at the development of my model in the carbon flame war thread. We have a good collaboration coming together with Roger Andrews, Vukcevic, lgl and myself. feel free to join the party.

  24. tallbloke says:

    Roger A: I’d really like to constrain to 11.08 and 11.86 if possible. But we’ll keep your numbers on the books for consideration.

  25. Gray says:

    Tim Cullen says:

    That deaf, dumb, and blind kid sure plays the mean pinball…

    It seems to me Tim that you may well be right. If the material that comprises the planets was originally flung from the Sun during its earlier more unstable days then the orbital rotations would have been an approximation of the Sun’s rotation at the time. Subsequent flares etc would have whipped the planets into a variety of positions some viable long term, others not.

    The parallels with Darwin here are clearly not precise but instead the solar system occupies that we’re-here-because-we’re-here realm that natural selection also occupies.

    It may be worth fathoming out more precisely how the process happens.

  26. Tim Cullen says:

    Gray says: October 25, 2012 at 5:43 pm
    That deaf, dumb, and blind kid sure plays the mean pinball…

    I wasn’t thinking so much of the “kid”…
    More about his mum: Mother Nature 🙂

    we’re-here-because-we’re-here realm that natural selection also occupies

    It’s a lottery… the odds are long…
    But someone has to win…
    Unless they get the short-straw.

    It may be worth fathoming out more precisely how the process happens.

    That is my [probably naive] intention…
    This means going back to basics and “weeding-out” the junk science…
    My “weeding-out” process has started with Newton:

    But there is a longgggggggggggg way to go…

  27. […] future data. I’m guessing he left it out because its inclusion was too encouraging to folks like Henry P who think that because they can achieve a crude approximate fit with a few hand-selected fourier […]