Cycles in Sunspot Number Reconstruction for 11,000 Years

This analysis is based on a Sunspot number reconstruction from Radiocarbon C14 in Tree Rings by Solanki, S.K., et al.  2005, and the data was obtained from NOAA. C14 is generally accepted as being a proxy for solar activity, possibly because of affects in cosmic rays. It will be seen that there are similar cycles in C14 to what are found in climate reconstructions.

The data extends over the period 9455 BCE to 1895 CE at decade spacing. Therefore it is not suitable for studying the 11 and 22 year cycles but is suitable for studying cycles longer than 30 years. This is a spectrum of the time series.

Because of the long period of data, it is possible to determine the cycles periods found with high precision, except for the longer cycles. Noticeable in the spectrum are a cluster of peaks around 55 to 60 years, one near 88 years, two near 200 years, one near 350 years, two near 500 years, one near 2300 years and one at over 6000 years. Taking these in turn we can compare them to known cycles.

Firstly, the 55 to 60 year cluster of cycles may be understood as a cycle in that range which is not strictly rhythmic. The last several centuries of climate data show a strong variation with a period in this range with temperature maxima around 1940 and 1998 and minima near 1910 and 1970.

A period of 208 years or thereabouts has been reported in climate and solar activity and is called the de Vries (or sometimes Suess) cycle. In this C14 series we see a strong 208 year period along with a stronger 224 year period. these two together will therefore form beats over a long cycle.

A period of 355 years was reported by Chizhevsky in climate and here we have a 352 year period in C14 which would seem to be related. Likewise, Wheeler reported a cycle of 510 years in climate and we find 520 and 560 years in C14.

A 2245 year cycle in C14 is quite close to the reported 2300 year cycle in climate called the Hallstatt cycle. This cycle has been suggested to be related to a 2300 year in alignments of the outer planets by Lamb and others.

The time series is not long enough to say that it is real, but there is a definite sign of a 6600 year cycle. Again, this is close to a 6000 year cycle reported by Xapsos & Burke in solar variation.

To gain some perspective of where we are in the longer cycles, here is a fit of a 6600 year cycle and a 2245 year cycle. On these long time frames, the cycle are still increasing.

The 208 year period or thereabout is reported much more often than a 224 year period. Two such periods together would be expected to produce beats, so it is worth looking at the time series filtered by a 210 years cycle smoothed over 3 successive cycles.

It is possible to look at this cycle and see a modulation that might be the 2300 year cycle. If the 2300 year cycle is indeed connected to a cycle of alignments of the 4 gas giant planets, then there needs to be some explanation of why there should be a 208 year cycle because the shorter gas giant cycle should average 171 years with a possible 179 year component. There is a cycle of that period of 171.0 years but its amplitude is not very high.

The cycles near 60 years have also been associated with gas giant alignments, specifically Jupiter and Saturn. These have conjunctions every 19.86 years which repeat in the same part of the sky very close to every third cycle or every 59.6 years, although the long term average would be 61 years.

About Ray Tomes

Ray's career was in computer software development including system software design, economic modeling, investments. He spent 15 years full time on cycles research and has spoken on cycles and related topics at conferences and seminars around the world. He retired at age 42 to study cycles full time and work out “The Formula for the Universe” and as a result developed the Harmonics Theory as an explanation for observed patterns of cycles and structure of the Universe. His current project is the development of CATS (Cycles Analysis & Time Series) software, and collecting and organizing large quantities of time series data and analyzing this data to test and confirm Dewey's findings in an organized way. Interested in all aspects of cycles especially climate change and causes.
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16 Responses to Cycles in Sunspot Number Reconstruction for 11,000 Years

  1. tallbloke says:

    Ray, thanks for a very interesting post. On the subject of the 2245 year cycle, Gray Stevens notes a cycle of that length in the variation of the Neptune Uranus synodic period:
    “The graphs suggest that individual pairs of planets produce cycles related to the synodic periods primarily of Jupiter and Saturn with interrelated timing. As such they offer an insight into long term Solar variability and its potential connection with our climate, geothermal activity and magnetosphere.”

    As you note, the longer cycles have only had a couple of occurences in the period of record, though your curve fit with the combined 6000yr and 2245yr looks very convincing! Hallstadt identified a 2300 year cycle in the C14 record but I think your figure is more accurate.

    Are you of the opinion that other quasi cyclic periods such as the ~1470 Bond Events and their glacial period equivalents Dansgaard-Oeschger events are just peaks in the interaction of these more fundamental cycles?

    • Ray Tomes says:

      This may be another case of what I call “average cycles” and “specific occurrences”. In the case of the short term approximate 4 giant planet line-ups, the average cycle must be the Uranus-Neptune synodic period of 171 years. However for Jupiter and Saturn to line up the period must be a multiple of 19.86 years. Therefore in the short term the cycle has 179 and 159 years mixed in the right proportion to produce a 171 years average. You can see this in the graph that you showed.

      For the longer term very good line-ups of the 4 gas giants, the cycle averages about 2315 years. However there is a period of 22xx years that is the most prominent specific occurrence. I need to write an article on this too, though it is addressed briefly in my paper

  2. tallbloke says:

    These guys sem to have managed to extract decadal solar activity data from the C14 record using wavelet methods with a band pass filter.
    Journal of Cosmology, 2010, Vol 8, 1970-1982., June, 2010
    Is the Sun Heading for Another Maunder Minimum?
    Precursors of the Grand Solar Minima

    Hiroko Miyahara, Ph.D.1, Kyohei Kitazawa, M.D.2, Kentaro Nagaya, M.D.2, Yusuke Yokoyama, Ph.D.3,4,5, Hiroyuki Matsuzaki, Ph.D.6, Kimiaki Masuda, Ph.D.2, Toshio Nakamura, Ph.D.7, Yasushi Muraki, Ph.D.8

  3. tallbloke says:

    My apolgies, the link somehow lost the ‘html’ part of the address

  4. tallbloke says:

    I came across this ice core reconstruction of geomagnetic activity compared to the 10Be records for the last 60k years. There seems to be an around 4k year periodicity in a long part of the series.

    What are the phasing and amplitudes for your 6000yr and 2245yr curve fit Ray?


  5. Ray Tomes says:

    Hi Rog, catching up with you at last!

    Lamb says there is a 4600 year climate cycle which is also a planetary cycle. I have been finding the climate cycle to be a bit shorter than that ~4450 years.

    If that Be10 measures temperature, then it was a lot hotter 2000 years ago.

    Phasing info is on the cycles fit graph. You can get an estimate of amplitudes from that too.


  6. tallbloke says:

    Hi Ray, ah, got it, thanks.

    Leif Svalgaard says The geomagnetic activity level modulates 10Be deposition rates, so that needs to be taken into account. See the graph linked above

    However, it was warmer 2000 years ago, certainly in the northern hemisphere. The Romans were growing grapes up at Hadrians wall. These days the quickest way to end up with a small fortune is to start with a large one and plant a vineyard in England…

  7. Ray Tomes says:

    Hi Rog, I have been looking at a couple of grape harvest date series from France and Switzerland that run back to about 1500. Interestingly they show that only in the 1990s did growing season temperatures in Europe exceed several of the peaks in the 16th, 17th and 18th centuries – times that are usually considered to be rather cool ones. Surely the hockey stick graphs are just the result of mixing proxies with direct temperature measurements for recent times. Proxies will always have less fluctuations because the correlations are not that high. It is a fundamental statistics error to mix these. Regards, Ray

  8. tallbloke says:

    Entire books have been written on the subject of the Principle Components analysis used by dendroclimatologists to create hockey stick graphs. The Hockey Stick Illusion by Andrew Montford is a recent one, which just took a beating from Grant Huchison on the realclimate website. A counterpoint debate is underway on the Bishop Hill blog as I write.

    This one will run and run, but personally I agree with you and the Wegman report, which was highly critical of the statistical methods used and the conflation of tree ring proxy reconstruction and thermometer data.

  9. Pingback: Analysis of BE10 records as a Solar Irradiance Proxy | Cycles Research Institute's Blog

  10. Pingback: Sunspot Number reconstruction by Leif Svalgaard and proxy cycles of 104 and 208 years | Cycles Research Institute's Blog

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  12. Peter Harris says:

    Hello Ray
    i would like to draw attention to the data and calibrations based on studies by Prof. Yavor Shopov et al in which 17 long term intense solar/climate cycles are found in cave speleothems as tabulated in this (and many other) study ::
    With few exceptions the magnitudes and periodicity do not agree with other studies, but his methods seem legitimate.
    In particular he cites a cycle of 11500Y with an relative intensity of 100W/M2.
    How do you find his data ?
    Peter .

  13. Ray Tomes says:

    Peter, thanks to the link to this interesting paper. I don’t see any link to a place to download the data. I would like to also do some analysis of this series. Regards, Ray

  14. Peter Harris says:

    Ray to be frank I am a bit wary about the data published by Stoykova, Shopov et al from studies on the speleothems in Duhata cave Bulgaria covering the period from present to 243KY because it refers to identical data which was published by Shopov in 2004 based on speleothem analysis in Jewel cave South Dakota covering the period 89300Y-133600Y. However the Stoykova study was accepted by JASTP and the data is here by NOAA :
    The original innovative calibration was conducted by Shopov and published in 2004 here:
    . (please let me know if this link does’nt work)
    The only match i could find with climate on a preliminary check was his 1460Y cycle which is probably the Bond cycle and which he calibrated as 10W/M2. I think surely these calibrations are overstated and yet his method seems unusual but OK to me. Maybe the Tallbloke might like to take a look too. I have further info if required.

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