Timo Niroma:
Sunspots: Summary of supercycles and a hypercycle of 2289 years.

Sunspot cycles and supercycles and their tentative causes.

  • 7. Summary of supercycles and a hypercycle of 2289 years.
  • PART 8: Organizing the cycles into a web.
  • Go to the
    beginning of the smoothing of the sunspots.

    Go to the
    beginning of the 200-year supercycle.

    -- The Roman Empire and its demise.
    -- The Mayan Classic Period.
    -- When the Nile froze in 829 AD.
    -- Why is it Iceland and Greenland and not vice versa?
    -- Tambora did not cause it.
    -- The spotless century 200 AD.
    -- The recent warming caused by Sun.
    -- The 200-year weather pattern.

    Go to the
    beginning of the basic cycles to supercycles.

    Go to the
    beginning of the minima, maxima and medians.

    Go to the
    beginning of the avg. influence of Jupiter.

    Go to the
    beginning of the sunspots.

    Comments should be addressed to timo.niroma@pp.inet.fi

    7. Summary of supercycles and a hypercycle of 2289 years

    7.1. Short supercycles

    The supercycle of Gleissberg (72-83 years) and the 200-year one (actually at least 180-220, possibly 170-230 years) are the most important short-range supercycles and have been treated in earlier parts. Albeit they have a connection, they appear very differently. Gleissberg has nearly clockwork sharp borderlines and as sharp a rhythm of oscillations (100/200 years). The 200-year cycle looks a little more irregular, but is both a determinant in superminima and supermaxima plus a determinant in the weather cycles on Earth. Despite its varying length in individual cases, in the long run the average seems to be very near 200 years (202 years?). In fact it looks like two cycles superimposed each other.

    But there are other short supercycles (by definition below 250 years), which are not so regular and not so apparent. They make the smoothed curves look chaos-like, but in fact that's only because they are not divisible by each other and overlap (and thus compromise) each other. Let's look also on these cycles.

    Now we have supercycles of 44 years (the deep superminimum 1790-1834), 50-51 years (the medium superminimum 1878-1928), 91 years (the interval between the minima of superminima 1810-1901), 120 years (the interval between maxima of supermaxima 1834-1954). The interval between the two highest supermaxima (1783-1954) is 171 years. From the superminimum of the Maunder minimum there was 210 years to the minimum of 1901. From the cycles 22 and 23 can be derived a supermaximum in about 1995-1996 exceeding that in 1954. This would also cause this smoothed supercycle to last 210 years.

    The three shortest supercycles in the Elatina study are 45, 52.5, and 63 years. The double of 52.5 or 105 years or half of the 210 years also appeared. With my interpretation these values were about 44, 52, and 62 (and 104) years. Now we have not only got 44- and 52-year supercycles from our analysis, but have given them also some ingredient. But what about the 60-year cycle? May it be the half of the 120-year cycle?

    By double smoothing, both with one Jovian year and with the cycle of 11.1 years, we get two superminima. The first one lasts from 1786 to 1838, the second one from 1838 to 1939. Thus we have cycles of 52 and 101 years. The two superminima are in 1813 and 1904 with an interval of 91 years.

    The cycles of 44 and 52 years are quite evident, but the 62-year seems to be hiding. But it is there, superimposed on the others. It is most clearly seen in when we study only the borderlines of active parts of the cycles (chapter 6.5). There we see 1784 and 1843 as well as 1901 and 1964. We have now got these values by smoothing, and found them in Elatina data and possibly in the Cole data plus in active parts of the cycles.

    Cole got two supercycles on the both sides of the Gleissberg cycle, 59 and 88 years. The 88 years could be a combination of 44+44 years. The 59 years could be a combination of 52 and 62 years. At the same time they can be cycles on their own right, as the series 50, 100 and 200 years or 77.5, 155 and 310 years.

    Are there other findings?

    Zhukov-Muzalevskii got in their analysis of the years 214 BC to 1947 cycles of 42.5 and 58.4 years. In their analysis of the years 850-1947 they got 43.1 years and a second high (after the 201.5 years) in around 50-51 years. The Yunnan group got a cycle of 62 years. Stuiver has a 46-year cycle. Besides Cole there are some cycle findings about 88-89 years. This can be seen in our smoothed data also.

    7.2. Supercycles from 250 years to a hypercycle of 2289 years

    The Cole cycle of 280 years is not a lonely observation. The Yunnan group, that estimated the 200-year cycle to be in the limits of 165 and 210 years, has found another cycle in the limits of 240 and 270 years. Damon has found in his 6000-year data a cycle of 286 years. Damon offered this cycle as an alternative to the 200-year cycle. The New York Academy has found a weather cycle of 270 years. Aaby (1976) has found a 260-year moisture cycle. There are some indications also of a half of this cycle, especially of a 133-year cycle (for example Stuiver). (All these values cited in Schove 1983).

    These values give credence to the idea, that this cycle is a combination of the 200-year cycle and the Gleissberg cycle or about 200-202 plus 78 years. There are indications that this cycle is a cycle of humidity, when the 200-year cycle is rather a temperature cycle.

    Cole got from his analysis also the double of his 280 years, or 560 years. Schove has estimated, that the interval between intense maxima is 554 years. The Kiral analysis is complicated to interpret, but his maxima may reflect the Jovian effect. In that case K in his analysis equals one Jovian year. On this condition, he has supercycles of 261, 308, 415, and 569 years.

    If we look at the auroral or weather data, a cycle in the order of about 1000 years is however more evident than a 560-year cycle. Cole has a 1050-year cycle. Zhukov-Muzalevskii have in their 2150-year data a 1072-year cycle. Suess has a 955-year cycle. The longest cycle in Schove data is 1265 years, but Schove himself regards it somewhat inaccurate. J. R. Bray (Cyclic temperature oscillation, Nature 237, pp. 277-279, 1972) has a cycle of 1325 years.

    To get something out of this mess, I decided to look at the auroral data. Auroral numbers smoothed by Gleissberg (Schove 1983, Introduction Figure 8, reprinted from Solar Physics 21, 1971) are not accurate enough to be used to derive a new value, but nevertheless indicate, that at least the superminima have a periodicity, that requires something like a thousand-year cycle: there is a long and low superminimum, the Wolf minimum in the 13th and in the early 14th century, a medium long and medium low superminimum, the Sporer minimum in the 15th century, and a very low and relatively short superminimum, the Maunder minimum in the late 17th century. The subsequent superminima are again higher than the previous ones as we observed by smoothing our data. The latest in about 1900 AD equals that one about 1050 AD.

    The auroral data of G. L. Siscoe of the years 450-1700 (Rev. Geophysics and Space Physics 18, 1980) give another chance to try to calculate a value for the 1000-year cycle. The lowest superminimum (smoothed) between 450 and 1450 appeared from 620 to 680. It precedes the lowest superminimum of this millennium, the Maunder Minimum in 1640-1700 by 1020 years. The next superminimum after this pre-Maunder is in 780-800, which apparently corresponds to the superminimum in 1800-1820 both by duration and relative height with a 1020 year delay. The third superminimum in the Siscoe data is in 850-880 corresponding to the superminimum in 1880-1920 about 1030 years later. The Siscoe supermaxima in 740-770, 820-850, and 900-930 correspond to supermaxima beginning 1030, 1010, and 1050 years later, so that a supercycle of 1020-1030 years in average length is rather apparent.

    There are very strong implications of a cold spell from 850BC to 800BC, from 200AD to 250AD and the Mediaval optimum beginning to turn into cold after about 1250.

    So a supercycle with a length of somewhere between 1020 and 1070 years gets support. But what about the Neftel-Suess value of 955 years, the Schove value of about 1265 years, or the Bray value of 1325 years? We apparently need a 2000-year cycle.

    The Neftel-Suess analysis has such a value: 2289 years or exactly 193 Jovian years. It's a rare cycle because of its length and still rarer in its accuracy in that magnitude. 2289 minus the Cole-Zhukov-Siscoe 1050 years gives about 1240 years or the Schove value within its accuracy limits. Futhermore, 1240 is 4 times the main Elatina cycle of 310 years or 16 Gleissbergs. 2289 minus the Neftel-Suess 955 years gives 1334 years or near the Bray value.

    1240 minus 1050 years equal 190 years or 16 Jovian years. Plus minus half of the 190 years or 8 Jovian years from 1240 and 1050 years, respectively, give the 1335 and 955 years. The difference between them is 32 Jovian years.

    1050:1240 years is 46:54. Our smoothed supercycles had that ratio also. The Elatina cycles of 26.25 and 29.2 have a relation of 47:53. Our Jovian rise lasted 65 months making the relation as 46:54. This is also the relation in Gleissberg cycle: 6.07:7 equals to 46:54.

    All this gives a hint of a web of interrelationships which I intend to elaborate in the final chapter 8.

    7.3. The long-range change in magnitude

    There has been an increase in the average Wolf number since probably at least the Maunder minimum, if the value is calculated with at least 200-year smoothing. What is the exact amount of this increase? What is the amplitude of this cycle, if it has such a regularity?

    If we count the change in R(M):s and compare the oldest and youngest cycles, the resulting difference depends on how many Jovian or how many mean cycles we use. Using 14 Jovian years, we get an average value of 44.8 Wolfs for the years 1774-1940 and 53.3 Wolfs for the years 1821-1987. This makes an increase of 1.8 Wolfs per decade. If we use R(M) or maxima, we get an average Wolf of 102 for 16 consecutive cycles in 1766-1944 and 119 in 1823-1996. This makes an increase in R(M) as 3.0 Wolfs per decade. Using 20 consecutive years we may dare to take the start from 1755 and now we get for 1755-1976 109 Wolfs and for 1775-1996 115 Wolfs, which makes the increase equally 3.0 Wolfs per decade. But using 18 consecutive cycles we lose the supercyclic rise. It is either 110 or 111 from 1766-1964 to 1798-1996.

    In fact the 16 consecutive cycles show no apparent rise from 1766-1944 to 1798-1976. It is all the time near 105 Wolfs. When this is also confirmed by the Gleissberg cycle and the slow rise of the 14 Jovian year cycle before 1963, something seems not to match.

    How can we explain this? If we take the period that begins in 1766 and use 18 cycles (ending thus in 1964) or 16 cycles (ending in 1944) we get 110 and 102 Wolfs, respectively. Thus it looks like the growth actually began only after 1944. But why then have the last 18 cycles (ending in 1996) from 1798 an average Wolf R(M) of 111, when the 16 last cycles from 1823 have a Wolf number of 119? Again a difference of 8 Wolfs between 16 and 18 cycles. The explanation lies in the fact that 18 cycles includes, but 16 cycles excludes the low values of the Dalton minimum from 1798 to 1823. So this all means that 16-18 cycles or 177-199 years is not enough to settle the value of the supercyclic rise (or fall).

    What about 20 cycles? Is 221 years enough to settle the question? I have in the first chapters regarded this as the magnitude cycle. In the beginning we already had 10.28 years for one of the two length cycles and 9.94 years as one of the two magnitude cycles. Now we have a 3 Wolf increase per decade with 20 cycles which corresponds the exactly same amount with 16 cycles. 16 cycles leave the Dalton minimum at the same time as they catch in their place the high cycles since 1976.

    The Gleissberg cycle can now be inspected in the light of this. Smoothing by Gleissberg in 1762- 1998 we get the years 1801-1959. The Wolf value oscillates between 42 and 52 until 1927. From 1927 to 1930 the Wolf value rises from 52 to 55-56, where it stands the whole decade of 1930's. A new rise begins in 1940 and the value is above 61 from 1943 until the studied period ends in 1959. In 1954-55 70 Wolfs is nearly reached. This stepwise rise is clearly seen in the 9.9 year cycle, where the other half is low and the other half high but where this is stepwise interrupted by rising both halves a couple of times.

    The 14 Jovian year rise shows also an increasing rise: The five series from 1774-1940 to 1821- 1987 show a rise from the previous series with amounts of 1.2, 1.0, 2.5 and 3.8 Wolfs or together 8.5 Wolfs. So this confirms the conclusion that the high sunspot values is a recent event, beginning about 1930 and accelerating since. But the 20 cycles or 221 years also show that although the Wolf values were high in 1775-1798 they have been still higher after about 1944 with intervening low periods in 1798-1833 and 1856-1933 (measured with unsmoothed values). The correlation with Earth's temperature is also apparent.

    In 1933-1996 the average R(M) was 151. This is about the same as 1775-1798, when it was 150. The 18th century high period lasted only 2 cycles, the 20th century high period has lasted 6 cycles. So it is not the the average height that makes the difference, but the amount of the high cycles. The two intervening lows had an R(M) of 57 (1798-1833) and 83 (1878-1933).

    If the Schove estimates of the 17th century covering the Maunder minimum are used, we get as the R(M) difference between the typical Gleissberg in 1766-1954 and the Gleissberg covering the Maunder minimum (100-43)/176 = 3.2 Wolfs per decade. So it seems likely that there has been an average increase of about 30 Wolfs per century in the R(M) since the Maunder minimum. The increase occurs stepwise;
    the R(M) has been:
    - 40 Wolfs during the Maunder minimum (1650-1718 from maximum to maximum),
    - 105 Wolfs from 1766 to 1976 if using the 16-cycle smoothing,
    - increasing by 7 Wolfs per cycle (50 Wolfs per Gleissberg) since 1976, if measured by the 16 cycle smoothing.

    From our supermaxima smoothed with one solar cycle we get (96-80)/170.8 = 0.9 Wolfs per decade. Superminima give (28.2-14.5)/90.8 = 1.5 Wolfs per decade. Smoothing with Gleissberg gives a value in the range of 40-50 Wolfs for the average R in 1801-1919. Then there begins an increase which in 1954 had reached a value of 69 Wolfs. From (69- 45)/(1954-1860) we get an increase of 2.6 Wolfs per decade. Half a Gleissberg gives (82-57)/(1965-1786) = 1.4 Wolfs. So we can see that rise there is from supermaximum to supermaximum, from superminimum to superminimum, be the smoothing amount one solar cycle or one or half a Gleissberg during the whole period from about 1760 when regular observations exist, if the measurement points are equal in character.

    The increase in R has also happened stepwise as with R(M). If we are to rely on Schove estimates, the R during the Maunder minimum with Gleissberg smoothing has been about 20, from 1720 to 1930 about 45 and reached 70 during the 1950's.

    But how long has this increase lasted and how long will it last? Both the Gleissberg (Solar Physics 21, 1971) and the Siscoe (Rev. Geophysics and Space Physics 18, 1980) auroral data suggest that the low in this millennium was during the Maunder minimum in the latter part of the 17th century and the millennium high in the former part of the 12th century the interval being about 570 (1690-1120) years.

    If we assume the 46:54 relation to apply here, the whole cycle would be 1050 years, in agreement with the results in chapter 7.2.

    7.4. Stuiver-Braziunas analysis: 9000 years?

    One of the few sunspot studies that has a perspective of millennia was published in Nature 338/6214 (March 1989). The article has a title of "Atmospheric 14C and century-scale solar oscillations" and is written by Minze Stuiver and Thomas F. Braziunas (pp. 405-407).

    My own conclusion about the 200-year cycle was that it oscillates at least from 180 to 220, possibly from 170 to 230 years. From the onset of the Maunder minimum in 1645 there was 170 years to the Napoleonian minimum in 1815. From the coldest decade of the Maunder minimum in 1690's there was 230 years to the end of the low cycles (and cold) in the 1920's. The difference of the ultimate borderlines, 60 years, seems also to be the interval between different climate types (1630, 1690, 1750, 1810, 1870, 1930, 1990)

    Stuiver-Braziunas: "The delta-14C oscillations of a few per cent ... have approximately equal rates of delta-14C increase and decrease. They differ slightly in length: the Maunder oscillations have a period of about 180 yr and the Sporer oscillations last about 40 years longer... Nine of the Maunder-type oscillations and eight of the Sporer variety are found in the 9600-yr record." Figure 1 in the article shows, that the Medieval maximum was of type Maunder. The fourth superminimum during this millennium occurred in the 11th century and was also of type Maunder. Before that there is a gap and the previous ones occurred about 350BC (Maunder-type) and 750BC (Sporer-type). However this gap may be a measurement problem and the Baillie event of 536 AD, that possibly has a cosmic origin, make the delta-14C measurements of these centuries a little complicate to interpret. Evidence of a Maunder-type minimum at least in the 7th century does exist.

    "From a Fourier analysis, spectral power exceeding the 2*sigma significance level was found at periods of 230-200, 150, 88 and 57 yr. The maximum entropy method (MEM or autoregressive (AR) model), using the Burg or FABNE algorithms and AR order 20, yields spectral power for similar periods [420, 218, 143, 85, 67, 57, 52 and 45 yr]... Virtually the same set of cycles (425, 227, 148, 85, 67, 58 and 45 yr) is found through the MEM approach (AR order 20) after de-trending Q... The fourth harmonic, with a calculated period of 105 yr, is not present in the entire spectrum..., but on subdividing the record into four equal parts we find 110- and 107-yr cycles in, respectively, the 5350 BC - 2970 BC and 570 BC - AD 1830 portions."

    Now we can compare the various results obtained previously with the cycles in this analysis. Using results of Stuiver-Braziunas (Fourier, MEM, MEM after detrending), Elatina, Schove, Cole, Kiral, Zhukov-Muzalevskii, Niroma (autocorrelation, smoothing) and Neftel-Suess, we get:

     1. 415-425 years
     2. 305-314 years
     3. 260-280 years, affects moisture
     4. 177-227 years, almost all, very pronounced, an intensity cycle,
        affects temperature
        (median 202 years)
     5. 154-157 years, a length cycle, 13 Jovian years             
     6. 143-148 years, a length cycle, 13 average cycles 
     7. 104-105 years, half of the 200-year cycle
     8.  85- 90 years 
     9.  78- 79 years, the Gleissberg cycle
    10.  63- 67 years, 1834-1901, (1954-?)
    11.  57- 59 years  
    12.  51- 52 years, 1783-1834, 1901-1954
    13.  43- 45 years

    "Sections of the record ... [6480-5800 BC, 3420-2740 BC, 880-200 BC and AD 920-1600] each of which contains at least two of the Maunder- and Sporer-type digressions, show clear similarities when viewed on an amplified timescale. A best fit to these segments, retaining their relative timing, yields equation (1), whereas the remaining sections are best represented by equation (2)... equation (1) (435, 207, 148 variant) ... equation (2) (456, 256, 143 variant)..." 207 and 256 years have the highest weights. My previous supposition of the relatedness of the 200- and 260-year cycles gets support from this split.

    But: "The Discussion so far has centred on the periodicities generated by the MEM method using moderate AR numbers. By increasing the AR order or using Fourier power spectra, additional periods become important. For instance, the single 420-yr peak splits into 504-, 355- and 299-yr peaks in the Fourier analysis of the complete de-trended Q record." ARMA- (auto-regressive-mo ving-average) methods are exactly as good as the used parameters. That's why I made the above comparison.

    Go to the
    beginning of organizing the cycles into a web.

    Go to the
    beginning of this part.

    Go to the
    beginning of the smoothing of the sunspots.

    Go to the
    beginning of the 200-year supercycle.

    Go to the
    beginning of the basic cycles to supercycles.

    Go to the
    beginning of the minima, maxima and medians.

    Go to the
    beginning of the avg. influence of Jupiter.

    Go to the
    beginning of the sunspots.

    Comments should be addressed to timo.niroma@pp.inet.fi