- Smoothing sunspot averages in 1768-1992 by one sunspot cycle.
- Smoothing by the Hale cycle.
- Smoothing by the Gleissberg cycle.
- Double smoothing.
- Omitting minima or taking into account only the active parts of the cycle.
- Short supercycles.
- Supercycles from 250 years to a hypercycle of 2289 years.
- The long-range change in magnitudes.
- Stuiver-Braziunas analysis: 9000 years?
PART 5. SUNSPOTS: A 200-YEAR CYCLE
5. The 200-year sunspot cycle is also a weather cycle.
The other supercycle, besides the Gleissberg, that most often is referred to in the present-day data, is a 200-year supercycle. The Gleissberg cycle is usually cited with one of two values, accurately as 78 years, inaccurately as 80 years, but the 200-year cycle has no agreed-upon value, mostly the values referred to are from 180 to 220 years.
Explicitly there is no 200-year cycle in the Elatina data, but I have interpreted that the 29.2 "sawtooth pattern" represents a cycle of 173 years, which means that it may be a variant of the 200-year cycle. In addition, the longest of the remaining Elatina supercycles is 105 years. There is also a 52-year cycle, which is not seen in today's data. One interpretation could be that the corresponding cycles today are 105 (weak) and 210 (strong) years. There are indications that the possible 200-year cycle really oscillates today. Would this hint to limits of 170 and 210 years in Elatina data, corresponding to from 180 to 220 years in today's data. That may mean a change in the Sun's cyclicity or in the Earth's rotation rate or rather a mixup of these both factors.
The Gleissberg cycle has no obvious subcycles (other than the seven basic cycles), but the 200-year cycle clearly consists of two parts of 100 years, which oscillate between 80 and 120 years and is intertwined with the Gleissberg cycle. It seems that the cycle 120/60/30 years or maybe more accurately 26.5/53/106/212 years are also weather cycles. At least at the moment (2001) the 200-year cycle seems to have a value of 211.4 years.
The following minima are minima smoothed by one sunspot cycle or 11 years (actually they are low maxima per cycle). The minima between the Sporer minimum in 1496+-1 and the Maunder minimum in 1695 is 198-200 years. The minima between the Maunder minimum and the Dalton minimum in 1815 is 120 years. There are indications of a warm spell beginning around 1755. Thus we have here a 55-60-year weather cycle: around 1870 began a cold spell which had its coldest phase around 1900, 1930's had a warm spell, 1960's had a cold spell, 1990's again a warm spell, which culminated in 1998. I predict that the Sun is now going towards low intensity, and the warm spell ends in the 2010's. The 2020's will again be a cold decade.
But everything is relative. The colder spells are not so cold as the earlier ones and warmer spells are a little warmer than the previous ones. This is caused by a larger oscillation, the 100/200/400-year oscillation. The Medieval warm lasted from about 930 to 1300, with an aftermath about 1350-1370. The Little Ice Age began after that getting a real escalation about 1400 and having two great (Sporer and Maunder) and some smaller really cold periods. After the first warm period about 1760-1800, there was the Dalton minimum from 1800 to 1830, from which we are now going again towards a warmer period, compared to the Medieval maximum.
"The disturbances of the early third century were nothing compared with what would follow the end of the Severan dynasty in 235 AD. The half century from 235 to 284 AD was a period of unparalleled crisis, during which the Roman Enmpire nearly came to an end... This is a period for which comparatively little documentation exists, but that in itself may be symptomatic... Barbarian incursions were frequent and ruinous between 248 and 268... It was Diocletian who, in a reign from 284 to his voluntary abdication in 305, quelled the barbarians, defeated usurpers, and at the same time initiated sweeping political and economic changes that transformed the nature of the Empire, and ensured its survival for a while longer... In the mid fifth century the West was gradually lost. Areas like Spain and Africa were temporarily or permanently lost to the barbarians... In 439 Vandals took Carthage... In the 20 years following the death of Valentinian III (455 AD), the Roman Army proper dwindled to nothing." (Tainter 1988, pp. 137-148).
Was there something like the Sporer minimum in the 200's and Maunder minimum in the 400's or rather vice versa as the following shows? What makes this a relevant question is that according to Schove there was only 7 cycles from 192 AD to 302 AD. This means that there most probably was 7 Jovian years plus a 27 year cessation. A real mother of all Maunders. Was this the reason for the Barbarian invasions at that time? Did they escape the terrible cold? And when the second cold spell came 200 years later, were also the Vandals attacking for the reason of the cold weather? Did the mighty Roman Army dwindle to nothing in just 20 years for this same reason?
There were 220 years between the Barbarian incursions from 230 AD to 270 AD and demise of the Roman Army after the Vandals from 450 AD to 490 AD.
Was it the warming of the climate that gave Diocletian and his followers the chance to revive The Roman Empire? There is one other historical moment whose simultaneous appearance gives this thought some credence. "The earliest inscriptions so far discovered in recognized Mayan lands are dated AD 292 and 320, dates on the threshold of the splendid Classic Period... The earliest date mentioned on inscriptions at Uaxactun is AD 328..." (Whitlock 1976). There is no known Columbus or other connector at that time between The Roman Empire and the Mayans.
Now it seems like this 100/200-year Maunder-like cyclity continued. The period of 200 years seems to oscillate between 180 and 220 years. The 220 is best approximated by 100+120 years and the 180 years by 60+120 years.
120 years of warm period passed. Then in 608 AD Euphrates froze. After the warm 700's, in 829 AD Nile froze (Cambridge CCNet 1998). The century of 800's belong to the dark ages. Again we have here 220 years.
"Another period of expansion [of the Mayas] extended from AD 731-90, when three splendid new centres were founded... Soon afterwards decline set in..." (Whitlock 1976)." "...the Maya of the Southern Lowlands, whose society underwent a rapid, dramatic, and justly famous collapse between about 790 and 890 AD." (Tainter 1988, pp. 152-153). "There is no trace of the large-scale destruction and fires which would have marked an invasion or an earth-quake." (Whitlock 1976, p. 26).
"The Norwegian farmer Folke Vilgerdson made the first attempt to settle in Iceland in about 865 AD... He lost his cattle in a severe winter and disappointed went back to Norway after having seen a fjord filled up by sea ice. Therefore he called the country Iceland. Only a few years later, in 874, Ingolf Arnason succeeded. He was followed by many others, and settlement was completed in 930 AD... In 982, Erik the Red discovered new land West of Iceland. He called it Greenland; according to the Greenlander Saga this was only to persuade people to follow him... But the O(18) curve suggests that the name described a reality... So the drastic climatic change [warming] late in the ninth century may be part of the reason why Iceland and Greenland did not get the opposite names." (Dansgaard: Palaeo-Climatic Studies on Ice Cores, in Oeschger, Messerli and Svilar, 1980).
"The beneficent times came to an end. Sea ice and stormier seas made the passages between Norway, Iceland and Greenland more difficult after AD 1200... In mainland Europe, disastrous harvests were experienced in the latter part of the thirteenth and in the early fourteenth century." (Grove 1988, pp. 1-2). The cold decades of 1680-1700 are very well documented, at least in Europe. (See for example Rothlisberger 1986). The glaciers in Alps increased, there was no good wine, harvests were a catastrophe and famine killed like the black death centuries before. Cold was also the decade of 1810-1820, including "the summer that did not come" or a "year without summer". The Tambora volcanic eruption has been accused for this summerless year 1816. Maybe it helped a little, but the cold spell had already begun from the spotless year 1810, with which Tambora had nothing to do.
If we take the Schove estimates of the maximum magnitudes (R(M)) from the period 1500-1750 and the measurements from 1750, we get (the rounding for exact centuries done only to make the general picture clear):
1410-1500 ? cold (Sporer minimum)
1510-1600 107 warm
1610-1700 61 cold (Maunder minimum)
1710-1800 114 warm
1810-1900 95 cold (Dalton minimum)
1910-2000 151 warm
2010-2100 ? cold?
So the supercyclic rise is a very long process, maybe a 1000- or a 2000-cycle or even longer. The Sun seems to be much more irregular than we ever have imagined. The historical data seem to show that the 200-year oscillation has been there at least since 200 AD. The even centuries seem to be have been cold, odd ones warm, not to the accuracy of year, but in the average anyway. If a spotless sun during the third century caused the process of the Great Roman Empire demise to begin, we have to write the history books anew.
The other thing that seems apparent is that the general warming trend has been going on at least 1,800 years so that the third century AD may be the coldest century for at least 2000 years. Its only rival is the latter part of the 17th century. 1690's may have been almost as cold as the years 250 to 270. The cold periods later during the first millennium AD are more dramatical than the Little Ice Age thousand years later. On the other hand we may now live in the second mildest climate Anno Domini.Warmer periods seem to have occurred only between 1000 to 1200 AD. This may even have greater implications to the whole Holocene climate study and possibly to ice age theories also. Considering the evidence it looks a bit exaggerated and hasty a conclusion that the recent rise of half a degree would have been caused by man. So great are the natural variations.
The evidence of man's role put into forefront in the IPCC Report 4 of 2007 is somewhat daring and based on very scanty evidence. If we compare the small warming and its oscillations during the 20th century with what has happened during the past, say 2000 years, we get a perspective that tells us how smooth and peaceful the, I would suggest, natural warming since the end of the Little Ice Age and especially Maunder Minimum has been. But man has always wanted to be in the center of the world. CO2 is the precondition for the multicellular life as we know it. Evidence is on the side that CO2 and its relation to Earth's temperature is a very complicated system. it's far from one-to-one relationship, there are so many intervening variables.
One solar-based climate change may have a period of about 1050 years. There are many reports of a cold period beginning about 850BC (Geel et al.: Solar Forcing of Abrupt Climate Change around 850 Calendar Years BC), there begins around 200 AD a period of low cycles which transforms into a cold period around 230 AD (see above), consisting of a maximum length Gleissberg cycle and lastly the low periods beginning in 1250 AD (Schove) leading to the rapid deterioration of the climate beginning about 1270-1280 AD, which led to the end for the Medieval Maximum and for example to the demise of the Greenland habitat and forced Europeans to invent the warming system for their houses. The cold period lasted in all cases about 80 years beginning an oscillating period of 660 years. So there are intervening some 400 years of a warm period (for example the Medieval maximum).
5.2. An autocorrelation analysis
To see the supercycles in my data I run an autocorrelation analysis of my 236-year data of the years 1762-1997. Primarily the purpose was to see, if and how (with which possible secondary harmonics) the 200-year cycle appears in this data and does it have some peak clearly over the others. I run the whole data (14,000 correlations), but because of the different character of the Gleissberg cycle and its double harmonics I expected to see only the 200-year variants not the Gleissberg, which almost also what was happened. Something was however expected to be seen near the basic cycle. Which of the many variants (4-5) has the highest autocorrelation, i.e. which is the "real" cycle? 11.1 years was condemned in the introduction to be only a compromise.
There are four cycles, whose correlation exceeds 40 %: Before inspecting them more throughly, I will notice that lowering the the limit to 35%, three more peaks appeared. They peak at 21.7 years (Hale), 120.3 years and 178.6 years. But the highest correlations are as follows:
TABLE 39. Cycles with autocorrelation above 40% in the 236-year data
1. cycle years (r**2 > .40) 2. cycle years (r**2 > .60) 3. cycle years (r**2 > .80) 4. the highest cycle year with one decimal 5. the highest correlation 1. 2. 3. 4. 5. 1. 8.9- 11.9y 10.2- 10.7y 10.3y 0.61 2. 199.4-203.1y 200.1-202.6y 201.0-201.7y 201.4y 0.83 3. 209.5-212.7y 209.8-212.2y 210.3-211.7y 211.1y 0.92 4. 219.2-221.7y 219.8-220.9y 220.2y 0.69
Immediately four things are apparent. 1. There is no 230-year cycle, and the 180-year cycle is weak. 2. The 211-year (210-212 y) cycle is very strong with two accompanying components of 201 years (201-202 y) and 220 years (220-221 y) which are so apparent in historical data. The 201-year cycle seems to be near 17 Jovian years, the 211-year cycle near 19 average basic cycles and 220-221-year cycle is near being both 20 average cycles and 18.5 Jovian years. 3. Gleissberg cycle has a higher level correlation. 4. The "real" basic cycle of Sun is 10.3 years.
As expected, the Gleissberg cycle didn't show up. It had its highest correlations, that were only 0.160, in the years 77.1-77.2, which corresponds to 6.50-6.51 Jovian years. Both of the limits of the Gleissberg cycle get negative correlations. On the upper limit the correlation is at its lowest or -0.130...-0.137 from 82.6 to 83.6 giving credibility to the limit being 7 Jovian years.
Because the average change in length from one Gleissberg cycle to the next is 0.07 Jovian years, this means that there are 13 Jovian years (154.2 years) and not 14 (meaning one full Jovian year) before there is a change of direction in the Gleissberg lengths. The whole round is done in 26.1 Jovian years or in 28 cycles or in 310 years. So this is what was seen in Elatina laminations.
If the low limit would have been 6 Jovian years, the prohibition of the exact meeting of the minimum and the Jovian perihelion would have been violated (See introduction). But which is the egg and which is the hen?
And one guess: the weak 179-year supercycle may bind the 9.9-year cycle with 15 1/14 Jovian years. This may have repercussions to the hypothesis that every 15th cycle among some others have the length of one Jupiter year.
And lastly one prediction. Since the ongoing cycle is the 13th cycle since the last long cycle in 1784-1867 this cycle is should reverse the trend, which means a long cycle probably ending somewhere in 2009-2010.
5.3. Some studies showing a 200-year cyclicity
Zhukov and Muzalevskii (Soviet Astronomy 13, 1969) have run several autocorrelation analysis based on the Schove series of data. The longest of these analysis, from 214 BC to AD 1947, has the highest spectral density at 200.4 years. From the smaller, but more reliable data from AD 850 to AD 1947, they got a value of 201.5 years. The former is 16.89 and the latter 16.99 Jovian years. My 201.4 years equal 16.98 Jovian years.
Peter Brockwell and Richard Davis have in their book "Time Series: Theory and Methods", 1987, (page 357) derived an autoregressive minimum AIC model for the Wolf numbers between 1770 and 1869 and got a value for the WN (white noise) as being 202.6 years or 17.08 Jovian years.
Houtermans, Suess, and Munk (Effect of Industrial Fuel Combustion on the Carbon-14 Level, in "Radioactive Dating and Methods", IAEA, 1967) have found a 200-year cycle. Neftel, Oeschger, and Suess (Secular Non-random Variations of Cosmogenic Carbon-14, in "Earth and Planetary Sci. Letters" 56, 1981) have in their 6000-year long study found a 202-year cycle. H. E. Suess has in two articles in 1980 (Schove 1983) considered a 203-year cycle as the most significant supercycle in eight millennia of Bristlecone history. M. Stuiver in Pepin et al.: "The Ancient Sun", 1980, has found a radiocarbon cycle of 202 years since AD 700.
Because 17 Jovian years equal 201.65 Earthly years, it is a good candidate for a supercycle.
Cole has two values, 190 and 196 years, but these I inspect later. Dansgaard et. al (Climatic record revealed, in Turekian: "The Late Cenozoic Glacial Ages", 1971) have found a 175-180 year cycle in the Greenland ice-cap since AD 1200, and a 380-year cycle in earlier times.
I had also a weak correlation near 180 years. May it be that this supercycle oscillates between 180 and 220 years?
After having remarked that according to Eddy there is a 180-y interval between the Maunder and Sporer minima, Paul Damon remarks (Solar Induced Variations of Energetic Particles at one AU, in White: "The Solar Output and Its Variation", 1977): "Damon, Long, and Grey (J. Geophys. Res. 71, 1966) showed that the best sinusoidal fit to the delta data for the Little Ice Age had a period of 200 y... using the Blackman-Tukey Fourier analysis. For the time from 0 to 2000 y [BP], 182-y periodicity is observed."
In the above-mentioned Kiral article ("Autocorrelation and Solar Cycles") there are several peaks between 177 and 222 years, which is in good agreement with my observations. A most interesting result comes from the Yunnan group, China (Yunnan Observatory: A Recompilation of our Country's Records of Sunspots Through the Ages, in "Chinese Astronomy" 1, 1977), which states that there is a peak
periodicity between 165 and 210 years. This study uses pre-telescopic sunspot sightings, of which the earliest is dated in May 28 BC.
The onset of the three great superminima in this millennium based on the 14C production according to Stuiver and Quay (Changes in atmosphere Carbon 14 attributed to a variable Sun, in Science 207, 1980) occurred in 1282 (medieval or Wolf), 1450 (Sporer), and 1645 (Maunder). From these we get intervals of 168 and 195 years.
In the Alps there has been retreats of the glaciers (Rothlisberger: 10000 Jahre Gletschergeschich te der Erde, 1986, page 76) between 1530 and 1565 and again between 1920 and 1960 with a short retreat between 1720 and 1730. The interval between the onsets is thus 190+200 years. The sudden advance of the glaciers began in 1680 and came to an end 195 years later in 1875. Between the three onsets in 1530 (retreat), in 1680 (advance), and in 1920 (retreat) elapsed 2 and 3 Gleissbergs, respectively.
If the 200-year cycle really oscillates, what is its present value, or if it has several interchanging values, how do the various variants interact today? To this purpose I have studied the lengths of 16, 18, and 20 consecutive cycles beginning in 1755.
TABLE 40. 18 consecutive cycles
1. cycles 2. years 3. total interval 4. mean sunspot cycle 5. mean smoothed magnitude maximum 1. 2. 3. 4. 5. 1-18 1755-1954 199.0 11.06 (104?) 2-19 1766-1964 198.2 11.01 110 3-20 1775-1976 201.0 11.17 110 4-21 1784-1986 202.0 11.22 110 5-22 1798-1996 198.1 11.01 111
Notice that there is no supercyclic rise in R(M).
TABLE 41. 16 consecutive cycles
1. cycles 2. years 3. total interval 4. mean sunspot cycle 5. mean smoothed magnitude maximum 1. 2. 3. 4. 5. 1-16 1755-1933 178.6 11.16 (100?) 2-17 1766-1944 177.7 11.11 102 3-18 1775-1954 178.7 11.17 104 4-19 1784-1964 180.0 11.25 107 5-20 1798-1976 178.2 11.14 105 6-21 1810-1986 176.1 11.01 112 7-22 1823-1996 173.1 10.82 119
This cycle shows both the supercyclic trend plus the possibility of the supercycle to be exceptionally low.
TABLE 42. 20 consecutive cycles
1. cycles 2. years 3. total interval 4. mean sunspot cycle 5. mean smoothed magnitude maximum 1. 2. 3. 4. 5. 1-20 1755-1976 221.3 11.065 (109?) 2-21 1766-1986 220.2 11.01 113 3-22 1775-1996 220.9 11.045 115
5.4. The periods of Cole
The analysis of T. W. Cole (Periodicities in Solar Activity, in "Solar Physics" 30, 1973, edited by D. J. Schove, 1983) is very interesting:
"Abstract. The techniques of power spectral analysis are used to determine significant periodicities in the annual mean relative sunspot numbers. The main conclusion is that a period of 10.45 yr is very basic and can be associated with an excitation of new solar cycles. When combined with a period of 11.8 yr, associated here with the free-running length of a solar cycle, the mean cycle length of 11.06 yr and a phase variation of 190 yr are explained."
"The strongest feature in the phase of the 11-yr cycle over the last 270 yr is a 190-yr periodicity... The form of the 190-yr variation is not sinusoidal... Given a 190-yr phase modulation, the power spectrum should show this as a series of peaks about the basic frequency of the cycle with a separation corresponding to a 190-yr period. Indeed, the peaks about the 10.45-yr peak are separated, on average, by this amount. Further, modulation theory indicates that the ratio of the various peaks is due to a phase modulation of +-90 degrees and the non-symmetry about the centre of the group of peaks at the 10.45-yr period indicates a non-sinusoidal form to the phase modulation."
"The autocorrelation function and the spectrum of [22-yr cycle] add to the argument in support of the real existence of a 190-yr phase modulation of the solar cycle... it can be seen that the phase is strongly modulated and that almost half of the time the sunspot cycle is, on average, closer to 10.45 yr than the mean, 11.06-yr period. The form of the 78.5-yr phase modulation is apparently sinusoidal..."
Thus Cole has deduced 190 years as the value for the 200-year cycle and 78.5 years as the value for the Gleissberg cycle. The affection of the mean cycle to 10.45 years corresponds to my introductory analysis of an affection to 10.3 years. The mean period of 11.06 years is close enough to my estimates for the results to support each other.
Furthermore the correlogram in Cole Fig. 1c exactly corresponds my autocorrelation analysis giving the cycles of 11 and 22 years, no cyclicity around 50 years, medium cycles around 100 years, no cyclicity around 150 years, and the highest correlations near 200 years. In the Cole figures 1b and 1d are power spectra that may reflect my 9.9-year cycle. The second highest peak in the Cole Fig. 1b after 11.1 years is 10.05 years.
But there is one inconsistency in the Cole analysis. As shown in Cole Fig. 2 he has run two autocorrelation analysis to reveal the Gleissberg and the 200-year cycle. In the first one there are two density peaks. The other one is at the 190 years, as he above analyzes, but the other one is at 84 years, and not at 78.5 years. On the other hand, the second run has produced the second highest peak at 78.5 years, but the highest peak is not 190, but 196 years. The difference between the analysis is that the first one has used data from 1626 to 1968, the other one from 300 to 1968. I would argue that the data from AD 300 is more accurate than the data from 1626, because the data from 1626 to about 1760 (40% of his data) is very unreliable. Of course the still earlier data are still more unreliable, but the law of great number of figures makes it a little paradoxically more reliable.
According to my analysis, the Gleissberg cycle can't be as long as 84 years, but the 78.5 years, which Cole himself uses, is a fairly good estimate. But then the 200-year cycle is not 190 years, as Cole supposes, but 196 years.
The end portion of the article has been omitted by Schove, but he remarks: "Cole concludes that the mean cycle length of 11.06 years and the 190-year phase modulation are a result of two periods of 11.8 and 10.45 years...". Apparently Cole sees no connection between the 11.8-year period and Jupiter, because the abstract ends: "The results dispute several associations of planetary position and solar activity." But there is again some inconsistency in his use of the 78.5 year period and in his claim in the abstract: "Similarly the amplitude variations with periods 88 and 59 yr (previously described as the 80-yr cycle) are due to an amplitude modulation of the solar cycle by a period of 11.9 +- 0.3 yr." The amplitude modulations of 59 and 88 years are most probably the half-periods of 120- and 180-year cycles.
I shall however postpone the discussion both of these two cycles and the very long cycles (280, 560 and 1050 yr) discovered by Cole into the chapter 6.
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