In an article on WUWT, “Solar Activity – Past, Present, Future“, Leif Svalgaard describes the problems of historical sunspot records because of changes in instrumentation and observers. He produces a new series which attempts to correct for the various problems. He has made the data available to me to perform a cycles analysis. This proves to be interesting as it enables linking our understanding of the telescopic record with the proxy records from C14 and Be10.
Before I performed a cycles analysis on the adjusted sunspot numbers, I took the square root of them. This has the result of making the 11 year cycle more symmetrical, and making typical fluctuations near minima and near maxima of about equal amounts. It does not have much effect on this particular analysis. Here is what the series looks like then:
It can be seen that the range of each cycle since about 1750 is quite similar. This is the result of using square root of sunspot numbers.
Next, a spectral analysis was done on this series using CATS. This allows finer resolution than with such tools as Fourier analysis or FFT. The location of peaks can be determined with high precision as shown here:
When analysis of shorter periods of sunspots are performed, the second highest peak here often appears only as a bump on the shoulder of the highest peak. Because of the longer period the peaks are able to be resolved clearly.
A number of researchers, myself included, have suggested that three of the periods found here might be related to planetary motions affecting the Sun. The periods are Jupiter’s period of 11.86 years, the Jupiter-Saturn conjunction period of 9.93 years, and the Jupiter-Venus-Earth syzygy cycle of 11.07 years (also happens to correspond to Jupiter + Neptune frequency). The increased precision of these estimates is almost able to rule out some of these suspected matches. In particular, the 10.01 year period should have uncertainty of +/-0.025 and it differs from 9.93 years by 0.08 years. Hard to say.
In order of strength the cycles periods are:
11.05, 10.49, 10.01, 11.79 years.
The interesting thing about these periods is the beats between them.
11.05 and 10.49 years gives 207 years beats.
11.05 and 10.01 years gives 106 year beats.
The other various pairs give beats of 220, 177, 95 and 66 years.
See previous articles about C14 cycles analysis and Be10 cycles analysis as these two series are considered to be proxies for the sunspot cycle. We see the strongest beats are very close to, and others are generally clustering around the C14 and Be10 periods of 208 and 104 years. This is very suggestive. The modern sunspot cycle has a high autocorrelation after a lag of 210 years.
We can use the 104 and 208 year cycles to make a crude cycles forecast. For this purpose the wilder fluctuations pre-1750 have been omitted. The result:
It can be seen that the 104 and 208 year lagged sunspot numbers give a reasonably good fit to the present weak cycle 24.
The most important conclusion is that the 104 and 208 year cycles are closely related to the beat cycles of the closely spaced strong cycles near 11 years. This type of behaviour is quite commonly found in cycles analysis.
This suggests that we will not return to strong solar cycles again until the 2040s.