Some Interesting Characteristics of Solar Cycle Lengths
G. E. Pease
The historical variation in solar cycle length has recently become a topic of interest to many. This 2009 paper, in particular, has caught my interest:
LONG-TERM VARIABILITY IN THE LENGTH OF THE SOLAR CYCLE
A very complete tabulation of solar cycle lengths from 1610 to 1996 is in Table 2 on page 3 of the paper. An un-trended scatter plot of the SSN lengths is included in Figure 5, page 5 and some plots of “normalized (O-C) Cycle Lengths” on page 7 produced some very pronounced sinusoidal plots that do not bear any resemblance to the raw data. The procedure for computing these plots involved computation of an “average cycle length of 10.95 years derived independently by the FFT and PDM analyses from the sunspot number data.”
Interesting, but I wondered if a more straightforward analysis could possibly yield similar results. Using Excel on the raw data, updated to 2008.9 for the solar minimum times, I obtained this plot:
A fourth order polynomial trend line was used. As I suspected, the raw data trend looks similar at the beginning and end, but shows only one shallow peak at 1800, whereas the elaborate procedure used in the paper produced two very distinct peaks, near 1725 and 1900, for both Pmin and Pmax data!
Here’s the Excel statistical analysis for the Pmin data:
Note that Excel agrees with the paper’s mean and standard deviation of 11.0+/-1.5 years.
Here is the Excel plot using solar max times:
As in the first plot, a fourth order polynomial trend line was used. Since cycle 24 max has evidently not yet occurred, for comparison purposes with the first plot I used a “guesstimate” of equal solar cycle length to that of the last Pmin, 12.4 years, which artificially guesses a cycle 24 max time of 2012.7. This was done solely for the purpose of producing an end-time trend comparable to the Pmin end-time trend. The actual Pmax times are historically likely to be significantly shorter or longer than Pmin times, but using the same number for extrapolation purposes does produce a very comparable trendline.
Here are the Pmax data Excel statistics:
The mean and median are the same as for the Pmin data, but the standard deviation is greater. The mean and standard deviation again agree with the numbers in the paper. Note the much greater sample variance and kurtosis of Pmax data, compared with Pmin data. Skewness is also slightly greater for the Pmax data.