On the longterm secular increase in sunspot number
Abstract
Correlated with the maximum amplitude (R _{max}) of the sunspot cycle are the sum (R _{sum}) and the mean (R _{mean}) of sunspot number over the duration of the cycle, having a correlation coefficient r equal to 0.925 and 0.960, respectively. Runs tests of R _{max}, R _{sum}, and R _{mean} for cycles 0 21 have probabilities of randomness P equal to 6.3, 1.2, and 9.2%, respectively, indicating a tendency for these solarcycle related parameters to be nonrandomly distributed. The past record of these parameters can be described using a simple twoparameter secular fit, one parameter being an 8cycle modulation (the socalled ‘Gleissberg cycle’ or ‘long period’) and the other being a longterm general (linear) increase lasting tens of cycles. For each of the solarcycle related parameters, the secular fit has an r equal to about 0.7 0.8, implying that about 50 60% of the variation in R _{max}, R _{sum}, and R _{mean} can be accounted for by the variation in the secular fit. Extrapolation of the twoparameter secular fit of R _{max} to cycle 22 suggests that the present cycle will have an R _{max} = 74.5 ± 49.0, where the error bar equals ± 2 standard errors; hence, the maximum amplitude for cycle 22 should be lower than about 125 when sunspot number is expressed as an annual average or it should be lower than about 130 when sunspot number is expressed as a smoothed (13month running mean) average. The longterm general increase in sunspot number appears to have begun about the time of the Maunder minimum, implying that the 314yr periodicity found in ancient varve data may not be a dominant feature of present sunspot cycles.
 Publication:

Solar Physics
 Pub Date:
 September 1988
 DOI:
 10.1007/BF00148736
 Bibcode:
 1988SoPh..115..397W
 Keywords:

 Secular Variations;
 Sunspot Cycle;
 Correlation Coefficients;
 Regression Analysis;
 Solar Physics