On the average rate of growth in sunspot number and the size of the sunspot cycle

Abstract

The average rate of growth during the ascending portion of the sunspot cycle, defined here as the difference in smoothed sunspot number values between elapsed time (in months) t and sunspot minimum divided by t, is shown to correlate (r ≥ 0.78) with the size of the sunspot cycle, especially for t ≥ 18 months. Also, the maximum value of the average rate of growth is shown to highly correlate (r = 0.98) with the size of the cycle. Based on the first 18 months of the cycle, cycle 22 is projected to have an R(M) = 186.0 ± 27.2 (at the ± 1σ level), and based on the first 24 months of the cycle, it is projected to have an R(M) = 201.0 ± 20.1 (at the ± 1σ level). Presently, the average rate of growth is continuing to rise, having a value of about 4.5 at 24 months into the cycle, a value second only to that of cycle 19 (4.8 at t = 24 and a maximum value of 5.26 at t = 27). Using 4.5 as the maximum value of the average rate of growth for cycle 22, a lower limit can be estimated for R(M); namely R(M) for cycle 22 is estimated to be ≳ 164.0 (at the 97.5% level of confidence). Thus, these findings are consistent with the previous single variate predictions that project R(M) for cycle 22 to be one of the greatest on record, probably larger than cycle 21 (164.5) and near that of cycle 19 (201.3).