On Determining the Rise, Size, and Duration Classes of a Sunspot Cycle

The behavior of ascent duration, maximum amplitude, and period for cycles 1 to 21 suggests that they are not mutually independent. Analysis of the resultant three-dimensional contingency table for cycles divided according to rise time (ascent duration), size (maximum amplitude), and duration (period) yields a chi-square statistic (= 18.59) that is larger than the test statistic (= 9.49 for 4 degrees-of-freedom at the 5-percent level of significance), thereby, inferring that the null hypothesis (mutual independence) can be rejected. Analysis of individual 2 by 2 contingency tables (based on Fisher's exact test) for these parameters shows that, while ascent duration is strongly related to maximum amplitude in the negative sense (inverse correlation) - the Waldmeier effect, it also is related (marginally) to period, but in the positive sense (direct correlation). No significant (or marginally significant) correlation is found between period and maximum amplitude. Using cycle 22 as a test case, we show that by the 12th month following conventional onset, cycle 22 appeared highly likely to be a fast-rising, larger-than-average-size cycle. Because of the inferred correlation between ascent duration and period, it also seems likely that it will have a period shorter than average length.