The G–O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

Abstract

We have analysed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874 -2011 and determined variations in the annual numbers (counts) of the small (maximum area A M < 100 millionth of solar hemisphere, msh), large (100 ≤ A M < 300 msh), and big (A M ≥ 300 msh) spot groups. We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule or G-O rule of solar cycles, generally described by using the Zürich sunspot number (R Z ). During cycles 12 -21 the G-O rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of R Z . This behavior of the variations in the small groups is largely responsible for the anomalous behavior of R Z in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This can be called as 'reverse G-O rule'. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G-O rule. In many cycles the positions of the peaks of the small, large, and big groups are different and considerably differ with respect to the corresponding positions of the R Z peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (Waldmeier effect is weak/absent) with their maxima taking place two years later than that of R Z . The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of R Z .

Sunspot Sizes and the Solar Cycle: Analysis Using Kodaikanal White-Light Digitized Data

“…However, at the cycle 22 maximum A ns attains a maximum value of ≈-0.5. This is consistent with the results, as obtained by Javaraiah (2005). This scenario changes a little as we move from small to large sunspot sizes.…”

“…The top panel in Figure 5 show the period obtained from the 'no thresholding' case where we see that the dominant period is 16.5 years (Javaraiah 2015) and the second highest period is 9 years (Chang 2009). Wavelet spectrum and the corresponding periods obtained for different sunspot sizes are shown in consecutive panels in Figure 5.…”

Will Solar Cycles 25 and 26 Be Weaker than Cycle 24?

“…Overall, this relationship has a large uncertainty. In the case of small sunspot groups (maximum area smaller than 100 MSH), the inverse G-O rule found to be valid throughout Cycles 12 -24 (Javaraiah, 2012). Using the relationships shown in Figure 3 and by knowing the epochs of violations of the G-O rule and the inverse G-O rule, it may be possible to predict the amplitude of a cycle from these rules (prediction for an evennumbered cycle is qualitative) except for the odd-and even-numbered cycles of the cycle pairs that violate the G-O rule and the inverse G-O rule.…”

Principal component analysis of sunspot cycle shape

“…Some papers have studied the Waldmeier rules using sunspot area (Dikpati et al 2008;Karak & Choudhuri 2011) separately for odd and even numbered cycles (Dikpati et al 2008) or separately for small and large sunspot groups (Javaraiah 2012). Dikpati et al (2008) concluded that Waldmeier rule 1 seems to be valid only for even numbered sunspot cycles.…”