Group sunspot numbers: Sunspot cycle characteristics

We examine the 'Group' sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group sunspot numbers to Zurich (International) sunspot numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zilrich numbers follow the 10.7-cm radio flux and total sunspot area measurements only slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zilrich numbers. We find that the 'Waldmeier Effect' - the anticorrelation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zilrich numbers. The 'Amplitude- Period Effect' - the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zilrich numbers. The 'Amplitude -Minimum Effect' - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zilrich numbers and the Group numbers. The 'Even-Odd Effect' - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zilrich numbers. The 'Secular Trend' - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80-year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zilrich numbers are slightly more useful for characterizing the on-going levels of solar activity.