Centennial variations in sunspot number, open solar flux and streamer belt width: 2. Comparison with the geomagnetic data

We investigate the relationship between interdiurnal variation geomagnetic activity indices, IDV and IDV(1d), corrected sunspot number, R{sub}C{\sub}, and the group sunspot number R{sub}G{\sub}. R{sub}C{\sub} uses corrections for both the “Waldmeier discontinuity”, as derived in Paper 1 [Lockwood et al., 2014c], and the “Wolf discontinuity” revealed by Leussu et al. [2013]. We show that the simple correlation of the geomagnetic indices with R{sub}C{\sub}{sup}n{\sup} or R{sub}G{\sub}{sup}n{\sup} masks a considerable solar cycle variation. Using IDV(1d) or IDV to predict or evaluate the sunspot numbers, the errors are almost halved by allowing for the fact that the relationship varies over the solar cycle. The results indicate that differences between R{sub}C{\sub} and R{sub}G{\sub} have a variety of causes and are highly unlikely to be attributable to errors in either R{sub}G{\sub} alone, as has recently been assumed. Because it is not known if R{sub}C{\sub} or R{sub}G{\sub} is a better predictor of open flux emergence before 1874, a simple sunspot number composite is suggested which, like R{sub}G{\sub}, enables modelling of the open solar flux for 1610 onwards in Paper 3, but maintains the characteristics of R{sub}C{\sub}