The Gnevyshev-Ohl rule for physical parameters of the solar magnetic field: The 400-year interval

Statistical Effects in the Solar Activity Cycles during AD 1823–1996

“…Other statistical effects (W1, AP1, and AP2) are sensitive to selection of solar index, interval of analysis, and way of the cycle parameter determination. The stability of the GO2 relation confirms the result of Nagovitsyn et al [21], who concluded that the GO2 rule could be considered as a rather strict principle of longterm solar magnetic field dynamics. The principle means that the 22-year cycle present in solar magnetic activity.…”

“…With the exception of this one pair, the correlation coefficients R l exceed 0.90 and are significant at more than 0.99 confidence level. That is in agreement with the result of Nagovitsyn et al [21] who analyzed GO2 effect in the reconstructed sunspot area over the last 400 years and obtained the corresponding correlation coefficient 0.907. It is remarkable that just for the cycles 4-5, we have the least reliable sunspot data.…”

“…Our results for W2 effect are in agreement with the results of Cameron and Schüssler [7] and Karak and Choudhuri [8]. Cameron and Schüssler [7] have analyzed four datasets: monthly Wolf sunspot numbers for cycles 7-23, monthly group sunspot numbers for cycles 7-22, sunspot areas for cycles 12-23, and 10.7-cm solar radio flux for cycles [19][20][21][22][23]. In all the cases, they obtained high (R l = 0.83-0.89) coefficient of correlation between rise rate and cycle amplitude.…”

“…That is why Usoskin et al [23] hypothesized that cycle 4 was actually double and one small cycle has been lost in the 1790s, because of sparse and unreliable observations. An inclusion of the new cycle 1793-1800 in sunspot number records restores the order of the GO2 rule, making it valid over the last 400 years [21,22].…”

New characteristics of the solar cycle and dynamo theory

“…These primarily include the Gnevyshev-Ohl rule (GOR) (Gnevyshev and Ohl 1948), according to which the area under the curve of Wolf numbers for an even cycle SR 2N correlates with that for the succeeding odd one SR 2N +1 , while SR 2N −1 does not correlate with SR 2N , with the GOR in such a formulation being valid for all cycles without exception (Nagovitsyn et al 2009). Its more popular but less accurate formulation states that each odd cycle is larger in amplitude than the preceding even one.…”