Amplitude variations of the 11 year cycle and the current solar maximum 23

We examined the conditions for violations of the Gnevyshev-Ohl rule, which states that the even-numbered 11 yr solar cycles have been followed by higher in amplitude odd-numbered ones. This regularity has been valid for the last 150 years, but it is very likely to be broken in the current 11 yr cycle 23. We used the Schove series, which includes the main macrocharacteristics of the 11 yr cycles and is continuous since the end of the third century. The reliability of these data has been discussed. A total of 152 cycles were investigated, the last one being cycle 21 in the International Sunspot Number series. We showed that there is a well-outlined group of even-numbered 11 yr cycles that are very likely to be followed by weaker odd-numbered ones. These are the most powerful even cycles, characterized by maximum monthly smoothed Wolf numbers exceeding 125 and decay times of 6 yr or more. The main factor for violations of the Gnevyshev-Ohl rule is a very high maximum of the even-numbered ii yr cycle. Applied to the present Hale cycle, which consists of ii yr cycles 22 and 23, our analysis implies a high probability for violation of the Gnevyshev-Ohl rule. The development of 11 yr cycle 23 confirms this conclusion. We argue that the present 11 yr cycle should not be qualified as "abnormal" when referring to the fact that it breaks a regularity that has lasted for 150 yr. The 11 yr cycle 23 might reveal a feature in the dynamics of the Hale cycle that the strongest even-numbered 11 yr cycles are likely to be followed by lower amplitude odd-numbered ones. We briefly discuss the relation between the long-term solar variability and the current violation of the Gnevyshev-Ohl rule.