The Link between Lengths and Amplitudes of the Eleven-Year Cycle for the Millennium Sunspot Index Series

In the recent work by Usoskin et al. (2021) a series of annual sunspot indices for the years 971 to 1899 was reconstructed. Using this series, we study behavior of the “length-amplidude rule” (LAR), according to which the mininum-to-minimum length of a given 11-year solar cycle anticorrelates with the amplitude of the next one. We show that approximately since the 14th century two regimes exist in the series: I) epochs of normal activity, when the LAR is observed; II) epochs of the Maunder, Spörer and Wolf grand minima, when there were no significant links between the amplitudes and lengths of the 11-year cycles. Before the 14th century the LAR and its relation to the level of global activity of the Sun is less pronounced, which, probably, is a consequence of inaccuracies of the 11-year cycle parameters determination in this epoch.