The Waldmeier Rule and its Modifications

We discuss the difference between the traditional Waldmeier rule and its various modifications related to the fact that the height of the 11-year cycle maxima is conditioned by the activity growth rates on the rising branches. We consider the closeness of the correlations between the Waldmeier effect, on the one hand, and its modifications that consider the activity growth rate from minimum to maximum instead of the length of the rising branch, on the other hand. Using Fisher’s test, we show that the traditional Waldmeier effect describes the observational data more poorly than does the modified one (with the argument of the maximum growth rate on the rising branch): the residual dispersion of data points for it is significantly larger (the significance level is $$\alpha=0.01$$ ). Based on a series of total sunspot areas on a 400-year time scale (Nagovitsyn and Osipova 2021), we consider the correlation of its values at activity maxima $$AR_{M}$$ with the mean rate of its change on the rising branches $$MAR$$ , including that during the Maunder minimum. We show that this correlation is nonlinear and close: the correlation coefficients for two different nonlinear fits, a parabola and a power law, are fairly large: $$R=0.97{-}0.98$$ .