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Abstract <p>We consider the applicability of the classical Waldmeier rule or effect, i.e., the relationship between the amplitude of the 11-year solar cycle and the length of its rising branch (rise time), to a series of total sunspot areas. We show that the absence of a correlation revealed by some authors is associated with the influence of quasi-biennial oscillations and the choice of a smoothing method. We propose a new proxy series of yearly mean sunspot group area that is free from the quasi-biennial component and Gnevyshev gaps. For this series we have estimated the correlation coefficient between the solar cycle amplitude and the length of the rising branch, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R\approx 0.8\)</EquationSource> <!--Letters2570064Osipova-m1--> </InlineEquation>, confirming the universality of the Waldmeier rule. Values of <i>R</i> up to 0.99 have been reached in the modified formulations that relate the amplitude to the maximum and mean activity growth rates, making them promising for an early prediction of the solar cycle amplitude.</p>

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Sunspot Group Area Index and the Waldmeier Rule

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. A. Osipova,
  • Yu. A. Nagovitsyn,
  • S. N. Fedoseeva

摘要

Abstract

We consider the applicability of the classical Waldmeier rule or effect, i.e., the relationship between the amplitude of the 11-year solar cycle and the length of its rising branch (rise time), to a series of total sunspot areas. We show that the absence of a correlation revealed by some authors is associated with the influence of quasi-biennial oscillations and the choice of a smoothing method. We propose a new proxy series of yearly mean sunspot group area that is free from the quasi-biennial component and Gnevyshev gaps. For this series we have estimated the correlation coefficient between the solar cycle amplitude and the length of the rising branch, \(R\approx 0.8\) , confirming the universality of the Waldmeier rule. Values of R up to 0.99 have been reached in the modified formulations that relate the amplitude to the maximum and mean activity growth rates, making them promising for an early prediction of the solar cycle amplitude.