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Correlation of Time Series of Wolf Numbers and their Derivatives

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Abstract

The results of the study of the correlation of the mean annual Wolf numbers W and their time derivatives W ' for time shifts of fragments of series W and W ' relative to each other are presented. The most significant (up to 0.88 and –0.85) correlation and anticorrelation coefficients are obtained with shifts of 2 or 3 years for fragments covering two 11-year cycles. For longer fragments, the coefficients remain significant (at levels of approximately ±0.8) at the same shifts. Therefore, the phase shift between W and W ' is approximately one-quarter of the solar cycle, which physically corresponds to the predominant connection of spots with magnetic energy. At the same time, there is also a significant shift by 8–9 years, which corresponds to correlation coefficients at levels of approximately ±0.75 associated with the magnetic energy variability. The prognostic potentials of the obtained correlation dependences are discussed.

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ACKNOWLEDGMENTS

We are grateful to an anonymous reviewer for providing useful links on the form of the solar activity cycle, comparative studies of derivatives of Wolf numbers, and for very constructive suggestions for the design of the paper.

We are grateful to another reviewer, Vitaly Nikitich Ishkov, for his advice to expand the graphical illustrations of correlations to the entire set of reliable series of Wolf numbers, and for considerations expressed about the possible nature of the phase shift between numbers and derivatives.

Funding

The study was supported by the Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation RAS within the framework of state funding.

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  1. Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, 108840, Moscow, Troitsk, Russia

    S. V. Starchenko & S. V. Yakovleva

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  1. S. V. Starchenko
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  2. S. V. Yakovleva
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Correspondence to S. V. Starchenko or S. V. Yakovleva.

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Starchenko, S.V., Yakovleva, S.V. Correlation of Time Series of Wolf Numbers and their Derivatives. Geomagn. Aeron. 62, 685–693 (2022). https://doi.org/10.1134/S0016793222050164

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  • DOI: https://doi.org/10.1134/S0016793222050164

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