Autocorrelation of Wolf Number Cycle Fragments and Solar Activity Half-Cycle Forecast

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Abstract

Autocorrelations of fragments of a series of Wolf numbers (Version 2) are considered for the purpose of forecasting for 6 years (half a solar activity cycle). Fragments similar to one and a half cycles were used for physical and optimal reasons. Testing was successfully carried out on fairly reliable pairs of series fragments, consisting of a fixed and a time-shifted fragment. Pairs were selected for testing if the correlation coefficient of their superposition was 0.91 or more. An original modification of the fixed fragment and the following segments of the series was used. Similarly, forecasts were made for 6 years after 2023, based on the fragment (2008.5−2023.5), which has correlation coefficients from 0.81 to 0.96 with fragments (1978.5−1993.5), (1901.5−1916.5), (1922.5−1937.5), (1964.5−1979.5), (1985.5−2000.5). The maximum value of the Wolf number (161 ± 30) is expected in mid-2024.

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S. V. Yakovleva

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences

Author for correspondence.
Email: svyakov@inbox.ru
Russian Federation, Troitsk

S. V. Starchenko

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences

Email: sstarchenko@mail.ru
Russian Federation, Troitsk

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2. Fig. 1. Variation of the mean annual Wolf numbers W from 1830 to 2023 in the V2 version of (http://sidc.oma.be/silso/datafiles). Numbers denote the maxima of the considered cycles, Wmax is the maximum value in the cycle, σ is the standard deviation.

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3. Fig. 2. Result of Test 1. The black colour shows a series of Wi values of the interval under study. The grey colour shows a series of Wj values of some interval in the past with a high pair correlation coefficient r = 0.93. This interval is shifted to coincide with the interval under study. The dashed line and the caption NORM denote the normalised series Fl. The numbers denote the maxima of the considered cycles. The coefficient of determination is respectively: 0.86 (left) and 0.75 (right), see Table 2 above.

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4. Fig. 3. Result of Test 2. The black colour shows a series of Wi values of the interval under study. The grey colour shows a series of Wj values of some interval in the past with a high pair correlation coefficient r = 0.93. This interval is shifted to coincide with the interval under study. The dashed line and the caption NORM denote the normalised series Fl. The numbers denote the maxima of the considered cycles. The coefficient of determination is 0.80 and 0.96, respectively (see Table 2 above).

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5. Fig. 4. Result of Test 3. The black colour shows a series of Wi values of the interval under study. The grey colour shows a series of Wj values of some interval in the past with a high pair correlation coefficient r = 0.93. This interval is shifted to coincide with the interval under study. The dashed line and the caption NORM denote the normalised series Fl. The numbers denote the maxima of the considered cycles. The coefficient of determination is 0.74 and 0.97, respectively (see Table 2 above).

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6. Fig. 5. Results of approximating the 16-year interval (2008.5-2022.5) through normalisation of correlated fragments: Fit1 (1878.5-1892.5), Fit2 (1901.5-1916.5), Fit3 (1922.5-1937.5), Fit4 (1964.5-1979.5), Fit5 (1985.5-2000.5) and the corresponding projections to 2029.5. In figure (a) from 2008.5, and in enlarged figure (b) from 2019.5. Mean Fit is the average of the normalised curve Fl. The standard deviation σ = ± 29.75. The average coefficient of determination R2 of the correlated fragments with the shifted fragment (2008.5-2022.5) is 0.8 ± 0.1 (see Table 3 for details).

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