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

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

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.

Full Text

Restricted Access

About the authors

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

References

  1. Бондарь Т.Н., Ротанова Н.М., Обридко В.Н. Прогнозирование временного ряда чисел Вольфа для 23-го солнечного цикла // Письма в Aстрон. журн. Т. 22. № 8. С. 628−630. 1996.
  2. Витинский Ю.И. Цикличность и прогнозы солнечной активности. Л.: Наука, 258 c. 1973.
  3. Ишков В.Н. Периоды “пониженной” и “повышенной” солнечной активности: наблюдательные особенности и ключевые факты / Сб. “Солнечная и солнечно-земная физика – 2013”. Ред. А.В. Степанов и Ю.А. Наговицын. СПб.: Изд. ВВМ. С. 111−114. 2013.
  4. Ишков В.Н., Шибаев И.Г. Циклы солнечной активности: общие характеристики и современные границы прогнозирования // Изв. РАН. Сер. физическая. Т. 70. № 10. С.1439–1442. 2006.
  5. Гневышев М.Н., Оль А.И. О 22-летнем цикле солнечной активности // Астрон. журн. Т. 25. № 1. С. 18−20. 1948.
  6. Наговицын Ю.А., Огурцов М.Г. Грандиозные минимумы и максимумы солнечной активности и климата Земли: последнее тысячелетие и картина будущего “в общих чертах” / Тр. 7-й Международной Пулковской конференции “Климатические и экологические аспекты солнечной активности”. Пулково, 7-11 июля 2003 г. СПб.: ГАО РАН. С. 321−326. 2003.
  7. Обридко В. Н., Наговицын Ю. А. Солнечная активность, цикличность и методы прогноза. СПб.: Изд. ВВМ, 466 c. 2017.
  8. Обридко В.Н., Шельтинг Б.Д. Об отрицательной корреляции между солнечной активностью и скоростью вращения Солнца // Письма в Aстрон. журн. Т. 42. № 9. С. 694–700. 2016. https://doi.org/10.7868/S0320010816080040
  9. Ожередов В.А., Бреус Т.К., Обридко В.Н. Прогнозирование полного 24-го цикла солнечной активности несколькими вариантами авторегрессии и методом предвестника // Геофизические процессы и биосфера. Т. 10. № 3. С. 51−65. 2011.
  10. Старченко С.В., Яковлева С.В. Корреляция временных рядов чисел Вольфа и их производных // Геомагнетизм и аэрономия. Т. 62. № 2. С. 144−154. 2022. https://doi.org/10.31857/S001679402202016X
  11. Abdel-Rahman H.I., Marzouk B.A. Statistical method to predict the sunspots number // NRIAG Journal of Astronomy and Geophysics. V. 7. N 2. P. 175−179. 2018. https://doi.org/10.1016/j.nrjag.2018.08.001
  12. Abdusamatov K.I. Optimal prediction of the peak of the next 11-year activity cycle and of the peaks of several succeeding cycles on the basis of long-term variations in the solar radius or solar constant // Kinemat. Phys. Celest. V. 23. N 3. P. 97–100. 2007. https://doi.org/10.3103/S0884591307030026
  13. Brajša R., Verbanac G., Bandić M., Hanslmeier A., Skokić I., Sudar D. A prediction for the 25th solar cycle maximum amplitude // Astron. Nachr. V. 343. N 3. ID e13960. 2022. https://doi.org/10.1002/asna.202113960
  14. Dmitrieva I.V., Kuzanyan K.M., Obridko V.N. Amplitude and period of the dynamo wave and prediction of the solar cycle // Sol. Phys. V.195. N 1. P. 209–218. 2000. https://doi.org/10.1023/A:1005207828577
  15. Hathaway D.H. The solar cycle // Living Rev. Sol. Phys. V. 12. N 1. ID 4. 2015. https://doi.org/10.1007/lrsp-2015-4
  16. Hathaway D.H., Wilson R.M. Geomagnetic activity indicates large amplitude for sunspot cycle 24 // Geophys. Res. Lett. V. 33. N 18 ID L18101. 2006. https://doi.org/10.1029/2006GL027053
  17. Hathaway D.H., Wilson R.M., Reichmann E.J. A synthesis of solar cycle prediction techniques // J. Geophys. Res. – Space. V. 104. N. 10. P. 22375–22388. 1999. https://doi.org/10.1029/1999JA900313
  18. Leamon R.J., McIntosh S.W., Chapman S.C., Watkins N.W. Response to “Limitations in the Hilbert transform approach to locating solar cycle terminators” by R. Booth // Sol. Phys. V. 296. N 10. ID 151. 2021. https://doi.org/10.1007/s11207-021-01897-z
  19. McIntosh S.W., Chapman S., Leamon R.J., Egeland R., Watkins N.W. Overlapping magnetic activity cycles and the sunspot number: Forecasting sunspot cycle 25 amplitude // Sol. Phys. V. 295. N 12. ID 163. 2020. https://doi.org/10.1007/s11207-020-01723-y
  20. Nagovitsyn Y.A., Ivanov V.G. Solar сycle рairing and рrediction of сycle 25 // Sol. Phys. V. 298. N 3. ID 37. 2023. https://doi.org/10.1007/s11207-023-02121-w
  21. Nandy D. Progress in solar cycle predictions: Sunspot cycles 24–25 in perspective // Sol. Phys. V. 296. N 3. ID 54. 2021. https://doi.org/10.1007/s11207-021-01797-2
  22. Pesnell W.D. Solar cycle predictions (invited review) // Sol. Phys. V. 281. N 1. P. 507–532. 2012. https://doi.org/10.1007/s11207-012-9997-5
  23. Petrovay K. Solar cycle prediction // Living Rev. Sol. Phys. V. 17. N 1. ID 2. 2020. https://doi.org/10.1007/s41116-020-0022-z
  24. Pishkalo M.I. Preliminary рrediction of solar cycles 24 and 25 dased on the correlation between сycle рarameters // Kinemat. Phys. Celest. V. 24. N 5. P. 242–247. 2008. https://doi.org/10.3103/S0884591308050036
  25. Zhu H., Zhu W., He M. Solar cycle 25 prediction using an optimized long short-term memory mode with F10.7 // Sol. Phys. V. 297. N 12. ID 157. 2022. https://doi.org/10.1007/s11207-022-02091-5

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
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.

Download (186KB)
Indexing metadata
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.

Download (128KB)
Indexing metadata
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).

Download (137KB)
Indexing metadata
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).

Download (152KB)
Indexing metadata
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).

Download (360KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences