14C-Based Sunspot Numbers for the Last Millennium Encompass the Full Range of Variability: Extreme Value Theory
Acero, F. J.; Carrasco, V. M. S.; Gallego, M. C.; Usoskin, I. G.; Vaquero, J. M. (2025-04-07)
Springer Publishing Company
07.04.2025
Acero, F.J., Carrasco, V.M.S., Gallego, M.C. et al. 14C-Based Sunspot Numbers for the Last Millennium Encompass the Full Range of Variability: Extreme Value Theory. Sol Phys 300, 50 (2025). https://doi.org/10.1007/s11207-025-02464-6.
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© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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https://urn.fi/URN:NBN:fi:oulu-202504102520
https://urn.fi/URN:NBN:fi:oulu-202504102520
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Abstract
We examine the statistical properties of extreme solar activity levels through the application of the extreme value theory to the annual sunspot number series reconstructed from 14C data spanning the last millennium. We have used the extreme value theory to study long-term solar variability by applying the peaks-over-threshold technique to an annual sunspot number series reconstructed from 14C data for the last millennium. We have obtained a negative value of the shape parameter of the generalized Pareto distribution implying that an upper bound has been reached by the extreme sunspot number value distribution during the past millennium. The results obtained from the same analysis applied to two subperiods of the series, are consistent with that considering the whole series. We have also estimated return levels and periods for the extreme sunspot numbers. The maximum annual sunspot number (273.6) observed during the past millennium is slightly higher (lower) than that considering a 1000-year (10,000-year) return level, but they are within the 95% confidence interval in both cases. It approximately corresponds to a 3500-year return period. Our result implies that solar activity has reached its upper limit, and it would be unlikely to observe, in the near future, sunspot numbers significantly higher than those already observed during the past millennium.
We examine the statistical properties of extreme solar activity levels through the application of the extreme value theory to the annual sunspot number series reconstructed from 14C data spanning the last millennium. We have used the extreme value theory to study long-term solar variability by applying the peaks-over-threshold technique to an annual sunspot number series reconstructed from 14C data for the last millennium. We have obtained a negative value of the shape parameter of the generalized Pareto distribution implying that an upper bound has been reached by the extreme sunspot number value distribution during the past millennium. The results obtained from the same analysis applied to two subperiods of the series, are consistent with that considering the whole series. We have also estimated return levels and periods for the extreme sunspot numbers. The maximum annual sunspot number (273.6) observed during the past millennium is slightly higher (lower) than that considering a 1000-year (10,000-year) return level, but they are within the 95% confidence interval in both cases. It approximately corresponds to a 3500-year return period. Our result implies that solar activity has reached its upper limit, and it would be unlikely to observe, in the near future, sunspot numbers significantly higher than those already observed during the past millennium.
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