14C-Based Sunspot Numbers for the Last Millennium Encompass the Full Range of Variability: Extreme Value Theory

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.