Extreme Value Theory and the New Sunspot Number Series

Abstract

Abstract Extreme value theory was employed to study solar activity using the new sunspot number index. The block maxima approach was used at yearly (1700–2015), monthly (1749–2016), and daily (1818–2016) scales, selecting the maximum sunspot number value for each solar cycle, and the peaks-over-threshold (POT) technique was used after a declustering process only for the daily data. Both techniques led to negative values for the shape parameters. This implies that the extreme sunspot number value distribution has an upper bound. The return level (RL) values obtained from the POT approach were greater than when using the block maxima technique. Regarding the POT approach, the 110 year (550 and 1100 year) RLs were lower (higher) than the daily maximum observed sunspot number value of 528. Furthermore, according to the block maxima approach, the 10-cycle RL lay within the block maxima daily sunspot number range, as expected, but it was striking that the 50- and 100-cycle RLs were also within that range. Thus, it would seem that the RL is reaching a plateau, and, although one must be cautious, it would be difficult to attain sunspot number values greater than 550. The extreme value trends from the four series (yearly, monthly, and daily maxima per solar cycle, and POT after declustering the daily data) were analyzed with the Mann–Kendall test and Sen’s method. Only the negative trend of the daily data with the POT technique was statistically significant.