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Solar activity, such as sunspots and flares, has a great impact on humans, living beings, and technologies in the whole world. Changes in sunspots will influence high-frequency and space-navigation radio communications. Based on the full-disk, southern and northern hemispheres sunspot areas (SAs) data in 1874–2023 from the Royal Observatory, Greenwich (RGO) USAF/NOAA, extreme value theory (EVT) is applied to predict the trend of the 25th and 26th solar cycles (SCs) in this work. Two methods with EVT, the block maxima (BM) approach and the peaks-over-threshold (POT) approach, are employed to research solar extreme events. The former method focuses on each block's maximum sunspot areas value and is applied for the generalized extreme value (GEV) distribution. The latter method aims to select the extreme values exceeding a threshold value and is used to obtain the generalized Pareto (GP) distribution. It is the first time that the EVT is applied on the sunspot areas data from the Royal Observatory, Greenwich (RGO) USAF/NOAA. The analysis indicates that the estimated 8-year return levels for sunspot areas are 5701 and 6258 using the two methods, while the estimated 19-year return levels are all 7165. This suggests that the trends of the 25th and 26th solar cycles will be stronger than that of the 24th solar cycle. [ABSTRACT FROM AUTHOR]

Based on the daily sunspot number (SN) data (1954–2011) from the Purple Mountain Observatory, the extreme value theory (EVT) is employed for the research of the long-term solar activity. It is the first time that the EVT is applied on the Chinese SN. Two methods are used for the research of the extreme events with EVT. One method is the block maxima (BM) approach, which picks the maximum SN value of each block. Another one is the peaks-over-threshold (POT) approach. After a declustering process, a threshold value (here it is 300) is set to pick the extreme values. The negative shape parameters are obtained by the two methods, respectively, indicating that there is an upper bound for the extreme SN value. Only one value of the N -year return level (RL) is estimated: N = 19 years. For N = 19 years, the RL values of SN obtained by two methods are similar with each other. The RL values are found to be 420 for the POT method and the BM method. Here, the trend of 25th solar cycle is predicted to be stronger, indicating that the length of meridional forms of atmospheric circulation will be increased. [ABSTRACT FROM AUTHOR]