Predicting the Maximum Amplitude of Solar Cycle 25 Using the Early Value of the Rising Phase

The rising rate [ β _a ] of a solar cycle is a good indicator for the subsequent maximum amplitude [ S_m ] of sunspot numbers. We compared the correlation between S_m and β _a and that between S_m and the early value of the smoothed monthly mean sunspot number [ S_N ] Δ m months after the solar minimum. Our main conclusions are as follows: i) The correlation coefficient [ r ] between S_m and S_N is slightly higher than that between S_m and β _a , and both increase with Δ m as the cycle progresses; ii) In the first year of the cycle, the correlation is weak [ r∼ 0.56]. At the inflection point [ Δ m=21 ], the correlation is stronger [ r = 0.83 ]. After the inflection point, r increases slowly with Δ m . Three years after the solar minimum, r⩾ 0.90 . Around the average rise time [52 months], r=0.95 ; iii) The correlation between S_m and S_N (or β _a ) in even-numbered cycles is stronger than that in odd-numbered ones, and the latter is slightly weaker than that for all the cycles; iv) The mean relative error [ η ] of S_m decreases and the MSE (Mean Square Error) skill score [ S_c ] increases with Δ m . One, two, three, and four years after the solar minimum: η⩽ 19% , 14% , 10% , and 6.5% , S_c⩾ 0.24 , 0.68, 0.86, and 0.97, respectively; v) Currently [ Δ m=20 ], the maximum amplitude of Cycle 25 is predicted to be 135.5± 33.2 and to occur around December 2024 (± 11 months).