Evolution of the Correlation Between the Amplitude of the Solar Cycle and the Sunspot Number Since the Previous Declining Phase in Both Hemispheres

nalyzing the variation in the correlation between the maximum amplitude [ R_max ] of the solar cycle and the hemispheric sunspot number [ R_H ], since the previous declining phase, is helpful in understanding the temporal evolution of the cycle and the possible different mechanisms at work in the two hemispheres. The correlation coefficient [ r ] between R_max and the smoothed monthly mean R_H as a function of m=- 50,- 49, … , 50 months from the solar minimum [ R_min ] is studied, and it is found that r is maximum about three years before R_min at the declining phase, falls to a minimum value around R_min , and increases with m during the rising phase in both hemispheres. Based on the highest correlations at the declining phase, the maximum amplitudes of Cycle 25 in the northern [NH] and southern hemisphere [SH] are predicted to be R_max,N(25)=85.6± 21.9 and R_max,S(25)=74.4± 17.9 , respectively. Using data at the rising phase, R_max,N(25)=84.0± 26.7 and R_max,S(25)=88.3± 16.8 . The average values are R_max,N(25)= 84.8± 24.3 and R_max,S(25)=81.4± 17.4 . According to the weak correlation between the rise time and R_max , the peak times of Cycle 25 in the NH and SH are predicted to be November 2023 ± 10 months and July 2024 ± 10 months, respectively. Employing the strong correlation between the amplitude of the total sunspot number [ R_max,T ] and those of R_H in both hemispheres ( r=0.99 ), the amplitude of Cycle 25 is predicted to be R_max,T(25)=139.7± 28.7 and 152.3± 31.5 using data at the declining and rising phases, respectively, with an average value of 146.0± 30.1 .