http://arxiv.org/abs/1804.03617
Solar cycles are studied with the new (version 2) monthly smoothed international sunspot number, the variations of which are found to be well represented by the modified logistic differential equation with four parameters: maximum cumulative sunspot number or total sunspot number $x_m$, initial cumulative sunspot number $x_0$, maximum emergence rate $r_0$, and asymmetry $\alpha$. A two-parameter function can be obtained by taking the parameters $\alpha$ and $r_0$ as fixed value. In addition, it is found that the two parameters $x_m$ and $x_0$ can be well determined at the start of a cycle based on the analysis of solar cycles $1-23$. Therefore, a prediction model of the sunspot number variations of solar cycles is established based on the two-parameter function. The prediction for cycles $4-23$ shows that the solar maximum can be predicted with relative error being 9\% at the start of the cycle, which is better than that of other fitting functions in the literature. Besides, our model can predict the cycle length with the relative error being 10\%. Furthermore, we predict the sunspot number variations of solar cycle 24 with the relative errors of the solar maximum and that of the ascent time being 8\% and 7\%, respectively, we also predict that the length of cycle 24 is $10.90\pm1.09$ years. The comparison to the observation of cycle 24 shows that our prediction model has good effectiveness.
G. Qin and S. Wu
Wed, 11 Apr 18
51/54
Comments: 24 pages, 7 figures, 4 tables