Modulation of the solar magnetic cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 +/- 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Sparer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950-2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.