Forecasting the 23 and 24 solar cycles on the basis of MGM spectrum

A new method of nonlinear spectral analysis (called the method of global minimum: MGM), based on the best presentation (in sense of minimal squares) of a given time data set as a sum of sinusoids whose frequencies, amplitudes and phases are to be determined, has been used to find periodicities in annual Wolf sunspot numbers (W) during the period 1700–1995. The possible future behaviour of the 11-year solar cycle (based on an extrapolation of the calculated model) is also presented. The main characteristics of the 23^rd solar cycle are as follows: the W maximum occurs about 2004, with a peak of nearly 220. An unusually large value of W will occur during the 23^rd cycle, which should be characterised by the longest maximum, specifically, W will be greater than 100 during the 11-year period from 1997 to 2007. The first sharp rise will occur during the period 1996–1998, the second sharp during 2002–2004. The main features of the 24 year cycle are as follows: the next minimum in W, associated with the 24^th solar cycle, should occur in the year 2008 and the maximum in 2014. W is expected to peak at about 180. The minimum value for the 25^th year cycle is expected to occur in the year 2019. It is shown that the accuracy of these predictions depends, first of all, on the extrapolation of the hyperlong harmonic of the calculated polyharmonic model fit of observed annual sunspot numbers during the period 1700–1995. The error bars in the definition of the maximum and minimum epochs can be as large as two years.