Predicting Solar Cycles with a Parametric Time Series Model

The objective of this paper is to reproduce and predict the series of solar cycle amplitudes using a simple time-series model that takes into account the variable time scale of the Gleissberg oscillation and the absence of clear evidence for odd–even alternation prior to Solar Cycle 9 (SC9). It is demonstrated that the Gleissberg oscillation can be quite satisfactorily modelled as a sinusoidal variation of constant amplitude with a period increasing linearly with time. Subtracting this model from the actual cycle amplitudes, a clear even–odd alternating pattern is discerned in the time series of the residuals since SC9. For this period of time, the mean value of the residuals for odd-numbered cycles is shown to exceed the value for even-numbered cycles by more than 4σ, providing the clearest evidence yet for a persistent odd–even–odd alternation in cycle amplitudes. Random deviations from these means are less than half the standard deviation of the raw cycle amplitude time series for the same period, which allows the use of these regularities for solar cycle prediction with substantially better confidence than the simple climatological average. Predicted cycle amplitudes are found to be robust against the addition or omission of some data points from the input set, and the method correctly hindcasts SC23 and SC24. The potential physical background of the regularities is also discussed. Our predictions for the amplitudes of SC25, SC26, and SC27 are 155.8±20.7, 96.9±25.1 and 140.8±20.7, respectively. This suggests that the amplitude of SC26 will be even lower than that of SC24, making it the weakest cycle since the Dalton Minimum.