Difference between even and odd cycles in the predictability of the amplitude of the around 11-year-period solar activity and prediction of the amplitude of cycle 25

The waxing and waning of the solar activity represented by a period of roughly 11 years is usually quantified by the change in the sunspot number (SSN). It is commonly held that these increases and decreases in the SSN as well as the changes in the general dipole-like magnetic field in the photosphere and corona are produced by a magneto-hydro dynamic process in the sun's underlying convection layer. Assuming this is the case, it follows that SSNs in past cycles should contain a certain kind of information that enables us to estimate the amplitudes of future cycles. We report here a set of new results along this line of research. The chief aim of this paper is to demonstrate a distinct difference in the predictability of solar activity between even and odd cycles. Yoshida and Yamagishi (2010) showed that the SSN at the point three years before a minimum is well correlated with the maximum SSN in the following cycle. Here, we show that the correlation between this locus and the average SSN supplies a higher correlation coefficient. Moreover, we demonstrate that the correlation coefficient for even cycles is far better than that for odd ones (i.e., 0.96 and 0.74, respectively). Though it has been known that the correlation between the SSN at a point three years after a minimum and the maximum SSN is high, we demonstrate here that taking this calculation along with the average SSN (instead of the maximum SSN), the correlation coefficient for even cycles (0.98) reveals itself to be noticeably larger than that for odd cycles (0.93). Furthermore, we have found that the average SSN of even cycles is highly correlated with that of succeeding odd cycles (i.e., the correlation coefficient - minus three outliers - is 0.99). Conversely, no correlation is observed between amplitudes of odd cycles and those of succeeding even cycles. These distinct differences between even-odd pairs and odd-even pairs in their connective features lead us to believe that pairs of even-odd cycles comprise an elementary unit in the self-dynamo mechanism. Although we cannot explain why outliers occasionally appear in such a tight relationship between amplitudes of even cycles and those of succeeding odd cycles, we can judge in the early stage of an even cycle, by looking at the increasing rate of the SSN, whether it will be followed by an outlier or not. Now that three years have past from the minimum SSN in the current even cycle, we can safely assume that the amplitude of cycle 25 will not be an outlier. If this is the case, we can predict the amplitude of cycle 25 through three steps. First, we estimate the amplitude of cycle 24 utilizing the high correlation between the SSN at three years after its minimum and the average SSN for even cycles. Secondly, based on the strong relationship between the amplitude of even cycles and that of succeeding odd cycles (between amplitudes of even-odd pairs), we calculate the amplitude of cycle 25. Thirdly, making note of the high correlation coefficient (0.98) between the average SSN and the maximum SSN (Yoshida and Sayre, 2012), we obtain the value of cycle 25's max SSN. Thus, we predict as of August 2012 that the maximum value of SSN of cycle 25 to be 112.0±15.1.