The correlation between solar and geomagnetic activity – Part 2: Long-term trends

Using lag-correlation function analysis, the correlation coefficient at zero lag (r0), the maximum (rm) and the corresponding lag time (Lm) between solar (Rz) and geomagnetic (aa) activity for a 528-month (44-year) running time window are shown to vary in a declining, declining and rising secular trend, respectively, before 1958. However, these trends changed since 1958 with a rising secular trend in both r0 and rm and without a significant trend in Lm, probably related to a periodicity longer than 140 years. An odd-numbered solar cycle tends to show a higher correlation and a shorter lag time between Rz and aa than the previous even-numbered one, suggesting a 2-cycle periodicity superimposed on secular trends. An even-numbered Hale cycle tends to show a higher correlation and a shorter lag time between Rz and aa than the previous odd-numbered one, suggesting a 4-cycle periodicity superimposed on secular trends. The variations in the correlations may be related to the non-linearity between Rz and aa, and the decreasing trend in the correlation (r0) is not exclusively caused by the increasing trend in the lag time of aa to Rz. These results represent an observational constraint on solar-dynamo models and can help us gain a better understanding of the long-term evolution of solar activities. In applications, therefore, cautions must be taken when using the correlation for molding the dynamical process of the Sun and for predicting solar activities.