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

Abstract. Using lag-correlation function analysis, the correlation coefficient at zero lag (r₀), the maximum (r_m) and the corresponding lag time (L_m) between solar (R_z) 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 r_m and without a significant trend in L_m, 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 R_z 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 R_z 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 R_z 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 R_z. 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.