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

Z L Du

doi:10.5194/angeo-29-1341-2011

Abstract

Abstract. 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.

Highlights

The aa geomagnetic index, calculated from the 3-hourly K indices measured at two near-antipodal midlatitude stations (Mayaud, 1972), has been used for analyzing long-term trends in the global geomagnetic activity and in its correlation with solar activity (Feynman, 1982; Legrand and Simon, 1989; Mursula et al, 2004; Lukianova et al, 2009)
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

Summary

Introduction

The aa geomagnetic index, calculated from the 3-hourly K indices measured at two near-antipodal midlatitude stations (Mayaud, 1972), has been used for analyzing long-term. Borello-Filisetti et al (1992) examined the secular variations in the correlation between aa and Rz in terms of ascending (A) and descending (D) phases of the solar cycle and pointed out that the linear correlation coefficient (r) during the Dphase tends to decrease. They suggested by visual inspection two periodicities of 5-cycle in A-phase, which they insist on later (Mussino et al, 1994), and 8-cycle in D-phase. In the following paper (Du, 2011b), we will present a model to explain these phenomena and the significant increase in the aa index (and its baseline) over the twentieth century

Correlation analysis for a 528-month running time window

Correlation analysis for solar cycles

Correlation analysis for Hale cycles

Findings

Discussions and conclusions