ANGEO Annales Geophysicae ANGEO Ann. Geophys. 1432-0576 Copernicus Publications Göttingen, Germany 10.5194/angeo-29-1341-2011 The correlation between solar and geomagnetic activity – Part 2: Long-term trends Du Z. L. 1 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 05 08 2011 29 8 1341 1348 Copyright: © 2011 Z. L. Du 2011 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://angeo.copernicus.org/articles/29/1341/2011/angeo-29-1341-2011.html The full text article is available as a PDF file from https://angeo.copernicus.org/articles/29/1341/2011/angeo-29-1341-2011.pdf

Using lag-correlation function analysis, the correlation coefficient at zero lag (<I>r</I><sub>0</sub>), the maximum (<I>r</I><sub>m</sub>) and the corresponding lag time (<I>L</I><sub>m</sub>) between solar (<I>R</I><sub>z</sub>) and geomagnetic (<I>aa</I>) 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 <I>r</I><sub>0</sub> and <I>r</I><sub>m</sub> and without a significant trend in <I>L</I><sub>m</sub>, 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 <I>R</I><sub>z</sub> and <I>aa</I> 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 <I>R</I><sub>z</sub> and <I>aa</I> 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 <I>R</I><sub>z</sub> and <I>aa</I>, and the decreasing trend in the correlation (<I>r</I><sub>0</sub>) is not exclusively caused by the increasing trend in the lag time of <I>aa</I> to <I>R</I><sub>z</sub>. 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.

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