ANGEO Annales Geophysicae ANGEO 1432-0576 Copernicus GmbH Göttingen, Germany 10.5194/angeo-29-1331-2011 The correlation between solar and geomagnetic activity – Part 1: Two-term decomposition of geomagnetic activity Du Z. L. 1 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 05 08 2011 29 8 1331 1340 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.ann-geophys.net/29/1331/2011/angeo-29-1331-2011.html The full text article is available as a PDF file from http://www.ann-geophys.net/29/1331/2011/angeo-29-1331-2011.pdf

By analyzing the logarithmic relationship between geomagnetic activity as represented by the annual <I>aa</I> index and solar magnetic field activity as represented by the annual sunspot number (<I>R</I><sub>z</sub>) during the period 1844–2010, <I>aa</I> is shown to lie in between two lines defined solely by <I>R</I><sub>z</sub>. Two ways can be used to decompose the <I>aa</I> index into two components. One is decomposing <I>aa</I> into the sum of the baseline (<I>aa</I><sub>b</sub>) and the remainder (<I>aa</I><sub>u</sub>) with a null correlation. Another is dividing the top-line (<I>aa</I><sub>t</sub>) into the sum of <I>aa</I> and the remainder (<I>aa</I><sub>d</sub>) with a null correlation. The first decomposition is similar to the traditional one. The second decomposition implies a nonlinear relationship of <I>aa</I> with <I>R</I><sub>z</sub> (<I>aa</I><sub>t</sub>) and a decay process (<I>aa</I><sub>d</sub>). Therefore, <I>aa</I><sub>t</sub>=<I>aa</I>+<I>aa</I><sub>d</sub>=<I>aa</I><sub>b</sub>+<I>aa</I><sub>u</sub>+<I>aa</I><sub>d</sub>: (i) <I>aa</I><sub>t</sub> is related to the solar energy potential of generating geomagnetic activity (associated with <I>R</I><sub>z</sub>); (ii) <I>aa</I><sub>b</sub> is related to transient phenomena; (iii) <I>aa</I><sub>u</sub> is related to recurrent phenomena; and (iv) <I>aa</I><sub>d</sub> is related to the energy loss in the transmission from solar surface to the magnetosphere and ionosphere that failed to generate geomagnetic activity.

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