The correlation between solar and geomagnetic activity – Part 1: Two-term decomposition of geomagnetic activity

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