Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

Abstract

This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (a p and AE), two solar indices (solar X-rays X l and solar flux F10.7), and two inner heliospheric indices (ion density Ni and flow speed Vs) over the period 1995-2001 by the universal multifractal approach and the traditional multifractal analysis. We found that the universal multifractal model (UMM) provides a good fit to the empirical K(q) and (q) curves of these time series. The estimated values of the Lévy index in the UMM indicate that multifractality exists in the time series for a p , AE, X l , and Ni, while those for F10.7 and Vs are monofractal.The estimated values of the nonconservation parameter H of this model confirm that these time series are conservative which indicate that the mean value of the process is constant for varying resolution. Additionally, the multifractal K(q) and (q) curves, and the estimated values of the sparseness parameter C 1 of the UMM indicate that there are three pairs of indices displaying similar scaling properties, namely a p and X l , AE and Ni, and F10.7 and Vs. The similarity in the scaling properties of pairs (a p , X l ) and (AE, Ni) suggests that a p and X l , AE and Ni are better correlated-in terms of scaling-than previous thought, respectively. But our results still cannot be used to advance forecasting of a p and AE by X l and Ni, respectively, due to some reasons.

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