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

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 A E ), two solar indices (solar X‐rays X l and solar flux F 10.7), and two inner heliospheric indices (ion density N i and flow speed V s ) 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 τ ( q ) curves of these time series. The estimated values of the Lévy index α in the UMM indicate that multifractality exists in the time series for a p , AE , X l , and N i , while those for F 10.7 and V s 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 τ ( 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 N i , and F 10.7 and V s . The similarity in the scaling properties of pairs ( a p , X l ) and ( A E , N i ) suggests that a p and X l , AE and N i 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 N i , respectively, due to some reasons.