Multifractal analysis of geomagnetic storm and solar flare indices and their class dependence

The multifractal properties of two indices of geomagnetic activity, D st (representative of low latitudes) and a p (representative of the global geomagnetic activity), with the solar X‐ray brightness, X l , during the period from 1 March 1995 to 17 June 2003 are examined using multifractal detrended fluctuation analysis (MF‐DFA). The h ( q ) curves of D st and a p in the MF‐DFA are similar to each other, but they are different from that of X l , indicating that the scaling properties of X l are different from those of D st and a p . Hence, one should not predict the magnitude of magnetic storms directly from solar X‐ray observations. However, a strong relationship exists between the classes of the solar X‐ray irradiance (the classes being chosen to separate solar flares of class X‐M, class C, and class B or less, including no flares) in hourly measurements and the geomagnetic disturbances (large to moderate, small, or quiet) seen in D st and a p during the active period. Each time series was converted into a symbolic sequence using three classes. The frequency, yielding the measure representations, of the substrings in the symbolic sequences then characterizes the pattern of space weather events. Using the MF‐DFA method and traditional multifractal analysis, we calculate the h ( q ), D ( q ), and τ ( q ) curves of the measure representations. The τ ( q ) curves indicate that the measure representations of these three indices are multifractal. On the basis of this three‐class clustering, we find that the h ( q ), D ( q ), and τ ( q ) curves of the measure representations of these three indices are similar to each other for positive values of q . Hence, a positive flare storm class dependence is reflected in the scaling exponents h ( q ) in the MF‐DFA and the multifractal exponents D ( q ) and τ ( q ). This finding indicates that the use of the solar flare classes could improve the prediction of the D st classes.