Hilbert–Huang transform analysis of periodicities in the last two solar activity cycles

Abstract

We investigated periodicities associated with the last two-and-a-half solar activity cycles with the novel Hilbert–Huang transform (HHT) method. Raw data signals of five different observational proxies: the 10.7 cm radio flux intensity, the helioseismic frequency shift, and the sunspot area signals recorded from the whole solar disc, and separately from the Northern and Southern hemispheres, were expanded into a set of intrinsic modes with the ensemble empirical mode decomposition technique. Instant and mean periods of each empirical mode were obtained with the use of the Hilbert transform applied independently to each separate mode. The periodicities were allocated to three distinct groups: short-term variations (with periods shorter than 0.5 yr), quasi-biennial oscillations (with typical periods from 0.5 yr to 3.9 yr), and longer periodicities, e.g. such as the 11 yr cycle. All periodicities detected in the examined solar cycles 22–24 are consistent with the well-known results found in the earlier solar epochs. We have demonstrated that the HHT method is a good tool for characterizing periodicities in the helioseismic data, which are necessarily relatively limited in terms of their time resolution. Periodicities obtained using the helioseismic data are, nevertheless, consistent with those found in other proxies. Since helioseismic oscillations are sensitive to the solar interior, this indicates that the behaviour of surface and atmospheric magnetic activity reflects that of the Sun's internal magnetic field. All identified intrinsic modes are seen to have clear amplitude modulation highly correlated with the 11 yr cycle. This amplitude modulation is most pronounced in the short-period modes. The short-term periodicities were found to be multiples of the shortest period, of 25 d. This ordering of the short-term periodicities is consistent with the previous findings. Signatures of the north–south asymmetry were detected in the individual hemisphere sunspot area indices. Furthermore, evidence of the last ‘extended’ solar minimum was detected too.