Multifractal properties of solar filaments and sunspots numbers

We analyze multifractal properties of low (LLSFNs; <50°), high (HLSFNs; ⩾50°), full-disk (FDSFNs; 0°∼90°) solar filament numbers (SFNs) and international sunspot numbers (ISNs) by estimating characteristic parameters (α0,Δα, spectrum skewness) of f(α) singularity spectrum. We find that the SFNs and ISNs have multifractal nature. The obtained α0 and Δα indicate that long-term behaviour of the solar filaments is more complex than that of the sunspots and the high-latitude filaments is the most complex in long-term behaviour. The spectrum skewnesses manifest that the ISNs display well symmetrical distribution in singularity strengths, whereas the SFNs are dominated by low singularity strengths, which means that the long-term behaviour of sunspots has homogenous structures and the filaments display averagely small fluctuations in amplitude. To detect the origin of their multifractality, we decompose the raw data of ISNs and SFNs: smoothed data represent ∼11-year cyclic activities and detrended data represent accidental activities. We also calculate their f(α) spectra, respectively. We find that the ∼11-year cyclic activities of filaments and sunspots tend to be a monofractal and display a bit predominance of low singularity strengths. Their accidental activities have the most complex behaviour than the raw and smoothed data. The accidental activities are dominated by high singularity strengths showing averagely large fluctuations in amplitude. Furthermore, multifractal properties from α0 and Δα of the accidental activities have the same features as that of raw data. We think that the ∼11-year periodic activity determines global fluctuations, while the accidental activities rule local complexity.