Empirical mode decomposition analysis of random processes in the solar atmosphere

Abstract

Context. Coloured noisy components with a power law spectral energy distribution are often shown to appear in solar signals of various types. Such a frequency-dependent noise may indicate the operation of various randomly distributed dynamical processes in the solar atmosphere. Aims. We develop a recipe for the correct usage of the empirical mode decomposition (EMD) technique in the presence of coloured noise, allowing for clear distinguishing between quasi-periodic oscillatory phenomena in the solar atmosphere and superimposed random background processes. For illustration, we statistically investigate extreme ultraviolet (EUV) emission intensity variations observed with SDO/AIA in the coronal (171 Å), chromospheric (304 Å), and upper photospheric (1600 Å) layers of the solar atmosphere, from a quiet sun and a sunspot umbrae region. Methods. EMD has been used for analysis because of its adaptive nature and essential applicability to the processing non-stationary and amplitude-modulated time series. For the comparison of the results obtained with EMD, we use the Fourier transform technique as an etalon. Results. We empirically revealed statistical properties of synthetic coloured noises in EMD, and suggested a scheme that allows for the detection of noisy components among the intrinsic modes obtained with EMD in real signals. Application of the method to the solar EUV signals showed that they indeed behave randomly and could be represented as a combination of different coloured noises characterised by a specific value of the power law indices in their spectral energy distributions. On the other hand, 3-min oscillations in the analysed sunspot were detected to have energies significantly above the corresponding noise level. Conclusions. The correct accounting for the background frequency-dependent random processes is essential when using EMD for analysis of oscillations in the solar atmosphere. For the quiet sun region the power law index was found to increase with height above the photosphere, indicating that the higher frequency processes are trapped deeper in the quiet sun atmosphere. In contrast, lower levels of the sunspot umbrae were found to be characterised by higher values of the power law index, meaning the domination of lower frequencies deep inside the sunspot atmosphere. Comparison of the EMD results with those obtained with the Fourier transform showed good consistency, justifying the applicability of EMD.

On the intrinsic timescales of temporal variability in measurements of the surface solar radiation

“…The short-term intrinsic periodicities in the solar proxies appear to be indicative of "randomly distributed dynamical processes in the solar atmosphere" that are closely related to the 11-year solar activity and therefore, unsurprisingly, the high-frequency modes are found to be modulated by this latter cycle (Kolotkov et al, 2016). But this phenomenon is not limited to solar activity signals and has also been identified in surface air temperature records (Paluš, 2014), and time series of the sea level (Liu et al, 2007), and may indicate crossscale nonlinear couplings (Paluš, 2014;Huang et al, 2016).…”

“…In Sect. 5.1, evidence is presented that the spectral band spanning from 2 to 300 days seems to be composed mostly of random realizations of stochastic background processes, which can be modeled following, e.g., Flandrin et al (2004a), Rilling et al (2005), Welter and Esquef (2013), and Kolotkov et al (2016).…”

“…A somewhat similar objective can be found in the work of Rios and de Mello (2016), though their method of discrimination between stochastic and deterministic components is fundamentally different. Kolotkov et al (2016) also propose a method for discriminating frequency-dependent stochastic components by empirically estimating their power law spectral energy distribution and respective confidence bounds. Approaches for discriminating high-frequency fluctuations from large timescale modulations are also described by Flandrin et al (2004b) and Alberti et al (2016).…”

Stellar flare oscillations: evidence for oscillatory reconnection and evolution of MHD modes

“…For instance, α = 0 corresponds to the case of white noise (with constant Fourier power S and E × P = constant), α = 1 is the pink (flicker) noise. Kolotkov, Anfinogentov & Nakariakov (2016) developed the EMD technique in the presence of coloured noise, allowing for clear distinguishing between quasi-periodic oscillatory phenomena in the solar atmosphere and superimposed random background processes; these results are given below with the derived periods given in the final plot for each flare.…”

Long-period quasi-periodic oscillations of a small-scale magnetic structure on the Sun

“…Lee et al 2015;Deng et al 2015;Qu et al 2015;Kolotkov et al 2015;Käpylä et al 2016;Xiang & Qu 2016, for the recent results). Testing the significance of the identified empirical modes with the approach developed in Wu & Huang (2004) and Kolotkov et al (2016), we managed to distinguish the white and pink noisy components superimposed and a single significant oscillatory mode.…”