23th February 2015, Warwick-Monash Seminar,
University of Warwick, UK
Hilbert-Huang analysis of
periodicities in the last two
solar activity cycles
Dmitrii Kolotkov1*
A.- M. Broomhall1, V. Nakariakov1.2
1 Centre for
Fusion, Space and Astrophysics, University of Warwick, UK
Pulkovo of the RAS, Russia
* D.Kolotkov@warwick.ac.uk
2 Central Astronomical Observatory at
Centre for Fusion, Space and Astrophysics
Outline
 Spectral analysis with the HHT method
 Application of HHT to solar activity cycles
 Discussion of results
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Hilbert-Huang Transform analysis
Empirical Mode Decomposition (EMD)+Hilbert transform
The main scheme of this technique:
• Decomposition of the initial data set into a number of intrinsic
mode functions (IMF) by applying EMD
• The subsequent Hilbert transformation of decomposed IMFs
Huang, N. E. et al. 1998, Royal Soc. of London Proc. Series A, 454, 903
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Empirical Mode Decomposition (EMD) step by step…
1. Identifying of all local extrema of original data X(t)
2. Define upper/lower envelopes connecting all maxima/minima
and their mean m1 . Then
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Empirical Mode Decomposition (EMD)
3. This “sifting process” must be repeated k times until the number of
extrema in residual h1k differs from the number of zero crossings by not
more than 1. Finally we have the first IMF:
Original
data
The first IMF
Data – 1st IMF
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Example of EMD expansion
Huang et al. (1998)
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Hilbert transformation
For each IMF:
Finally we have frequency-time distribution for each IMF designated as
Hilbert spectrum
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Data
10. 7 cm radio flux1
helioseismic
frequency shift2
Sunspot area 3
from South hemisphere
from North hemisphere
from the whole Sun
3http://solarscience.msfc.nasa.gov/
greenwch.shtml
2Birmingham Solar
Oscillations Network
1 http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solarfeatures/solar-radio/noontime-flux/penticton/
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Results
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Samples of identified modes
mean period of
626 days (~ 2 yr)
10. 7 cm radio flux
total sunspot area
sunspot area from
North
mean period of
903 days (~ 2.5 yr)
10. 7 cm radio flux
helioseismic
frequency shift
10. 7 cm radio flux
mean period of
~ 11 yr
sunspot area from
North
sunspot area from
South
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Mean mode period determination
Hilbert spectrum and its probability histogram of the 690 days 10.7 radio flux
mode, allowing one to determine the average mode period
Colour gradient on the Hilbert spectrum shows variations of a spectral power
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Conclusions
• Example of the successful use of the HHT method for analysing of
the last two solar cycles was demonstrated
• The periodicities were found to be allocated in three distinct
groups: short-term variations (with periods less than 0.5 yr),
quasi-biennial oscillations (periods from 0.5 yr up to 3.9 yr), and
longer periodicities, e.g. such as 11-year cycle
• Signatures of the N-S asymmetry were clearly revealed
• Kolotkov et al. 2015 (in prep.)
• Kolotkov et al., Multi-mode quasi-periodic pulsations in a solar
flare, 2015, A&A, 574, A53
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