Proper orthogonal and dynamic mode decomposition of sunspot data

A. B. Albidah, W. Brevis, V. Fedun, I. Ballai, D. B. Jess, Marco Stangalini, J. Higham, G. Verth*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


High-resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here, we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

Original languageEnglish
Article number20200181
Number of pages11
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2190
Publication statusPublished - 08 Feb 2021

Bibliographical note

Funding Information:
Data accessibility. The data used in this paper are from an observing campaign using the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument based at the Dunn Solar Telescope, USA, during December 2011. The Dunn Solar Telescope at Sacramento Peak/NM was operated by the National Solar Observatory (NSO). NSO is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under cooperative agreement with the National Science Foundation (NSF). The NSO historical data archive and its public directory can be found here ROSA is a six-camera high-cadence solar imaging instrument developed by Queen’s University Belfast. Although Queen’s University currently do not have the facilities to host such large datasets publicly for download, the ROSA data archive and ROSA reconstructed data are documented and can be requested and transferred (e.g. FTP or on a physical disk drive) from here solar_physics/rosa_archive. Authors’ contributions. G.V. and V.F. initiated the overall research in MHD mode identification. A.B.A. and W.B. carried out the POD and DMD analysis. V.F., I.B., G.V. and A.B.A. provided the theoretical background and physical interpretation of obtained results. D.J. and M.S. provided datasets and participated in data interpretation. J.H. provided his expertise in the methodology of mode decomposition. All the Authors participated in discussing the results and editing the draft. Competing interests. We declare we have no competing interests. Funding. V.F. and G.V. thank to The Royal Society, International Exchanges Scheme, collaboration with Chile (IE170301) and Brazil (IES/R1/191114), and Science and Technology Facilities Council (STFC) grant no. ST/M000826/1. This research is also partially funded by the European Union’s Horizon 2020 research and innovation program under grant agreement no. 824135 (SOLARNET). D.B.J. is grateful to Invest NI and Randox Laboratories Ltd for the award of a Research & Development grant no. (059RDEN-1). Acknowledgements. A.B.A. acknowledges the support by Majmaah University (Saudi Arabia) to carry out his PhD studies. V.F. and G.V. are thankful for support provided by The Royal Society and Science and Technology Facilities Council (STFC) and the European Union’s Horizon 2020 (SOLARNET). The authors

Funding Information:
wish to acknowledge scientific discussions with the Waves in the Lower Solar Atmosphere (WaLSA; www. team, which is supported by the Research Council of Norway (project number 262622), and The Royal Society through the award of funding to host the Theo Murphy Discussion Meeting ‘High-resolution wave dynamics in the lower solar atmosphere’ (grant no. Hooke18b/SCTM).

Publisher Copyright:
© 2020 The Author(s).

Copyright 2021 Elsevier B.V., All rights reserved.


  • dynamic mode decomposition
  • magnetohydrodynamic
  • proper orthogonal decomposition
  • sunspots
  • waves

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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