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

doi:10.1098/rsta.2020.0181

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 journal › Article › peer-review

18 Citations (Scopus)

Abstract

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 language	English
Article number	20200181
Number of pages	11
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	379
Issue number	2190
DOIs	https://doi.org/10.1098/rsta.2020.0181
Publication status	Published - 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 https://www.nso.edu/data/historical-archive/. 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 https://star.pst.qub.ac.uk/wiki/doku.php/public/research_areas/ 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. WaLSA.team) 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:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

dynamic mode decomposition
magnetohydrodynamic
proper orthogonal decomposition
sunspots
waves

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rsta.2020.0181Licence: Unspecified

Cite this

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title = "Proper orthogonal and dynamic mode decomposition of sunspot data",

abstract = "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'. ",

keywords = "dynamic mode decomposition, magnetohydrodynamic, proper orthogonal decomposition, sunspots, waves",

author = "Albidah, {A. B.} and W. Brevis and V. Fedun and I. Ballai and Jess, {D. B.} and Marco Stangalini and J. Higham and G. Verth",

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 https://www.nso.edu/data/historical-archive/. ROSA is a six-camera high-cadence solar imaging instrument developed by Queen{\textquoteright}s University Belfast. Although Queen{\textquoteright}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 https://star.pst.qub.ac.uk/wiki/doku.php/public/research_areas/ solar_physics/rosa_archive. Authors{\textquoteright} 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{\textquoteright}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{\textquoteright}s Horizon 2020 (SOLARNET). The authors Funding Information: wish to acknowledge scientific discussions with the Waves in the Lower Solar Atmosphere (WaLSA; www. WaLSA.team) 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 {\textquoteleft}High-resolution wave dynamics in the lower solar atmosphere{\textquoteright} (grant no. Hooke18b/SCTM). Publisher Copyright: {\textcopyright} 2020 The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

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doi = "10.1098/rsta.2020.0181",

language = "English",

volume = "379",

journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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T1 - Proper orthogonal and dynamic mode decomposition of sunspot data

AU - Albidah, A. B.

AU - Brevis, W.

AU - Fedun, V.

AU - Ballai, I.

AU - Jess, D. B.

AU - Stangalini, Marco

AU - Higham, J.

AU - Verth, G.

N1 - 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 https://www.nso.edu/data/historical-archive/. 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 https://star.pst.qub.ac.uk/wiki/doku.php/public/research_areas/ 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. WaLSA.team) 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: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2/8

Y1 - 2021/2/8

N2 - 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'.

AB - 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'.

KW - dynamic mode decomposition

KW - magnetohydrodynamic

KW - proper orthogonal decomposition

KW - sunspots

KW - waves

U2 - 10.1098/rsta.2020.0181

DO - 10.1098/rsta.2020.0181

M3 - Article

C2 - 33342375

AN - SCOPUS:85098745489

SN - 1364-503X

VL - 379

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2190

M1 - 20200181

ER -

Proper orthogonal and dynamic mode decomposition of sunspot data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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