pith. sign in

arxiv: 2605.23599 · v1 · pith:BP424MINnew · submitted 2026-05-22 · 🌌 astro-ph.SR

Investigation of the Two-Dimensional Velocity Field of the Large-Scale Coronal Wave from September 6, 2011 using the SOLERwave Tool

Markus Baumgartner-Steinleitner , Astrid M. Veronig , Karin Dissauer , Jens Pomoell This is my paper

Pith reviewed 2026-05-25 02:58 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords coronal wavessolar coronaMHD modelvelocity fieldmagnetosonic speedSeptember 2011 eventwave propagation
0
0 comments X

The pith

The two-dimensional velocity field of the September 6 2011 coronal wave differs by over 40 percent between directions because of variations in magnetosonic speed.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper maps the motion of a fast large-scale coronal wave across the solar surface on September 6 2011. It applies both a standard perturbation-profile method and a new multi-sector technique inside the SOLERwave tool that places wavefront locations from multiple angular sectors and connects nearest points between successive times to obtain the local velocity vector. The resulting speeds range from 750 to 1500 km/s and show more than 40 percent higher values in the northwestward sector than in the northward sector. The authors compare the observed speeds with coronal structures, the photospheric magnetic field, and the Alfvén and magnetosonic speeds taken from a steady-state MHD model and conclude that the background magnetosonic-speed difference is the most likely cause.

Core claim

For the event under study the resulting two-dimensional velocity field shows a significant difference between the northward traveling and the northwestward traveling part of the wave front of over 40 percent, in the range of 750 to 1500 km/s. The large difference in magnetosonic speed found in the investigated sector is the most likely explanation for the velocity difference.

What carries the argument

The multi-sector method inside the SOLERwave tool, which extracts perturbation profiles along many angular sectors, locates the wavefront at each time via a Huygens construction, and computes the two-dimensional velocity at each point by measuring the distance to the nearest point on the prior wavefront divided by the time step.

If this is right

  • Wave propagation speed is not uniform but depends on local background plasma properties along each direction.
  • Differences in magnetosonic speed can produce observed velocity variations larger than 40 percent even for a single wave front.
  • The multi-sector technique yields a full two-dimensional velocity map rather than a single average speed.
  • Steady-state MHD models supply a practical way to interpret directional speed differences in coronal waves.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same directional velocity contrast should appear in other events whenever the wave crosses regions of strong coronal inhomogeneity.
  • The method could be used to test whether waves slow or speed up when they encounter coronal holes or active-region boundaries.
  • Replacing the steady-state MHD background with a time-evolving simulation would show how much the attribution to magnetosonic speed changes.
  • If the velocity field can be predicted from the background model, the tool offers a route to forecast wave arrival times at specific solar locations.

Load-bearing premise

The steady-state coronal MHD solution gives an accurate picture of the magnetosonic speed along the paths the wave actually followed at the moment it passed.

What would settle it

A direct comparison of the observed wave velocities against magnetosonic speeds measured or modeled from dynamic, time-dependent coronal conditions at the exact times and locations of the wave passage.

Figures

Figures reproduced from arXiv: 2605.23599 by Astrid M. Veronig, Jens Pomoell, Karin Dissauer, Markus Baumgartner-Steinleitner.

Figure 1
Figure 1. Figure 1: Two AIA 211 ˚A base ratio images (base image at 22:15:50 UT) of the large-scale coronal wave observed on September 6, 2011. A single-sector is overplotted with an angular extent between −15° and 0° with respect to the great circle intersection both the presumed wave origin at (N14°, W18°) and the solar north pole. The markers on the sector show 100 Mm increments. Within the sector a single segment with 1° … view at source ↗
Figure 2
Figure 2. Figure 2: Demonstration of the Gauss fitting and peak finding of the perturbation profiles. The left panels shows the perturbation profile for three time steps. The red solid line shows the Gaussian fit to the measurements (black line), the red dashed line denotes the pre-event level. The blue crosses indicates the peak identified by the peak finding algorithm, the green crosses the front and trailing edges (defined… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the wave tracing algorithm. Left: The peaks circled in blue are found to be part of a wave by the tracing algorithms, as they follow each other within a minimum and maximum distance moving forward in time. The two peaks towards the bottom left did not move between time steps and are therefore not marked as a wave. Right: The blue dashed line circles an example for a two-peak start, where both … view at source ↗
Figure 4
Figure 4. Figure 4: Octant plot for the large-scale coronal wave on September 6, 2011 showing the wave evolution in SDO/AIA 211 ˚A in eight sectors, each with a width of 45° (the sector boundaries are illustrated in the base image shown in the middle panel). The directions are counted from solar North (0°) in counter-clockwise direction. The color bar below quantifies the corresponding intensity values from base ratio images … view at source ↗
Figure 5
Figure 5. Figure 5: Perturbation profiles derived from SDO/AIA 211 ˚A base ratio images for the wave observed on September 6, 2011 along the sector between −15° to 0° (North; see also [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Kinematics of the wave in the north direction, as provided by the SOLERwave output plots. From top to bottom: distance of the peak of the wave, the front of the wave, the wave width, and amplitude. Shown are only points associated to waves detected by the wave tracing algorithm. The color shows the association to a continuous wave detection. Two waves have been detected, which can be assumed being part of … view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Multi-sector analysis in the SDO/AIA 211˚A passband: velocity of wave front. The arrows connect the closest wave front between time steps, the color shows the velocity based on the distance and time difference between observations. The shown map is the result of all time steps. A movie of this plot is available in the online version showing the stepwise creation. filter the resulting profile with running a… view at source ↗
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The left plot shows the SDO/HMI LOS magnetogram observed at 22:00:00 UT in the range of [−1000, 1000] Gauss. The right plot shows a map of the Alfv´en speed at a height of 1.07 R⊙, derived from a thermodynamic MAST model for Carrington rotation 2114. Overplotted are the sectors towards the north and northwest as used in this study. direction coinciding with an elevated Alfv´en speed, the north direction a… view at source ↗
Figure 11
Figure 11. Figure 11: Kinematics of the wave front in the north direction in the upper panel (same as [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Distributions of the base ratio values, with counts on the y-axis and base ratio values on the x-axis. For each panel two ensembles with 200000 normal distributed numbers were created. The mean of the first ensemble is given by µ = 50, 100, 200 from the left to the right column, the standard deviation is given by σ = √µ. The mean of the second ensemble is given by µ ′ = µ · cratio with cratio changing for… view at source ↗
Figure 14
Figure 14. Figure 14: One dimensional sketch of the effects of the distance between segment centers. The blue curve represents the original wave front. Applying a running median filter to it would reproduce the exact curve, as it is monotonically falling. Applying the filter only in certain steps, represented by the orange boxes, results in only the values marked with orange crosses. The supremum of the distance between the re… view at source ↗
Figure 15
Figure 15. Figure 15: Two dimensional representation of the schematics for the direction error depend￾ing on the wave origin. The inner blue semi circle represents the wave front at time ti, the outer blue semi circle at ti+1. The green cross is the position of the true center of the circular wave, the red cross the position of the shifted center from which the velocity is estimated. All Latin letters indicate angular distance… view at source ↗
Figure 16
Figure 16. Figure 16: Relative velocity error between parts of the wave assumed to travel at heights ∆h above the photosphere and parts of wave traveling at photospheric height, i.e. R⊙. The left plot follows the centerline of the northward sector investigated in Section 4.1, the right plot the centerline of the north-westward sector investigated. The x-axis shows distance from the wave origin along these centerlines measured … view at source ↗
read the original abstract

We investigate the two-dimensional velocity field of the fast and complex large-scale coronal wave observed on September 6, 2011. We use both a classical perturbation profile approach and the newly developed multi-sector method of the SOLERwave tool, using a Huygens-plotting-based approach. The multi-sector method utilizes perturbation profiles derived in multiple directions (sectors) to determine the location of the wavefront at a given time. The two-dimensional velocity vector at each point along the wavefront is derived by identifying the point closest to it along the wavefront observed one time step earlier and dividing the distance between the two points along the solar surface by the time difference between the observations. For the event under study the resulting two-dimensional velocity field shows a significant difference between the northward traveling and the northwest ward traveling part of the wave front of over 40%, in the range of 750 to 1500 km/s. To determine the cause of this difference in speed, we investigate the coronal structures, the photospheric magnetic field distribution and the Alfv\'en speed derived from a steady-state coronal magneto hydro dynamic (MHD) solution along different propagation directions of the wave. We find the large difference in magnetosonic speed found in the investigated sector as the most likely explanation for the velocity difference.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes the two-dimensional velocity field of the fast large-scale coronal wave of 6 September 2011 using both classical perturbation profiles and the multi-sector Huygens-plotting method implemented in the SOLERwave tool. The central result is a >40% speed contrast (750–1500 km/s) between the northward and northwestward segments of the wavefront; this contrast is attributed to a corresponding difference in magnetosonic speed extracted from a steady-state coronal MHD solution.

Significance. If the attribution is shown to be robust, the work would supply direct observational support for the role of local magnetosonic-speed variations in shaping the propagation of coronal waves, with implications for MHD wave theory in structured corona. The multi-sector technique itself is a methodological contribution that could be adopted more widely once its accuracy and error budget are quantified.

major comments (2)
  1. [Abstract] Abstract (final sentence): the attribution of the observed >40% velocity difference to the magnetosonic-speed contrast rests on the untested premise that the steady-state MHD solution accurately represents Alfvén and sound speeds along the actual propagation paths at the time of wave passage. No quantitative comparison between model speeds and observed wave speeds, nor any sensitivity test to flare-induced perturbations, is reported.
  2. [Method] Method (multi-sector wavefront location and velocity derivation): the procedure of identifying the closest point on the preceding wavefront and dividing distance by time step is described without an accompanying error propagation analysis or validation against synthetic wavefronts, making it impossible to assess whether the reported 40% contrast exceeds the method’s uncertainty.
minor comments (2)
  1. [Abstract] Abstract contains the typographical split 'northwest ward'; correct to 'northwestward'.
  2. The manuscript does not state the number or angular width of the sectors used in the multi-sector method, nor the cadence of the EUV images employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. Below we provide point-by-point responses to the major comments and indicate the planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final sentence): the attribution of the observed >40% velocity difference to the magnetosonic-speed contrast rests on the untested premise that the steady-state MHD solution accurately represents Alfvén and sound speeds along the actual propagation paths at the time of wave passage. No quantitative comparison between model speeds and observed wave speeds, nor any sensitivity test to flare-induced perturbations, is reported.

    Authors: We acknowledge that the manuscript does not include a direct quantitative comparison between the MHD-derived magnetosonic speeds and the observed wave speeds, nor sensitivity tests to flare-induced perturbations. The attribution is based on the spatial correspondence between sectors of high/low magnetosonic speed and the observed velocity contrast. We will revise the manuscript to add a quantitative comparison of magnetosonic speeds extracted along the specific northward and northwestward paths versus the measured wave speeds, and we will include a discussion of the steady-state assumption as a limitation. revision: yes

  2. Referee: [Method] Method (multi-sector wavefront location and velocity derivation): the procedure of identifying the closest point on the preceding wavefront and dividing distance by time step is described without an accompanying error propagation analysis or validation against synthetic wavefronts, making it impossible to assess whether the reported 40% contrast exceeds the method’s uncertainty.

    Authors: We agree that a formal error propagation analysis is needed to allow readers to assess whether the >40% contrast exceeds methodological uncertainty. We will expand the method section to include an error budget based on observational resolution, time cadence, and the closest-point identification step. Validation against synthetic wavefronts lies outside the scope of the present observational study; however, we will note the consistency between the multi-sector results and the classical perturbation-profile method as supporting evidence for robustness. revision: partial

Circularity Check

0 steps flagged

No significant circularity: velocity field derived directly from observations; MHD comparison is post-hoc interpretation

full rationale

The paper computes the two-dimensional velocity field by tracking wavefront positions across time steps using the multi-sector Huygens-plotting method on observational data; this step contains no reference to the steady-state MHD solution and does not reduce to any fitted parameter or self-defined quantity from the model. The subsequent examination of photospheric B, coronal structures, and Alfvén/magnetosonic speeds extracted from the MHD run is presented only as an explanatory comparison after the velocity difference has already been measured. No equations equate the observed speeds to the model outputs by construction, no self-citation chain justifies a uniqueness theorem or ansatz that forces the result, and the central claim remains an independent data-driven measurement rather than a renaming or tautological prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5786 in / 1365 out tokens · 27788 ms · 2026-05-25T02:58:40.647603+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

171 extracted references · 171 canonical work pages · 2 internal anchors

  1. [1]

    and Warmuth, A

    Vršnak, B. and Warmuth, A. and Temmer, M. and Veronig, A. and Magdalenić, J. and Hillaris, A. and Karlický, M. , month = mar, year =. Multi-wavelength study of coronal waves associated with the. , publisher =. doi:10.1051/0004-6361:20053740 , abstract =

    work page doi:10.1051/0004-6361:20053740

  2. [2]

    , author =

    On the. , author =. 2012 , keywords =. doi:10.1007/s11207-012-9988-6 , abstract =

    work page doi:10.1007/s11207-012-9988-6 2012

  3. [3]

    and Podladchikova, Tatiana and Dissauer, Karin and Temmer, Manuela and B

    Veronig, Astrid M. and Podladchikova, Tatiana and Dissauer, Karin and Temmer, Manuela and B. Seaton, Daniel and Long, David and Guo, Jingnan and Vršnak, Bojan and Harra, Louise and Kliem, Bernhard , month = nov, year =. Genesis and. , publisher =. doi:10.3847/1538-4357/aaeac5 , abstract =

    work page doi:10.3847/1538-4357/aaeac5

  4. [4]

    Piantschitsch, Isabell and Vršnak, Bojan and Hanslmeier, Arnold and Lemmerer, Birgit and Veronig, Astrid and Hernandez-Perez, Aaron and Čalogović, Jaša and Žic, Tomislav , month = nov, year =. A. , publisher =. doi:10.3847/1538-4357/aa8cc9 , abstract =

    work page doi:10.3847/1538-4357/aa8cc9

  5. [5]

    Total reflection of a flare-driven quasi-periodic extreme ultraviolet wave train at a coronal hole boundary , volume =

    Zhou, Xinping and Shen, Yuandeng and Tang, Zehao and Zhou, Chengrui and Duan, Yadan and Tan, Song , month = mar, year =. Total reflection of a flare-driven quasi-periodic extreme ultraviolet wave train at a coronal hole boundary , volume =. , publisher =. doi:10.1051/0004-6361/202142536 , abstract =

    work page doi:10.1051/0004-6361/202142536

  6. [6]

    Impacts of

    Liu, Rui and Wang, Yuming and Lee, Jeongwoo and Shen, Chenglong , month = dec, year =. Impacts of. , publisher =. doi:10.3847/1538-4357/aaf04e , abstract =

    work page doi:10.3847/1538-4357/aaf04e

  7. [7]

    , author =

    Extreme-. , author =. 2022 , keywords =. doi:10.1007/s11207-022-02082-6 , abstract =

    work page doi:10.1007/s11207-022-02082-6 2022

  8. [8]

    , author =

    Ion. , author =. 2025 , keywords =. doi:10.1007/s11207-025-02522-z , abstract =

    work page doi:10.1007/s11207-025-02522-z 2025

  9. [9]

    and Gallagher, P

    Rigney, J. and Gallagher, P. T. and Ramsay, G. and Doyle, J. G. and Long, D. M. and Stepanyuk, O. and Kozarev, K. , month = apr, year =. Tracking the motion of a shock along a channel in the low solar corona , volume =. , publisher =. doi:10.1051/0004-6361/202348452 , abstract =

    work page doi:10.1051/0004-6361/202348452

  10. [10]

    Kalenská, Petra Kosová and Rajmic, Pavel and Gebrtová, Karolína and Druckmüller, Miloslav , month = nov, year =. A. Supplement Series , publisher =. doi:10.3847/1538-4365/ad8633 , abstract =

    work page doi:10.3847/1538-4365/ad8633

  11. [11]

    Multi-scale image preprocessing and feature tracking for remote

    Stepanyuk, Oleg and Kozarev, Kamen and Nedal, Mohamed , year =. Multi-scale image preprocessing and feature tracking for remote. J. Space Weather Space Clim. , publisher =. doi:10.1051/swsc/2022020 , abstract =

    work page doi:10.1051/swsc/2022020

  12. [12]

    2019 , keywords =

    , author =. 2019 , keywords =. doi:10.1007/s11207-019-1505-8 , abstract =

    work page doi:10.1007/s11207-019-1505-8 2019

  13. [13]

    and Reid, Hamish A

    Long, David M. and Reid, Hamish A. S. and Valori, Gherardo and O’Kane, Jennifer , month = nov, year =. Localized. , publisher =. doi:10.3847/1538-4357/ac1cdf , abstract =

    work page doi:10.3847/1538-4357/ac1cdf

  14. [14]

    Kraaikamp, Emil and Verbeeck, Cis , year =. Solar. J. Space Weather Space Clim. , publisher =. doi:10.1051/swsc/2015019 , abstract =

    work page doi:10.1051/swsc/2015019

  15. [16]

    FLCT: A Fast, Efficient Method for Performing Local Correlation Tracking

    Subsurface and Atmospheric Influences on Solar Activity , author =. 2008 , pages =. doi:10.48550/arXiv.0712.4289 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.0712.4289 2008

  16. [17]

    The. Front. Astron. Space Sci. , publisher =. 2023 , keywords =. doi:10.3389/fspas.2023.1076726 , abstract =

    work page doi:10.3389/fspas.2023.1076726 2023

  17. [18]

    EGU General Assembly Conference Abstracts , year = 2025, series =

    The Horizon Europe SOLER project (2024-2027): project objectives and first results. EGU General Assembly Conference Abstracts , year = 2025, series =. doi:10.5194/egusphere-egu25-11202 , adsurl =

    work page doi:10.5194/egusphere-egu25-11202 2024

  18. [19]

    Simple magnetohydrodynamic waves , volume =. J. Plasma Phys. , author =. 1995 , pages =. doi:10.1017/S0022377800018043 , abstract =

    work page doi:10.1017/s0022377800018043 1995

  19. [20]

    Bayesian

    Linden, Wolfgang Von Der and Dose, Volker and Toussaint, Udo Von , month = jun, year =. Bayesian. doi:10.1017/CBO9781139565608 , abstract =

    work page doi:10.1017/cbo9781139565608

  20. [21]

    , Scherrer , P.H

    Design and. , author =. 2012 , keywords =. doi:10.1007/s11207-011-9842-2 , abstract =

    work page doi:10.1007/s11207-011-9842-2 2012

  21. [22]

    , author =

    The. , author =. 2014 , keywords =. doi:10.1007/s11207-014-0516-8 , abstract =

    work page doi:10.1007/s11207-014-0516-8 2014

  22. [23]

    , author =

    The. , author =. 2012 , keywords =. doi:10.1007/s11207-011-9834-2 , abstract =

    work page doi:10.1007/s11207-011-9834-2 2012

  23. [24]

    , author =

    Observables. , author =. 2016 , keywords =. doi:10.1007/s11207-016-0957-3 , abstract =

    work page doi:10.1007/s11207-016-0957-3 2016

  24. [25]

    Roddanavar, Arpita and Inoue, Satoshi and Hayashi, Keiji and Jing, Ju and Cao, Wenda and Wang, Haimin , month = jan, year =. Large. , publisher =. doi:10.3847/1538-4357/ae2122 , abstract =

    work page doi:10.3847/1538-4357/ae2122

  25. [26]

    and Dissauer, Karin and Temmer, Manuela , month = apr, year =

    Vanninathan, Kamalam and Veronig, Astrid M. and Dissauer, Karin and Temmer, Manuela , month = apr, year =. Plasma. , publisher =. doi:10.3847/1538-4357/aab09a , abstract =

    work page doi:10.3847/1538-4357/aab09a

  26. [27]

    The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package

    The. , author =. 2022 , keywords =. doi:10.3847/1538-4357/ac7c74 , abstract =

    work page internal anchor Pith review doi:10.3847/1538-4357/ac7c74 2022

  27. [28]

    and Mann, G

    Warmuth, A. and Mann, G. , month = jun, year =. A model of the. , publisher =. doi:10.1051/0004-6361:20042169 , abstract =

    work page doi:10.1051/0004-6361:20042169

  28. [29]

    , author =

    Large-scale Coronal Propagating Fronts in Solar Eruptions as Observed by the Atmospheric Imaging Assembly on Board the Solar Dynamics Observatory. , author =. 2013 , pages =. doi:10.1088/0004-637X/776/1/58 , abstract =

    work page doi:10.1088/0004-637x/776/1/58 2013

  29. [30]

    Secondary

    Olmedo, Oscar and Vourlidas, Angelos and Zhang, Jie and Cheng, Xin , month = aug, year =. Secondary. , publisher =. doi:10.1088/0004-637X/756/2/143 , abstract =

    work page doi:10.1088/0004-637x/756/2/143

  30. [31]

    Veronig, A. M. and Muhr, N. and Kienreich, I. W. and Temmer, M. and Vršnak, B. , month = may, year =. First. Letters , publisher =. doi:10.1088/2041-8205/716/1/L57 , abstract =

    work page doi:10.1088/2041-8205/716/1/l57 2041

  31. [32]

    Veronig, A. M. and Gömöry, P. and Kienreich, I. W. and Muhr, N. and Vršnak, B. and Temmer, M. and Warren, H. P. , month = nov, year =. Plasma. Letters , publisher =. doi:10.1088/2041-8205/743/1/L10 , abstract =

    work page doi:10.1088/2041-8205/743/1/l10 2041

  32. [33]

    Thompson, B. J. and Myers, D. C. , month = jul, year =. A. Supplement Series , publisher =. doi:10.1088/0067-0049/183/2/225 , abstract =

    work page doi:10.1088/0067-0049/183/2/225

  33. [34]

    and Veronig, A

    Vanninathan, K. and Veronig, A. M. and Dissauer, K. and Madjarska, M. S. and Hannah, I. G. and Kontar, E. P. , month = oct, year =. Coronal. , publisher =. doi:10.1088/0004-637X/812/2/173 , abstract =

    work page doi:10.1088/0004-637x/812/2/173

  34. [35]

    1998 , keywords =

    Geophysical Research Letters , author =. 1998 , keywords =. doi:10.1029/98GL50429 , abstract =

    work page doi:10.1029/98gl50429 1998

  35. [36]

    Patsourakos, Spiros and Vourlidas, Angelos , month = jul, year =. ". , publisher =. doi:10.1088/0004-637X/700/2/L182 , abstract =

    work page doi:10.1088/0004-637x/700/2/l182

  36. [37]

    Kienreich, I. W. and Temmer, M. and Veronig, A. M. , month = sep, year =. , publisher =. doi:10.1088/0004-637X/703/2/L118 , abstract =

    work page doi:10.1088/0004-637x/703/2/l118

  37. [38]

    and Golub, Leon and Lin, Jun and Chen, Huadong and Grigis, Paolo and Testa, Paola and Long, David , month = aug, year =

    Ma, Suli and Raymond, John C. and Golub, Leon and Lin, Jun and Chen, Huadong and Grigis, Paolo and Testa, Paola and Long, David , month = aug, year =. Observations and. , publisher =. doi:10.1088/0004-637X/738/2/160 , abstract =

    work page doi:10.1088/0004-637x/738/2/160

  38. [39]

    Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J

    Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and van der Walt, Stéfan J. and Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and K...

    work page doi:10.1038/s41592-019-0686-2 2020

  39. [40]

    , author =

    H\. , author =. 2013 , keywords =. doi:10.1051/0004-6361/201118001 , abstract =

    work page doi:10.1051/0004-6361/201118001 2013

  40. [41]

    , author =

    Evolution of Two EIT/H. , author =. 2001 , keywords =. doi:10.1086/324055 , abstract =

    work page doi:10.1086/324055 2001

  41. [42]

    and Yashiro, S

    Gopalswamy, N. and Yashiro, S. and Temmer, M. and Davila, J. and Thompson, W. T. and Jones, S. and McAteer, R. T. J. and Wuelser, J.-P. and Freeland, S. and Howard, R. A. , month = jan, year =. , publisher =. doi:10.1088/0004-637X/691/2/L123 , abstract =

    work page doi:10.1088/0004-637x/691/2/l123

  42. [43]

    and Mikić, Zoran , month = jan, year =

    Lionello, Roberto and Linker, Jon A. and Mikić, Zoran , month = jan, year =. Multispectral. , publisher =. doi:10.1088/0004-637X/690/1/902 , abstract =

    work page doi:10.1088/0004-637x/690/1/902

  43. [44]

    , author =

    Flare waves observed in Helium I 10 830. , author =. 2002 , pages =. doi:10.1051/0004-6361:20021121 , abstract =

    work page doi:10.1051/0004-6361:20021121 2002

  44. [45]

    , author =

    Interpreting. , author =. 2013 , keywords =. doi:10.1007/s11207-013-0276-x , abstract =

    work page doi:10.1007/s11207-013-0276-x 2013

  45. [46]

    and Dissauer, Karin and Podladchikova, Tatiana and Jain, Shantanu , month = jul, year =

    Razquin, Amaia and Veronig, Astrid M. and Dissauer, Karin and Podladchikova, Tatiana and Jain, Shantanu , month = jul, year =. Coronal dimmings from active region 13664 during the. , publisher =. doi:10.1051/0004-6361/202554772 , abstract =

    work page doi:10.1051/0004-6361/202554772

  46. [47]

    and Bhunia, Shilpi and Zucca, Pietro and Gallagher, Peter T

    Nedal, Mohamed and Cuddy, Catherine and Long, David M. and Bhunia, Shilpi and Zucca, Pietro and Gallagher, Peter T. , month = apr, year =. Multiple shocks generated by the 2024. , publisher =. doi:10.1051/0004-6361/202556266 , abstract =

    work page doi:10.1051/0004-6361/202556266 2024

  47. [48]

    and Thalmann, J

    Jarolim, R. and Thalmann, J. K. and Veronig, A. M. and Podladchikova, T. , month = oct, year =. Probing the solar coronal magnetic field with physics-informed neural networks , volume =. Nature Astronomy , publisher =. doi:10.1038/s41550-023-02030-9 , abstract =

    work page doi:10.1038/s41550-023-02030-9

  48. [49]

    Physics-informed machine learning

    Karniadakis, George Em and Kevrekidis, Ioannis G. and Lu, Lu and Perdikaris, Paris and Wang, Sifan and Yang, Liu , month = jun, year =. Physics-informed machine learning , volume =. Nature Reviews Physics , publisher =. doi:10.1038/s42254-021-00314-5 , abstract =

    work page doi:10.1038/s42254-021-00314-5

  49. [50]

    Thompson, B. J. and Gurman, J. B. and Neupert, W. M. and Newmark, J. S. and Delaboudinière, J.-P. and Cyr, O. C. St and Stezelberger, S. and Dere, K. P. and Howard, R. A. and Michels, D. J. , month = apr, year =. , publisher =. doi:10.1086/312030 , abstract =

    work page doi:10.1086/312030

  50. [51]

    1995 , keywords =

    , author =. 1995 , keywords =. doi:10.1007/BF00768758 , abstract =

    work page doi:10.1007/bf00768758 1995

  51. [52]

    , author =

    Sun. , author =. 2008 , keywords =. doi:10.1007/s11214-008-9341-4 , abstract =

    work page doi:10.1007/s11214-008-9341-4 2008

  52. [53]

    , author =

    The. , author =. 2008 , keywords =. doi:10.1007/s11214-007-9277-0 , abstract =

    work page doi:10.1007/s11214-007-9277-0 2008

  53. [54]

    , author =

    Statistical. , author =. 2014 , keywords =. doi:10.1007/s11207-014-0594-7 , abstract =

    work page doi:10.1007/s11207-014-0594-7 2014

  54. [55]

    , month = aug, year =

    Mann, Gottfried and Veronig, Astrid M. , month = aug, year =. Propagation of a dome-shaped, large-scale extreme-ultraviolet wave in the solar corona , volume =. , publisher =. doi:10.1051/0004-6361/202245688 , abstract =

    work page doi:10.1051/0004-6361/202245688

  55. [56]

    Hudson, H. S. and Warmuth, A. , month = sep, year =. Coronal. , publisher =. doi:10.1086/425314 , abstract =

    work page doi:10.1086/425314

  56. [57]

    , author =

    Automated. , author =. 2005 , keywords =. doi:10.1007/s11207-005-5373-z , abstract =

    work page doi:10.1007/s11207-005-5373-z 2005

  57. [58]

    and Temmer, Manuela and Vršnak, Bojan , month = jun, year =

    Veronig, Astrid M. and Temmer, Manuela and Vršnak, Bojan , month = jun, year =. High-. , publisher =. doi:10.1086/590493 , abstract =

    work page doi:10.1086/590493

  58. [59]

    and Li, Yuying , month = jan, year =

    Branch, Mary Ann and Coleman, Thomas F. and Li, Yuying , month = jan, year =. A. SIAM J. Sci. Comput. , publisher =. doi:10.1137/S1064827595289108 , abstract =

    work page doi:10.1137/s1064827595289108

  59. [60]

    Asymmetrical uncertainties , volume =

    Possolo, Antonio and Merkatas, Christos and Bodnar, Olha , month = jul, year =. Asymmetrical uncertainties , volume =. Metrologia , publisher =. doi:10.1088/1681-7575/ab2a8d , abstract =

    work page doi:10.1088/1681-7575/ab2a8d

  60. [61]

    Wills-Davey, M. J. , month = jul, year =. Tracking. , publisher =. doi:10.1086/504144 , abstract =

    work page doi:10.1086/504144

  61. [62]

    1982 , keywords =

    Similarity. 1982 , keywords =

    work page 1982

  62. [63]

    and Wills-Davey, M

    Ma, S. and Wills-Davey, M. J. and Lin, J. and Chen, P. F. and Attrill, G. D. R. and Chen, H. and Zhao, S. and Li, Q. and Golub, L. , month = nov, year =. A. , publisher =. doi:10.1088/0004-637X/707/1/503 , abstract =

    work page doi:10.1088/0004-637x/707/1/503

  63. [64]

    , Thompson , B.J

    The. , author =. 2012 , keywords =. doi:10.1007/s11207-011-9841-3 , abstract =

    work page doi:10.1007/s11207-011-9841-3 2012

  64. [65]

    and Nightingale, Richard W

    Aschwanden, Markus J. and Nightingale, Richard W. and Tarbell, Ted D. and Wolfson, C. J. , month = jun, year =. Time. , publisher =. doi:10.1086/308866 , abstract =

    work page doi:10.1086/308866

  65. [66]

    Applications of

    Javaherian, Mohsen and Bashiri Mosavi, Seyed Alireza and Mohammadi, Parsa and Eskandari, Zahra , month = aug, year =. Applications of. Iranian Journal of Astronomy and Astrophysics , publisher =. doi:10.22128/ijaa.2025.1013.1212 , abstract =

    work page doi:10.22128/ijaa.2025.1013.1212 2025

  66. [67]

    and Warmuth, Alexander and Veronig, Astrid M

    Pesce-Rollins, Melissa and Omodei, Nicola and Krucker, Säm and Di Lalla, Niccolò and Wang, Wen and Battaglia, Andrea F. and Warmuth, Alexander and Veronig, Astrid M. and Baldini, Luca , month = apr, year =. The. , publisher =. doi:10.3847/1538-4357/ac5f0c , abstract =

    work page doi:10.3847/1538-4357/ac5f0c

  67. [68]

    Recent advances in solar coronal extreme ultraviolet waves , volume =

    Zheng, Ruisheng , month = oct, year =. Recent advances in solar coronal extreme ultraviolet waves , volume =. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , publisher =. doi:10.1098/rspa.2023.0950 , abstract =

    work page doi:10.1098/rspa.2023.0950 2023

  68. [69]

    , year =

    Beck, James Vere and Arnold, Kenneth J. , year =. Parameter

    work page

  69. [70]

    Measurement Science and Technology , author =

    When errors in both coordinates make a difference in the fitting of straight lines by least squares , volume =. Measurement Science and Technology , author =. 1998 , pages =. doi:10.1088/0957-0233/9/12/012 , abstract =

    work page doi:10.1088/0957-0233/9/12/012 1998

  70. [71]

    Metrologia , author =

    Correlations in primary spectral standards , volume =. Metrologia , author =. 2003 , keywords =. doi:10.1088/0026-1394/40/1/338 , abstract =

    work page doi:10.1088/0026-1394/40/1/338 2003

  71. [72]

    Measurement Science and Technology , author =

    The propagation of uncertainty with calibration equations , volume =. Measurement Science and Technology , author =. 2007 , keywords =. doi:10.1088/0957-0233/18/7/047 , abstract =

    work page doi:10.1088/0957-0233/18/7/047 2007

  72. [73]

    International Journal of Thermophysics , author =

    Propagation of. International Journal of Thermophysics , author =. 2017 , keywords =. doi:10.1007/s10765-016-2174-6 , abstract =

    work page doi:10.1007/s10765-016-2174-6 2017

  73. [74]

    IEEE Transactions on Visualization and Computer Graphics , author =

    Positional. IEEE Transactions on Visualization and Computer Graphics , author =. 2011 , keywords =. doi:10.1109/TVCG.2010.247 , abstract =

    work page doi:10.1109/tvcg.2010.247 2011

  74. [75]

    IEEE Transactions on Visualization and Computer Graphics , author =

    On the. IEEE Transactions on Visualization and Computer Graphics , author =. 2012 , keywords =. doi:10.1109/TVCG.2012.249 , abstract =

    work page doi:10.1109/tvcg.2012.249 2012

  75. [76]

    IEEE Transactions on Visualization and Computer Graphics , author =

    Uncertainty. IEEE Transactions on Visualization and Computer Graphics , author =. 2013 , keywords =. doi:10.1109/TVCG.2013.208 , abstract =

    work page doi:10.1109/tvcg.2013.208 2013

  76. [77]

    Ratios of. J. Stat. Softw. , author =. 2006 , keywords =. doi:10.18637/jss.v016.i04 , abstract =

    work page doi:10.18637/jss.v016.i04 2006

  77. [78]

    , author =

    Propagation of hydromagnetic disturbances in the solar corona and. , author =. 1968 , keywords =. doi:10.1007/BF00146996 , abstract =

    work page doi:10.1007/bf00146996 1968

  78. [79]

    , author =

    Recent. , author =. 1960 , keywords =. doi:10.1086/127549 , urldate =

    work page doi:10.1086/127549 1960

  79. [80]

    1995 , keywords =

    , author =. 1995 , keywords =. doi:10.1007/BF00733432 , abstract =

    work page doi:10.1007/bf00733432 1995

  80. [81]

    , author =

    Origin of. , author =. 2008 , keywords =. doi:10.1007/s11207-008-9241-5 , abstract =

    work page doi:10.1007/s11207-008-9241-5 2008

Showing first 80 references.