Abstract
We employ different shapes of apodizing windows in the local correlation tracking (LCT) routine to retrieve horizontal velocities using numerical simulations of convection. LCT was applied on a time sequence of temperature maps generated by the Nirvana code with four different apodizing windows, Gaussian, Lorentzian, trapezoidal, and triangular, with varying widths. In terms of correlations (between the LCT-retrieved and simulated flow field), the triangular and the trapezoidal perform the best and worst, respectively. By segregating the intrinsic velocities in the simulations on the basis of their magnitudes, we find that for all windows a significantly higher correlation is obtained for the intermediate and high-velocity bins and only modest or weak values in the low-velocity bins. The differences between the LCT-retrieved and simulated flow fields were determined spatially. They show large residuals at or close to the boundary of granules. The extent to which the horizontal flow vectors retrieved by LCT are similar to the simulated values entirely depends on the width of the central peak of the apodizing window for a given σ. Even though LCT suffers from a lack of spatial content, as seen in simulations, its simplicity and speed could serve as a viable first-order tool to probe horizontal flows. This would be an ideal tool for large data sets.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Similar content being viewed by others
Notes
Available as online material.
References
Barthol, P., Gandorfer, A., Solanki, S.K., Schüssler, M., Chares, B., Curdt, W., Deutsch, W., Feller, A., Germerott, D., Grauf, B., Heerlein, K., Hirzberger, J., Kolleck, M., Meller, R., Müller, R., Riethmüller, T.L., Tomasch, G., Knölker, M., Lites, B.W., Card, G., Elmore, D., Fox, J., Lecinski, A., Nelson, P., Summers, R., Watt, A., Martínez Pillet, V., Bonet, J.A., Schmidt, W., Berkefeld, T., Title, A.M., Domingo, V., Gasent Blesa, J.L., Del Toro Iniesta, J.C., López Jiménez, A., Álvarez-Herrero, A., Sabau-Graziati, L., Widani, C., Haberler, P., Härtel, K., Kampf, D., Levin, T., Pérez Grande, I., Sanz-Andrés, A., Schmidt, E.: 2011, The Sunrise mission. Solar Phys. 268, 1. DOI . ADS .
Beeck, B., Collet, R., Steffen, M., Asplund, M., Cameron, R.H., Freytag, B., Hayek, W., Ludwig, H.-G., Schüssler, M.: 2012, Simulations of the solar near-surface layers with the CO5BOLD, MURaM, and Stagger codes. Astron. Astrophys. 539, A121. DOI . ADS .
Cheung, M.C.M., Rempel, M., Title, A.M., Schüssler, M.: 2010, Simulation of the formation of a solar active region. Astrophys. J. 720, 233. DOI . ADS .
Danilovic, S., Gandorfer, A., Lagg, A., Schüssler, M., Solanki, S.K., Vögler, A., Katsukawa, Y., Tsuneta, S.: 2008, The intensity contrast of solar granulation: Comparing hinode SP results with MHD simulations. Astron. Astrophys. 484, L17. DOI . ADS .
Fisher, G.H., Welsch, B.T.: 2008, FLCT: A fast, efficient method for performing local correlation tracking. In: Howe, R., Komm, R.W., Balasubramaniam, K.S., Petrie, G.J.D. (eds.) Subsurface and Atmospheric Influences on Solar Activity, Astronomical Society of the Pacific Conference Series 383, 373. ADS .
Freytag, B., Steffen, M., Ludwig, H.-G., Wedemeyer-Böhm, S., Schaffenberger, W., Steiner, O.: 2012, Simulations of stellar convection with CO5BOLD. J. Comput. Phys. 231, 919. DOI . ADS .
Georgoulis, M.K., LaBonte, B.J.: 2006, Reconstruction of an inductive velocity field vector from Doppler motions and a pair of solar vector magnetograms. Astrophys. J. 636, 475. DOI . ADS .
Hart, A.B.: 1956, Motions in the Sun at the photospheric level. VI. Large-scale motions in the equatorial region. Mon. Not. Roy. Astron. Soc. 116, 38. ADS .
Kusano, K., Maeshiro, T., Yokoyama, T., Sakurai, T.: 2002, Measurement of magnetic helicity injection and free energy loading into the solar corona. Astrophys. J. 577, 501. DOI . ADS .
Lantz, S.R., Fan, Y.: 1999, Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. 121, 247. DOI . ADS .
Leighton, R.B., Noyes, R.W., Simon, G.W.: 1962, Velocity fields in the solar atmosphere. I. Preliminary report. Astrophys. J. 135, 474. DOI . ADS .
Longcope, D.W.: 2004, Inferring a photospheric velocity field from a sequence of vector magnetograms: The minimum energy fit. Astrophys. J. 612, 1181. DOI . ADS .
Moll, R., Cameron, R.H., Schüssler, M.: 2011, Vortices in simulations of solar surface convection. Astron. Astrophys. 533, A126. DOI . ADS .
Nisenson, P., van Ballegooijen, A.A., de Wijn, A.G., Sütterlin, P.: 2003, Motions of isolated G-band bright points in the solar photosphere. Astrophys. J. 587, 458. DOI . ADS .
November, L.J.: 1986, Measurement of geometric distortion in a turbulent atmosphere. Appl. Opt. 25, 392. DOI . ADS .
November, L.J., Simon, G.W.: 1988, Precise proper-motion measurement of solar granulation. Astrophys. J. 333, 427. DOI . ADS .
Potts, H.E., Barrett, R.K., Diver, D.A.: 2004, Balltracking: An highly efficient method for tracking flow fields. Astron. Astrophys. 424, 253. DOI . ADS .
Rempel, M., Schüssler, M., Cameron, R.H., Knölker, M.: 2009, Penumbral structure and outflows in simulated sunspots. Science 325. DOI . ADS .
Rieutord, M., Roudier, T., Ludwig, H.-G., Nordlund, Å., Stein, R.: 2001, Are granules good tracers of solar surface velocity fields? Astron. Astrophys. 377, L14. DOI . ADS .
Rüdiger, G., Küker, M., Schnerr, R.S.: 2012, Cross helicity at the solar surface by simulations and observations. Astron. Astrophys. 546, A23. DOI . ADS .
Schuck, P.W.: 2005, Local correlation tracking and the magnetic induction equation. Astrophys. J. Lett. 632, L53. DOI . ADS .
Schuck, P.W.: 2006, Tracking magnetic footpoints with the magnetic induction equation. Astrophys. J. 646, 1358. DOI . ADS .
Simon, G.W., Leighton, R.B.: 1964, Velocity fields in the solar atmosphere. III. Large-scale motions, the chromospheric network, and magnetic fields. Astrophys. J. 140, 1120. DOI . ADS .
Stangalini, M.: 2014, Photospheric supergranular flows and magnetic flux emergence. Astron. Astrophys. 561, L6. DOI . ADS .
Steiner, O., Franz, M., Bello González, N., Nutto, C., Rezaei, R., Martínez Pillet, V., Bonet Navarro, J.A., del Toro Iniesta, J.C., Domingo, V., Solanki, S.K., Knölker, M., Schmidt, W., Barthol, P., Gandorfer, A.: 2010, Detection of vortex tubes in solar granulation from observations with SUNRISE. Astrophys. J. Lett. 723, L180. DOI . ADS .
Strous, L.H.: 1995, Feature tracking: Deriving horizontal motion and more. In: Helioseismology, ESA SP-376, 213. ADS
Verma, M., Steffen, M., Denker, C.: 2013, Evaluating local correlation tracking using CO5BOLD simulations of solar granulation. Astron. Astrophys. 555, A136. DOI . ADS .
Vögler, A., Shelyag, S., Schüssler, M., Cattaneo, F., Emonet, T., Linde, T.: 2005, Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code. Astron. Astrophys. 429, 335. DOI . ADS .
Welsch, B.T., Fisher, G.H., Abbett, W.P., Regnier, S.: 2004, ILCT: Recovering photospheric velocities from magnetograms by combining the induction equation with local correlation tracking. Astrophys. J. 610, 1148. DOI . ADS .
Welsch, B.T., Abbett, W.P., De Rosa, M.L., Fisher, G.H., Georgoulis, M.K., Kusano, K., Longcope, D.W., Ravindra, B., Schuck, P.W.: 2007, Tests and comparisons of velocity-inversion techniques. Astrophys. J. 670, 1434. DOI . ADS .
Yelles Chaouche, L., Moreno-Insertis, F., Bonet, J.A.: 2014, The power spectrum of solar convection flows from high-resolution observations and 3D simulations. Astron. Astrophys. 563, A93. DOI . ADS .
Ziegler, U.: 2004, A central-constrained transport scheme for ideal magnetohydrodynamics. J. Comput. Phys. 196, 393. DOI . ADS .
Acknowledgements
R.E. Louis is grateful for the financial assistance from the German Science Foundation (DFG) under grant DE 787/3-1 and the European Commission’s FP7 Capacities Programme under Grant Agreement number 312495. M.K. Georgoulis acknowledges support by the European Commission’s FP7 Marie Curie Programme under grant agreement no. PIRG07-GA-2010-268245. This work used the Nirvana code developed by Udo Ziegler at the Leibniz-Institut für Astrophysik Potsdam (AIP). We thank the referee for the useful suggestions and comments.
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Louis, R.E., Ravindra, B., Georgoulis, M.K. et al. Analysing the Effects of Apodizing Windows on Local Correlation Tracking Using Nirvana Simulations of Convection. Sol Phys 290, 1135–1146 (2015). https://doi.org/10.1007/s11207-015-0659-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-015-0659-2