Analysing the Effects of Apodizing Windows on Local Correlation Tracking Using Nirvana Simulations of Convection

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.

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Notes

  1. 1.

    Available as online material.

References

  1. 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 .

    Article  ADS  Google Scholar 

  2. 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 .

    Article  ADS  Google Scholar 

  3. 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 .

    Article  ADS  Google Scholar 

  4. 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 .

    Article  ADS  Google Scholar 

  5. 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 .

    Google Scholar 

  6. 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 .

    Article  ADS  MATH  Google Scholar 

  7. 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 .

    Article  ADS  Google Scholar 

  8. 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 .

    Article  ADS  Google Scholar 

  9. 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 .

    Article  ADS  Google Scholar 

  10. Lantz, S.R., Fan, Y.: 1999, Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. 121, 247. DOI . ADS .

    Article  ADS  Google Scholar 

  11. 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 .

    Article  ADS  Google Scholar 

  12. 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 .

    Article  ADS  Google Scholar 

  13. Moll, R., Cameron, R.H., Schüssler, M.: 2011, Vortices in simulations of solar surface convection. Astron. Astrophys. 533, A126. DOI . ADS .

    Article  ADS  Google Scholar 

  14. 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 .

    Article  ADS  Google Scholar 

  15. November, L.J.: 1986, Measurement of geometric distortion in a turbulent atmosphere. Appl. Opt. 25, 392. DOI . ADS .

    Article  ADS  Google Scholar 

  16. November, L.J., Simon, G.W.: 1988, Precise proper-motion measurement of solar granulation. Astrophys. J. 333, 427. DOI . ADS .

    Article  ADS  Google Scholar 

  17. 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 .

    Article  ADS  Google Scholar 

  18. Rempel, M., Schüssler, M., Cameron, R.H., Knölker, M.: 2009, Penumbral structure and outflows in simulated sunspots. Science 325. DOI . ADS .

  19. 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 .

    Article  ADS  Google Scholar 

  20. Rüdiger, G., Küker, M., Schnerr, R.S.: 2012, Cross helicity at the solar surface by simulations and observations. Astron. Astrophys. 546, A23. DOI . ADS .

    Article  Google Scholar 

  21. Schuck, P.W.: 2005, Local correlation tracking and the magnetic induction equation. Astrophys. J. Lett. 632, L53. DOI . ADS .

    Article  ADS  Google Scholar 

  22. Schuck, P.W.: 2006, Tracking magnetic footpoints with the magnetic induction equation. Astrophys. J. 646, 1358. DOI . ADS .

    Article  ADS  Google Scholar 

  23. 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 .

    Article  ADS  Google Scholar 

  24. Stangalini, M.: 2014, Photospheric supergranular flows and magnetic flux emergence. Astron. Astrophys. 561, L6. DOI . ADS .

    Article  ADS  Google Scholar 

  25. 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 .

    Article  ADS  Google Scholar 

  26. Strous, L.H.: 1995, Feature tracking: Deriving horizontal motion and more. In: Helioseismology, ESA SP-376, 213. ADS

    Google Scholar 

  27. Verma, M., Steffen, M., Denker, C.: 2013, Evaluating local correlation tracking using CO5BOLD simulations of solar granulation. Astron. Astrophys. 555, A136. DOI . ADS .

    Article  ADS  Google Scholar 

  28. 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 .

    Article  ADS  Google Scholar 

  29. 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 .

    Article  ADS  Google Scholar 

  30. 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 .

    Article  ADS  Google Scholar 

  31. 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 .

    Article  ADS  Google Scholar 

  32. Ziegler, U.: 2004, A central-constrained transport scheme for ideal magnetohydrodynamics. J. Comput. Phys. 196, 393. DOI . ADS .

    Article  ADS  MATH  Google Scholar 

Download references

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

Affiliations

Authors

Corresponding author

Correspondence to Rohan E. Louis.

Electronic Supplementary Material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

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

Download citation

Keywords

  • Velocity fields
  • Photosphere