Solar Physics

, Volume 254, Issue 1, pp 101–125 | Cite as

Statistical Assessment of Photospheric Magnetic Features in Imminent Solar Flare Predictions

  • Hui Song
  • Changyi Tan
  • Ju Jing
  • Haimin Wang
  • Vasyl Yurchyshyn
  • Valentyna Abramenko


In this study we use the ordinal logistic regression method to establish a prediction model, which estimates the probability for each solar active region to produce X-, M-, or C-class flares during the next 1-day time period. The three predictive parameters are (1) the total unsigned magnetic flux T flux, which is a measure of an active region’s size, (2) the length of the strong-gradient neutral line L gnl, which describes the global nonpotentiality of an active region, and (3) the total magnetic dissipation E diss, which is another proxy of an active region’s nonpotentiality. These parameters are all derived from SOHO MDI magnetograms. The ordinal response variable is the different level of solar flare magnitude. By analyzing 174 active regions, L gnl is proven to be the most powerful predictor, if only one predictor is chosen. Compared with the current prediction methods used by the Solar Monitor at the Solar Data Analysis Center (SDAC) and NOAA’s Space Weather Prediction Center (SWPC), the ordinal logistic model using L gnl, T flux, and E diss as predictors demonstrated its automatic functionality, simplicity, and fairly high prediction accuracy. To our knowledge, this is the first time the ordinal logistic regression model has been used in solar physics to predict solar flares.


Sun: Activity Sun: Flares Sun: Magnetic fields Magnetic observables 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramenko, V.I.: 2005, Astrophys. J. 629, 1141. CrossRefADSGoogle Scholar
  2. Abramenko, V.I., Gopasyuk, S.I., Ogir’, M.B.: 1991, Solar Phys. 134, 287. CrossRefADSGoogle Scholar
  3. Abramenko, V.I., Yurchyshyn, V.B., Wang, H., Spirock, T.J., Goode, P.R.: 2003, Astrophys. J. 597, 1135. CrossRefADSGoogle Scholar
  4. Agresti, A.: 1996, An Introduction to Categorical Data Analysis, Wiley, New York zbMATHGoogle Scholar
  5. Alzola, C.F., Harrell, F.E.: 2004, An Introduction to S and the Hmisc and Design Libraries, Free available electronic book. Google Scholar
  6. Antalova, A.: 1996, Contrib. Astron. Obs. Skaln. Pleso 26, 98. ADSGoogle Scholar
  7. Berger, T.E., Lites, B.W.: 2003, Solar Phys. 213, 213. CrossRefADSGoogle Scholar
  8. Bornmann, P.L., Shaw, D.: 1994, Solar Phys. 150, 127. CrossRefADSGoogle Scholar
  9. Breiman, L.: 1992, J. Am. Stat. Assoc. 87, 738. zbMATHCrossRefMathSciNetGoogle Scholar
  10. Brueckner, G.E., Delaboudiniere, J.P., Howard, R.A., Paswaters, S.E., St. Cyr, O.C., Schwenn, R., Lamy, P., Simnett, G.M., et al.: 1998, Geophys. Res. Lett. 25, 3019. CrossRefADSGoogle Scholar
  11. Cane, H.V., Richardson, I.G., St. Cyr, O.C.: 2000, Geophys. Res. Lett. 27, 3591. CrossRefADSGoogle Scholar
  12. Canfield, R.C., Hudson, H.S., McKenzie, D.E.: 1999, Geophys. Res. Lett. 26, 627. CrossRefADSGoogle Scholar
  13. Cragg, J.G., Uhler, R.: 1970, Can. J. Econ. 3, 386. CrossRefGoogle Scholar
  14. Efron, B.: 1986, J. Am. Stat. Assoc. 81, 461. zbMATHCrossRefMathSciNetGoogle Scholar
  15. Falconer, D.A.: 2001, J. Geophys. Res. 106, 25185. CrossRefADSGoogle Scholar
  16. Falconer, D.A., Moore, R.L., Gary, G.A.: 2003, J. Geophys. Res. 108, SSH11. CrossRefGoogle Scholar
  17. Gallagher, P.T., Moon, Y.J., Wang, H.: 2002, Solar Phys. 209, 171. CrossRefADSGoogle Scholar
  18. Gary, G.A., Hagyard, M.J.: 1990, Solar Phys. 126, 21. CrossRefADSGoogle Scholar
  19. Gopalswamy, N., Lara, A., Lepping, R.P., Kaiser, M.L., Berdichevsky, D., St. Cyr, O.C.: 2000, Geophys. Res. Lett. 27, 145. CrossRefADSGoogle Scholar
  20. Hagyard, M.J., Teuber, D., West, E.A., Smith, J.B.: 1984, Solar Phys. 91, 115. CrossRefADSGoogle Scholar
  21. Harrell, F.E.: 2001, Regression Modeling Strategies with Application to Linear Models, Logistic Regression, and Survival Analysis, Springer, Berlin. Google Scholar
  22. Hess, W.N. (ed.): 1964, The Physics of Solar Flares, NASA, Washington. Google Scholar
  23. Jing, J., Song, H., Abramenko, V.I., Tan, C., Wang, H.: 2006, Astrophys. J. 644, 1273. CrossRefADSGoogle Scholar
  24. Kim, R.S., Cho, K.S., Moon, Y.J., Kim, Y.H., Yi, Y., Dryer, M., Bong, S.C., Park, Y.D.: 2005, J. Geophys. Res. 110, 11104. CrossRefGoogle Scholar
  25. Leka, K.D., Barnes, G.: 2003a, Astrophys. J. 595, 1277. CrossRefADSGoogle Scholar
  26. Leka, K.D., Barnes, G.: 2003b, Astrophys. J. 595, 1296. CrossRefADSGoogle Scholar
  27. Leka, K.D., Canfield, R.C., McClymont, A.N., de La Beaujardiere, J.F., Fan, Y., Tang, F.: 1993, Astrophys. J. 411, L370. CrossRefADSGoogle Scholar
  28. McCullagh, P.: 1980, J. Roy. Stat. Soc. B 42, 109. zbMATHMathSciNetGoogle Scholar
  29. McIntosh, P.S.: 1990, Solar Phys. 125, 251. CrossRefADSGoogle Scholar
  30. Moreton, G.E., Severny, A.B.: 1968, Solar Phys. 3, 282. CrossRefADSGoogle Scholar
  31. Nagelkerke, N.J.D.: 1991, Biometrika 493, 205–247. MathSciNetGoogle Scholar
  32. Priest, E., Forbes, T.: 2000, Magnetic Reconnection: MHD Theory and Applications, Cambridge Univ. Press, Cambridge. zbMATHGoogle Scholar
  33. Sawyer, C., Warwick, J.W., Dennett, J.T.: 1986, Solar Flare Prediction, Colorado Assoc. Univ. Press, Boulder. Google Scholar
  34. Schrijver, C.J.: 2007, Astrophys. J. 662, L119. CrossRefADSGoogle Scholar
  35. Scott, S.C., Goldberg, M.S., Mayo, N.E.: 1997, J. Clin. Epidemiol. 50, 45. CrossRefGoogle Scholar
  36. Song, H., Yurchyshyn, V., Yang, G., Tan, C., Chen, W., Wang, H.: 2006, Solar Phys. 238, 141. CrossRefADSGoogle Scholar
  37. Stone, C.J., Koo, C.Y.: 1985, In: Proceeding of the Statistics Computing Section ASA, Washington, DC 45. Google Scholar
  38. Svestka, Z.: 1976, Solar Flares, Reidel, Dordrecht Google Scholar
  39. Tan, C., Jing, J., Abramenko, V.I., Pevtsov, A.A., Song, H., Park, S.-H., Wang, H.: 2007, Astrophys. J. 665, 1460. CrossRefADSGoogle Scholar
  40. Tian, L., Liu, Y., Wang, J.: 2002, Solar Phys. 209, 361. CrossRefADSGoogle Scholar
  41. Wang, H.: 2006, Astrophys. J. 649, 490. CrossRefADSGoogle Scholar
  42. Wang, T., Xu, A., Zhang, H.: 1994, Solar Phys. 155, 99. CrossRefADSGoogle Scholar
  43. Wang, J., Shi, Z., Wang, H., Lü, Y.: 1996, Astrophys. J. 456, 861. CrossRefADSGoogle Scholar
  44. Wang, Y.M., Ye, P.Z., Wang, S., Zhou, J.P., Wang, J.: 2002, J. Geophys. Res. 107, 2. Google Scholar
  45. Wang, H., Song, H., Yurchyshyn, V., Deng, Y., Zhang, H., Falconer, D., Li, J.: 2006, Chin. J. Astron. Astrophys. 6, 477. CrossRefADSGoogle Scholar
  46. Webb, D.F., Cliver, E.W., Crooker, N.U., Cry, O.C.S., Thompson, B.J.: 2000, J. Geophys. Res. 105, 7491. CrossRefADSGoogle Scholar
  47. Wheatland, M.S.: 2004, Astrophys. J. 609, 1134. CrossRefADSGoogle Scholar
  48. Zhang, J., Dere, K.P., Howard, R.A., Bothmer, V.: 2003, Astrophys. J. 582, 520. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Hui Song
    • 1
  • Changyi Tan
    • 1
  • Ju Jing
    • 1
  • Haimin Wang
    • 1
  • Vasyl Yurchyshyn
    • 2
  • Valentyna Abramenko
    • 2
  1. 1.Space Weather Research Laboratory, Center for Solar-Terrestrial ResearchNew Jersey Institute of TechnologyNewarkUSA
  2. 2.Big Bear Solar ObservatoryNew Jersey Institute of TechnologyBig Bear CityUSA

Personalised recommendations