Solar Physics

, Volume 289, Issue 11, pp 4137–4150 | Cite as

Predictive Capabilities of Avalanche Models for Solar Flares

Article

Abstract

We assess the predictive capabilities of various classes of avalanche models for solar flares. We demonstrate that avalanche models cannot generally be used to predict specific events because of their high sensitivity to the embedded stochastic process. We show that deterministically driven models can nevertheless alleviate this caveat and be efficiently used for predictions of large events. Our results suggest a new approach for predictions of large (typically X-class) solar flares based on simple and computationally inexpensive avalanche models.

Keywords

Flares, forecasting Flares, models Self-organized criticality 

Notes

Acknowledgements

The authors thank an anonymous referee for valuable comments. The authors acknowledge stimulating discussions during the ISSI Workshops on Turbulence and Self-Organized Criticality (2012 – 2013) held in Bern, Switzerland; and during the “Festival de théorie” (2013) held in Aix-en-Provence, France. This research has made use of SunPy, an open-source and free community-developed solar data analysis package written in Python (Mumford et al., 2013). AS acknowledges financial support from CNES via a Solar Orbiter grant. We also acknowledge support from the Natural Sciences and Engineering Research Council of Canada.

References

  1. Aschwanden, M.J.: 2011, The state of self-organized criticality of the Sun during the last three solar cycles. I. Observations. Solar Phys. 274(1), 99. ADS. DOI. ADSCrossRefMathSciNetGoogle Scholar
  2. Aschwanden, M.J., Charbonneau, P.: 2002, Effects of temperature bias on nanoflare statistics. Astrophys. J. Lett. 566(1), L59. ADS. DOI. ADSCrossRefGoogle Scholar
  3. Aschwanden, M.J., Freeland, S.L.: 2012, Automated solar flare statistics in soft X-rays over 37 years of GOES observations: the invariance of self-organized criticality during three solar cycles. Astrophys. J. 754(2), 112. ADS. DOI. ADSCrossRefGoogle Scholar
  4. Aschwanden, M.J., McTiernan, J.M.: 2010, Reconciliation of waiting time statistics of solar flares observed in hard X-rays. Astrophys. J. 717(2), 683. ADS. DOI. ADSCrossRefGoogle Scholar
  5. Aschwanden, M.J., Parnell, C.E.: 2002, Nanoflare statistics from first principles: fractal geometry and temperature synthesis. Astrophys. J. 572(2), 1048. ADS. DOI. ADSCrossRefGoogle Scholar
  6. Aschwanden, M.J., Crosby, N., Dimitropoulou, M., Georgoulis, M.K., Hergarten, S., McAteer, R.T.J., Milovanov, A., Mineshige, S., Morales, L., Pruessner, G., Sanchez, R., Strugarek, A., Uritsky, V.: 2014, 25 years of self-organized criticality: solar and astrophysics. Space Sci. Rev., in press. arXiv
  7. Bak, P., Tang, C., Wiesenfeld, K.: 1987, Self-organized criticality – an explanation of 1/f noise. Phys. Rev. Lett. 59, 381. ADS. DOI. ADSCrossRefMathSciNetGoogle Scholar
  8. Barnes, G., Leka, K.D.: 2008, Evaluating the performance of solar flare forecasting methods. Astrophys. J. Lett. 688(2), L107. ADS. DOI. ADSCrossRefGoogle Scholar
  9. Bélanger, E., Vincent, A., Charbonneau, P.: 2007, Predicting solar flares by data assimilation in avalanche models. I. Model design and validation. Solar Phys. 245(1), 141. ADS. DOI. ADSCrossRefGoogle Scholar
  10. Bloomfield, D.S., Higgins, P.A., McAteer, R.T.J., Gallagher, P.T.: 2012, Toward reliable benchmarking of solar flare forecasting methods. Astrophys. J. Lett. 747(2), L41. ADS. DOI. ADSCrossRefGoogle Scholar
  11. Charbonneau, P.: 2013, SOC and solar flares. In: Aschwanden, M.J. (ed.) Self-Organized Criticality Systems, Academic Press, San Diego, 404. ADS. Google Scholar
  12. Charbonneau, P., McIntosh, S.W., Liu, H.-L., Bogdan, T.J.: 2001, Avalanche models for solar flares (invited review). Solar Phys. 203(2), 321. ADS. DOI. ADSCrossRefGoogle Scholar
  13. Chen, P.F.: 2011, Coronal mass ejections: models and their observational basis. Liv. Rev. Solar Phys. 8, 1. ADS. DOI. ADSMATHGoogle Scholar
  14. Georgoulis, M.K.: 2012, On our ability to predict major solar flares. In: The Sun: New Challenges 3, 93. ADS. DOI. Google Scholar
  15. Georgoulis, M.K., Vlahos, L.: 1996, Coronal heating by nanoflares and the variability of the occurrence frequency in solar flares. Astrophys. J. Lett. 469, L135. ADS. DOI. ADSCrossRefGoogle Scholar
  16. Georgoulis, M.K., Vlahos, L.: 1998, Variability of the occurrence frequency of solar flares and the statistical flare. Astron. Astrophys. 336, 721. ADS. ADSGoogle Scholar
  17. Jensen, H.J.: 1998, Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems, Cambridge University Press, Cambridge. books.google.com/books?hl=en&lr=&id=ODJWWKd1JtIC&oi=fnd&pg=PP11&dq=jensen&ots=TGNyQq5K6h&sig=9_VMLDvpmDuHT0cZbDJBs5LoBjA. CrossRefMATHGoogle Scholar
  18. Kadanoff, L.P., Nagel, S.R., Wu, L., Zhou, S.-M.: 1989, Scaling and universality in avalanches. Phys. Rev. A 39(1), 6524. ADS. DOI. ADSCrossRefGoogle Scholar
  19. Lu, E.T.: 1995, The statistical physics of solar active regions and the fundamental nature of solar flares. Astrophys. J. Lett. 446, L109. ADS. DOI. ADSCrossRefGoogle Scholar
  20. Lu, E.T., Hamilton, R.J.: 1991, Avalanches and the distribution of solar flares. Astrophys. J. Lett. 380, L89. ADS. DOI. ADSCrossRefGoogle Scholar
  21. Lu, E.T., Hamilton, R.J., McTiernan, J.M., Bromund, K.R.: 1993, Solar flares and avalanches in driven dissipative systems. Astrophys. J. 412, 841. ADS. DOI. ADSCrossRefGoogle Scholar
  22. Mumford, S., Pérez-Suárez, D., Christe, S., Mayer, F., Hewett, R.J.: 2013, SunPy: python for solar physicists. In: van der Walt, S., Millman, J., Huff, K. (eds.) 12th Python in Science Conference, 74. conference.scipy.org/proceedings/scipy2013/mumford.html. Google Scholar
  23. Norman, J.P., Charbonneau, P., McIntosh, S.W., Liu, H.-L.: 2001, Waiting-time distributions in lattice models of solar flares. Astrophys. J. 557(2), 891. ADS. DOI. ADSCrossRefGoogle Scholar
  24. Shibata, K., Magara, T.: 2011, Solar flares: magnetohydrodynamic processes. Liv. Rev. Solar Phys. 8, 6. ADS. DOI. ADSGoogle Scholar
  25. Strugarek, A., Charbonneau, P.: 2014, Predictions of solar flares with avalanche models. Solar Phys. (to be submitted). Google Scholar
  26. Strugarek, A., Charbonneau, P., Joseph, R., Pirot, D.: 2014, Deterministically driven avalanche models of solar flares. Solar Phys. 289, 2993. ADS. DOI. ADSCrossRefGoogle Scholar
  27. Vlahos, L., Georgoulis, M., Kluiving, R., Paschos, P.: 1995, The statistical flare. Astron. Astrophys. 299, 897. ADS. ADSGoogle Scholar
  28. Weibull, W.: 1951, A statistical distribution function of wide applicability. J. Appl. Mech., 293. Google Scholar
  29. Wheatland, M.S.: 2000, The origin of the solar flare waiting-time distribution. Astrophys. J. Lett. 536(2), L109. ADS. DOI. ADSCrossRefGoogle Scholar
  30. Wheatland, M.S.: 2005, A statistical solar flare forecast method. Space Weather 3(7), 07003. ADS. DOI. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Département de PhysiqueUniversité de MontréalMontréalCanada

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