Skip to main content
Log in

Predictive Capabilities of Avalanche Models for Solar Flares

  • Published:
Solar Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  • 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 .

    Article  ADS  MathSciNet  Google Scholar 

  • Aschwanden, M.J., Charbonneau, P.: 2002, Effects of temperature bias on nanoflare statistics. Astrophys. J. Lett. 566(1), L59. ADS . DOI .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • Aschwanden, M.J., Parnell, C.E.: 2002, Nanoflare statistics from first principles: fractal geometry and temperature synthesis. Astrophys. J. 572(2), 1048. ADS . DOI .

    Article  ADS  Google Scholar 

  • 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

  • Bak, P., Tang, C., Wiesenfeld, K.: 1987, Self-organized criticality – an explanation of 1/f noise. Phys. Rev. Lett. 59, 381. ADS . DOI .

    Article  ADS  MathSciNet  Google Scholar 

  • Barnes, G., Leka, K.D.: 2008, Evaluating the performance of solar flare forecasting methods. Astrophys. J. Lett. 688(2), L107. ADS . DOI .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • Charbonneau, P.: 2013, SOC and solar flares. In: Aschwanden, M.J. (ed.) Self-Organized Criticality Systems, Academic Press, San Diego, 404. ADS .

    Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • Chen, P.F.: 2011, Coronal mass ejections: models and their observational basis. Liv. Rev. Solar Phys. 8, 1. ADS . DOI .

    ADS  MATH  Google Scholar 

  • Georgoulis, M.K.: 2012, On our ability to predict major solar flares. In: The Sun: New Challenges 3, 93. ADS . DOI .

    Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • Georgoulis, M.K., Vlahos, L.: 1998, Variability of the occurrence frequency of solar flares and the statistical flare. Astron. Astrophys. 336, 721. ADS .

    ADS  Google Scholar 

  • 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 .

    Book  MATH  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • Lu, E.T., Hamilton, R.J.: 1991, Avalanches and the distribution of solar flares. Astrophys. J. Lett. 380, L89. ADS . DOI .

    Article  ADS  Google Scholar 

  • 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 .

    Article  ADS  Google Scholar 

  • 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 

  • 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 .

    Article  ADS  Google Scholar 

  • Shibata, K., Magara, T.: 2011, Solar flares: magnetohydrodynamic processes. Liv. Rev. Solar Phys. 8, 6. ADS . DOI .

    ADS  Google Scholar 

  • Strugarek, A., Charbonneau, P.: 2014, Predictions of solar flares with avalanche models. Solar Phys. (to be submitted).

  • Strugarek, A., Charbonneau, P., Joseph, R., Pirot, D.: 2014, Deterministically driven avalanche models of solar flares. Solar Phys. 289, 2993. ADS . DOI .

    Article  ADS  Google Scholar 

  • Vlahos, L., Georgoulis, M., Kluiving, R., Paschos, P.: 1995, The statistical flare. Astron. Astrophys. 299, 897. ADS .

    ADS  Google Scholar 

  • Weibull, W.: 1951, A statistical distribution function of wide applicability. J. Appl. Mech., 293.

  • Wheatland, M.S.: 2000, The origin of the solar flare waiting-time distribution. Astrophys. J. Lett. 536(2), L109. ADS . DOI .

    Article  ADS  Google Scholar 

  • Wheatland, M.S.: 2005, A statistical solar flare forecast method. Space Weather 3(7), 07003. ADS . DOI .

    Article  ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Strugarek.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Strugarek, A., Charbonneau, P. Predictive Capabilities of Avalanche Models for Solar Flares. Sol Phys 289, 4137–4150 (2014). https://doi.org/10.1007/s11207-014-0570-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-014-0570-2

Keywords

Navigation