Abstract
Data assimilation techniques, developed in the past two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the possibility of applying the four-dimensional variational data assimilation (4D-VAR) technique to the prediction of solar flares. We do so in the context of a continuous version of the classical cellular-automaton-based self-organized critical avalanche models of solar flares introduced by Lu and Hamilton (Astrophys. J. 380, L89, 1991). Such models, although a priori far removed from the physics of magnetic reconnection and magnetohydrodynamical evolution of coronal structures, nonetheless reproduce quite well the observed statistical distribution of flare characteristics. We report here on a large set of data assimilation runs on synthetic energy release time series. Our results indicate that, despite the unpredictable (and unobservable) stochastic nature of the driving/triggering mechanism within the avalanche model, 4D-VAR succeeds in producing optimal initial conditions that reproduce adequately the time series of energy released by avalanches and flares. This is an essential first step toward forecasting real flares.
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References
Anderson, J.: 2003, In: Predictability of a Data Assimilation/Prediction System, NCAR Data Assimilation Initiative, Boulder.
Aschwanden, M., Charbonneau, P.: 2002, Astrophys. J. 566, L59.
Aschwanden, M., Tarbell, T., Nightingale, R., et al.: 2000, Astrophys. J. 535, 1047.
Bak, P.: 1996, How Nature Works: The Science of Self-Organized Criticality, Springer, New York.
Bak, P., Tang, C., Wiesenfeld, K.: 1987, Phys. Rev. Lett. 59, 381.
Bertino, L., Evensen, G., Wackernagel, H.: 2002, Inverse Probl. 18, 1.
Carton, J., Chepurin, G., Cao, X.: 2000, J. Phys. Oceanogr. 30, 311.
Charbonneau, P., McIntosh, S., Liu, H.-L., Bogdan, T.: 2001, Solar Phys. 203, 321.
Courtier, P., Talagrand, O.: 1990, Tellus 42A, 531.
Cressman, G.: 1959, Mon. Weather Rev. 87, 367.
Daley, R.: 1991, Atmospheric Data Analysis, Cambridge Atmospheric and Space Science Series, Cambridge University Press, Cambridge.
Dennis, B.: 1985, Solar Phys. 100, 465.
Ehrendorfer, M.: 1992, Quart. J. Roy. Meteorol. Soc. 118, 673.
Errico, R.: 1997, Bull. Am. Meteorol. Soc. 78, 2577.
Eymin, C., Fournier, A.: 2005, In: Abstract Book/CD IAGA 2005, IAGA2005, Toulouse.
Georgoulis, M., Vlahos, L.: 1998, Astron. Astrophys. 336, 721.
González, Á., Vázquez-Prada, M., Gómez, J., Pacheco, A.: 2006, Tectonophysics 424, 319.
Isliker, H., Anastasiadis, A., Vlahos, L.: 2000, Astron. Astrophys. 363, 1134.
Jensen, H.: 1998, Self-Organized Criticality, Cambridge University Press, Cambridge.
Kadanoff, L., Nagel, S., Wu, L., Zhou, S.: 1989, Phys. Rev. A 39, 6524.
Kalnay, E.: 2003, Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge.
Kantha, L., Clayson, C.: 2000, Numerical Models of Oceans and Oceanic Processes, International Geophysics Series 66, Academic Press, New York.
Le Dimet, F.-X., Talagrand, O.: 1986, Tellus 38A, 97.
Lions, J.: 1968, Contrôle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles, Dunod, Paris.
Liu, H.-L., Charbonneau, P., Pouquet, A., Bogdan, T., McIntosh, S.: 2002, Phys. Rev. E 66, 056111.
Lu, E., Hamilton, R.: 1991, Astrophys. J. 380, L89.
Lu, E., Hamilton, R., McTiernan, J., Bromund, K.: 1993, Astrophys. J. 412, 841.
Mitchell, A., Griffiths, D.: 1980, The Finite Difference Method in Partial Differential Equations, Wiley, Toronto.
Moore, A., Arango, H., Lorenzo, E. et al.: 2004, Ocean Model. 7, 227.
Nichols, N.: 2003, In: Swinbank, R., Shutyaev, V., Lahoz, W. (eds.) Data Assimilation for the Earth System, Kluwer, Dordrecht, 9.
Norman, J., Charbonneau, P., McIntosh, S., Liu, H.-L.: 2001, Astrophys. J. 557, 891.
Parker, E.: 1983, Astrophys. J. 264, 635.
Parker, E.: 1988, Astrophys. J. 330, 474.
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, New York.
Rundle, J., Klein, W., Tiampo, K., Donnellan, A., Fox, G.: 2003, In: Computational Science – ICCS 2003, Lecture Notes in Computer Science 2659, Springer, Berlin/Heidelberg, 827.
Sanders, B., Katopodes, N.: 1999, J. Irrig. Drainage Eng. 125, 287.
Sanders, B., Katopodes, N.: 2000, J. Eng. Mech. 126, 909.
Schrijver, C., DeRosa, M.: 2003, Solar Phys. 212, 165.
Schröter, J., Seiler, U., Wenzel, M.: 1993, J. Phys. Oceanogr. 23, 925.
Siscoe, G., Solomon, S.: 2006, Space Weather 4, S04002.
Talagrand, O., Courtier, P.: 1987, Quart. J. Roy. Meteorol. Soc. 113, 1311.
Wheatland, M.: 2000, Astrophys. J. 536, L109.
Wiltberger, M., Baker, D.: 2006, Space Sci. Rev. 124, 217.
Zirker, J., Cleveland, F.: 1993, Solar Phys. 145, 119.
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Bélanger, E., Vincent, A. & Charbonneau, P. Predicting Solar Flares by Data Assimilation in Avalanche Models. Sol Phys 245, 141–165 (2007). https://doi.org/10.1007/s11207-007-9009-3
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DOI: https://doi.org/10.1007/s11207-007-9009-3