Text Box: Over the past decades, humankind has become more and more dependent on space systems, satellite-based services, and various ground-based facilities. All these technologies are influenced by Sun – Earth interactions. Therefore, one of the primary objectives in space weather research is to predict the occurrence of solar flares and coronal mass ejections (CMEs), which are believed to be the major causes of geomagnetic disturbances (e.g., Brueckner et al., 1998; Cane, Richardson, and St. Cyr, 2000; Gopalswamy et al., 2000; Webb et al., 2000; Wang et al., 2002; Zhang et al., 2003).

It has long been known that solar flares tend to occur along magnetic polarity inversion lines where the magnetic field lines are often highly sheared, with the transverse field directed nearly parallel to the polarity inversion line. Canfield, Hudson, and McKenzie (1999) showed that CMEs also tend to arise in connection with active regions (ARs) exhibiting strong sheared and/or twisted coronal loops called sigmoids. The twisting, tangling, and shearing of magnetic loops lead to magnetic topological complexities and build up a stressed flux system (and excess energy). Subsequent destabilizing events such as local emergence of new magnetic flux from below the photosphere or changes in magnetic connectivity owing to magnetic field reorganization elsewhere on the Sun may result in the release of energy (Priest and Forbes, 2000). To date, various observational studies have explored the connection between photospheric magnetic fields and solar flares, supporting the hypothesis that solar flares are driven by the nonpotentiality of magnetic fields. Through five solar flares, Wang (2006) found there are obvious changes of the magnetic gradient occurring immediately and rapidly following the onset of each flare. Falconer (2001) measured the lengths of strong-sheared and strong-gradient magnetic neutral line segments and found that they are strongly correlated with CME productivity of an active region and both might be prospective predictors. In a study of six large (X5 or larger) flares, Wang et al. (2006) reported a positive linear relationship between the magnetic shear and the magnetic gradient and that the latter seems to be a better tool to predict the occurrence of flares and CMEs in an active region.  Jing et al. (2006) analyzed three magnetic parameters – i) the mean spatial magnetic field gradient at the strong-gradient magnetic neutral line, Mgnl; ii) the length of a strong-gradient magnetic neutral line, Lgnl; and iii) the total magnetic energy dissipation, Ediss, which describes magnetic field features of nonpotentiality and turbulence – and found that these parameters have a positive correlation with the overall flare productivity of ARs. Active regions with larger Mgnl, Lgnl, and Ediss generally show a higher incidence of flaring activity. The purpose of this study is to find out whether statistical methods that are conceptually simple and algorithmically fast are able to provide a feasible way to evaluate the probability of an active region in producing solar flares. The ordinal logistic regression model satisfies our criteria. The model describes the relationship between an ordered response variable and a set of predictive variables. In our case, the ordered response variable represents four different energy levels of solar flares. We assign numerical values 3, 2, 1, and 0 to represent X-, M-, C-, and B-class flares, respectively. The predictive variables so far include Lgnl.

Our group uses the ordinal logistic regression method to establish a prediction model (Song et al., 2009), 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 Tflux, which is a measure of an active region’s size, (2) the length of the strong-gradient neutral line Lgnl, which describes the global nonpotentiality of an active region, and (3) the total magnetic dissipation Ediss, 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, Lgnl 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 Lgnl, Tflux, and Ediss as predictors demonstrated its automatic functionality, simplicity, and fairly high prediction accuracy. This is the first time the ordinal logistic regression model has been used in solar physics to predict solar flares (For the detail of the method, please see Song et al. 2009). 

The ordinal logistic regression method is proven to be a viable, practical, and competitive approach to automated flare prediction. The results are better than those data published by the NASA/SDAC service and are comparable to the data provided by the NOAA/SWPC complicated expert system (see the figure blow).

 

                                                                                 (Courtesy of Dr. Changyi Tan)
References:
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.
Cane, H.V., Richardson, I.G., St. Cyr, O.C.: 2000, Geophys. Res. Lett. 27, 3591.
Canfield, R.C., Hudson, H.S., McKenzie, D.E.: 1999, Geophys. Res. Lett. 26, 627.
Falconer, D.A.: 2001, J. Geophys. Res. 106, 25185.
Gopalswamy, N., Lara, A., Lepping, R.P., Kaiser, M.L., Berdichevsky, D., St. Cyr, O.C.: 2000, Geophys. Res. Lett. 27, 145.
Jing, Ju, Song, Hui, Abramenko, Valentyna, Tan, Changyi, Wang, Haimin: 2006, Astrophys. J. 644, 1273.
Priest, E., Forbes, T.: 2000, Magnetic Reconnection: MHD Theory and Applications, Cambridge Univ. Press, Cambridge.
Song, Hui, Tan, Changyi, Jing, Ju, Wang, Haimin, Yurchyshyn, Vasyl, Abramenko, Valentyna: 2009, Solar Physics, 254, 101.
Wang, H., Song, H., Yurchyshyn, V., Deng, Y., Zhang, H., Falconer, D., Li, J.: 2006, Chin. J. Astron. Astrophys. 6, 477.
Wang, Y.M., Ye, P.Z., Wang, S., Zhou, J.P., Wang, J.: 2002, J. Geophys. Res. 107, 2.
Webb, D.F., Cliver, E.W., Crooker, N.U., Cry, O.C.S., Thompson, B.J.: 2000, J. Geophys. Res. 105, 7491.
Zhang, J., Dere, K.P., Howard, R.A., Bothmer, V.: 2003, Astrophys. J. 582, 520.
              http://swrl.njit.edu/h2f/flare.jpg (Courtesy of NASA)