Jingjing Wang1,2, Yuhang Zhang3, Shea A. Hess Webber4, Siqing Liu1,2,5, Xuejie Meng1,2, & Tieyan Wang6
1. National Space Science Center, Chinese Academy of Sciences, Beijing, People’s Republic of China
2. Key Laboratory of Science and Technology on Environmental Space Situation Awareness, Chinese Academy of Sciences, Beijing, People’s Republic of China
3. School of Computer Science and Technology, Xidian University, Xi’an, 710126, People’s Republic of China.
4. W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA
5. University of Chinese Academy of Sciences, Beijing, People’s Republic of China
6. RAL Space, Rutherford Appleton Laboratory, Harwell Oxford, Didcot, OX11 0QX, UK
Solar magnetic field observations have been widely used to search for magnetic properties that are related to solar eruptions. The Space-weather HMI Active Region Patches data product (SHARP), a set of proxies for magnetic field parameters, is one of the key datasets used to derive physical properties and develop flare prediction models.
Properties of the polarity inversion line (PIL) in solar active regions (ARs) are strongly correlated to flare and CME occurrences. The SHARP R-value, one of the best predictors in flare prediction, is the sum of flux near the PIL from the full SHARP AR region that is calculated using the method described in Ref [1]. In Ref [2], the PIL masks (bottom-left panel in Fig. 1), are produced using the same method but using the radial magnetic field, Br (top-left panel in Fig. 1), from the SHARP vector magnetic field products. The values (from 0 to 1) in a PIL mask indicate the gradient between the positive and negative magnetic field regions. The standard SHARP parameters are then modified by multiplying them with a PIL mask. The modified parameters discriminate between non-eruptive and eruptive ARs much better than the standard SHARP parameters. This indicates that the immediate PIL regions possess the potential to improve machine-learning-based solar flare prediction models.
In this work, an unsupervised machine-learning algorithm, Kernel Principle Component Analysis (KPCA), is adopted to directly derive features from the PIL mask and difference PIL mask (bottom-left and bottom right panels in Fig. 1), and those features are used to classify ARs into two categories—non-strong flaring ARs and strong-flaring (M-class and above flares) ARs—for time-in-advance from 1hr to 72hr with a 1hr cadence. KPCA can automatically reconstruct two-dimensional images and then obtain one-dimensional features from each image, after which the two-dimensional images are represented by several one-dimensional features. The features are learned without supervision, i.e., without preset labels for the images.
In Fig. 1, the red squares enclose a sub-image with an area of 250×250 pixels centered at the centroid of the PIL mask. The centroid of the PIL mask is taken as the pixel with the largest gradient, determined by averaging the gradient values from the nine neighboring pixels surrounding the center pixel. The sub-images of the PIL mask and the difference PIL mask (bottom row) are the data to be used for the unsupervised KPCA feature derivation in this study.
Figure 1| Top left: radial magnetic field, Br, in the active region AR 12673 taken at 11:48 UT, 2017 September 6. The minimum and maximum of the image are −1000 G and 1000 G, respectively. Top right: positive/negative magnetic polarity mask derived from the Br image. Bottom left: PIL mask derived from the Br polarity mask. Bottom right: the corresponding 48-hour difference PIL mask.
Standardized sub-images are used instead of the entire PIL mask (with different image sizes of SHARP patches) to avoid image distortion problems during the process of scaling inputs into a standard uniform size for machine learning. We also note the benefit of the decreased computational cost by using sub-images, while still being able to maintain strong predictive capability.
Two best features are selected from the KPCA results. Feature 1 is the best feature derived from the PIL masks. Figure 2 is the best feature derived from the difference PIL masks.
We first use a statistical characterization metric, the Fisher ranking score (F-score), to compare the distinguishing capability of the two KPCA-derived features, the SHARP R-value and the difference R-value (dR). The larger the F-score, the better the feature performs at distinguishing between groups.
Figure 2| Top panel: F-score for Feature 1 derived from the PIL masks corresponding to the time-in-advance (from 1 to 72 hr at 1 hr cadence). Bottom panel: F-score for Feature 2 derived from difference PIL masks corresponding to the time difference (from 1 to 48 hr at 1 hr cadence), simplified by choosing the time-difference as 0.
As a comparison, the top panels in Fig. 2 and Fig. 3 show the F-score of Feature 1 and the SHARP R-value corresponding to the time-in-advance (from 1 to 72hr at 1hr cadence), respectively. The bottom panels in Fig. 2 and Fig. 3 show the F-score of Feature 2 and dR corresponding to the time difference of calculating the difference dataset (from 1 to 48hr at 1hr cadence), respectively. The top panels emphasize prediction dependence on the amount of time before an AR flare; the bottom panels emphasize prediction dependence on changes over time during an AR flare. We find that the features derived from the PIL masks and the difference PIL masks achieves larger F-scores than the SHARP R-value and dR, respectively, and therefore should be more capable of distinguishing between the strong flaring and non-strong-flaring ARs.
Figure 3| . Top panel: F-score for the SHARP R-value corresponding to the time-in-advance (from 1 to 72 hr at 1 hr cadence). Bottom panel: F-score for dR corresponding to the time difference (from 1 to 48 hr at 1 hr cadence), simplified by choosing the time-difference as 0.
We then employ a random forest machine-learning method, taking each of the four predictors (the two derived features, the SHARP R-value and dR) as input, to develop a separate feature-based flare forecasting model. The model is tested based on hourly data between 1hr to 72hr before the flare events. Our simple evaluative prediction test yields similar metric results for all four predictors. One explanation is that only using one predictor as model input may cause an increased number of false alarms and could be improved by inputting multiple predictors as inputs in the future.
This study demonstrates that both the PIL mask and the difference PIL mask are very useful for strong-flare prediction. Useful features can be derived from the masks using unsupervised machine-learning algorithms and those derived features can then be used to develop improved supervised flare prediction models.
For more details of this work, please refer to our recent publication Ref. [3].
References
[1] Schrijver, C. J. 2007, ApJL, 655, L117
[2] Wang, J., Liu, S., Ao, X., et al. 2019, ApJ, 884, 175
[3] Wang, J., Zhang, Y., Hess Webber, S., et al. 2020, ApJ, 892, 140