Addressing Known Challenges in Solar Flare Forecasting I: Limb-Flare Prediction with a 4-pi Full-Heliosphere Framework

TL;DR

This study tackles the limb-flare forecasting challenge by developing a $4\pi$ full-Heliosphere framework that merges a high-resolution, Earth-facing Advective Flux Transport (AFT) magnetic field map with far-side helioseismology to produce synchronic full-Sun AR information. AFT-based AR detection and a novel $4\pi$ AR labeling system feed two key parameters, the total unsigned flux $\Phi$ and the Schrijver $R$ near strong-gradient PILs, into a NWRA nonparametric discriminant analysis that yields probabilistic flare forecasts. The authors curate GOES flare events to create limb- and Earth-visible event lists, and evaluate performance across disk-only and limb-inclusive configurations, using ROCSS, BSS, and related metrics. Results from two limb cases and a larger sample show modest yet consistent improvements in limb-ward predictions when far-side information is included, with particularly notable gains for East-limb events, suggesting practical value in extending operational flare forecasting to the full solar sphere. The work demonstrates a viable path toward operational $4\pi$ space-weather forecasting by integrating physics-based transport, seismology-derived data, robust AR labeling, and probabilistic validation, and lays groundwork for incorporating additional limb-visible data streams in the future.

Abstract

A demonstrated failure mode for operational solar flare forecasting is the inability to forecast flares that occur near, or just beyond, the solar limb. To address this shortcoming, we develop a "4pi" full-heliosphere event forecasting framework and evaluate its statistical classification ability against this specific challenge. A magnetic surface flux transport model is used to generate full-sun maps of the photospheric radial magnetic field from which active regions (ARs) are identified and tracked using a new labeling scheme that is observer-location agnostic and allows for post-facto modifications. Flare-relevant magnetic parameters couple to a "visibility" index that specifies AR location relative to the visible solar limb and expected flare detection. Flare labels are assigned according to peak Soft X-ray flux, and a statistical classification is performed using nonparametric discriminant analysis. A version where new or emerging ARs on the far ("invisible" side of the Sun are incorporated into the model by way of far-side helioseismology, is also tested. We evaluate the new framework by its performance specifically including the limb areas using Brier Skill Score and ROC Skill Score, finding improvement at the 2-sigma level or less. However, we do find that the number of False Negatives, or "missed" forecasts decreases, and find strong evidence that the additional information provided by the far-side helioseismology can help predict near- and just-beyond-limb flares, particularly for East-limb events. While individual components of this framework could be improved, we demonstrate that a known failure mode for solar flare forecasting can be mitigated with available resources.

Figures (8)

• Figure 1: An example AFT full-Sun (or "4$\pi$") magnetic field map on 2014.01.04 18:00 UT, scaled to $\pm 1,000\,{\rm Mx\,cm}^{-2}$, with the solar limb (grey), the AFT assimilation window (magenta) and identified AFT active regions, or AFT-ARs (blue). Note that the b0-angle on this day is such that the south pole is slightly visible. In this example, the regions fully within the assimilation window would be assigned Disk, the two regions on the far-side (at CL=[$0^\circ,280^\circ$]) would be assigned Far, and the region centered at ${\rm CL}\approx230^\circ$ that spans both the assimilation and limb terminators would be assigned Occ, or "occulted" (see Section \ref{['sec:vis']} for details).
• Figure 3: Cartoon representation (with absolutely no scale intended) of a far-side AR region (purple) and an occulted region (green), and the effective Stonyhurst longitude $\theta>90^\circ$ indicated. For both loops, red line-segments indicate the minimum height that an AR loop system would need to achieve to be visible from Earth. As the cartoon indicates, our model that assesses whether an AR is to be labeled "Far-Side" or "Occulted" depends on the AR size and location.
• Figure 4: ROC plots for the region-based forecasts, comparing the paired tests as indicated ( c.f. Table \ref{['tbl:tests']}). For each, the $P_{\rm th}$ location on the ROC curve is indicated, where the TSS = POD-FAR is maximum, is indicated. The associated ROCSS and the differences between the paired tests are provided in Table \ref{['tbl:results_region']}.
• Figure 5: Same as Figure \ref{['fig:roc']} but for full-disk forecasts, with associated ROCSS given in Table \ref{['tbl:results_FD']}.
• Figure 6: Reliability Plots for the AFT-HMI Baseline data without (F10, left) and with (F11, right), the occulted-region data included, for C1.0+ flares (top) and M1.0+ flare (bottom). The predicted probabilities are divided into 20 bins, and the error bars reflect the sample size of that bin Wheatland2005. Also shown are the sample-size histograms (red), the climatology (blue) and the "no-skill" line (green).