Global Energetics of Solar Flares. XI. Flare Magnitude Predictions of the GOES Class

Abstract

Abstract In this study we determine scaling relationships of observed solar flares that can be used to predict upper limits of the Geostationary Orbiting Earth Satellite (GOES)–class magnitude of solar flares. The flare prediction scheme is based on the scaling of the slowly varying potential energy E p (t), which is extrapolated in time over an interval of Δt ≤ 24 hr. The observed scaling of the dissipated energy E diss scales with the potential field energy as . In addition, the observed scaling relationship of the flare volume, , the multi-thermal energy, E th ∝ V 0.76, the flare emission measure , the EM-weighted temperature T w , and the GOES flux, , allows us then to predict an upper limit of the GOES-class flare magnitude in the extrapolated time window. We find a good correlation (cross-correlation coefficient (CCC) ≈ 0.7) between the observed and predicted GOES-class flare magnitudes (in 172 X- and M-class events). This is the first algorithm that employs observed scaling laws of physical flare parameters to predict GOES flux upper limits, an important capability that complements previous flare prediction methods based on machine-learning algorithms used in space-weather forecasting.