Using Extreme Value Theory for Determining the Probability of Carrington-Like Solar Flares

Abstract: Space weather events can negatively affect satellites, the electricity grid, satellite navigation systems and human health. As a consequence, extreme space weather has been added to the UK and other national risk registers. However, by their very nature, extreme events occur rarely and statistical methods are required to determine the probability of occurrence solar storms. Space weather events can be characterised by a number of natural phenomena such as X-ray (solar) flares, solar energetic particle (SEP) fluxes, coronal mass ejections and various geophysical indices (Dst, Kp, F10.7). Here we use extreme value theory (EVT) to investigate the probability of extreme solar flares. Previous work has suggested that the distribution of solar flares follows a power law. However such an approach can lead to overly "fat-tails" in the probability distribution function and thus to an under estimation of the return time of such events. Using EVT and GOES X-ray flux data we find that the expected 150 year return level is an X60 flare (6x10^-3 Wm-2, 1-8 Å X-ray flux). We also show that the EVT results are consistent with flare data from the Kepler space telescope mission.