Using extreme value theory for determining the probability of carrington‐like solar flares

By their very nature, extreme space weather events occur rarely and, therefore, statistical methods are required to determine the probability of their occurrence. 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). In this paper extreme value theory (EVT) is used to investigate the probability of extreme solar flares. Previous work has assumed that the distribution of solar flares follows a power law. However such an approach can lead to a poor estimation of the return times of such events due to uncertainties in the tails of the probability distribution function. Using EVT and GOES X‐ray flux data it is shown that the expected 150‐year return level is approximately an X60 flare whilst a Carrington‐like flare is a one in a 100‐year event. In the worst case the 150‐year return level is an X90 flare whist a Carrington flare is a one in 30‐year event. It is also shown that the EVT results are consistent with flare data from the Kepler space telescope mission.