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 characterized by a number of natural phenomena such as X-ray (solar) flares, solar energetic particle fluxes, coronal mass ejections, and various geophysical indices (such as Dst, Kp, and 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 flares due to uncertainties in the tails of the probability distribution function. Using EVT and Geostationary Operational Environmental Satellites X-ray flux data, it is shown that the expected 150 year return level is approximately an X60 flare while 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 while 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.