Statistics of the extreme events with extreme value theory

Measuring the probability of extreme space weather events poses a challenge due to their infrequency. However, these rare events significantly and extensively impact various facilities in modern society. Extreme space weather events from the Sun have the potential to push the magnetosphere into an extreme state, where electromagnetic fields and particle environments behave differently than predicted by conventional theory, potentially causing more severe impacts than anticipated. In this study, we applied Extreme Value Theory to geomagnetic indices (such as the AE index, Aa index) derived from ground-based magnetometer observations spanning various solar cycles. We obtained the return levels of the indices with different return periods and identified an upper bound for the time series. Diligent precautions are necessary to mitigate the consequences of such extreme events, and surpassing the upper limit becomes increasingly challenging over time.