Estimating the Occurrence of Geomagnetic Activity Using the Hilbert-Huang Transform and Extreme Value Theory

In this paper extreme value theory (EVT) has been used to estimate the return levels for geomagnetic activity based on the aa index. The aa index is the longest, continuously recorded, geomagnetic data set (from 1868 to present). This long, 150-year data set is an ideal candidate for extreme value analysis. However, the data are not independent and identically distributed as required for EVT since they are impacted by the approximately 11-year solar cycle. The Hilbert-Huang transform has been used to identify the solar cycle component in the data, and the data have been split into solar maximum and minimum times. In these two regimes the generalized extreme value distribution has been fit to the data sets. These have also been combined for an estimate of the overall return times. The results suggest that the largest event in the database (March 1989) is a 1-in-25-year event. However, considering separate solar maximum and minimum times has a large impact on the return times. During solar minimum conditions the return time of the March 1989 event is 130 years. This suggests that the occurrence of extreme space weather events is conditionally dependent on where in the solar cycle we are.