Variation of geomagnetic index empirical distribution and burst statistics across successive solar cycles

The overall level of solar activity, and space weather response at Earth, varies within and between successive solar cycles and can be characterized by the statistics of bursts, i.e., time series excursions above a threshold. We consider nonoverlapping 1‐year samples of the auroral electrojet index (AE) and the SuperMAG‐based ring current index (SMR), across the last four solar cycles. These indices, respectively, characterize high latitude and equatorial geomagnetic disturbances. We suggest that average burst duration τ ̄ $\bar{\tau }$ and burst return period R ̄ $\bar{R}$ form an activity parameter, τ ̄ / R ̄ $\bar{\tau }/\bar{R}$ which characterizes the fraction of time the magnetosphere spends, on average, in an active state for a given burst threshold. If the burst threshold takes a fixed value, τ ̄ / R ̄ $\bar{\tau }/\bar{R}$ for SMR tracks sunspot number, while τ ̄ / R ̄ $\bar{\tau }/\bar{R}$ for AE peaks in the solar cycle declining phase. Level crossing theory directly relates τ ̄ / R ̄ $\bar{\tau }/\bar{R}$ to the observed index value cumulative distribution function (cdf). For burst thresholds at fixed quantiles, we find that the probability density functions of τ and R each collapse onto single empirical curves for AE at solar cycle minimum, maximum, and declining phase and for (−)SMR at solar maximum. Moreover, underlying empirical cdf tails of observed index values collapse onto common functional forms specific to each index and cycle phase when normalized to their first two moments. Together, these results offer operational support to quantifying space weather risk which requires understanding how return periods of events of a given size vary with solar cycle strength