Robust Features of the Size-Above-Threshold Distribution of Space Weather Events Seen in Geomagnetic Indices

Abstract:

Quantifying the large scale dynamic response of the magnetosphere to solar wind driving is central to our understanding of solar wind-magnetosphere coupling. Auroral geomagnetic indices provide a comprehensive dataset of substorm and storm events spanning several solar cycles. We can characterize these observations in terms of 'space climate' by quantifying how the statistical properties of ensembles of these observed variables vary between different phases of the solar cycle.
We present novel comparative statistical techniques which characterize secular changes in the distribution of geomagnetic indices. We first threshold these timeseries to generate a sequence of 'bursts' or events and find the statistical distributions of event size. The event size distribution is robustly multicomponent, and we find that for all thresholds above 1000nT the mean event size-above-threshold tends to a constant value. This 'tail' in the distribution of large events is found to be present in all phases of the solar cycle but is more populated (there are more, larger events) at solar maximum. Successive solar maxima and minima also show the same 'tail' in the distribution but again it is populated to different extents; some maxima or minima are stronger than others in terms of space weather impact as seen in auroral indices. By plotting the distribution of event sizes normalised to the first two monents we can compare the functional form of one distribution with another. We then find that these large (>1000nT threshold) events all share the same functional form for their probability distribution; it is independent of threshold. Thus, for a given solar cycle, once a sufficient number of events have been observed to determine the first two moments, the likelihood of an event of given size-above-threshold is determined for that solar cycle. This can parameterize the exceedence likelihood of events of a given size and how this is changing, with implications for space weather applications.