The Tsallis statistical distribution applied to geomagnetically induced currents

Geomagnetically induced currents (GICs) have been long recognized as a ground effect arising from a chain of space weather events. GICs have been measured and modeled in many countries, resulting in a considerable amount of data. Previous statistical analyses have proposed various types of distribution functions to fit long-term GICs data sets. However, these extensive statistical approaches have been only partially successful in fitting the data sets. Here we use modeled GICs data sets calculated in four countries (Brazil, South Africa, United Kingdom, and Finland) using data from solar cycle 23 to show a plausible function based on a nonextensive statistical model of the q-exponential Tsallis function. The fitted q-exponential parameter is approximately the same for all locations, and the Lilliefors test shows good agreement with the q-exponential fits. From this fit, we compute that the likely numbers of extreme GICs events over the next ten solar cycles are 1–2 for both Finland and United Kingdom, at least one for Brazil and less than one event for South Africa. Our results indicate that the nonextensive statistics are a general characteristic of GICs, suggesting that the ground current intensity has a strong temporal correlation and long-range interaction.