The Tsallis statistical distribution applied to geomagnetically induced currents

Abstract

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.

A Statistical Model of Vorticity in the Polar Ionosphere and Implications for Extreme Values

“…We have shown that the measured PDFs of ionospheric vorticity fluctuations are well modeled by q-exponential probability distributions at all locations in the polar ionosphere. These distributions have previously been shown to successfully model fluctuations in other space plasma measurements (e.g., Barbosa et al, 2017;Burlaga et al, 2007;Esquivel & Lazarian, 2010). The parameter E q is associated with the level of kurtosis in the distribution, and hence, the amount of turbulent intermittency.…”

“…turbulence has significant consequences for forecasting the impact of space weather on space-and groundbased technological systems, such as the impact of geomagnetically induced currents (GICs) on power grids (Barbosa et al, 2017;Freeman et al, 2019).…”

“…Chisham and Freeman (2010) successfully modeled ionospheric vorticity PDFs using Tsallis q-exponential distributions (Picoli et al, 2009;Tsallis, 2009). In space plasmas, q-distributions have been used to characterize interstellar turbulence (Esquivel & Lazarian, 2010), turbulence in the solar wind (Burlaga et al, 2007), and geomagnetically induced currents (GICs) (Barbosa et al, 2017).…”

Geomagnetically Induced Currents Caused by Interplanetary Shocks With Different Impact Angles and Speeds

“…This constant and imminent threat has led to regulatory actions not only in the United States but also at an international level (see, e.g., Cassak et al, 2017;Jonas & McCarron, 2015;Knipp, 2015;Pulkkinen et al, 2017). GICs are also a very common subject for modeling studies whose goal corresponds to the improvement of GIC forecasting (Barbosa et al, 2015(Barbosa et al, , 2017Blake et al, 2016;Ngwira et al, 2009;Pulkkinen, 2015;Torta et al, 2017;Zhang et al, 2015Zhang et al, , 2016.…”

Tsallis Entropy for Cross-Shareholding Network Configurations

“…Within a long list, we may mention systems involving long-range interactions (see e.g. [59,5]), non-Markovian stochastic processes, like financial markets (see e.g. [60,61,62,8,68,40]), dissipative systems in a phase space which has some underlying looking (multi)fractal-like structure (see e.g.…”