Extreme Value Analysis of Solar Flare Events

Abstract

Space weather events such as solar flares can be harmful for life and infrastructure on Earth or in near‐Earth orbit. In this paper we employ extreme value theory to model extreme solar flare events; extreme value theory offers the appropriate tools for the study and estimation of probabilities for extrapolation to ranges outside of those that have already been observed. In this work the data points used are inherently independent and realistic confidence intervals are offered with respect to the estimates of future solar flare events. The data used in this study are peak X‐ray fluxes provided by National Oceanic and Atmospheric Administration that form a series of distinct flare events. The expected return levels for Carrington‐ or Halloween storm‐like events were calculated with the outcome that the existing data predict similar events happening in 110 and 38 years, respectively, which are consistent with the results and inferences provided by Elvidge and Angling (2018, https://doi.org/10.1002/2017SW001727). We also make a preliminary analysis of the implications of solar seasonality and found its effect on extreme flare events to be statistically insignificant.

A global climatological model of extreme geomagnetic field fluctuations

“…In previous studies, EVT has been used to examine the likelihood of extreme values of geomagnetic indices including D st (Silbergleit, 1996;Tsubouchi & Omura, 2007), the Auroral Electrojet indices (AU, AL, and AE) (Nakamura et al, 2015), A p (Koons, 2001), and the aa and AA* indices (Siscoe, 1976;Silbergleit, 1999), although the location and timing of large jdB H =dtj events are not well predicted by geomagnetic index statistics (e.g., Kozyreva et al, 2018). In related space weather fields, EVT has characterised the probability of extreme solar flare X-ray flux (Elvidge & Angling, 2018;Tsiftsi & De la Luz, 2018) and extreme high-energy (>2 MeV) radiation-belt "killer" electron fluxes (Koons, 2001;O'Brien et al, 2007;Meredith et al, 2015). N.C. Rogers et al: J.…”

Extreme value theory in the solar wind: the role of current sheets

“…Since rotations of the magnetic field vector generate a current density, intense current sheets are usually associated with large rotations of B, resulting in large fluctuations or bursts in time series of two-point differences of the form where τ is a time lag. In the context of financial sciences, the bursts are known as volatility (Poon 2005;Tsay 2010), which is usually associated with violent changes in the financial market, such as a financial crisis. The two-point difference series is known as the financial return (Tsay 2010), therefore we call r mag the magnetic return.…”

“…For instance, in Chian & Miranda (2009) a time series of normalized magnetic-field differences was used, while in Greco et al (2009Greco et al ( , 2018 the partial variance of increments method was adopted. In the present work, we propose a new technique based on the volatility (Poon 2005), a statistical tool widely employed to detect and predict sudden changes in financial markets (Tsay 2010). This analysis is based on so-called return time series (Tsay 2010), which present interesting statistical properties such as stationarity and ergodicity.…”

“…In the present work, we propose a new technique based on the volatility (Poon 2005), a statistical tool widely employed to detect and predict sudden changes in financial markets (Tsay 2010). This analysis is based on so-called return time series (Tsay 2010), which present interesting statistical properties such as stationarity and ergodicity. The measure of the bursts of those return time series is called volatility (Poon 2005) and displays the clustering (or memory) effect (Tsay 2010).…”

“…This analysis is based on so-called return time series (Tsay 2010), which present interesting statistical properties such as stationarity and ergodicity. The measure of the bursts of those return time series is called volatility (Poon 2005) and displays the clustering (or memory) effect (Tsay 2010). In other words, the volatility at a certain time depends on the volatility at previous times.…”