Distributions of Birkeland Current Density Observed by AMPERE are Heavy‐Tailed or Long‐Tailed

Abstract

The way in which field-aligned currents, or Birkeland currents, are distributed in Earth's magnetosphere is critical to understanding the times at which Earth feels the largest effects from space weather. This is because Birkeland currents close through Hall and Pedersen currents flowing in Earth's ionosphere (Cowley, 2000). Ampère's law means that these currents cause magnetic perturbations that can be measured on Earth's surface, and Faraday's law in turn means that those magnetic perturbations induce currents on the surface, commonly known as geomagnetically induced currents (GICs). GICs are a key area of scientific interest and have been reviewed on multiple occasions (Ngwira & Pulkkinen, 2019;Pirjola, 2002;Thomson et al., 2009); they are also a key area of policy interest, due to the adverse impact of GICs on electrical power networks and the associated risk of high economic costs (Eastwood et al., 2018). Several authors have previously examined the average behavior of Birkeland currents. Christiansen et al. (2002) reported maximum average current densities of ∼0.2 μA m −2 observed by Ørsted and MAGSAT during quiet times as opposed to average densities of ∼0.5 μA m −2 during disturbed times. Juusola et al. (2014) reported maximum average current densities of ∼0.7 μA m −2 using CHAMP data during 2000-2010. Workayehu et al. (2019) used Swarm data from 2014 to 2017 and reported maximum means of 0.4 μA m −2 which is lower than Juusola et al. (2014) but consistent with Christiansen et al. (2002); this may indicate that CHAMP overestimated the current densities or may indicate that 2000-2010 was generally more active than 2014-2017, consistent with Solar Cycle 24 being generally quieter than the preceding solar cycle. Xiong et al. (2020) used DMSP data during 2010-2014, and reported the maximum average current density as ∼0.2 μA m −2 , which is lower than both Juusola et al. (2014) and Workayehu et al.

Separating Contributions to Plasma Vorticity in the High‐Latitude Ionosphere From Large‐Scale Convection and Meso‐Scale Turbulence

“…FACs are intimately related to vorticity, being proportional in the limit of uniform ionospheric conductance, and the results presented by Coxon et al. (2022) showed that PDFs of FAC are similarly leptokurtic, with a similar spatial variation of q ‐exponential fit parameters across the northern hemisphere polar ionosphere. They used these results to identify regions of the ionosphere where there is a high likelihood of extreme FACs.…”

Extreme Birkeland Currents Are More Likely During Geomagnetic Storms on the Dayside of the Earth

“…We calculate the probability for any appreciable current flow by using a threshold J = 0.2 µA m −2 in Section 4.1; for high current flow by using a threshold J = 1.0 µA m −2 in Section 4.2; and for extreme current flow by using a threshold J = 4.0 µA m −2 in Section 4.3. We select these thresholds to enable comparison to the figures presented in Coxon et al (2022). We only show plots for the Northern Hemisphere; the corresponding probabilities for the Southern Hemisphere are generally lower, consistent with Coxon et al (2022), and are presented in Supporting Information S1.…”

“…We refer to these probabilities as P(J) where J is the threshold we set. This method was described fully in Coxon et al (2022), but briefly recapping it here: we use maximum likelihood estimation to estimate the probability distribution of the underlying data, and then apply the survival function using the probability distribution to recover the probabilities P(J). We fit the probability distribution on either side of the mode current j m separately, such that we derive the probability distributions for j > j m and j < j m ; for ease of discussion we will refer to these as positive and negative current respectively through the rest of this manuscript.…”

“…The former assumption is valid because Ridders' Method only fails to converge when q is close to 1. Therefore, the white "holes" in the maps of the probabilities seen in Coxon et al (2022) are not reproduced here. We note that we are modeling the underlying probability distributions, rather than applying probability thresholds to the data directly; this means we can extrapolate to events more extreme than those seen in our interval, but that our selected thresholds do not map to percentiles of the data.…”

“…Chisham and Freeman (2021) fit q-exponential functions to the distributions to obtain the survival function of the distributions, and therefore the probabilities of observing extreme values of ionospheric vorticity. Coxon et al (2022) performed a similar analysis on AMPERE-derived Birkeland currents from 2010 to 2012, and found that they are also well-described by a q-exponential distribution. They found that the probability of current densities above a given threshold was higher in the Northern Hemisphere than in the Southern for currents at multiple amplitude thresholds, and that the disparity was greater at larger thresholds.…”