- Open Access
Statistical analysis of extreme auroral electrojet indices
© Nakamura et al. 2015
Received: 29 December 2014
Accepted: 2 September 2015
Published: 16 September 2015
Extreme auroral electrojet activities can damage electrical power grids due to large induced currents in the Earth, degrade radio communications and navigation systems due to the ionospheric disturbances and cause polar-orbiting satellite anomalies due to the enhanced auroral electron precipitation. Statistical estimation of extreme auroral electrojet activities is an important factor in space weather research. For this estimation, we utilize extreme value theory (EVT), which focuses on the statistical behavior in the tail of a distribution. As a measure of auroral electrojet activities, auroral electrojet indices AL, AU, and AE, are used, which describe the maximum current strength of the westward and eastward auroral electrojets and the sum of the two oppositely directed in the auroral latitude ionosphere, respectively. We provide statistical evidence for finite upper limits to AL and AU and estimate the annual expected number and probable intensity of their extreme events. We detect two different types of extreme AE events; therefore, application of the appropriate EVT analysis to AE is difficult.
Extreme auroral electrojet activities can induce rapid variations in geomagnetic fields and ionospheric disturbances. These rapid variations in the geomagnetic fields induce large geomagnetically induced currents (GIC), which can damage high-voltage power transformers of power grids and increase steel corrosion of pipeline networks (e.g., Lanzerotti 2001). The ionospheric disturbances due to Joule heating associated with auroral electrojets can degrade radio communications and interfere with precise navigation (e.g., Ding et al. 2008). The characterization of extreme GIC events is central to quantifying the technological impacts and societal consequences of extreme space weather. Recently, Thomson et al. (2011), Viljanen et al. (2013), and Pulkkinen et al. (2012) used the European magnetic observatory network to study extreme geomagnetic activities and to assess their hazard in Europa. In the present study, we focus on auroral latitude geomagnetic activity caused by auroral electrojets. Because they cause intense GIC, the effect of auroral latitude geomagnetic activity on GIC has been intensively studied by many researchers (e.g., Beggan 2015). This auroral activity also causes polar-orbiting satellite anomalies due to the enhanced auroral electron precipitation. Auroral electrojets are horizontal electric currents that flow in the ionosphere of the auroral zone; their indices were introduced by Davis and Sugiura (1966) as a measure of global electrojet activity. These indices are derived from geomagnetic variations in the horizontal component observed at 12 observatories in a geomagnetic latitude range of 61°–70° in the Northern Hemisphere. The AU and AL indices are defined by the largest and the smallest values of the data, respectively. The symbols AU and AL represent values forming the upper and lower envelopes of the superposed plots of all data from these stations as functions of universal time (UT). The AU and AL indices are believed to describe the maximum strength of eastward and westward electrojet currents in the auroral latitude ionosphere, respectively. The difference, AU minus AL, defines the auroral electrojet (AE) index (AE = AU − AL). The AE index describes the sum of the maximum current strength of the two oppositely directed currents at two different points in local time and is commonly used as an index of global aurora activities. When a substorm is initiated, auroral electrojets are developed. Westward (eastward) electrojets lead to decreases (increases) in AL (AU), resulting in an increase in AE at the substorm onset. A commonly used method for identifying substorm onsets based on the AE index is to detect prompt decreases (increases) in AL (AE). Moreover, these extreme auroral electrojet activities represent extreme substorm activities. These substorms cause the stored energy in the magnetosphere to be released from the magnetotail to be injected into the auroral latitude ionosphere. The mechanisms of this energy injection have not been fully resolved. The study of extreme auroral geomagnetic activities allows for GIC hazard assessment in the auroral latitude and provides physical insight into the energy release and injection mechanisms in place during extreme substorms.
To estimate the occurrence of extreme auroral electrojet activities, we utilize extreme value theory (EVT) for AL, AU, and AE. EVT, a statistical theory that focuses on the behavior of the upper tail of a distribution function, has been previously applied to geomagnetic data for space weather studies. Tsubouchi and Omura (2007) evaluated long-term occurrence probabilities of extremely intense geomagnetic storm events by using the Dst index, which is a global geomagnetic index used in measuring geomagnetic storm magnitude. Thomson et al. (2011) studied extreme variations in magnetic fields by using digital 1-min data from 28 European observatories in a geomagnetic latitude range of 40.3°–73.9°. They evaluated the return level of the horizontal and declination of magnetic field variations at each observatory that might be observed once every 100 and 200 years. Other applications of EVT have been used in the context of space weather (energetic electrons) for satellite designs. O’Brien et al. (2007) estimated the extremely high fluxes of MeV electrons in the outer zone of radiation belts. In addition, Nakamura and Yoneda (2014) estimated the worst electron temperatures in the geostationary orbit.
In the present study, we begin with an analysis of AL and AU indices by outlining a statistical model of EVT. Next, we analyze the AE index, and we discuss the physical meaning of the statistical results.
The AL, AU, and AE datasets used in this study are available from the World Data Center for Geomagnetism (WDCG), Kyoto University, Japan (http://swdcwww.kugi.kyoto-u.ac.jp/index.html). The datasets consist of 1-min values of the auroral indices in 1996–2012, giving a total of 8,942,400 data points for each index. These datasets have been systematically calculated from digitally recorded data. Older datasets from 1975 to 1995 are also available from WDCG. However, because much of the older data is digitized from analog magnetogram paper records, it is not clear whether their accuracy is sufficient for an extreme region.
AL and AU indices
Numerical techniques are required to solve this. We use the R package “ismev” and “extRemes”; “R” is a free software environment for statistical computing and graphics (http://www.r-project.org/).
Generalized Pareto distribution (GPD) parameters for −AL and AU
−0.544 ± 0.097
654 ± 87
−1.180 ± 0.001
663 ± 0
Generalized Pareto distribution (GPD) parameters for AE
0.409 ± 0.338
97.0 ± 37.9
Influence of clustering
Event lists of −AL >3000 nT and AU >1500 nT
hh:mm (−hh:mm) UT
Number of data
We utilized the POT model of EVT for the AL, AU, and AE indices and presented statistical evidence for finite upper limits to AL and AU. The results suggest that the westward and eastward electrojet currents in the auroral latitude ionosphere have finite upper limits. These results appear to be contradictory to those reported by Thomson et al. (2011). In their research, the return levels of the horizontal magnetic field variations in the auroral latitude gradually increased with the return periods and appeared to have no upper limits. We attribute this discrepancy to differences in determining the GPD threshold μ. Although they set the threshold μ at 99.97 % for each variable at most observatories, we set the value at ~99.999 % for −AL. Because the auroral indices were derived from 12 stations and provided a substantially larger amount of information than that obtained by using the data of a single station, the number of data points in the extreme range was insufficient in the previous study.
Thomson et al. (2011) determined that the magnetic field return levels in the mid-latitude range of 53°–62° increase more than those in other latitude ranges. They suggest that the extreme auroral electrojet currents move southward from the normal auroral latitude to the mid-latitude as the active auroral oval extends and moves southward. The southward movement of the auroral electrojet currents is a possible explanation for the upper limits of −AL and AU because the induced field variations decrease with distance even if the auroral electrojet currents strengthen over mid-latitudes. However, the limited amount of further extreme data prevents us from concluding that the magnetic field variation has no upper limits. Therefore, we offer an additional possible hypothesis: the auroral electrojet currents themselves have upper limits. In text books (e.g., Baumjohann and Treumann 1997), substorms cause part of the stored energy in the magnetosphere to be released from the magnetotail to be injected into the auroral latitude ionosphere. The energy is dissipated by Joule heating due to auroral electrojet current flows in the ionosphere and the additional heating of the upper atmosphere. Although these mechanisms have not been fully resolved, it appears reasonable that the aural electrojet currents have upper limits because the stored energy in the earth’s finite-sized magnetosphere should have a physical upper limit. These analyses will provide physical insight into the energy release and injection mechanisms in place during extreme substorms.
Finally, we discuss the older dataset of the auroral indices. We determined that the mean excess function of −AL including the older dataset before 1995, particularly that before 1992, does not show a simple negative tendency linear slope shape in the extreme range; rather, the slope shape resembled that of AE. However, there is no method available to check the validity of the extreme dataset owing to difficulties in the digitization of the analog magnetogram data and the calibration of the data. Our findings of the auroral electrojet analysis are given as preliminary and not as final results. That is, new datasets should be added, and the influence of the clusters of extreme values requires more precise evaluation. Further research should include such improvements.
The authors thank Dr. Masahito Nosé for providing information on the extreme auroral electrojet indices events. The authors are also grateful to the referees for their constructive comments. The authors acknowledge World Data Center for Geomagnetism (Kyoto) for the use of the auroral electrojet index database. This work was partly supported by the NICT Science Cloud at National Institute of Information and Communications Technology.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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