Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Viljanen, A.; Pulkkinen, A.; Amm, O.; Pirjola, Risto; Korja, T.

doi:10.5194/angeo-22-101-2004

Cited by 105 publications

(112 citation statements)

References 39 publications

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“…Then we interpolated the magnetic field at VKH and calculated GIC from the electric field applying Eq. (10) (this simplification is a good approximation as shown by Viljanen et al 2004). We tested two different conductivity models.…”

Section: Gic In the North-west Russian Power Gridmentioning

confidence: 99%

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Continental scale modelling of geomagnetically induced currents

Viljanen

Pirjola

Wik³

et al. 2012

J. Space Weather Space Clim.

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The EURISGIC project (European Risk from Geomagnetically Induced Currents) aims at deriving statistics of geomagnetically induced currents (GIC) in the European high-voltage power grids. Such a continent-wide system of more than 1500 substations and transmission lines requires updates of the previous modelling, which has dealt with national grids in fairly small geographic areas. We present here how GIC modelling can be conveniently performed on a spherical surface with minor changes in the previous technique. We derive the exact formulation to calculate geovoltages on the surface of a sphere and show its practical approximation in a fast vectorised form. Using the model of the old Finnish power grid and a much larger prototype model of European high-voltage power grids, we validate the new technique by comparing it to the old one. We also compare model results to measured data in the following cases: geoelectric field at the Nagycenk observatory, Hungary; GIC at a Russian transformer; GIC along the Finnish natural gas pipeline. In all cases, the new method works reasonably well.

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Section: Gic In the North-west Russian Power Gridmentioning

confidence: 99%

“…We apply the method of spherical elementary current systems (SECS) to calculating the geoelectric field as outlined by Viljanen et al (2004). The first task is to determine ionospheric equivalent currents in terms of elementary systems.…”

Section: Geoelectric Fieldmentioning

confidence: 99%

Continental scale modelling of geomagnetically induced currents

Viljanen

Pirjola

Wik³

et al. 2012

J. Space Weather Space Clim.

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“…Although modelling of GIC for past events is fairly straightforward (e.g. Pirjola, 2002;Viljanen et al, 2004), forecasting GIC based on physical models from the solar wind down to the ground is still highly challenging (e.g. Pulkkinen et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Climatology of rapid geomagnetic variations at high latitudes over two solar cycles

Viljanen

Tanskanen

2011

Ann. Geophys.

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Abstract.We investigate the characteristics of rapid geomagnetic variations at high latitudes based on the occurrence of large time derivatives of the horizontal magnetic field (dH /dt exceeding 1 nT s −1 ). Analysis of IMAGE magnetometer data from North Europe in 1983-2010, covering more than two solar cycles, confirms and specifies several previous findings. We show that dH /dt activity is high around the midnight and early morning hours, and nearly vanishes at noon and early afternoon. This happens during all seasons, although the midnight maximum is nearly invisible during summer. As indicated by modelled ionospheric equivalent currents, large dH /dt values occur predominantly during westward ionospheric electrojets. Before and around midnight, dH /dt tends to be north-south oriented, whereas in the morning hours, its direction is more west-east directed. dH /dt tends to be more strictly north-south oriented during winter than other seasons. The seasonal occurrence of large dH /dt values is similar to the variation of the maximum amplitude of westward equivalent currents. The yearly fraction of east-west directed large dH /dt vectors at the Kilpisjärvi station (MLAT 65.88) varies from 31 to 47 % without any clear correlation with the general geomagnetic activity nor with the yearly averages of solar wind parameters.

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“…We begin by showing that in 1-D cases, the divergencefree currents determined from satellite data with the relatively new 1-D SECS method equal the equivalent currents obtained from ground measurements with the already wellestablished 2-D SECS method (Amm, 1997;Amm and Viljanen, 1999;Pulkkinen et al, 2003;Viljanen et al, 2004). For this purpose, we have used 124 1-D passes of the CHAMP satellite over the IMAGE (International Monitor for Auroral Geomagnetic Effects; Lühr et al, 1998; http://space.fmi.fi/ image/) magnetometer network during 2001 and2002.…”

Section: Introductionmentioning

confidence: 99%

A model for estimating the relation between the Hall to Pedersen conductance ratio and ground magnetic data derived from CHAMP satellite statistics

et al. 2007

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Abstract. The goal of this study is to find a way to statistically estimate the Hall to Pedersen conductance ratio α from ground magnetic data. We use vector magnetic data from the CHAMP satellite to derive this relation. α is attained from magnetic satellite data using the 1-D Spherical Elementary Current Systems (SECS). The ionospheric equivalent current density can either be computed from ground or satellite magnetic data. Under the required 1-D assumption, these two approaches are shown to be equal, which leads to the advantage that the statistics are not restricted to areas covered by ground data. Unlike other methods, using magnetic satellite measurements to determine α ensures reliable data over long time sequences. The statistical study, comprising over 6000 passes between 55 • and 76.5 • northern geomagnetic latitude during 2001 and 2002, is carried out employing data from the CHAMP satellite. The data are binned according to activity and season. In agreement with earlier studies, values between 1 and 3 are typically found for α. Good compatibility is found, when α attained from CHAMP data is compared with EISCAT radar measurements. The results make it possible to estimate α from the east-west equivalent current density J φ [A/km]: α=2.07/(36.54/|J φ |+1) for J φ <0 (westward) and α=1.73/(14.79/|J φ |+1) for J φ >0 (eastward). Using the same data, statistics of ionospheric and field-aligned current densities as a function of geomagnetic latitude and MLT are included. These are binned with respect to activity, season and IMF B Z and B Y . For the first time, all three current density components are simultaneously studied this way on a comparable spatial scale. With increasing activity, the enhancement and the equatorward expansion of the electrojets and the R1 and R2 currents is observed, and in the nightside, possible indications of a Cowling channel appear. During southward IMF B Z , the electrojets and the R1 and R2 currents are stronger and clearer than during northward B Z . IMF B Y affects the orientation of the pattern.

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Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Cited by 105 publications

References 39 publications

Continental scale modelling of geomagnetically induced currents

Continental scale modelling of geomagnetically induced currents

Climatology of rapid geomagnetic variations at high latitudes over two solar cycles

A model for estimating the relation between the Hall to Pedersen conductance ratio and ground magnetic data derived from CHAMP satellite statistics

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