 Article
 Open Access
Towards quantitative assessment of the hazard from space weather. Global 3D modellings of the electric field induced by a realistic geomagnetic storm
 Christoph Püthe^{1}Email author and
 Alexey Kuvshinov^{1}
https://doi.org/10.5047/eps.2013.03.003
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2013
 Received: 14 December 2012
 Accepted: 6 March 2013
 Published: 9 October 2013
Abstract
In order to estimate the hazard to technological systems due to geomagnetically induced currents (GIC), it is crucial to understand the response of the geoelectric field to a geomagnetic disturbance and to provide quantitative estimates of this field. Most previous studies on GIC and the geoelectric field generated during a geomagnetic storm assume a 1D conductivity structure of Earth. This assumption however is invalid in coastal regions, where the lateral conductivity contrast is large. In this paper, we investigate the global spatiotemporal pattern of the surface geoelectric field induced by a typical major geomagnetic storm in a conductivity model of Earth with realistic laterallyheterogeneous oceans and continents. Exploiting this model makes the problem fully 3D. Data from worldwide distributed magnetic observatories are used to construct a realistic model of the magnetospheric source. The results of our numerical studies show large amplification of the geoelectric field in many coastal regions. Peak amplitudes obtained with 3D modelling exceed the amplitudes obtained in a 1D model by at least a factor 2, even if the latter makes use of the local vertical conductivity structure. Lithosphere resistivity is a critical parameter, which governs both amplitude and penetration width of the anomalous electric field inland.
Key words
 Geomagnetic storms
 GIC
 geoelectric field
 3D modelling
1. Introduction
Eruptions at Sun’s surface (coronal mass ejections) blow large quantities of charged particles into space. The particle streams interact with Earth’s magnetic field, intensifying the westward directed magnetospheric ring current (Love, 2008). This phenomenon, leading to substantial temporal variations of the geomagnetic field, is known as geomagnetic storm. According to Faraday’s law of induction, the fluctuating geomagnetic field in turn generates an electric field and induces currents in Earth and grounded conducting networks, such as power grids and pipelines (Pirjola, 2000). These geomagnetically induced currents (GIC) can lead to severe damages of the power network, as happened, for example, 1989 in Quebec (Kappenman et al., 1997). Understanding the properties of the geoelectric field is a key consideration in estimating the hazard to technological systems from space weather (Pulkkinen et al., 2007).
So far, most studies of the geoelectric field in connection with GIC were performed on a regional or local scale, considering rather simplified models of the inducing geomagnetic source (see review paper of Thomson et al. (2009) for more details). In addition, most of the studies (except for the works by Beamish et al., 2002; Thomson et al., 2005 and Gilbert, 2005) employed the assumption of a onedimensional (1D) conductivity structure of Earth. But it is wellknown that the lateral conductivity contrast is large at oceanland interfaces, making the 1D assumption invalid in many coastal areas. The literature contains many publications (Parkinson and Jones, 1979; Cox, 1980; Fainberg, 1980; Rikitake and Honkura, 1985; Kuvshinov, 2008; among others) dealing with the study of the coastal (ocean) effect. However, these studies mainly concentrate on either the investigation of Earth’s mantle structure in the presence of oceans or the influence of the ocean effect on the geomagnetic field.
In this paper, we discuss a rigorous numerical scheme that aims to model on a global scale the geoelectric field induced by a geomagnetic storm as close to reality as possible. Based on this scheme, we investigate the global pattern of the geoelectric field during the main phase of the storm (when the largest amplitudes are expected), using a conductivity model of Earth with realistic laterallyheterogeneous oceans and continents, and exploiting a realistic model of the magnetospheric source. Note that estimating the geoelectric field during geomagnetic substorms (i.e. when the auroral currents are intensified, but not necessarily the ring current) is out of scope of this study. In Section 4.3 of this paper, we discuss how our approach could be modified in order to estimate the electric field induced by geomagnetic substorms.
The paper is organized as follows. Section 2 describes the conductivity model and explains the approach to construct the spatiotemporal model of the magnetospheric source and to calculate the geoelectric field. Section 3 presents the results of our numerical studies, both in terms of modelled time series at specific locations and of modelled snapshots of the global pattern. Discussion and conclusions are presented in Section 4.
2. Methods
2.1 Conductivity model
The importance of the underlying conductivity structure was tested by simulating induction in models with different 1D sections. Our basic 1D profile consists of a resistive lithosphere with a thickness of 100 km and a layered model underneath, derived from 5 years of CHAMP, Ørsted and SACC magnetic data by Kuvshinov and Olsen (2006). Previous model studies that aimed to investigate the ocean effect in S_{q} and D_{st} geomagnetic variations (Kuvshinov et al., 1999) demonstrated that the resistivity of the lithosphere is a key parameter, which governs the behaviour of the magnetic field at oceanland contacts. In order to investigate the effect of this parameter, lithosphere resistivities of 300 Ωm and 3000 Ωm were tested. Note that we do not account for lateral variations in the thickness and resistivity of the lithosphere; the reasoning for this is discussed in Section 4.2.
 (a)
Model derived by Kuvshinov and Olsen (2006) from satellite data with lithosphere of 300 Ωm (R = 3 · 10^{7} Ωm^{2})
 (b)
Model derived by Kuvshinov and Olsen (2006) from satellite data with lithosphere of 3000 Ωm (R = 3 · 10^{8} Ωm^{2})
 (c)
Model derived by Baba et al. (2010) for the Philippine Sea with lithosphere of 300 Ωm (R = 3 · 10^{7} Ωm^{2})
 (d)
Model derived by Baba et al. (2010) for the North Pacific with lithosphere of 3000 Ωm (R = 3 · 10^{8} Ωm^{2})
 (e)
Model derived by Baba et al. (2010) for the Philippine Sea (R = 5 · 10^{7} Ωm^{2})
 (f)
Model derived by Baba et al. (2010) for the North Pacific (R = 4 · 10^{8} Ωm^{2})
2.2 Derivation of the source model
A major geomagnetic storm, which had its maximum on November 20, 2003 with amplitudes of about 300 nT at Earth’ surface, is used as basis to construct a spatiotemporal model of the magnetospheric source. We have selected this storm due to its classical temporal form with clearly distinguishable main and recovery phases. For a tenday time segment starting on November 18, 2003, we assembled minute mean magnetic data of 72 worldwide distributed observatories, situated at geomagnetic latitudes equatorward of ±55° (cf. Fig. 1(a)). What follows is an explanation how we derive the spatiotemporal structure of the source using these data.
Finally we estimate the external coefficients by fitting the available data from the global net of observatories using the system of equations (17). We use an iteratively reweighted least squares algorithm (e.g. Aster et al., 2005) to assure the stability of the solution.
Two comments are relevant at this point. First, note that the source of geomagnetic storm variations is assumed to be largescale (at least at nonpolar latitudes), and therefore external coefficients of relatively low n and m (≤ 3) are used to describe its spatial structure. Second, to solve numerically Maxwell’s equations (15)–(16), i.e. to calculate and at Earth’s surface on a 1° × 1° mesh, an integral equation approach (Kuvshinov, 2008) is used. Values of at observatory locations are obtained by interpolation of the results obtained on the 1° × 1° mesh.
2.3 Calculation of the electric field
3. Results
3.1 Time series of the electric field at observatory locations

The electric field is subject to highfrequency oscillations during the geomagnetic storm, a clear peak phase (as usually observed for the magnetic field, cf. Fig. 3) is in general not recognizable.

1D modelling yields peak amplitudes of about 50 mV/km for both components in LZH. Peak amplitudes in HER are about 50 mV/km for E_{ φ } and about 20 mV/km for E_{ ϑ }. 1D modelling here implies the use of the local normal 1D structure of the 3D model (including the local conductance of the surface shell S, cf. Fig. 1(a)) and an individual solution of Maxwell’s equations at each grid point according to the methodology first presented by Srivastava (1966).

3D modelling increases the amplitudes of both field components by roughly a factor 2 in HER, but has only minor effects in LZH.

An increase in lithosphere resistivity from 300 Ωm to 3000 Ωm has virtually no effect for the 1D modelling results and only minor effects for the 3D modelling results obtained in LZH. However, both field components obtained with 3D modelling in HER are amplified, roughly by a factor 1.5.
3.2 Snapshots of the global pattern of the electric field
The results obtained in models (a) and (c) are very similar. As both models have the same lithosphere conductivity, but a different 1D stratification at greater depths, we conclude that the conductivity structure at depths greater than 100 km has only minor effects on the field pattern. The same conclusions can be made when comparing the results obtained in models (b) and (d). The field pattern obtained in model (e) (the original model derived by Baba et al. (2010) for the Philippine Sea) is similar to those obtained in models (a) and (c), but amplitudes appear to be slightly lower. Similarly, the pattern obtained in model (f) (the original model derived by Baba et al. (2010) for the North Pacific) is slightly less pronounced than the patterns obtained in models (b) and (d), and amplitudes are slightly lower. We attribute this difference to the increase in conductivity at shallow depths in the models derived by Baba et al. (2010) (cf. Fig. 1(b)).
A crosscomparison of both rows in Fig. 6 indicates that stronger and more pronounced fields are obtained in models with larger transversal resistance of the lithosphere. As the differences between the rows are significantly larger than those within each row, we conclude that our basic models (a) and (b) are good representatives and will thus in the following concentrate on the results obtained in models (a) and (b). Note that a comparison of E_{ φ } in the various models leads to the same conclusions, as well as the examination of snapshots at different instants.
We are especially interested in investigating the effects arising from the laterally nonuniform surface layer S. To this purpose, we present results in form of the “anomalous” electric field, which is computed as difference between our 3D modelling results and results obtained in a “local 1D” model. Local 1D modelling here implies the use of the local normal 1D structure of the 3D model (including the local conductance of the surface shell S) and a solution of Maxwell’s equations separately performed at each grid point. Expressions for the (frequency domain) electric field emerging due to induction by a source of our type in 1D conductivity models are presented in Appendix H of Kuvshinov and Semenov (2012).

As expected, the anomalous field is very small inside continents and oceans, but pronounced in regions where conductance varies laterally on short scales, especially at the coasts.

Largest amplitudes are observed at long east and west coasts, e.g. the Americas or southern Africa. This reflects the geometry of the source (the magnetospheric ring current).

An increase of lithosphere resistivity from 300 Ωm to 3000 Ωm leads to an amplification of the components of the anomalous electric field by roughly a factor 2 at coastal sites.

The penetration width of the anomalous field is also governed by lithosphere resistivity. Dependent on the site, massive enhancements are observed up to 400 km inland in the case of a 300 Ωm lithosphere and up to 600 km inland in the more resistive case (Fig. 8; note that 1° of longitude corresponds to 100 km in the profile through Australia and to 85 km in the profile through North America).

In latitudeparallel profiles through continents, the anomalous E_{ φ } exhibits an axial symmetry, while the anomalous E_{ ϑ } is antisymmetric. This observation confirms previous results by Kuvshinov et al. (1999) obtained in simplified conceptual models. Note that there is no enhancement of E_{ ϑ } at the Australian west coast for the chosen moment, cf. Fig. 8.
Our results stress the need of 3D modelling in an environment with large lateral variations in conductivity. The amplifications observed at coasts are at least on the same level as the maximum amplitudes obtained in 1D models. As previously shown in Fig. 4, using a 1D model might results in an underestimation of the peak amplitudes of the geoelectric field during a geomagnetic storm by a factor 2–3 at coastal sites. Due to the high temporal variability of the geoelectric field, coastal enhancements vary significantly during a geomagnetic storm.
4. Discussion and Conclusions
4.1 Summary
We have presented a numerical scheme for a time domain estimation of the global electric field induced by a geomagnetic storm with realistic spatiotemporal structure, derived from measurements of the horizontal component of the magnetic field at worldwide distributed observatories. A conductivity model of Earth’s interior with a realistic laterally heterogeneous surface layer representing oceans and continents was used.
The results could be obtained within a few hours, if the observatory data were available and preprocessed (edited, checked for consistency etc.). It is noteworthy that this estimate does not depend on the complexity and resolution of the 3D conductivity model, since the responses for induction in a given 3D model by elementary sources (in case of a geomagnetic storm described by spherical harmonics) can be calculated beforehand and archived. To obtain the geoelectric field for a specific storm, it is just necessary to reconstruct the spatiotemporal form of the external source responsible for this storm and to convolve the source field with the precomputed 3D responses. We believe that our numerical scheme would be a useful tool to estimate quantitatively the space weather hazard associated with excessive GIC arising in groundbased conductor networks (such as power lines) during major geomagnetic storms.
4.2 Effect of oceans and lithosphere
Model studies based on our numerical scheme revealed substantial differences between the electric fields generated in 3D and 1D models, even if the 1D model makes use of the local vertical conductivity structure. As expected, the differences are mainly marked at the coasts. The anomalous electric field, computed as difference between the electric fields obtained in 3D and 1D models, can penetrate up to more than 500 km inland (depending on the site and the local conductivity structure). Anomalous amplitudes are at least as large as the amplitudes calculated in a 1D model. Peak amplitudes of a geomagnetic storm at coastal sites are hence underestimated by a factor 2–3 when using a 1D model. The 3D modelling results state that coastal areas are in danger of experiencing electric field amplitudes of up to 200 mV/km during a typical magnetic storm. Long east and west coasts like the Americas, southern Africa or Australia and narrow land bridges like Panama seem to be especially endangered.
The resistivity of the lithosphere is a critical parameter when estimating amplitudes of the electric field. Resistivities of 300 Ωm and 3000 Ωm, representing realistic boundary values for Earth’s lithosphere, were tested in this study. Lithosphere resistivity mainly affects the electric field at coastal sites. The amplitudes of the anomalous electric field were doubled in the model with a lithosphere of 3000 Ωm, and the “coastal region”, in which the anomalous field shows enhanced amplitudes, was significantly wider. The influences of the conductivity distribution at greater depths and the precise stratification within the lithosphere on the results were minor in comparison with the integrated lithosphere resistivity.
According to our modelling results, a precise estimate of the lithosphere resistivity in the region of interest is crucial in order to obtain a trustworthy estimate of the actual electric field. In this study, we considered a model with a lithosphere of laterally uniform thickness and resistivity. While the chosen lithosphere thickness of 100 km agrees with the global average, it is wellknown that lithosphere thickness is very variable on Earth and ranges from few km at midocean ridges to several 100 km below old continental shields. The choice of a laterally uniform lithosphere is thus a limitation of our work; it was however necessary, since thickness and resistivity of the lithosphere are poorly resolved on a global scale. We want to stress in this context that the numerical solution discussed in this paper is fully 3D and thus can readily adopt models with a laterally variable lithosphere once reliable information about such variability is available.
4.3 Estimates of the electric field at polar latitudes
In this paper, we discussed the geoelectric field induced by a largescale magnetospheric source that dominates in midlatitudes. However, it is well known that one can expect larger signals in polar regions due to substorm geomagnetic disturbances (Pirjola and Viljanen, 1994). The recovery of the spatiotemporal structure of the auroral ionospheric source, which is responsible for this activity, is more challenging due to the large variability of the auroral source both in time and space.
One of the ways to determine realistic auroral currents on a semiglobal scale (in the whole polar cap) consists of collecting the data from highlatitude geomagnetic observatories and polar magnetometer arrays (e.g. IMAGE and MIRACLE arrays in Scandinavia, DTU and MAGIC arrays in Greenland, CARISMA array in Canada etc.) and then reconstructing the auroral current, for example by exploiting an approach based on elementary current systems (e.g. Amm, 2001; Sun and Egbert, 2012). Note that this approach was used by Pulkkinen and Engels (2005), who analysed the influence of 3D induction effects on ionospheric currents during geomagnetic substorms.
Once the auroral source is quantified, a similar numerical scheme as described above, however with two modifications, can be implemented in order to calculate the geoelectric field caused by a geomagnetic substorm. One modification concerns the description of the substorm source— instead of using a spherical harmonics representation, one can mimic the auroral ionospheric current by elementary current systems. Another modification applies to the 3D conductivity model. Since substorm magnetic variations are characterized by periods between a few tens of seconds and tens of minutes, one cannot exploit a model in which the surface layer is approximated by a thin shell, as it was done in this paper. The variable thickness of this layer is important in this period range, thus a full 3D model (including bathymetry) should be considered. However, as mentioned in Section 4.1, the complexity and resolution of the 3D conductivity model has no effect on the computational cost of the source modelling for a specific substorm. As in the case of a largescale geomagnetic storm, a model of the electric field due to a specific substorm for the whole polar cap could be obtained within a few hours when using a standard workstation for computations. Note again that this estimate does not account for the efforts of collecting and preprocessing the data and for the 3D calculations of the magnetic field due to elementary sources.
Semiglobal estimates of the geoelectric field induced by a realistic geomagnetic substorm in a realistic 3D conductivity model accounting for bathymetry and nonuniform lithosphere will be the subject of a subsequent publication.
Declarations
Acknowledgments
The authors express their gratitude to the staff of the geomagnetic observatories who have collected and distributed the data. We thank Dr. Alan Thomson for discussion on the manuscript and Dr. Ikuko Fujii and an anonymous reviewer for helpful comments. This work has been supported by the Swiss National Science Foundation under grant No. 2000021140711/1.
Authors’ Affiliations
References
 Amm, O., The elementary current method for calculating ionospheric current systems from multisatellite and ground magnetometer data, J. Geophys. Res., 106, 24843–24855, 2001.View ArticleGoogle Scholar
 Aster, R. C., B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, Elsevier Academic Press, 2005.Google Scholar
 Baba, K., H. Utada, T. Goto, T. Kasaya, H. Shimizu, and N. Tada, Electrical conductivity imaging of the Philippine Sea upper mantle using seafloor magnetotelluric data, Phys. Earth. Planet. Inter., 183, 44–62, 2010.View ArticleGoogle Scholar
 Beamish, D., T. D. G. Clark, E. Clarke, and A. W. P. Thomson, Geomagnetically induced currents in the UK: Geomagnetic variations and surface electric fields, J. Atmos. Sol. Terr. Phys., 64, 1779–1792, 2002.View ArticleGoogle Scholar
 Cox, C. J., Electromagnetic induction in the oceans and inferences on the constitution of the earth, Geophys. Surv., 7, 137–156, 1980.View ArticleGoogle Scholar
 Everett, M. E., S. Constable, and C. G. Constable, Effects of nearsurface conductance on global satellite induction responses, Geophys. J. Int., 153, 277–286, 2003.View ArticleGoogle Scholar
 Fainberg, E. B., Electromagnetic induction in the world ocean, Geophys. Surv., 4, 157–171, 1980.View ArticleGoogle Scholar
 Gilbert, J., Modeling the effect of the oceanland interface on induced electric fields during geomagnetic storms, Space Weather, 3, doi:10.1029/2004SW000120, 2005.Google Scholar
 Kappenman, J., L. Zanetti, and W. Radasky, Geomagnetic storms can threaten electric power grid, Earth in Space, 9, 9–11, 1997.Google Scholar
 Kuvshinov, A., 3D Global induction in the oceans and solid Earth: recent progress in modeling magnetic and electric fields from sources of magnetospheric, ionospheric and oceanic origin, Surv. Geophys., 29, 139–186, 2008.View ArticleGoogle Scholar
 Kuvshinov, A. and N. Olsen, A global model of mantle conductivity derived from 5 years of CHAMP, Ørsted, and SACC magnetic data, Geophys. Res. Lett., 33, doi:10.1029/2006GL027083, 2006.Google Scholar
 Kuvshinov, A. and A. Semenov, Global 3D imaging of mantle electrical conductivity based on inversion of observatory Cresponses I. An approach and its verification, Geophys. J. Int., 189, doi:10.1111/j.1365–246X.2011.05349.x, 2012.Google Scholar
 Kuvshinov, A. V., D. B. Avdeev, and O. V. Pankratov, Global induction by Sq and Dst sources in the presence of oceans: bimodal solutions for nonuniform spherical surface shells above radially symmetric Earth models in comparison to observations, Geophys. J. Int., 137, 630–650, 1999.View ArticleGoogle Scholar
 Laske, G. and G. Masters, A global digital map of sediment thickness, Eos Trans. AGU, 78, F483, 1997.Google Scholar
 Love, J. J., Magnetic monitoring of Earth and space, Physics Today, 61, 31–37, 2008.View ArticleGoogle Scholar
 Manoj, C, A. Kuvshinov, S. Maus, and H. Luehr, Ocean circulation generated magnetic signals, Earth Planets Space, 58, 429–437, 2006.View ArticleGoogle Scholar
 Olsen, N. and A. Kuvshinov, Modeling the ocean effect of geomagnetic storms, Earth Planets Space, 56, 525–530, 2004.View ArticleGoogle Scholar
 Parkinson, W. D. and F. W. Jones, The geomagnetic coast effect, Rev. Geophys., 17, 1999–2015, 1979.View ArticleGoogle Scholar
 Pirjola, R., Geomagnetically induced currents during magnetic storms, IEEE Trans Plasma Sci, 28, 1867–1873, 2000.View ArticleGoogle Scholar
 Pirjola, R. and A. Viljanen, Geomagnetically induced currents in the Finnish highvoltage power system, a geophysical review, Surv. Geophys., 15, 383–408, 1994.View ArticleGoogle Scholar
 Pulkkinen, A. and M. Engels, The role of 3D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data, Ann. Geophys., 23, 909–917, 2005.View ArticleGoogle Scholar
 Pulkkinen, A., M. Hesse, M. Kuznetsova, and L. Rastatter, First principles modeling of geomagnetically induced electromagnetic fields and currents from upstream solar wind to the surface of the Earth, Ann. Geophys., 25, 881–893, 2007.View ArticleGoogle Scholar
 Rikitake, T. and Y. Honkura, Developments in Earth and planetary sciences, in Solid Earth Geomagnetism, vol. 5, edited by Rikitake, T., Terra Scientific Publishing Company, 1985.Google Scholar
 Srivastava, S. P., Theory of the magnetotelluric method for a spherical conductor, Geophys. J. R. Astron. Soc., 11, 373–387, 1966.View ArticleGoogle Scholar
 Sun, J. and G. Egbert, Spherical decomposition of electromagnetic fields generated by quasistatic currents, Int. J. Geomath., 3, 279–295, 2012.View ArticleGoogle Scholar
 Thomson, A. W. P., A. J. McKay, E. Clarke, and S. J. Reay, Surface electric fields and geomagnetically induced currents in the Scottish Power grid during the 30 October 2003 geomagnetic storm, Space Weather, 3, doi:10.1029/2005SW000156, 2005.Google Scholar
 Thomson, A. W. P., A. J. McKay, and A. Viljanen, A review of progress in modelling of induced geoelectric and geomagnetic fields with special regard to induced currents, Acta Geophys., 57, 209–219, 2009.View ArticleGoogle Scholar