© A. Viljanen et al., Published by EDP Sciences 2026

1 Introduction

1.1 General

A severe space storm is likely to cover a wide variety of physical phenomena and has the potential to cause significant technological and economic impacts in space and on the ground (cf. Schrijver et al., 2015; Eastwood et al., 2017; Oughton et al., 2018; Hapgood et al., 2021). Geomagnetically induced currents (GIC) are a well-known and widely investigated example of the impacts of space weather (Boteler et al., 1998; Molinski, 2002; Pulkkinen et al., 2017). The 1859 Carrington storm (Carrington, 1859; Hodgson, 1859) has become a standard benchmark of an extreme event (Clauer & Siscoe, 2006). Sporadic magnetic field recordings of the event show that it clearly exceeded the magnitude of any storm recorded during the Space Age. Quite a comparable geomagnetic storm occurred in 1921 (Hapgood, 2019), causing global impacts on the most advanced technology at the time (telegraph and telephone systems, radio communication). There is also a lot of evidence that the storm on 4 February 1872 belongs to the group of similar extreme cases (Hayakawa et al., 2023; Usoskin et al., 2023, Sect. 7.3.4). The estimated probability of a Carrington-class event is approximately 10% in a decade, although this contains fairly large uncertainties (e.g., Riley & Love, 2017). Consequently, a Carrington-class superstorm is a low probability, high-impact event. In particular, its global consequences could be unequalled.

GIC can potentially cause substantial problems in power grids. This was demonstrated by the province-wide blackout in Québec, Canada, in Mar 1989 (Bolduc, 2002) and a local disturbance in Malmö, Sweden, during the Halloween storm on 29–31 Oct 2003 (Pulkkinen et al., 2005). However, extreme solar storms, as witnessed in the past, have not occurred since the introduction of the extensive high-voltage power grids in the mid-1900s, and the technological development that has taken place since.

Many countries have identified space weather in general, and GIC in particular, as a potential hazard in national risk assessments (Cabinet Office, 2023; Kevin, 2023; Ministry of the Interior, 2023). In Finland, the National Emergency Supply Agency commissioned a study in 2022 to gather information about extreme space weather storms and their impacts on vital technological systems, concentrating on power grids and satellites (Viljanen et al., 2022). Hapgood et al. (2021) describe how worst-case scenarios of a wide variety of space weather phenomena have been developed in the UK to support risk assessments, and a recent extensive update focusing on the UK critical infrastructure has been compiled by Allcock et al. (2025). In the European context, GIC-related problems with their indirect impacts have been estimated to cause expensive problems for modern society (European Commission, 2024, p. 345–350, p. 365), leading to costs of about 400–500 MEUR.

The goal of this paper is to provide a quantitative estimate of the magnitude of a Carrington-scale storm. We focus on the GIC aspect and consider the time derivative of the ground magnetic field and especially the modelled geoelectric field, which is the driver of GIC. We utilize a global simulation of the Carrington event in 1859 (Blake et al., 2021), from which we obtain the modelled ground magnetic field around the world. When combined with a 3-dimensional (3-D) ground conductivity model, this results in an estimated electric field. It is then compared to data-based results of the Halloween storm, of which extensive magnetometer recordings are available in Fennoscandia.

Next, in Section 1.2 we discuss some of the largest historic storms and extreme value estimates to provide a reference point to the magnetic field values simulated by Blake et al. (2021). Then in Section 2 we present an overview of the simulated ground magnetic field as it is used as input to the modelling of the geoelectric field (Sect. 3). In Discussion (Sect. 4), we describe uncertainties and challenges related to present simulations of extreme events.

1.2 Historic storms

We describe briefly three very large historic magnetic storms, which were also considered by Kappenman (2005). Magnetic activity in the northern hemisphere is summarised by the SuperMAG (Gjerloev, 2012) indices SMU and SML. These indices, with their extensive latitudinal coverage are more useful in characterizing extreme storm activity in the expanded auroral oval than the traditional AE-indices (Davis & Sugiura, 1966). As explained in Newell & Gjerloev (2011), baseline subtracted magnetometer data are transformed into coordinates with the H component pointing toward local magnetic north. Then the station with the largest H value gives the SMU value, while the station with the smallest value gives SML. The SuperMAG portal provides these indices based on northern hemisphere stations within the geomagnetic latitude range 40–80 (see https://supermag.jhuapl.edu/indices/?tab=description).

Figure 1 shows the SMU and SML indices during the most intense phases of three storms: 13–14 Jul 1982, 13–14 Mar 1989, and 29–30 Oct 2003. The first event is the largest one in terms of these indices: SMU reaches values up to about 2000 nT, and SML nearly reaches −5000 nT. The number of magnetometer stations was slightly more than 15 for the 1982 event, about 30 for the 1989 event, and about 100 for the 2003 event. Therefore, it is possible that, especially for the 1982 event, SMU and SML are not fully representative due to a sparse coverage of observations. It is good to recognize that the capability of SuperMAG to catch activity at lower latitudes has also improved with years. The number of stations below the magnetic latitude 60° has increased from ~10 to ~70 from the year 1982 to 2003.

Figure 1 SuperMAG activity indices SMU and SML during the most intense phases of three geomagnetic storms. From top: 13–14 Jul 1982, 13–14 Mar 1989, 29–30 Oct 2003. Black arrows indicate the times of the power grid impacts mentioned in the text. On 13–14 Jul 1982, the smallest value of SML is −4714 nT, and the largest value of SMU is 2131 nT.

All three storms have some reported GIC impacts on power grids. During the 1982 event, four transformers and 15 power lines were tripped in the Swedish high-voltage power system (Wik et al., 2009). Furthermore, Swedish railways experienced some traffic light signals erroneously turning red. The 1989 storm can be regarded as the most severe example as it caused a province-wide blackout of several hours in Québec, Canada (Bolduc, 2002). The 2003 storm caused a regional blackout in Malmö in southern Sweden (Pulkkinen et al., 2005).

The largest GIC event in the Finnish natural gas pipeline occurred on 29–31 Oct 2003 (Fig. 2). The maximum value of about 57 A was reached soon after the beginning of the storm, followed by nearly continuous high activity for approximately 24 h. Consistent with a lower global activity as indicated by the SML index in Figure 1, the daytime of 30 Oct was rather quiet. Another major activation occurred in the evening and continued until the early afternoon of 31 Oct.

Figure 2 Measured GIC along the Finnish natural gas pipeline at Mäntsälä in southern Finland on 29–31 Oct 2003. The time cadence was 10 s. Dashed lines indicate the magnetic midnight (blue) and noon (red). Positive GIC flows to the east.

Large GIC values are more likely during local night time (Viljanen et al., 2014), associated with auroral substorms and pulsations (Juusola et al., 2023). The GIC events described above seem to belong to this category as they appeared during pre- or post-midnight local times and at magnetic latitudes 50–60° which refers to substorm activity in an expanded auroral oval. However, the largest storms can additionally show high GIC activity at any other time of the day, as the Halloween example demonstrates. It is also possible that impacts occur predominantly in the daytime, as witnessed during the March 1940 storm with numerous distortions in long-line US communication systems as driven by two subsequent Sudden Storm Commencements (SSCs) and dayside reconnection (Love et al., 2023).

During the storm on 10–11 May 2024, there were a large number of public and social media reports of aurora displays down to exceptionally low magnetic latitudes around 30° (e.g., Grandin et al., 2024). In terms of the Dst index, this event was equally large to the Halloween storm in 2003 (Lazzús & Salfate, 2024). Substantial GICs of up to 30 A were measured on 10 May 2024 in Mexico at a low-latitude substation at (19.72° N, 96.41° W), corresponding to the geomagnetic latitude ~28° according to https://wdc.kugi.kyoto-u.ac.jp/igrf/gggm/ (Caraballo et al., 2025). In New Zealand, the national grid operator enacted a country‐wide GIC mitigation plan (Clilverd et al., 2025; Mac Manus et al., 2025). In Sweden, GIC disturbances in the 400 kV power grid led to a disconnection of a DC cable between Sweden and Poland on 10 May 2024 at 22:29 UT (Rosenqvist et al., 2025). Additionally, citizen scientists have reported on a few incidents of power cuts or unstable power (Grandin et al., 2024, Table 1), but their connection to geomagnetic variations is not confirmed. This storm will obviously become a benchmark thanks to comprehensive availability of abundant space weather data.

1.3 Extreme value estimates

The three large events discussed above represent some of the largest geomagnetic storms within the modern high-technological era. However, there is clear evidence based on sporadic data that the Sep 1859 Carrington storm (Clauer & Siscoe, 2006), a comparable event in May 1921 (Hapgood, 2019; Love et al., 2019) and the storm in Feb 1872 (Hayakawa et al., 2023) were stronger. To assess the magnitude of very rare events, statistical extrapolations of high-cadence geomagnetic data have been widely performed. We do not discuss the details of these studies, but refer to the investigation by Rogers et al. (2020), who produced a global model of extreme geomagnetic field variations. Especially, they considered the time derivative of the horizontal field vector ($|\mathrm{d}\mathbf{H}/\mathrm{d}t|\mathrm{ }=\sqrt{(\mathrm{d}{B}_x/\mathrm{d}t{)}^2+(\mathrm{d}{B}_y/\mathrm{d}t{)}^2}$), which is a proxy for GIC (B_x and B_y are the north and east components of the ground magnetic field variation).

A relevant result for our case is presented in Figure 3. It shows how the expected magnitude of |dH/dt| increases as a function of the return period, which is intuitively clear. More importantly, the location of the largest |dH/dt| moves equatorward with an increasing return period. Figure 3 represents an averaged result based on spline fit, so much larger estimates of |dH/dt| appear at some locations (see Rogers et al., 2020, for detailed results). As Love & Mursula (2024, Sect. 9) note, the largest measured rate of change at Colaba on 2 Sep 1859 was ~245 nT/min, which corresponds to a 1-in-500 year event (Fig. 3, CGM latitude ~10°; Rogers et al. (2020)).

Figure 3 Return levels of |dH/dt| for a range of return periods as derived by Rogers et al. (2020, Fig. 4d).

We note that extreme value estimates are based on statistical methods, so they may fail for really extraordinary events (cf. Sornette & Ouillon, 2012). Furthermore, these methods cannot provide snapshot estimates of vectors over a region. For GIC modelling, the horizontal geoelectric field is needed to be able to calculate voltages in technological conductors and further calculate induced currents. So, we prefer first-principle methods as described next.

2 Data

We will now summarise the most relevant characteristics of the simulated ground magnetic field by Blake et al. (2021). A global overview of the time derivative of the horizontal ground magnetic field (|dH/dt|) from the simulation is presented. Since the simulation plays a central role in our study, we will assess its validity and provide arguments to justify its use separately in Section 4.

2.1 Simulated Carrington storm

A physics-based description of an extreme magnetic storm was presented by Blake et al. (2021). They carried out simulations using the Space Weather Modeling Framework (SWMF) (Gombosi et al., 2021) with an aim to reproduce the horizontal magnetic field disturbance measured at Colaba, India, at the beginning of the Carrington event. The disturbance was observed near the magnetic equator at noon, and consisted of a sharp decrease of ~1600 nT over two hours followed by a rapid increase of ~1250 nT over 20 min.

Blake et al. (2021) used synthetic solar wind conditions at L1 to drive the Block-Adaptive-Tree-Solar wind-Roe-Upwind-Scheme (BATS-R-US) magnetohydrodynamic (MHD) magnetosphere model coupled to the Rice Convection Model (RCM) for the inner magnetosphere and the Ridley Ionosphere Model (RIM). As noted by the authors, this combination has been shown to perform well when statistically replicating geomagnetic disturbances. Because the aim of Blake et al. (2021) was to reproduce the Colaba disturbance by extreme compression of the magnetopause due to extreme solar wind dynamic pressure, they used the measured horizontal magnetic field time series from Colaba as a template for the shape of the solar wind magnetic field, velocity, particle density, and temperature. The resulting peak values for the solar wind velocity (2500 km/s), density (96 cm⁻³), and Bz (−116 nT) were large, but not unreasonable, as discussed by the authors. Blake et al. (2021) used three scenarios, of which we have applied results from their “Scenario 1”, in which the solar wind parameters follow the measured magnetic field at Colaba around the peak period.

In Blake et al. (2021), the position of the magnetic axis at the start of the run was set such that the magnetic north pole was at its approximate position in 1859: (69.174° N, 96.757° W), based on the International Geomagnetic Reference Field (IGRF) model. However, a more physical choice would obviously have been the IGRF geomagnetic north pole. Its location in 1900 was about (78.68° N, 68.79° W) and presently (2025) about (80.8° N, 72.8° W), i.e., only slightly changed in 125 years (Alken et al., 2021, Table 4). The dipole strength of the Earth was 32000 nT, whereas it is presently approximately 29400 nT, i.e., about 10% weaker (Alken et al., 2021, Table 2). To mimic the present conditions, we shifted the original simulation results to a spherical coordinate system with its north pole equal to the IGRF geomagnetic north pole in 2025. This is a minor change, since we assume that the difference in the dipole tilt angle does not have any significant effect on the simulated ground magnetic field. We also note that the geomagnetic latitude is relevant for our purposes. So, for example, maps with polar views shown later in this paper can be rotated around the geomagnetic pole to place maximal disturbances at a desired location.

In this study, we use the simulated horizontal ground magnetic field (north and east components) expressed in geomagnetic coordinates (see Acknowledgements for the link to the data). We use northern hemisphere data given at latitudes from 0.5 to 84.5 deg at 1 deg step and at longitudes from 0.5 to 359.5 deg at 1 deg step. Altogether, there are 30 600 ground points. The time cadence is 1 min.

2.2 Global magnetic field variations according to the Carrington simulation

In Figure 4, we show the maximum and minimum variation of the northward ground magnetic field in the northern hemisphere, i.e., activity indicators similar to the SMU and SML indices (one minute resolution in time, one degree resolution in latitude and longitude). To be consistent with the online SuperMAG indices, data within the geomagnetic latitude range 40–80 were used. However, including all northern hemisphere data gives nearly identical curves. The smallest SML is −5146 nT, and the largest SMU is 3369 nT. For comparison, the range of the northward variation field based on all SuperMAG stations in the northern hemisphere from 1976 to 2023 was from −4712 nT to 2180 nT and of the eastward field, the range was from −2514 nT to 2734 nT (Rodríguez-Zuluaga et al., 2024, Fig. 7). The times of these values are not given, but the extremes of the northward field are very close to the SML and SMU indices on 13–14 Jul 1982 (Fig. 1). Consequently, the simulated values of the northward field variation during the Carrington storm are not very much larger than the most extreme ones observed since 1976. We remark that the simulated field is only due to the external sources in the ionosphere and magnetosphere, i.e. the contribution by telluric currents is omitted. Consequently, the SML and SMU indices in Figure 4 may be underestimated (cf. Juusola et al., 2020). Additionally, the incapability of the simulation to model substorms may produce underestimation. For more details, see the discussion about these issues in Section 4.1.

Figure 4 Maximum and minimum northward variation of the ground magnetic field in the northern hemisphere as calculated from a simulated Carrington event and mimicking the SuperMAG activity indices SMU (red) and SML (blue).

The time derivative of the horizontal field components is shown in Figure 5 at the location (62.5 N, −95.5 E) where |dH/dt| reaches its maximum (5044 nT/min) in the northern hemisphere. It is noteworthy that the time derivative of the geomagnetic east component (dY/dt) is notably larger than that of the north component (dX/dt). However, further elaboration of this feature is beyond the scope of this study. The largest |dH/dt| in the northern hemisphere as a function of geomagnetic latitude is shown in Figure 6. The largest measured $|d\mathbf{H}/\mathrm{dt}|$ from 1-min data known to the authors is marked in the plot as well (about 2700 nT/min; see Kappenman, 2005). This is later used as a threshold of an extremely large event. We concentrate here only on the northern hemisphere, from which most of the measured data are available.

Figure 5 Time derivative of the north (dX/dt) and east (dY/dt) component of the magnetic field at the location in the northern hemisphere with the largest |dH/dt| of the simulated Carrington event.

Figure 6 The largest time derivative of the horizontal ground magnetic field (|dH/dt|) in the northern hemisphere as calculated from a simulated Carrington event. The red dot shows the largest known 1-min value, which was recorded at the Lovö observatory in Sweden on 13 Jul 1982.

In terms of |dH/dt|, the largest phase of the simulated storm concentrates on 2 Sep 1859 at 06:10–06:38 UT when it exceeded 2700 nT/min at least at one location. Simulated activity indices (Fig. 4) show another smaller activation after about 12 UT, seen as the general downward trend of SML, upward trend of SMU and a sharper dip in SML and SMU at 14 UT. However, there is no large |dH/dt| (Fig. 5), so we do not discuss these features further. Figure 7 shows the largest |dH/dt| along each meridian at 1° separation in the northern hemisphere at 06:10–06:38 UT. At about half of all meridians, the maximum |dH/dt| exceeds the known historic record of 2700 nT/min. Figure 8 shows all locations where |dH/dt| exceeded 2700 nT/min at 06:10–06:38 UT. The largest continuous “hot spot” covers an area corresponding to a continental size and lasts for 3–4 h in MLT. As the snapshot at 06:28 UT of Figure 8 indicates, very large |dH/dt| occur simultaneously at a very wide range of longitudes.

Figure 7 Upper panel: The largest time derivative of the horizontal ground magnetic field (|dH/dt|) along each meridian (1° separation) in the northern hemisphere as calculated from the simulated Carrington event at 06:10–06:38 UT on 2 Sep 1859. Red dots indicate values exceeding the largest known measured value (2700 nT/min) at the Lovö observatory in Sweden on 13 Jul 1982 and also marked as a dashed line. Lower panel: geomagnetic latitude of the site of maximum |dH/dt| at each longitude. Red colour is used similarly to the upper panel.

Figure 8 Left: Polar view of “hot spots” where |dH/dt| exceeded 2700 nT/min (red) or 1350 nT/min (black) at least once at 06:10–06:38 UT during the simulated Carrington storm on 2 Sep 1859. Right: Snapshot at 06:28 UT, when the number of points with |dH/dt| > 2700 nT/min reached its maximum of the whole event. Geomagnetic latitudes are used.

Some relation between |dH/dt| and GIC risk can be based on Rosenqvist et al. (2022, Table 5), who state that |dH/dt| exceeding 1500 nT/min could cause large voltage fluctuations and temporary loss of the 400 kV and 220 kV lines across Sweden. Therefore, we show in Figure 8 also regions with |dH/dt| exceeding 1350 nT/min (half of the known record), which is close to the aforementioned threshold.

Broadly speaking, the simulated Carrington storm shows similar features to observed events. The SMU and SML indicators of Figure 4 reach slightly larger values than the historic events in Figure 1. The time derivative |dH/dt| in Figure 6 has quite a similar overall latitudinal distribution as extreme value estimates suggest (Fig. 3). A small difference is that the simulation does not show an increase of |dH/dt| close to the equator, which may be due to technical limitations of the simulation. We do not discuss these very low latitude regions in this paper. However, we note a possibility of GIC effects during extreme events at those locations based on the impacts on telegraph communication between Cairo and Khartoum on 4 Feb 1872 (Hayakawa et al., 2023). Even less extreme storms can cause cumulative damages to transformers at low latitudes as reported from South Africa after large geomagnetic storms in 2003 to 2004 (Gaunt & Coetzee, 2007).

Interestingly, the maximum value from the simulation (about 5000 nT/min) is roughly twice the extreme estimate of a 500-year return level (Fig. 3). However, Figure 3 is a smoothed spline fit, and a more detailed plot in Rogers et al. (2020, Fig. 4c) indicates that a 500-year return level could exceed 5000 nT/min, especially at locations close to the latitude of 55°.

Geomagnetic superstorms are likely to begin with an SSC. This was the case, for example, for the Halloween storm in 2003 (Juusola et al., 2023, Fig. 14). At Nurmijärvi, southern Finland, |dH/dt| reached about 180 nT/s (as calculated from 1-s data, which gives much larger derivatives than 1-min data). Even stronger impulses could be possible as the simulation by Welling et al. (2021) indicates for an idealised coronal mass ejection, with 1-s |dH/dt| reaching about 500 nT/s, i.e., about three times the above-mentioned Halloween value. Recently, Zhang et al. (2023) suggested that the Québec blackout in 1989 could have been related to an SSC which caused vortex-type ionospheric currents propagating from the dayside to the nightside (the blackout occurred at 02:45 local time, see Bolduc, 2002). The tendency of having the highest |dH/dt| not in the same MLT sector with the solar wind pressure impacts is visible also in the simulation by Blake et al. (2021): the hotspot region of Figure 8 at geomagnetic dipole longitudes 270–280° corresponds to pre-midnight MLT sector around the time of the magnetopause re-expansion.

3 Modelling of the geoelectric field

As the main new result, we will now estimate the maximal geoelectric field in Fennoscandia based on the simulated magnetic field and a detailed complex 3-D ground conductivity model. For comparison, we perform the same modelling for the Halloween storm in Oct 2003, but using the measured ground magnetic field.

We apply procedures described in detail in Appendices A and B based on the modelling approaches presented by Kruglyakov et al. (2022) and Marshalko et al. (2023). Our modelling takes into account the lateral non-uniformity of the source of electromagnetic induction as well as a 3-D distribution of the Earth’s electrical conductivity. The difference between the events lies in how we deal with the modelling input, which is the magnetic field. For the Carrington storm, the geoelectric field modelling is based on the output of the geospace simulation of Blake et al. (2021) (external magnetic field). For the Halloween storm, the geoelectric field modelling is performed using the total magnetic field variation measured by the IMAGE magnetometer network, so it contains both an external and an induced component.

We are interested in the largest magnetic field variations and their time derivatives. So for the Carrington storm, the external magnetic field data are rotated with respect to the Earth’s dipole axis in such a way that the biggest “hot spot” in terms of |dH/dt| is shifted to the study region in Fennoscandia (see Appendix B for details).

The spatial resolution of the geoelectric field grid is 0.03° × 0.07° in latitudinal and longitudinal directions, correspondingly. We perform a point-by-point comparison of the geoelectric fields simulated for the Halloween and Carrington storms by calculating the ratio between the maximum magnitudes (over the whole modelling period) of the horizontal geoelectric field (|E_h|) during the considered events. According to our modelling results, the maximum |E_h| in Fennoscandia during the Carrington storm is 201 V/km. During the Halloween storm, the maximum is 41.6 V/km. Figure 9 shows snapshots of the external ionospheric current and the modelled electric field at the time of the largest modelled electric field. As the upper row plots indicate, there was an intense westward electrojet across Fennoscandia during the Halloween storm, whereas the main current was directed northward during the Carrington storm.

Figure 9 Snapshots of the equivalent ionospheric current (top) and geoelectric field (bottom) in Fennoscandia at the moments of the maximum geoelectric field amplification during the Halloween (left) and Carrington (right) storms. Equivalent current and geoelectric field distributions are obtained using procedures described in Appendices A and B. Note that UT for the Carrington storm refers to the time stamp in the original data.

For the sake of comparison, Lucas et al. (2020) estimated the electric field across large areas in the United States based on empirical magnetotelluric impedances at 1079 locations. As a case study, they considered the storm on 13–14 Mar 1989, during which the maximum of the modelled 1-min geoelectric field varies from 0.02 V/km to 22.4 V/km. Then, based on the geomagnetic data of 31 years, they extrapolated the value of the 1-in-100 years geoelectric field, which varies from 0.02 V/km to 27.2 V/km. In our modelling, the largest values occur at the Norwegian coast, where the conductivity has a large lateral gradient. The electric field increases there at a narrow zone along the coast, but its magnitude decreases quickly within a few tens of km away from the coastline. We remark that the conductivity model has uncertainties in this region, as discussed more in Section 4.1.3.

Harang (1941) reports on the March 1940 geomagnetic storm, which he estimated to have caused an electric field of ~50 V/km or more in northern Norway in an 80 km long telephone line. This is an indirect estimate based on the impacts on the equipment. It should be considered with some caution, since the reported maximum values of other events are closer to ~10 V/km (Pulkkinen et al., 2008).

Figure 10 shows the ratio of the maximum magnitudes of the geoelectric field during the Carrington and Halloween storms, along with the conductivity distribution in the upper layer of the conductivity model of Fennoscandia. In several areas, the ratio is affected by large conductivity contrasts. For example, in southern Finland (latitudes 60–62, longitudes 22–28), it is larger closer to the coastline (smaller conductivity) than inland (larger conductivity). The choice of the analysis area is discussed in Appendix B. Only land areas are considered. The mean ratio is 6.7, and the standard deviation is 2.7. The minimum value is 1.4, and the maximum value is 20.4, so the Carrington event exceeds the Halloween event everywhere in this region (remembering that we rotated the maximal magnetic field variations of the Carrington storm to Fennoscandia). Figure 11 shows the histogram of the geoelectric field ratio values.

Figure 10 The ratio between the maximum magnitudes of the geoelectric field during the Carrington and Halloween storms (black points), along with conductivity distribution (in S/m) in the upper layer of the conductivity model of Fennoscandia used for the geoelectric field simulation. For visual clarity, the ratio is shown only for 1% of points considered in the analysis.

Figure 11 The number of points for different values of the ratio between maximum magnitudes of the horizontal geoelectric field during the Carrington and Halloween geomagnetic storms.

When we perform a similar analysis for the northward (E_x) and eastward (E_y) components of the geoelectric field separately, we obtain the following results: for |E_x|, the mean Carrington to Halloween ratio is 10.6 and the standard deviation is 4.7. For |E_y|, the mean ratio is 4.0 and the standard deviation is 2.0.

We also calculated the ratio between the maximum external magnetic field time derivatives (|dH/dt|) during the two events. For this purpose, we obtain magnetic field data produced by the ionospheric equivalent current on a 0.03° × 0.07° grid as described in Vanhamäki & Juusola (2020). For the Halloween storm, the equivalent current is constructed using the procedure described in Appendix A. For the Carrington storm, the equivalent current is obtained using the Spherical Elementary Current Systems (SECS) method (Vanhamäki & Juusola, 2020) based on the external magnetic field data by Blake et al. (2021). Figure 12 presents the ratio in a similar format to Figure 10. The mean ratio is 6.5 and the standard deviation is 2.0. The minimum ratio is 2.8 and the maximum is 17.2. The maximum |dH/dt| ratio has less spatial variability than the maximum horizontal geoelectric field ratio, but the average values are almost equal. Naturally, if we consider a smaller area with large lateral conductivity contrasts, the difference between |dH/dt| and |E_h| ratio values will be more prominent. Referring again to southern Finland, the ratio for |dH/dt| has clearly less spatial variation than the corresponding ratio for |E_h|. The former is only affected by external currents, while the latter has contributions induced currents and charges in the conducting ground too (cf. Juusola et al., 2025).

Figure 12 The ratio between maximum external magnetic field time derivatives during the Carrington and Halloween storms (black points), along with conductivity distribution (in S/m) in the upper layer of the conductivity model of Fennoscandia used for the geoelectric field simulation. For visual clarity, the ratio is shown only for 1% of points considered in the analysis.

For a more quantitative link to GIC, we also calculated the voltage along straight lines in the eastward and northward directions (Fig. 13) (cf. Dimmock et al., 2020, Fig. 8). We limited this experiment to the approximate area of Finland. The length of northward lines was set to 1.20°, i.e., about 133 km, independently of the longitude. This represents quite a typical length of a high-voltage transmission line. The southernmost line started at latitude 59.62, the next line at latitude 59.65, and so on. A similar setup was used for the eastward lines, of which the westernmost line started at longitude 20.66, the next line at longitude 20.73, and so on. The length of these lines varied between 106 and 157 km, depending on the latitude. For example, the voltage along a northward line is simply obtained by summing E_x at the corresponding grid points and multiplying by the uniform spacing. In this way, there are hundreds of lines across Finland at very different locations with respect to the ground conductivity. Figure 13 shows histograms of the Carrington to Halloween ratio of the maximum absolute voltages of each line. The voltages in northward lines are, on average, 12.5 times larger for the Carrington storm. In the eastward lines, the corresponding ratio is “only” 4.0 on average, although still being quite large. The Carrington to Halloween ratios are quite equal independently of whether we consider the electric field at single points or the voltage. We also made tests with shorter and longer lines, and came practically to the same conclusion for the ratio. It does not seem to matter much whether we use a sparser grid of the electric field. Further investigation of GIC and analysis of its impacts due to a Carrington-scale storm is left for a later study.

Figure 13 Left: Sketch of a grid of electric field vectors (blue arrows) and eastward and northward lines (red) along which the voltage is determined. Right: Carrington to Halloween ratio of the maximum absolute voltages along northward and eastward lines.

As already noticed, there are clear differences in the external driving of these storms around the peak time of the geoelectric field (Fig. 9). During the observed Halloween storm, there was a very large-scale westward electrojet across Fennoscandia, whereas the most intense phase of the simulated Carrington storm was dominated by a spectacular northward ionospheric current. This makes it understandable that the northward electric field and voltages in northward lines are much larger during the Carrington storm. It is noteworthy that the eastward electric field and voltages in eastward lines are also clearly larger during the Carrington storm, even in the lack of a pronounced conventional electrojet.

The electric field in southern Finland in the region of the natural gas pipeline (close to latitude 61, not drawn for clarity) could be even 10–20 times larger than during the Halloween storm (Fig. 10). Since the observed GIC on 29–31 Oct 2003 exceeded 30 A at several moments (Fig. 2), a Carrington scale storm could produce GIC of several 100 A, assuming that the driving electric field is oriented to a suitable direction. For a quantitative estimate, we calculated GIC at the Mäntsälä recording point of the pipeline during the Halloween and Carrington storms as described in Marshalko et al. (2023) based on the modelled geoelectric field. The maximum simulated GIC values during these storms are 31.5 A and 520.5 A, respectively. The ratio between the maximum values is 16.5. Time series of GIC simulated during these two storms and GIC recorded during the Halloween geomagnetic storm (1-min averages) are plotted in Figure 14.

Figure 14 Top: GIC modelled (red curve) and observed (black curve) due to the Halloween storm on 29–31 Oct 2003. Bottom: GIC modelled due to the Carrington storm on 2 September 1859. Values are 1-min data. The modelled and observed values for the Halloween storm are very close to each other and nearly indistinguishable.

In southern Sweden, GIC exceeding 150 A was measured on 29 Oct 2003 at a transformer neutral, Simpevarp-2, close to the nuclear power plant OKG in Oskarshamn (Wik et al., 2009, Fig. 8). The coordinates of OKG and the measurement site are approximately (57.4° N, 16.7° E). According to our modelling results, the ratio between the maximum magnitudes of the geoelectric field during the Carrington and Halloween storms at this location is ~10. Thus, during a Carrington-scale event, GIC could exceed 1000 A assuming a similar power grid configuration as in 2003.

Our results are schematically summarized as a risk map (Fig. 15). It is primarily based on Figures 7–8 related to the maximum value of |dH/dt| from the simulation by Blake et al. (2021). Regions where |dH/dt| can exceed the largest measured value known from data archives are marked by red. In the yellow region, at least half of the historic record could be reached. We have assumed hemispherical symmetry with respect to geomagnetic latitudes. For the sake of clarity, the schematic drawing does not mean that extremely large |dH/dt| would occur simultaneously across the whole coloured regions. As our modelling results of the geoelectric field show, the whole of Fennoscandia north of ~55° N belongs to a very high risk region (Figs. 10 and 12). This modelling indicates that other regions at about the same magnetic latitudes can also experience much larger GIC impacts than during the Halloween storm. A more quantitative statement would require similar electric field modelling as performed in this investigation and applying ground conductivity models valid for each region. Finally, we remind that the equatorial region is not considered in our study. However, it is also likely significantly affected as the direct observations of the 1859 storm indicate.

Figure 15 Geographic map of the estimated risk level of the impacts on power grids due to an extreme geomagnetic storm, based on Figures 7–8. Red refers to regions where |dH/dt| is likely to exceed the Space Age record. In the yellow regions, at least half of the Space Age record is reached. Note that our study does not consider equatorial regions.

4 Discussion

We have performed modelling of the geoelectric field based on the reproduced Carrington storm in 1859. This has been done following first-principle physics. However, there are limitations and uncertainties which are discussed below. We consider first items related to near-space simulations. Then we discuss other studies which have investigated historic intense events or are based on other simulations, and have focused on estimating the geoelectric field or GIC.

4.1 Remarks on uncertainties

4.1.1 MHD models

In the MHD approach, space plasma processes are modelled with a fluid approximation which combines properties of electron and ion populations. This is useful for describing the main features of space weather phenomena on global scales, but fails to capture the physics of different particle populations, particularly in near-Earth space. These phenomena most likely have an important role in the generation of high |dH/dt| values. One way to resolve this issue is to handle plasma populations in near-Earth space with velocity distribution functions similar to the Vlasiator hybrid simulation (Palmroth et al., 2018). It is a computationally demanding approach, but it offers a way to gain a better understanding of those magnetospheric processes that have relevant spatiotemporal scales for accurate GIC studies.

The simulations by Blake et al. (2021) were able to reproduce the intense dip and rapid recovery of the magnetic field at Colaba relatively well as a combination of the magnetic fields due to magnetopause and field-aligned currents during the magnetopause compression and re-expansion. However, the simulations were not able to recreate the horizontal magnetic field recordings available from other locations during the event (and suffering from off-scale periods). It is evident that the simulation is not a perfect global recreation of the Carrington event. As discussed by Blake et al. (2021), this is to be expected, given the simplifications in the chosen solar wind profile and the physical limitations of the SWMF model. Consequently, Blake et al. (2021) conclude that their result should not be interpreted as “an accurate replication of the magnetospheric and ionospheric conditions during the Carrington event”. Keeping this in mind, the simulated field still shows reasonable features as discussed above. The physical explanation for the exceptionally large magnetic field variation at Colaba is still under lively discussion, as demonstrated, for example, by Ohtani (2022) versus Tsurutani et al. (2023), or Love & Mursula (2024) and Ohtani et al. (2024). It is also uncertain how the Colaba observations should be properly interpreted as a measure of global magnetic activity, such as the Dst index (Love et al., 2024; Love & Mursula, 2024).

Thomas et al. (2024) analyse the northward ground magnetic field from Blake et al. (2021) and from a “Carrington-type” simulation by Ngwira et al. (2014). The latter investigation did not aim at reproducing the exact magnetic field variation at Colaba. Despite substantial differences in the solar wind parameters, both simulations produce a comparable global magnetic field pattern, and field magnitudes are quite equal in size around the peak time of the event. Based on the analysis of the simulated geospace currents, Thomas et al. (2024) suggest that the Carrington event was due to a combination of magnetospheric and ionospheric currents, which both contribute to ground magnetic field variations of the same order of magnitude, although details depend on the region considered. They also state that these conclusions may not be applicable to smaller storms, because the scenarios involve only Carrington-like events, i.e., something completely different from typical events.

A typical intense geomagnetic storm is driven by a fast CME preceded by a sheath of compressed solar wind. The storm starts with an SSC, i.e., a step-like intensification of the horizontal magnetic field at low latitudes, as the shock in front of the sheath impacts the magnetopause. Large geomagnetic disturbances are caused by the SSC and other variations of the solar wind dynamic pressure on the dayside and by substorm activity on the nightside (e.g., Juusola et al., 2023). In addition, enhancement of the ring current creates geomagnetic disturbances particularly at low latitudes. Studies of other major storms since 1859, e.g., May 1921 and March 1989, indicate that within each storm the impacts occurred as a series of localised (a few 100 to 1000 km) events (Boteler, 2019; Hapgood, 2019), possibly associated with the dynamics of the auroral oval, auroral electrojets, and omega bands (Apatenkov et al., 2020).

The solar wind of Blake et al. (2021) does not describe a typical CME. There is no shock that would cause an SSC, but instead, the solar wind dynamic pressure increases steadily for two hours. Neither does the structure of the solar wind parameter profiles reflect that of a realistic CME. However, Blake et al. (2021) have identified a physical mechanism that might have created the geomagnetic disturbance at Colaba. Unlike the typically localized disturbances created by the previously identified mechanisms, the intense geomagnetic disturbances created by the severe compression and re-expansion of the magnetopause affect a wide area simultaneously.

As a side note, a thorough analysis of SSCs would require the use of high temporal resolution. Using one-minute averages may smooth all rapid variations (e.g., Juusola et al., 2023, Fig. 14), so one-second sampling would be a better choice (cf. Trichtchenko (2021)). In the present study, we have only 1-min values for the Carrington storm, so we use 1-min data for the Halloween storm too.

Thus, although the simulations by Blake et al. (2021) should not be considered a globally accurate description of the historical Carrington event, they describe global geomagnetic disturbances due to extreme, but not unreasonable, solar wind conditions. The simulations were able to reproduce the geomagnetic disturbance recorded close to the geomagnetic equator at noon by a physical mechanism that is distinct from those generally thought to create intense geomagnetic variations. There is a possibility that a truly extreme storm is not simply an intense version of a typical storm but includes elements different from those of typical cases (cf. Sornette & Ouillon, 2012). As Ohtani et al. (2024) state about the Carrington storm, “the event itself was extreme, and therefore, no idea should be precluded only because it requires something extraordinary”. Because of that, we consider the geomagnetic variations provided by Blake et al. (2021) worth applying to geoelectric field estimations while waiting for the next iteration of the simulated Carrington event. Absence of solar wind data is, however, a deficiency that cannot be overcome. From that perspective, adjusting solar wind conditions so that they reproduce a relatively good match with dayside magnetometer observations can be considered as an equally feasible way forward as constructing the solar wind input by educated guessing.

There is also an indication of a ~3000 nT variation of the horizontal magnetic field on 2 Sep 1859 at Rome simultaneously to the large variations at Colaba (Blake et al., 2020). This is a huge value at such a mid-latitude location (magnetic latitude ~38.6° N in 1859) and no corresponding events are obviously known. The simulation by Blake et al. (2021) produces “only” ~1000 nT at Rome, which is still a very large value. There are recently digitized data by Beggan et al. (2024) of two observatories close to London during the Carrington storm. Unfortunately, there is a gap in the horizontal component within the most active period. The vertical component is available from Greenwich and shows a 1000 nT variation.

Al Shidi et al. (2022) conducted an extensive simulation of over 100 geomagnetic storms between 2010 and 2019, for which they determined ground magnetic field variations but not the time derivatives, which are still a challenge. They assessed the modelled fields with respect to the measurements by using Heidke skill score values. In general, they found that the simulations predict quite well the magnetic field variations at low and mid-latitudes, but the regions near the equatorward edge of the auroral oval show lower accuracy. According to Al Shidi et al. (2022), this is due to the fact that ionospheric currents, which dominate the contribution to the ground field in the auroral region, have a sharp equatorward boundary. If the simulation model fails to predict the location of the auroral oval, significant errors may appear in the modelled field. A case study related to a major GIC event in the Kola Peninsula in May 2017 showed that MHD simulations may underestimate the magnitude of the time derivative of the magnetic field (dB/dt) related to small-scale impulsive structures such as Pi3 pulsations (Pilipenko et al., 2023). Challenges in the present simulations have also been highlighted by Engebretson et al. (2024), who investigated large nighttime magnetic field disturbances at high latitudes in Canada. As Figure 5 shows, the simulation by Blake et al. (2021) produces very large dB/dt only within a short period at the beginning of the Carrington event. On the other hand, the SMU and SML indices are quite large throughout the storm, being comparable to the Halloween storm (Fig. 1). Consequently, we could expect long-term high dB/dt and GIC activity as in Finland on 29–31 Oct 2003 (Fig. 2). Since this is not the case with the simulated values, the simulation cannot obviously fully reproduce small-scale structures of high-latitude ionospheric currents.

MHD models can predict some characteristic features of substorms, such as onset times (Haiducek et al., 2020). However, Gordeev et al. (2017) demonstrated that the global MHD model BATS-R-US (Powell et al., 1999), which is part of the SWMF, does not realistically reproduce the substorm-related loading-unloading cycle, representing a principal large-scale perturbation in the magnetosphere. This applies to BATS-R-US model versions available at the NASA Community Coordinated Modeling Center (CCMC), which Blake et al. (2021) used to carry out their simulation. One may then argue that the magnetic field variations and their time derivatives (Figs. 4–6) during the Carrington storm are underestimated, since the simulation lacks proper substorm features. It follows that the geoelectric field is also underestimated. For the Halloween event, at ~87% of the land area grid points, the peak electric field value occurs at 20:03–20:11 UT on 30 Oct 2003 (a little before the local MLT midnight). The rest occur at 19:50–20:00 UT on 30 Oct 2003 and a small number at 06:15–07:00 UT on 29 Oct 2003. Consequently, nearly all maximum values of the Halloween storm are related to an obvious substorm. For the Carrington storm, the maximum electric field at all grid points occurs within a short time window at 06:23–06:42 UT on 2 Sep 1859 (especially, ~76% of all points have a maximum at 06:31 UT).

To perform additional comparison of the geoelectric field during the two geomagnetic storms without taking substorms into account, we calculated the ratio between the maximum magnitude of the geoelectric field during the Carrington storm and the first phase of the Halloween storm (29 Oct 2003 06:00–13:59 UT). The latter is daytime (approximately 08:30–16:30 MLT), i.e., outside of the occurrence time of substorms. The largest electric field values in the region studied occur within a narrow interval at 06:30–06:50 UT. In this case, the mean value of the Carrington to Halloween ratio of |E_h| is as high as 12.2, and the standard deviation is 5.2. The minimum ratio is 2.6, and the maximum is 37.7. Whether such a large ratio is realistic cannot be solved here, but next-generation simulations capable of dealing with substorms should be applied.

The Carrington simulation by Blake et al. (2021) assumed a different location of the geomagnetic north pole from the present one. A potential future task is to rerun the same simulation with the present location of the pole and dipole strength. Additionally, a large number of different extreme solar wind inputs should be used to mimic the wide variety of possible events. This could also include a rerun of Ngwira et al. (2013a) of the 2012 near miss event with modern simulation resources.

4.1.2 Estimation of the external magnetic field

The ground magnetic field provided by the Carrington simulation is produced only by the external currents in the ionosphere and magnetosphere. This implies that the contribution by the internal induced currents in the conducting ground to the magnetic field is omitted. Generally, this leads to an underestimation of horizontal field variations and their time derivative (cf. Juusola et al., 2020). However, there is a slightly tricky point here. The simulated (external) magnetic field by Blake et al. (2021) matches the measurement at Colaba. The measured field contains both the external and internal contributions, so a slightly smaller external driver would actually produce the observed total field. We considered the simulated ground magnetic field by Blake et al. (2021) at the geographic location (18.5° N, 72.5° E), which is the closest available point to the Colaba observatory (18.9° N, 72.8° E). The largest horizontal field variation (|H|) is 1847 nT (mostly due to the northward component), and the largest |dH/dt| is ~170 nT/min ≈2.8 nT/s (from 1-min data). Although the field variation at Colaba is about 1/3 of the global maximum, its time derivative is only 1/30 of the global maximum (Figs. 4–5). Consequently, the (simulated) ionospheric/magnetospheric currents obviously have large differences in their characteristics depending on the latitude, and this affects dH/dt more strongly than H. We also note that the largest derivative of the measured H component at Colaba was ~6 nT/s calculated from two successive spot values separated by 2 min (Love et al., 2024, Sect. 9). As Juusola et al. (2020, Table 1) show, the internal contribution to the magnetic field (B_x, B_y) is typically 30–40% at moments when |dH/dt| exceeds 1 nT/s (calculated from 10-s data) at auroral and subauroral locations in North Europe. However, we do not know how large the internal contribution would be at the specific location of Colaba. Consequently, we have interpreted the simulated magnetic field by Blake et al. (2021) to be purely of external origin without trying to scale it in a more or less arbitrary way.

4.1.3 Modelling of the geoelectric field

As discussed in Appendices A and B, the external ionospheric equivalent current is used as input to geoelectric field modelling. For the Carrington event, it is directly obtained from the simulation (Blake et al., 2021), while it is based on the measured ground magnetic field for the Halloween event. Furthermore, the geoelectric field calculation during both storms is performed with the use of spatial modes obtained using the Principal Component Analysis (PCA) of the external current in Fennoscandia during the Halloween storm (29–31 Oct 2003). Even though this introduces some error to the results of the geoelectric field of the Carrington storm, the spatial modes approximate the external current reasonably well. We limit our analysis to areas where the fit between the original external magnetic field and the external magnetic field produced by the external current approximated with spatial modes is good.

A considerable issue in the geoelectric field and GIC modelling arises due to the imperfectness of the conductivity model of the region. Although a rather extensive set of conductivity models was available from electromagnetic investigations at the time of the compilation of the conductivity model of Fennoscandia (Korja et al., 2002), the spatial coverage of experimental data was still far from complete. This was especially true in the westernmost part of Fennoscandia, where the data were almost absent (see Fig. 2 in Korja et al., 2002). Other geophysical and geological data were used to assign a most likely resistivity model in areas where electromagnetic data were not available. Thus, the conductivity distribution along the Norwegian coast may not be entirely accurate, and our geoelectric field modelling results are the least reliable in this area. This means that the magnitudes of the modelled electric field are uncertain. However, the ratio of the Carrington to Halloween storm in terms of the maximum electric field has quite a narrow distribution as Figure 11 demonstrates. Figure 10 shows that this ratio does not vary very strongly as a function of the ground conductivity, although the Fennoscandian region represents a large variety of conductivities: there are very different local vertical profiles as well as strong lateral gradients.

The external driver of the two events is very different around the time of the maximum geoelectric field. The consequent ground response can also be very different, which could cause some randomness in the ratio between the events. For example, a specific site can experience especially large variations during the Halloween storm, but happen to be less affected during the Carrington storm. However, our results do not show very rapid variation in the ratio between the storms when nearby ground points are compared (see Fig. 10 for the electric field). It is also worth noting that the external |dH/dt| provides a reasonable proxy for the geoelectric field, although there is no simple relation between simultaneous values of dH/dt and E.

Concerning the implementation of the modelling method, there are a few additional approximations that we use compared to an approach to 3-D geoelectric field modelling described in Marshalko et al. (2021):

1. Approximation of the inducing source with a small number of spatial modes.

2. Approximation of an improper integral with a definite integral in formula A.10 (discussed in Kruglyakov et al., 2022).

3. The use of regularisation when solving equation A.9.

All these approximations do not significantly affect modelling results and can lead to slight underestimation of electric field values as shown in Kruglyakov et al. (2022).

4.1.4 Summary of uncertainties

Finally, we summarize the identified uncertainties in an indicative order of importance:

• 1 (major): Limited capability of MHD applied in the simulation by Blake et al. (2021).

• 2 (major): Imperfect ground conductivity model.

• 3 (major): Simplified model of the solar wind driver in the simulation.

• 4 (minor): Separation of the external magnetic field from measurements for the Halloween event versus the direct use of the external field from the Carrington simulation.

• 5 (minor): Interpretation of the simulated ground magnetic field of the Carrington event as representing a purely external contribution.

• 6 (minor): Shift of the original simulated ground magnetic field to a spherical coordinate system with its north pole at the present (2025) IGRF geomagnetic north pole.

• 7 (minor): Use of the same spatial modes of external equivalent currents for the Carrington event as derived for the Halloween event.

• 8 (minor): A few technical approximations in the version of the first-principle model used in this study.

4.2 Remarks on GIC risk estimations of intense and extreme storms

4.2.1 Significance of magnetotelluric data

Outlining the GIC impacts in a quantitative and comprehensive way is demanding and beyond the scope of this study. It would require extensive power system analysis based on a given geoelectric field and exactly known power grid parameters (e.g., Mac Manus et al., 2023; Oyedokun & Jankee, 2023; Schachinger et al., 2023). This would allow us to calculate the GIC and assess its effects on transformers and power transmission. This should be conducted for a large region, up to continental scales, since an extreme magnetic storm covers a large geographical range, and power grids are widely interconnected across national borders. In any case, accurate estimates of the geoelectric field would be of a key importance. Magnetotelluric measurements facilitate reaching this goal. The extensive MT surveys performed in the United States (The USArray MT data, Kelbert et al., 2018) and Australia (The Australian Lithospheric Architecture Magnetotelluric Project, AusLAMP, https://www.ga.gov.au/about/projects/resources/auslamp) are leading examples of recent progress in this field.

Love et al. (2022) present the modelled geoelectric field in North America during the Mar 1989 storm together with publicly known GIC impacts in the same region. There is a clear tendency for the effects on the power grid to predominantly concentrate in regions where the electric field is enhanced. More or less the same locations experienced problems also during the very intense storms in Aug 1972 and Mar 1940. Love et al. (2022) base their modelling on empirical magnetotelluric transfer functions, so they do not use an explicit ground conductivity model, and they assume (implicitly) a spatially uniform external source, i.e., a plane wave. Kelbert et al. (2019) have constructed a 3-D conductivity model of the continental United States. This conductivity map confirms the general fact that large electric fields occur at regions of low conductivity in the uppermost part of the subsurface. This is also observed in our results when comparing the electric field in Figure 9 with the ground conductivity in Figure 10. We also remark that the empirical magnetotelluric transfer functions can involve correction for galvanic distortions, which could be an order of magnitude greater than the regional field (Malone-Leigh et al., 2024, Sect. 2.3). First-principle modelling does not try to eliminate such very localized enhancements occurring at sharp lateral gradients of the conductivity. However, the conductivity models are, in turn, typically based on distortion corrected magnetotelluric data (Bonner & Schultz, 2017, Sect. 2.1), so there is inevitable uncertainty in the resulting geoelectric field.

In Europe, there is no such detailed analysis of the GIC risk as for North America. Viljanen et al. (2014) estimated the magnitude of GIC in different parts of the continent based on a simplified power grid model, geomagnetic data between 1996–2008 and 1-D ground conductivity models by Ádám et al. (2012). However, electric field estimations based on 1-D models inevitably neglect the effects due to the true 3-D ground conductivity (Kelbert, 2020, Sect. 4). A problem in Europe is that information on the ground conductivity or empirical MT impedances is scattered. Although there are regions (Fennoscandia) or countries (e.g., the UK, Hübert et al., 2025, Portugal) with quite much data collected (Grayver, 2024, Fig. 3), there is no centralized data bank covering the whole continent, contrary to the United States or Australia.

4.2.2 Extreme geoelectric field and GIC simulations

Ebihara et al. (2022) estimated GIC in Japan due to a Carrington-like storm. As the starting point, they used the recorded field (H variation) at Colaba on 2 Sep 1859. They assumed that the transverse horizontal component D is half of H. The difference in the magnetic latitude between Colaba and a Japanese observatory at Kakioka is about 18°, so they made a small correction for the magnetic latitude effect, and then derived an estimate for the horizontal field components (B_x,B_y) in Japan. With an empirical model, they calculated the electric field and finally GIC at a few substations of the Japanese power grid. Based on the observed magnetic field at Kakioka, Japan, they calculated GIC during the 13–14 Mar 1989 and 29–30 Oct 2003 magnetic storms. They found that a Carrington-like storm produces 4–6 times larger GIC than the two other events, which is quite similar to our result giving a mean ratio 6.7 ± 2.7 (Fig. 11). The method by Ebihara et al. (2022) is a simplification, since it assumes that the temporal development of the magnetic field during a Carrington-like event in Japan follows the one observed at Colaba in 1859 (with small modifications).

Love et al. (2025) provide a statistical estimate of the electric field during a Carrington-scale storm. They use 40 strong storms within 1989–2024, and based on empirical MT impedances, calculate the electric field across the contiguous United States. Using the storm intensity (maximum of the 1-hour -Dst index) as a parameter, they extrapolate the results to the Carrington event for which a storm intensity of 964 nT is assumed. Expressed in relative terms, they state that a Carrington‐class storm would likely induce geoelectric fields with strengths 55% greater than for the 13–14 March 1989 storm. This is quite similar to the previous investigation by Lucas et al. (2020). Consequently, it is much more conservative than our estimate, or the result by Ebihara et al. (2022) discussed above.

Recently, Mac Manus et al. (2022) conducted a study on the New Zealand power grid. They combined extreme estimates of a geomagnetic storm with modelled GIC in the grid, and also incorporated “danger threshold” GIC levels provided by the grid operator. Extreme storm scenarios were based on three real events, whose geomagnetic variations were scaled to produce a maximum horizontal field component rate of change of 4000 nT/min applicable to the geomagnetic latitudes of New Zealand (cf. Thomson et al., 2011). This is also consistent with the simulation by Blake et al. (2021), which produces a comparable maximum of dH/dt at a wide latitude range as summarised in Figure 6. However, a simple direct scaling of a historic event may not be the most physical approach, since it assumes that there is no change in the spatial configuration of ionospheric currents driving geomagnetic disturbances. Mac Manus et al. (2022) then modelled GIC at all substations of the New Zealand grid, and sites reaching any of the five danger levels were identified. Extreme storm scenarios predict that at 13–35% of transformers, GIC can experience dangerous levels. This confirms further that an extreme magnetic storm can lead to major GIC problems around the globe. Concerning mitigation strategies, power grid operators can adopt some general hints from these scenarios similarly to what has been done in New Zealand (Mac Manus et al., 2023; Clilverd et al., 2025). Of course, each region has its specific features, including the ground conductivity as well as technical details of power grids and transformers, so any universally valid single recommendation is obviously not available.

On 23 July 2012, an exceptionally fast CME hit the NASA STEREO-A satellite, which was monitoring solar activity at the same distance but in a different longitude sector than the Earth. This CME hit the satellite 19 h after its launch from the solar surface. In the literature, it is often referred to as the “Carrington storm that missed the Earth”. Unlike the original Carrington event, the July 2012 storm offers an opportunity to use authentic solar wind observations as input to MHD simulations. Simulation results by Ngwira et al. (2013a) suggest that substorm activity at local midnight sector is the primary cause for high |dH/dt| and consequent enhancements in the geoelectric field. Largest values of the geoelectric field by the simulation, based on a simplified 1-D ground conductivity model, are observed around geomagnetic latitudes around 55°, and they are within the range of 8–13 V/km. Therefore, the maximum exceeds the global extreme of 11.4 V/km estimated for the Halloween storm in a separate study by Ngwira et al. (2013b).

Noteworthy in both simulations by Ngwira et al. (2013a) and Blake et al. (2021) is a rather short period of ~1 h during which the extreme |dH/dt| values occur, compared to the entire storm duration, which is typically 1–2 days (cf. Fig. 1). However, it should be recognized that CMEs can occur in sequences which may either strengthen their joint capability to cause geomagnetic activity, like in the case of July 2012 (Liu et al., 2014), or lengthen the time periods of harmful GIC effects (cf. Figs. 1–2 indicating long-term high activity).

Extreme geomagnetic storms, typically associated with strong radiation and high-energy particle phenomena, have both scientific and societal significance. They provide a challenge to our ability to model events which are much more intense than average cases. The practical motivation to investigate them follows from their capability to cause damage to modern technological systems. The Carrington storm in Sep 1859 has become a popular benchmark for such an extreme event (Clauer & Siscoe, 2006; Usoskin et al., 2023, Sect. 7.3). However, there are very few measurements available of that storm or other comparable historic events, so its rigorous analysis is a big challenge. Major uncertainty also arises from the fact that the modern infrastructure has not experienced a solar superstorm of a similar magnitude to the Carrington event. Consequently, we do not have any first-hand knowledge of what such a superstorm could cause in the modern world.

This study concentrated on the geomagnetic and GIC viewpoints. During highly active space weather periods, there is also a large chance for severe radiation and particle events leading to different technological impacts both in space, atmosphere, and ground (e.g., Usoskin et al., 2023). For example, variations in the ionospheric conditions can affect radio wave propagation and impede the availability of satellite-based services.

5 Conclusions

In this paper, we have utilised results from the best available first-principle simulation of the Carrington event (Blake et al., 2021). We have used the simulated ground magnetic field variations to estimate the related geoelectric field based on a detailed 3-D ground conductivity model of Fennoscandia. For a maximal impact, we rotated the Earth with respect to the geomagnetic dipole axis so that the strongest simulated magnetic field variations and their largest time derivatives are concentrated on Fennoscandia. To make our results more tangible, we have compared them to the Halloween storm in Oct 2003, for which a good coverage of geomagnetic recordings is available in North Europe.

According to our modelling results, the Carrington to Halloween ratio of the maximum horizontal electric field is 6.7 ± 2.7. Thus, we can conclude that in Fennoscandia, the Carrington-scale geomagnetic storm can be about 4–10 times stronger than the Halloween storm in Oct 2003 in terms of the horizontal geoelectric field magnitude. Since GIC is basically determined by linear spatial integration of the electric field, a corresponding estimate can be given for GIC too.

As a final remark, we acknowledge that there are notable uncertainties in modelling extreme geomagnetic storms and geoelectric fields, which remain a challenge to researchers. However, decision-makers need to consider the significance of the present knowledge concerning the protection of modern infrastructure. An option is to apply the precautionary principle, which is a strategy for managing potential risks when scientific understanding is incomplete or uncertain. It emphasizes taking preventive action in the face of possible harm to human health, the environment, or the technological infrastructure, even when some cause-and-effect relationships are not fully established.

Acknowledgments

We acknowledge Theresa Hoppe for helping with the paper by Harang (1941), written in German. We thank the reviewers for raising different viewpoints, which helped us improve the paper. The editor thanks Ciaran D. Beggan and an anonymous reviewer for their assistance in evaluating this paper.

Funding

This study was supported by the Academy of Finland grant no. 339329 and by the ALBATROS project (https://www.albatros-horizon.eu/) with funding from the Horizon Europe Research and Innovation Programme under grant agreement no. 101077071. Some key results of this paper are also summarised in an as yet unpublished deliverable of the ALBATROS project.

Conflicts of interest

The authors declare no conflict of interest.

Data availability statement

Recordings of geomagnetically induced currents in the Finnish natural gas pipeline were performed in collaboration with Gasum Oy (data available at https://space.fmi.fi/gic/). We gratefully acknowledge the SuperMAG collaborators for providing geomagnetic data around the world (https://supermag.jhuapl.edu/info/?page=acknowledgement). We thank the institutes who maintain the IMAGE magnetometer array (https://space.fmi.fi/image/): Tromsø Geophysical Observatory of UiT the Arctic University of Norway (Norway), Finnish Meteorological Institute (Finland), Institute of Geophysics Polish Academy of Sciences (Poland), GFZ German Research Centre for Geosciences (Germany), Geological Survey of Sweden (Sweden), Swedish Institute of Space Physics (Sweden), Sodankylä Geophysical Observatory of the University of Oulu (Finland), Polar Geophysical Institute (Russia), DTU Technical University of Denmark (Denmark), and Science Institute of the University of Iceland (Iceland). Simulation data used in this study was provided by the Community Coordinated Modeling Center (https://ccmc.gsfc.nasa.gov/results/viewrun.php?runnumber=Elena_Marshalko_20211014_PP_1). The SMAP model (Korja et al., 2002) is available via the European Plate Observing System (EPOS) portal (https://www.epos-eu.org/dataportal) at https://mt.research.ltu.se/MT/Models/2000_BEAR_SMAP_Fennoscandia.json.bz2 (stored in JSON format and compressed with bzip2) under CC BY-NC 4.0. PGIEM2G 3-D EM forward modeling code is developed openly at Gitlab and is available at https://gitlab.com/m.kruglyakov/PGIEM2G under GPLv2. Python wrapper of the AACGMv2 C library is openly available at https://doi.org/10.5281/zenodo.14582758 under MIT license. Geoelectric fields simulated due to the Carrington and Halloween geomagnetic storms are available at Zenodo under CC BY NC 4.0: https://doi.org/10.5281/zenodo.14743724.

References

Appendix A: Modelling of the geoelectric field during the Halloween geomagnetic storm

Electric and magnetic fields obey Maxwell’s equation. In the frequency domain, these equations read as

$$\frac{1}{{\mu }_0}\nabla \times \mathbf{B}=\sigma \mathbf{E}+{\mathbf{j}}^{\mathrm{ext}},$$(A.1)

$$\nabla \times \mathbf{E}=\mathrm{i\omega }\mathbf{B},$$(A.2)

where σ(r) is the spatial distribution of electrical conductivity, j^ext (r,ω) is the external (inducing) electric current density, E(r, ω; σ) and B(r, ω; σ) are electric and magnetic fields, correspondingly, ω is angular frequency, r = (x, y, z) is a position vector, and μ₀ is the magnetic permeability of free space.

We neglect displacement currents and adopt the following Fourier convention:

$$f\left(t\right)=\frac{1}{2\pi }\underset{-\infty }{\overset{\infty }{\int }}\mathrm{}f\left(\omega \right)e^{-\mathrm{i}\omega t}\mathrm{d}\omega .$$(A.3)

The current density, j^ext (r, ω), can be represented as a linear combination of so-called spatial modes j_i (r),

$${\mathbf{j}}^{\mathrm{ext}}(\mathbf{r},\omega )=\sum _{i=1}^L\mathrm{}{c}_i\left(\omega \right){\mathbf{j}}_i\left(\mathbf{r}\right).$$(A.4)

The form of spatial modes j_i (r) (and their number, L) varies with application. In this study, spatial modes are obtained using the SECS method and PCA of the SECS ionospheric equivalent current as described in Kruglyakov et al. (2022). We use the same L = 34 spatial modes that were previously identified by Marshalko et al. (2023) via the time-domain PCA of the SECS ionospheric equivalent current in Fennoscandia during three days of the Halloween geomagnetic storm (29–31 Oct 2003). These spatial modes describe 99.9% of the inducing source variability during the considered geomagnetic storm.

By virtue of the linearity of Maxwell’s equations with respect to j^ext (r, ω) term, we can expand electric and magnetic fields as linear combinations of individual fields E_i and B_i:

$$\mathbf{E}(\mathbf{r},\omega ;\sigma )=\sum _{i=1}^L\mathrm{}{c}_i\left(\omega \right){\mathbf{E}}_i(\mathbf{r},\omega ;\sigma ),$$(A.5)

$$\mathbf{B}(\mathbf{r},\omega ;\sigma )=\sum _{i=1}^L\mathrm{}{c}_i\left(\omega \right){\mathbf{B}}_i(\mathbf{r},\omega ;\sigma ),$$(A.6)

where the E_i (r, ω; σ) and B_i (r, ω; σ) are “electric” and “magnetic” solutions of the following Maxwell’s equations:

$$\frac{1}{{\mu }_0}\nabla \times {\mathbf{B}}_i=\sigma {\mathbf{E}}_i+{\mathbf{j}}_i,$$(A.7)

$$\nabla \times {\mathbf{E}}_i=\mathrm{i\omega }{\mathbf{B}}_i.$$(A.8)

In this study, we utilise the approach to the geoelectric field modelling with the use of the “conductivity-based” inducing source (Marshalko et al., 2023) in order to calculate the horizontal geoelectric field in Fennoscandia during the Halloween storm. Marshalko et al. (2023) demonstrated that this approach allows for reproducing the GIC observed at the Mäntsälä recording point of the Finnish natural gas pipeline with a high level of accuracy. The approach includes the following steps:

1. Horizontal total (the sum of external and induced) magnetic field data H^obs (r_j, t), j = 1,…, N, recorded at IMAGE magnetometer sites are converted from the time to frequency domain using the fast Fourier transform (FFT). In our case, N is equal to 23. The northernmost sites Ny Ålesund, Longyearbyen, and Hornsund fall outside the modelling region.

2. At each FFT frequency ω, we estimate c_i (ω) by solving the over-determined system of linear equations (2 × 23 equations, 34 unknowns)

$$\sum _{i=1}^L\mathrm{}{c}_i\left(\omega \right){\mathbf{H}}_i({\mathbf{r}}_j,\omega ;\sigma )={\mathbf{H}}^{\mathrm{obs}}({\mathbf{r}}_j,\omega ),\hspace{1em}j=1,...,N.$$(A.9)

by means of the regularised least squares method. FFT frequencies range between $\frac{1}{S}$ and $\frac{1}{2\Delta t}$ where S is the length of the event (72 h in the case of the Halloween storm) and Δt = 1 min.

3. Time series c_i (t), i = 1,…, L, are then obtained by means of the inverse FFT of frequency domain coefficients c_i (ω).

4. Finally, the geoelectric field at a given time instant t and location r is computed by calculating the following convolution integral numerically

$$\mathbf{E}(\mathbf{r},t;\sigma )\approx \sum _{i=1}^L\mathrm{}\underset{0}{\overset{T}{\int }}\mathrm{}{c}_i(t-\tau ){\mathbf{E}}_i(\mathbf{r},\tau ;\sigma )\mathrm{d}\tau .$$(A.10)

as discussed in Marshalko et al. (2023) and Kruglyakov et al. (2022).

In the case of Fennoscandia, T can be taken as equal to only 15 min (for the justification of the choice of T, see Kruglyakov et al., 2022).

Note that in Marshalko et al. (2023), all 3 magnetic field components were used to construct the inducing source. The vertical component of the magnetic field is more sensitive to 3-D variations of conductivity than the horizontal components (Koch & Kuvshinov, 2013). That is why the inducing source obtained using all 3 components of the magnetic field is more affected by the difference between the actual conductivity distribution in the ground and available conductivity model, trying to compensate for this difference by design. In the current study, we would like to calculate the external equivalent ionospheric current as accurately as possible and model the geoelectric field in the given conductivity model of the region of interest, to carry out the comparison of the Halloween and Carrington storm (Appendix B) geoelectric fields consistently. That is why we construct the current using only the horizontal components of magnetic field.

Estimation of coefficients c_i (t) and electric field E(r, t; σ) implies computation of H_i (r_j, ω; σ) and E_i (r, ω; σ) in a given conductivity model σ(r) of the region of interest. We perform these computations using the scalable 3-D electromagnetic forward modelling code PGIEM2G (Kruglyakov & Kuvshinov, 2018) based on a method of volume integral equations with a contracting kernel (Pankratov & Kuvshinov, 2016). The computations are carried out for the variant of the conductivity model of Fennoscandia (based on the SMAP model, Korja et al., 2002) previously used by Marshalko et al. (2021, 2023) and Kruglyakov et al. (2022, 2023). The 3-D part of the model is underlain by a 1-D conductivity profile from Kuvshinov et al. (2021).

Appendix B: Modelling of the geoelectric field during the Carrington geomagnetic storm

The geoelectric field during the Carrington storm on 2 September 1859 (04:10–15:45 UT) is calculated based on the SWMF simulation results (Blake et al., 2021) in the following way:

1. The outputs of the SWMF (time-varying 3-D currents in the magnetosphere, horizontal currents in the ionosphere and field-aligned currents flowing between the magnetosphere and ionosphere) are used to calculate (through the Biot-Savart law) the external magnetic field perturbations at the ground. This is done using the CalcDeltaB tool (Rastätter et al., 2014). Time series of the external magnetic field are calculated globally at 1° × 1° spatial grid in geomagnetic dipole coordinates with a sampling rate of 1 min. These values are available at CCMC, as mentioned in Acknowledgements.

2. The coordinate transformation and the corresponding vector rotation are performed for the external magnetic field to obtain the data in geographic coordinates. In this study, we set the coordinates of the geomagnetic north pole to be 80.8° N, 72.8° W (coordinates of the north geomagnetic pole in 2025 according to the IGRF model; Alken et al., 2021), because we would like to simulate ground effects of a Carrington-scale geomagnetic storm under modern conditions. Figure B1 demonstrates |dH/dt| values in geographic coordinates before and after a 150° westward rotation with respect to the geomagnetic dipole axis. The figure also shows the point with the largest simulated |dH/dt|. In geographic coordinates, the location of the point is 62° N and 150.75° W. MLT of this point, for example, at 06:31 UT, 2 Sep 2025, is 19:30. We calculated MLT using the aacgmv2 (Burrell et al., 2024), a Python wrapper for the AACGMv2 C library (Shepherd, 2014).

3. As in this study, we are interested in the largest and magnetic field perturbations, magnetic field data are rotated 150° westward with respect to the dipole axis. As a result, the biggest “hot spot” in terms of |dH/dt| (Fig. 8) is shifted to our study region in Fennoscandia.

4. After this, we carry out geoelectric field modelling as described in Kruglyakov et al. (2022). That is, we:

• Calculate the so-called scalar (or scaling) factors S_m (t), m = 1,…, M (where M is the number of SECS poles), based on external magnetic field data (see Vanhamäki & Juusola, 2020, for more information).

• Calculate coefficients c_i (t) from equation 4 using scalar factors S_m (t) and pre-identified principal components v_i (r_m), I = 1,…, L, corresponding to spatial modes j_i (r), as follows:

Figure B1 Time derivative of the horizontal external magnetic field |dH/dt| in geographic coordinates at 06:31 UT, 2 Sep 1859 (the moment of the largest |dH/dt| during the Carrington event simulation), before (left) and after 150° westward rotation (right) with respect to the geomagnetic dipole axis. The yellow star indicates the point with the largest simulated |dH/dt|. dX/dt and dY/dt time series at this point are shown in Figure 5. The transformation from the geomagnetic to geographic coordinate system was performed using the position of the geomagnetic north pole in 2025 according to the IGRF model (80.8° N, 72.8° W).

$$c_i\left(t\right)=\sum _{l=1}^M\mathrm{}{S}_m\left(t\right)v_i\left({\mathbf{r}}_m\right).$$(B.1)

• Compute the geoelectric field in the time domain using coefficients c_i (t) and convolution integrals 10 as described in Kruglyakov et al. (2022).

The approach used in the current study for the calculation of the geoelectric field during the Carrington storm has several differences from the approach described in Kruglyakov et al. (2022):

1. In Kruglyakov et al. (2022), geoelectric field modelling is carried out based on the IMAGE magnetometer data. In the current study, magnetic field data are provided on a grid of locations, and we use the data from points that fall within the modelling domain (latitude range: 55–72° N, longitude range: 4–42° E).

2. As we obtain external magnetic field data based on the SWMF outputs, we do not perform magnetic field separation into external and internal parts, as it was done in Kruglyakov et al. (2022), where the total magnetic field was used as an input. Thus, we use only a horizontal magnetic field components to obtain S_m (t).

3. We use the same 34 spatial modes that are used for geoelectric field modelling during the Halloween storm in this study (Appendix A), whereas Kruglyakov et al. (2022) used 21 spatial modes obtained on the basis of 7–8 September 2017 geomagnetic storm.

The sampling rate of the external magnetic field time series is 1 min. Just like in the case of the Halloween storm, geoelectric field calculation “memory” is set to 15 min.

It is important to understand how well the spatial modes are obtained based on the Halloween storm magnetic field data approximate the external source of the more intense Carrington event. To figure this out, we first calculate the external magnetic field (following Vanhamäki & Juusola, 2020) corresponding to

$$S({\mathbf{r}}_m,t)=\sum _{l=1}^L\mathrm{}{c}_i\left(t\right)v_i\left({\mathbf{r}}_m\right),m=1,...,M.$$(B.2)

Then we calculate the fitting error between the original external horizontal magnetic field time series H(r, t) and external horizontal magnetic field H^appr (r, t) obtained using the SECS method and pre-identified principal components in the following way:

$$\mathrm{err}(\mathbf{H},{\mathbf{H}}^{\mathrm{appr}})=\frac{\sum _{i=1}^{N_t}\mathrm{}\sqrt{\left(B_x^{\mathrm{appr}}\right(\mathbf{r},t_i)-B_x(\mathbf{r},t_i){)}^2+(B_y^{\mathrm{appr}}(\mathbf{r},t_i)-B_y(\mathbf{r},t_i){)}^2}}{\sum _{i=1}^{N_t}\mathrm{}\sqrt{B_x^2(\mathbf{r},t_i)+B_y^2(\mathbf{r},t_i)}},$$(B.3)

where N_t is the number of time steps in the magnetic field time series, B_x (r, t) and B_y (r, t) are the original horizontal external magnetic field components and $B_x^{\mathrm{appr}}(\mathbf{r},t)$ and $B_y^{\mathrm{appr}}(\mathbf{r},t)$ are the horizontal external magnetic field components obtained using the approximation described above.

Figure B2 demonstrates the fitting error in the modelling region. Figure B3 shows the time series of the original horizontal external magnetic field components H(r, t) and horizontal external magnetic field components ${\mathbf{H}}^{\mathrm{appr}}(\mathbf{r},t)$ obtained using the SECS method and pre-identified principal components at the external magnetic field grid points closest to Nurmijärvi (NUR) and Abisko (ABK) geomagnetic observatories. It is clear that the fit is good (fitting error is less than 0.2) in the area covered by the IMAGE magnetometers, the data from which were used to obtain the 34 principal components and corresponding spatial modes via the PCA of the SECS ionospheric equivalent current in Marshalko et al. (2023). In Section 3, we perform an analysis of the geoelectric field modelling results for this area.

Figure B2 Fitting error between the original horizontal external magnetic field time series H(r, t) and horizontal external magnetic field time series ${\mathbf{H}}^{\mathrm{appr}}(\mathbf{r},t)$ obtained using the SECS method and pre-identified principal components. The locations of magnetometers in Fennoscandia, the data from which were used for the PCA, are marked with blue and red (ABK, NUR) triangles.

Figure B3 Time series of the original horizontal external magnetic field components H(r, t) (blue) and approximated horizontal external magnetic field components ${\mathbf{H}}^{\mathrm{appr}}(\mathbf{r},t)$ (red) obtained using the SECS method and pre-identified principal components. Time series are demonstrated for the external magnetic field grid points closest to Nurmijärvi (NUR) and Abisko (ABK) geomagnetic observatories. The observatories are marked with red triangles in Figure B2. The original and approximated curves are nearly indistinguishable.

All Figures

	Figure 1 SuperMAG activity indices SMU and SML during the most intense phases of three geomagnetic storms. From top: 13–14 Jul 1982, 13–14 Mar 1989, 29–30 Oct 2003. Black arrows indicate the times of the power grid impacts mentioned in the text. On 13–14 Jul 1982, the smallest value of SML is −4714 nT, and the largest value of SMU is 2131 nT.
In the text

	Figure 2 Measured GIC along the Finnish natural gas pipeline at Mäntsälä in southern Finland on 29–31 Oct 2003. The time cadence was 10 s. Dashed lines indicate the magnetic midnight (blue) and noon (red). Positive GIC flows to the east.
In the text

	Figure 3 Return levels of |dH/dt| for a range of return periods as derived by Rogers et al. (2020, Fig. 4d).
In the text

	Figure 4 Maximum and minimum northward variation of the ground magnetic field in the northern hemisphere as calculated from a simulated Carrington event and mimicking the SuperMAG activity indices SMU (red) and SML (blue).
In the text

	Figure 5 Time derivative of the north (dX/dt) and east (dY/dt) component of the magnetic field at the location in the northern hemisphere with the largest |dH/dt| of the simulated Carrington event.
In the text

	Figure 6 The largest time derivative of the horizontal ground magnetic field (|dH/dt|) in the northern hemisphere as calculated from a simulated Carrington event. The red dot shows the largest known 1-min value, which was recorded at the Lovö observatory in Sweden on 13 Jul 1982.
In the text

Figure 7 Upper panel: The largest time derivative of the horizontal ground magnetic field (|dH/dt|) along each meridian (1° separation) in the northern hemisphere as calculated from the simulated Carrington event at 06:10–06:38 UT on 2 Sep 1859. Red dots indicate values exceeding the largest known measured value (2700 nT/min) at the Lovö observatory in Sweden on 13 Jul 1982 and also marked as a dashed line. Lower panel: geomagnetic latitude of the site of maximum |dH/dt| at each longitude. Red colour is used similarly to the upper panel.

In the text

	Figure 8 Left: Polar view of “hot spots” where |dH/dt| exceeded 2700 nT/min (red) or 1350 nT/min (black) at least once at 06:10–06:38 UT during the simulated Carrington storm on 2 Sep 1859. Right: Snapshot at 06:28 UT, when the number of points with |dH/dt| > 2700 nT/min reached its maximum of the whole event. Geomagnetic latitudes are used.
In the text

Figure 9 Snapshots of the equivalent ionospheric current (top) and geoelectric field (bottom) in Fennoscandia at the moments of the maximum geoelectric field amplification during the Halloween (left) and Carrington (right) storms. Equivalent current and geoelectric field distributions are obtained using procedures described in Appendices A and B. Note that UT for the Carrington storm refers to the time stamp in the original data.

In the text

	Figure 10 The ratio between the maximum magnitudes of the geoelectric field during the Carrington and Halloween storms (black points), along with conductivity distribution (in S/m) in the upper layer of the conductivity model of Fennoscandia used for the geoelectric field simulation. For visual clarity, the ratio is shown only for 1% of points considered in the analysis.
In the text

	Figure 11 The number of points for different values of the ratio between maximum magnitudes of the horizontal geoelectric field during the Carrington and Halloween geomagnetic storms.
In the text

	Figure 12 The ratio between maximum external magnetic field time derivatives during the Carrington and Halloween storms (black points), along with conductivity distribution (in S/m) in the upper layer of the conductivity model of Fennoscandia used for the geoelectric field simulation. For visual clarity, the ratio is shown only for 1% of points considered in the analysis.
In the text

	Figure 13 Left: Sketch of a grid of electric field vectors (blue arrows) and eastward and northward lines (red) along which the voltage is determined. Right: Carrington to Halloween ratio of the maximum absolute voltages along northward and eastward lines.
In the text

	Figure 14 Top: GIC modelled (red curve) and observed (black curve) due to the Halloween storm on 29–31 Oct 2003. Bottom: GIC modelled due to the Carrington storm on 2 September 1859. Values are 1-min data. The modelled and observed values for the Halloween storm are very close to each other and nearly indistinguishable.
In the text

	Figure 15 Geographic map of the estimated risk level of the impacts on power grids due to an extreme geomagnetic storm, based on Figures 7–8. Red refers to regions where |dH/dt| is likely to exceed the Space Age record. In the yellow regions, at least half of the Space Age record is reached. Note that our study does not consider equatorial regions.
In the text

Figure B1 Time derivative of the horizontal external magnetic field |dH/dt| in geographic coordinates at 06:31 UT, 2 Sep 1859 (the moment of the largest |dH/dt| during the Carrington event simulation), before (left) and after 150° westward rotation (right) with respect to the geomagnetic dipole axis. The yellow star indicates the point with the largest simulated |dH/dt|. dX/dt and dY/dt time series at this point are shown in Figure 5. The transformation from the geomagnetic to geographic coordinate system was performed using the position of the geomagnetic north pole in 2025 according to the IGRF model (80.8° N, 72.8° W).

In the text

Figure B2 Fitting error between the original horizontal external magnetic field time series H(r, t) and horizontal external magnetic field time series ${\mathbf{H}}^{\mathrm{appr}}(\mathbf{r},t)$ obtained using the SECS method and pre-identified principal components. The locations of magnetometers in Fennoscandia, the data from which were used for the PCA, are marked with blue and red (ABK, NUR) triangles.

In the text

Figure B3 Time series of the original horizontal external magnetic field components H(r, t) (blue) and approximated horizontal external magnetic field components ${\mathbf{H}}^{\mathrm{appr}}(\mathbf{r},t)$ (red) obtained using the SECS method and pre-identified principal components. Time series are demonstrated for the external magnetic field grid points closest to Nurmijärvi (NUR) and Abisko (ABK) geomagnetic observatories. The observatories are marked with red triangles in Figure B2. The original and approximated curves are nearly indistinguishable.

In the text