# Reproducibility of the Geomagnetically Induced Currents at Middle Latitudes During Space Weather Disturbances

^{1}Institute for Sun-Earth Environmental Research, Nagoya University, Nagoya, Japan^{2}Research Institute for Sustainable Humanosphere, Kyoto University, Kyoto, Japan^{3}School of Agriculture, Kibi International University, Minamiawaji, Japan^{4}National Institute of Technology, Tokuyama College, Shunan, Japan^{5}Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu, Japan^{6}National Institute of Information and Communications Technology, Koganei, Japan

Watari et al. (Space Weather, 2009, 7) found that the geomagnetically induced current (GIC) in Hokkaido, Japan (35.7° geomagnetic latitude (GML)), is well correlated with the y-component magnetic field (*T*) of disturbances, we made correlation analyses for the geomagnetic sudden commencements and pulsations (*T* = 1–10 min), quasi-periodic DP2 fluctuations (30 min), substorm positive bays (60 min), geomagnetic storms (1–20 h), and quiet-time diurnal variations (8 h). The linear correlation is found to be valid for short periods (cc > 0.8 for *T* < 1 h) but not for long periods (cc < 0.3 for *T* > 6 h). To reproduce the GIC with any periods, we constructed one-layer model with uniform conductor and calculated the electric field (IEF) induced by *B*_{y} dependence. The mechanism of the strong *B*_{y} dependence of the GIC remains an issue, but a possible mechanism for the daytime GIC is due to the zeroth-order transverse magnetic (TM_{0}) mode in the Earth-ionosphere waveguide, by which the ionospheric currents are transmitted from the polar to equatorial ionosphere.

## Key Points

1. The geomagnetically induced currents in Hokkaido, Japan (35.7° GML), are correlated with *B*_{y} (cc > 0.8) for short periods (*T* < 1 h), while the correlation is poor (cc < 0.3) for long periods (*T* > 6 h).

2. The GICs with periods of 1 min to 24 h are well correlated with the electric field, *E*_{x}, induced by *B*_{y} in the semi-infinite one-layer conductivity model (cc > 0.85) and two-layer model (cc > 0.95) composed of highly conductive upper layer.

3. The strong *B*_{y} dependence of the GIC is also observed at lower latitude in Japan (25.3° GML) with cc > 0.85.

4. The *B*_{y} dependence of the midlatitude GIC may be associated with the ionosphere-ground currents transmitted by the TM_{0} mode waves in the earth-ionosphere waveguide from high latitude to the equator.

## Introduction

Geomagnetic disturbances have been known to induce electric fields on the surface of the Earth, which create a potential difference between transformers in the power transmission line system. The potential difference drives electric currents [geomagnetically induced currents (GICs)] in the power lines through the Earthing lines of the transformers (Pirjola, 1983). The GIC is a quasi-steady current, compared to the frequency (50 Hz or 60 Hz) of the power system, and has the larger magnitude at higher latitudes, particularly at the auroral latitudes where the auroral electrojets cause large-amplitude disturbances in the northward magnetic field (

The GIC is derived from formula relating the GIC and the surface electric field; *a* and *b* are the parameters, which depend on the topology and the electrical characteristics of the system (Pulkkinen et al., 2007; Viljanen et al., 2012; Wei et al., 2013). The surface impedance has been widely used to estimate the electric fields from the magnetic fields through the relationship; *E*_{x,y} = Z·*B*_{y}*,*_{x}/*μ*, where *B*_{y}*,*_{x}, *μ*, and Z are the horizontal magnetic field, magnetic permeability, and surface impedance, respectively. The surface impedance is derived from the ground conductivity and layer thickness through the complex-image method (Boteler and Pirjola, 1998) and from the measured GIC and surface magnetic fields (Pulkkinen et al., 2007).

On the other hand, it was reported that the GIC is much more closely related to time derivatives (*dB/dt*) than *B* (deflection from the pre-event value) (Viljanen, 1997; Trichtchenko and Boteler, 2006) and the GIC has been evaluated by quite a few papers from *dB/dt* using the Faraday’s law (Viljanen, 1997; Pirjola, 2000; Carter et al., 2016; Kozyreva et al., 2018). It should be noted, on the other hand, that *dB/dt* is related to the spatial derivative of the electric field, *E*, in the Faraday’s law. No clear correspondence between the GIC and *dB/dt* to the GIC. The *dB/dt* method has been used to assess the GIC even under the equatorial electrojet where the GIC has never been measured (Ngwira et al., 2013; Carter et al., 2016). It should be noted that the induction theory tells us that *dB/dt* should be convolved with the function of 1/*t*: time) (Cagniard, 1953; Viljanen and Pirjola, 1989) that is a response of the conductor to step function-like magnetic field changes (Cheng, 1959). Thus, the sole usage of *dB/dt* does not meet the induction theory except that the model is composed of two layers with less conductive upper layer over the highly conductive lower layer (Pirjola, 2010).

Watari et al. (2009) demonstrated that the middle latitude GIC in Hokkaido (35.7° GML), Japan, is not correlated with _{0} mode waves in the Earth-ionosphere waveguide, which was applied to explain the instantaneous transmission of the polar electric field and currents to the equator (Kikuchi et al., 1978). Brändlein et al. (2012) also suggested that the GIC is closely associated with the ionospheric currents by showing diurnal and seasonal variations of the GIC observed at low latitude in northern Chile.

The Hokkaido GIC has been reproduced from the ground magnetic fields using the surface impedance (Pulkkinen et al., 2010). Furthermore, Love and Swidinski (2015) reproduced the geoelectric field (GEF) measured at Kakioka, Japan (27.8° GML), from the magnetic fields at Kakioka using the convolution of *dB/dt* and the response of the semi-infinite one-dimensional flat Earth. Love and Swidinski (2014) solved the diffusion equation using the Laplace transformation and applied the function of *dB/dt*. The reproduced IEF was plotted in good shape with the observed GEF, but the correlation is not evaluated quantitatively.

As overviewed above, there are various methods to reproduce the GIC/GEF from the surface magnetic field such as from *dB/dt*, surface impedance and from the convolution of *dB/dt* and response functions. The variety of the method may be due to many factors affecting the GIC such as directions of power lines and coastlines, 3-D structures of Earth’s conductivities (Goto, 2015; Nakamura et al., 2018; Ivannikova et al., 2018), and the propagation mode that transports magnetic disturbances from the ionosphere and magnetosphere into the Earth. In this study, we revisit the GIC in Hokkaido to construct a model that reproduces the GIC from the observed magnetic field, *B*_{y}. The model is not to clarify the structure of the Earth’s conductivity that has been made by other methods like the magneto-telluric (MT) method but is rather a tool designed so as to reproduce the GIC from the surface magnetic field as accurately as possible. As a next step to the accomplishment of the good correlations between the GIC and *B*_{y} (Watari et al., 2009), we examine if the GIC-*B*_{y} correlations are valid for any space weather disturbances with different period/time scales ranging from 1 min to 24 h. As shown in the following sections, we found that the GIC-*B*_{y} correlation depends on the period of disturbances such that cc > 0.8 for short periods (<1 h) and cc < 0.3 for long periods (>6 h). To construct a model capable of reproducing the long period GIC, we calculated the IEF, *Derivation of the IEF from the Observed Magnetic field*, we formulate equations that derive the IEF from the observed magnetic field in one- and two-layer models. Then, we calculate correlation coefficients of the GIC with *B*_{x,y} and *E*_{y,x} induced in the one- and two-layer models in *Correlations among Observed GIC, B*_{x,y} *and E*_{y,x}. In order to evaluate the capability of the model for various types of space weather events, we analyzed impulsive geomagnetic sudden commencement (SC), short-period (1 min) geomagnetic Pi2 pulsations, longer-period (30 min-8 hours) DP2 fluctuations, and solar quiet diurnal variations (Sq), isolated substorm magnetic bays, and long-lasting storm disturbances (1–24 h). To examine the generality of the model, we applied the model to the GIC measured at the Shin-Yamaguchi (SYG) substation of the Chugoku Electric Company located at lower latitudes in Japan (25.3° GML). We found that the model well reproduced the GIC at SYG with high correlation coefficients (cc = 0.87–0.95) for DP2 and SC events with strong *B*_{y} dependence. In *Discussion*, we discuss that the daytime GIC can be connected with the ionospheric currents by the TM_{0} mode waves in the Earth-ionosphere waveguide, which carry the ionospheric currents from the polar ionosphere to the equator (Kikuchi et al., 1978; Kikuchi, 2014). We further stress that large-amplitude GICs tend to occur around the midnight during substorms, which raises an issue on the propagation mode from the magnetospheric currents to the ground on the nightside.

## Derivation of the IEF from the Observed Magnetic field

### Convolution Theorem

The magnetic field, *s* (*s* is the complex number used in the Laplace transformation), and integration is multiplication of 1/*s*. Following the theory of response of the linear system (Cheng, 1959), the induced electric field (IEF),

Here, we note that the impulse response is a response of the system to the external excitation in a form of the delta function,

where ∗ refers to the convolution of two functions. The convolution (2) implies that *t*.

We may write the Eq. 1 in a different form including 1/s (time integral) and s (time derivative) as

Using Eq. 3, we can write the convolution (2) in a different form as

where *G*(*t*) denotes the step response of the conductor, a response to the excitation function in a form of the unit step function, *B*_{y}(0) is the initial value of *B*_{y}. In the following, *B*_{y}(0) is assumed to be zero since *t* = 0 is set to the quiet time before the arrival of the disturbances. The convolution (4) is identical to the Eq. 12 of Cagniard (1953). It should be stressed that the IEF is obtained from *dB/dt* convolved with the step response of the conductor. In the following, we use Eq. 4 to derive the IEF, while Eq. 2 works the same way. Since the GIC and magnetometer data at Memambetsu (MMB), Hokkaido are sampled every one second, the time *t* is discrete, and the time derivative and integral in Eq. 4 are replaced with a difference and summation, respectively, as follows.

where we start the summation from *i* = 1 since

### IEF in One-Layer Model

The diffusion equation in the conductor is derived from the Faraday’s law, Ampere’s law, and Ohm’s law as listed below.

where ** J** are electric conductivity and current in the conductor, respectively.

The Eq. 6 leads to the following diffusion equations for *x, y*, and *z* directed toward the north, east, and down, respectively.

The Laplace transforms of Eq. 7 are given by

where the initial value of *B*_{y} is assumed to be zero as mentioned above. Transformed solutions are obtained in the following form:

We give the unit step function for *z* = 0 to obtain the step response function, which is used to derive the IEF from the convolution with *z* = 0 and

We thus have the transformed solutions as

Substituting *z* = 0 for Eq. 10 and applying the inverse transformation,

Substituting (11) for (5), we obtain the IEF as

### IEF in the Two-Layer Model

Using the earth-currents and magnetometer data, Owada (1972) showed that the subterranean electric conductivity at Memambetsu has a structure of three layers with depths of 8–20 km, 20–90 km, and 90–170 km and with conductivities higher in the top layer than in the lower layers. The MT method has revealed inhomogeneous distribution of the Earth’s conductivity in Hokkaido not only in the vertical but also in the horizontal directions (Satoh et al., 2000; Uyeshima et al., 2001; Uyeshima, 2007). However, since our purpose is to construct a model that is capable of reproducing the observed GIC, we pay our attention to the vertical profile of Owada (1972)’s results and construct a two-layer model with thickness, *d* = 20 km and

We assume the magnetic field be a fixed value at *z* = 0 in the same way as in the one-layer model, and the magnetic permeability is common in both layers. The Laplace-transformed solutions in the layer 1 and layer 2 are given as follows:

We give the unit step function for

We obtain

where

Under the condition,

where *j* refers to the number of reflections and *n* is chosen so that the summation approaches a steady value (*n* = 50 in the calculation below). Then, we have the coefficients as follows:

Substituting Eq. 18 for Eq. 13, we obtain the transformed solutions as follows:

The Laplace transform of the step response function, *z* = 0 for

Using the inverse Laplace transform,

Using Eq. 21 in Eq. 5, we obtain the IEF from the convolution,

## Correlations among Observed GIC, B_{x,y}, and E_{y,x}

The GIC was measured on the grounding conductor in the transformer of the 187 kV power line systems at the Memambetsu substation of Hokkaido Electric Power Co. Inc. (35.7° GML). The direction of the power line is southwestward, and the length of the line is approximately 100 km (Watari et al., 2009). The magnetometer observations were made at the Memambetsu magnetic observatory (http://www.kakioka-jma.go.jp/en/index.html) close to the GIC measurements.

### Pi2 and SC (1–10 min)

To confirm the high correlation between the GIC and *B*_{y} (Watari et al., 2009), we picked out a Pi2 event with the period of 1 min recorded at Memambetsu (MMB) in the morning sector (0600 MLT) and a geomagnetic sudden commencement (SC) with the preliminary impulse (PI, 1 min) followed by the main impulse (MI, 5–10 min) in the morning sector (0630 MLT). Figure 1 shows *B*_{y} (cc = 0.90), while almost nothing with *B*_{x} (cc = -0.21). The Pi2 often occurs on the nightside during substorms, while also observed on the dayside as the event in Figure 1 is the case (e.g., Han et al., 2004). The daytime Pi2 has been attributed to ionospheric currents flowing from the polar ionosphere to the equator carried by the TM_{0} mode waves in the Earth-ionosphere waveguide (Sutcliffe and Lühr, 2010; Imajo et al., 2015). The TM_{0} mode waves propagating southward (-x direction) have the magnetic field _{0} mode waves as suggested by Watari et al. (2009) and Brändlein et al. (2012).

**FIGURE 1**. **(A)** X- and Y-components of the magnetic field (*B*_{x}, *B*_{y}) observed at the Memambetsu (MMB) magnetic observatory during the Pi2 event with the period of 1 min in the morning sector (21 UT, 06 MLT). **(B)** GIC observed at the Memambetsu substation of the Hokkaido Electric Company (solid curve). *E*_{x2} scaled to the GIC is plotted with the dotted curve in the frame of the GIC, so that one can see the high correlation between the GIC and *E*_{x2}. **(C, D)** The induced electric fields (IEF), *E*_{y,x} induced by *B*_{x,y} at the surface of the Earth in the one- and two-layer models. Sig1 = 10^{–4} mho/ m in the one-layer model denotes the conductivity of the semi-infinite uniform conductor. The parameters of the two-layer model are sig1 = 10^{–4} mho/ m and depth = 20 km of the upper layer and sig2 = 10^{–8} mho/ m of the semi-infinite lower layer. The cc refers to the correlation coefficient between the GIC and *B*_{x,y}/*E*_{y,x}.

Figure 1 also shows the IEF in one-layer model,

Figure 2 shows the SC event with the positive PI followed by the negative MI in _{0} mode waves (Kikuchi, 2014), the GIC is consistent with being the ground surface currents carried by the TM_{0} mode waves.

**FIGURE 2**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB, and **(B)** *E*_{x} and *E*_{y} calculated in the one- and two-layer models for the SC event with time scales of 1–10 min observed in the morning sector (2130 UT, 0630 MLT). The parameters and formats of the plots are the same as in Figure 1.

Figure 2 (right panels) shows the IEF in one- and two-layer models. The correlation of the GIC with

### Quasi-Periodic DP2 Fluctuations (30 min)

Figure 3 shows periodic fluctuations with periods of 30 min in both

**FIGURE 3**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB, and **(B)** *E*_{x} and *E*_{y} calculated in the one- and two-layer models for the DP2 fluctuation event with periods of 30 min in the evening sector (10-12 UT, 19-21 MLT). The parameters and formats of the plots are the same as in Figure 1.

The correlation of the GIC with

### Substorm Bays (60 min)

Figure 4 shows two successive substorm positive bays in _{0} mode wave scenario since the magnetic bays on the nightside are caused not by ionospheric currents but primarily by field-aligned currents. It remains an issue what kind of propagation mode explains the

**FIGURE 4**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB, and **(B)** *E*_{x} and *E*_{y} calculated in the one- and two-layer models for the substorm positive bay events with time scales of 60 min in the pre-midnight (14 UT, 23 MLT) and post-midnight (17 UT, 02 MLT). The parameters and formats of the plots are the same as in Figure 1.

### Geomagnetic Storms (1–20 h)

Figure 5 shows a geomagnetic storm event, where

**FIGURE 5**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB, and **(B)** *E*_{x} and *E*_{y} calculated in the one- and two-layer models for the geomagnetic storm events with the main phase (00-10 UT, 09-19 MLT) followed by the recovery phase (10-18 UT, 19-03 MLT) superimposed by the substorm positive bay (10-11 UT, 19-20 MLT). The parameters and formats of the plots are the same as in Figure 1.

### Solar Quiet Geomagnetic Variations (8 h)

Figure 6 shows an example of the solar quiet geomagnetic variations (Sq). The period of Sq is 24 h, while significant changes occur over 8 h in the daytime (00-08 UT, 09-17 MLT).

**FIGURE 6**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB, and **(B)** *E*_{x} and *E*_{y} calculated in the one- and two-layer models for the solar quiet diurnal variations with time scales of 8 h (00-08 UT, 09-17 MLT). The parameters and formats of the plots are the same as in Figure 1.

## Discussion

The GIC in Hokkaido, Japan, can be reproduced from

**TABLE 1**. Correlation coefficients between the GIC and surface magnetic fields, *B*_{x} and *B*_{y} and the electric field, *E*_{y} and *E*_{x} induced by *B*_{x} and *B*_{y}, respectively, calculated in one (I)- and two (II)-layer models for space weather (SW) events with periods ranging from 1min to 24 h.

To address this issue, we constructed the two-layer model composed of higher conductivity in the upper layer, following the previous works on the geoelectric conductivity at Memambetsu (Owada, 1972). Fujii et al. (2015), using the MT method, clarified that the apparent resistivity of the Earth increases with an increasing period of geomagnetic disturbances at Memambetsu. This result is qualitatively consistent with the two-layer model with lower conductivity in the lower layer. The two-layer model with higher conductivity in the upper layer well explains the linear relationship with *B* (Pirjola, 2000). As summarized in Table 1, the induced electric field in the two-layer model,

**FIGURE 7**. Observed GIC (solid curve) and *E*_{x2} scaled to the GIC (dotted curve) during space weather disturbances; SC, Pi2, substorms, and storms with different time scales. The cc (gic-ex2) refers to the correlation coefficient between the GIC and *E*_{x2}, and sampling = 1 s refers to that the original 1 s sampled GIC and *B*_{y} data are used. Note that MLT = UT + 9.

We here check parameter dependence of the correlation coefficients (*cc*) in the two-layer model. Provided that the conductivities are fixed, major parameters responsible for cc are the number of reflections (*n*) and the depth of the upper layer (*d*_{1}) in the Eq. 22. Using the DP2 event in Figure 3, we calculated *cc* with *d*_{1} = 20 km and different n. The *cc* increases as *n* increases such that *cc* = 0.94, 0.96, 0.96, 0.97, 0.97 for *n* = 20, 30, 40, 50, 100, respectively. We then calculated cc with fixed *n* = 50 and different *d*_{1}. The cc increases as *d*_{1} increases such that *cc* = 0.94, 0.96, 0.97, 0.97 for *d*_{1} = 10, 15, 20, 30 km, respectively. Thus, we fixed *n* = 50 and *d*_{1} = 20 km in the two-layer model used for the calculation of the correlation coefficients.

Here, we make a brief comment on the singularity of *t* = 0 included in the step response function. Love and Swidinsky (2014), Love and Swidinsky (2015) introduced the ramp function, *t* with *t* + 0.0001 to avoid *t* = 0. This approximation worked well to achieve the excellent correlations between the IEF and GIC, while it is just technical so that 0.0001 can be replaced with another small value.

We next examine if we can estimate the GIC that could have occurred during the past major storms. For this examination, we fix scale factors, *k*_{1} (GIC/*E*_{x1}) = 8.0 [A/(mV/m)] and *k*_{2} (=GIC/*E*_{x2}) = 0.17 [A/(mV/m)], derived from the isolated substorm event in Figure 8. The observed GIC is well reproduced by both the one-layer and two-layer models with cc (GIC- *E*_{x1}) = 0.97 and cc (CIC- *E*_{x2}) = 0.99 as shown in the bottom left and right panels of Figure 8, respectively. For the sake of visual comparison, the observed GIC is plotted with dotted curves in each of the panels. Then, we used the scale factors, *k*_{1} and *k*_{2}, to reproduce the GIC observed during the SC event (Figure 2). As shown in Figure 9, the GIC is well reproduced by the two-layer model with the same amplitude and high cc (=0.99), whereas the GIC is not well reproduced by the one-layer model with lower cc (= 0.88) and overestimation of the rapid changes at the onset of the SC. The good correlation between the GIC and *E*_{x2} for the bay and SC events would allow us to use the scale factor *k*_{2} to estimate the GIC for the past major storms. Figure 10 shows two examples of the estimated GIC during the storms on November 6, 2001 (panel (a)) and October 30, 2003 (panel (b)). It is interesting to note that the GIC estimated for the October 2003 storm has the largest magnitude at 20 UT because of the large magnitude of *B*_{y}, when the storm ring current had not fully developed yet. This result suggests strong local time dependence of the GIC at MMB, which raises an important issue from the space weather forecasting point of view.

**FIGURE 8**. **(A, B)** *B*_{x}, *B*_{y} and GIC observed at MMB in the evening (10 UT, 19 MLT) during the substorm bay event. **(C)** GIC estimated from *E*_{x1} scaled to the GIC with the scale factor, *k*_{1} = 8.0 [A/(mV/m)] (solid line) and observed GIC (dotted line). **(D)** GIC estimated from *E*_{x2} scaled to the GIC with the scale factor, *k*_{2} = 0.17 [A/(mV/m)] (solid line) and observed GIC (dotted line).

**FIGURE 9**. **(A)** *B*_{x}, *B*_{y} and GIC observed at MMB during the SC event same as in Figure 2. **(B)** GIC estimated from *E*_{x1} and *E*_{x2} scaled with the same scale factors as in Figure 8.

**FIGURE 10**. **(A)** Geomagnetic storms recorded at MMB in the daytime (01-09 UT, 10-18 MLT) on November 06, 2001 and **(B)** in the midnight-morning (16-24 UT, 01-09 MLT) on October 30, 2003. **(C) (D)** GICs estimated from *E*_{x2} with the scale factor same as in Figures 8, 9.

The parameters used in the two-layer model may not represent the ones estimated by the MT method (Fujii et al., 2015), but the excellent correlations in Table 1 allow us to use the model to reproduce the GIC from the observed magnetic field disturbances. Therefore, the model should be referred to as an empirical model that works for MMB. Although the model is not a commonly applicable model, we check the model with GICs measured at the Shin-Yamaguchi (SYG) substation of the Chugoku Electric Power Company in Yamaguchi prefecture in the western-southern part of Japan (34.16°N, 131.09°E GR; 25.25°N, 201.67°E GM). The power transmission line extends in the east-west direction along the coastline. Figure 11 shows a DP2 fluctuation event (T = 80 min) observed at Kakioka (KAK, 36.23°N,140.19°E GR; 27.95°N,209.77°E GM) and the GIC at SYG, where the high frequency components are removed by applying the moving average over the window of 10 min. The KAK observatory is separated from SYG by 2.7° in GML, but the GIC is well correlated with the IEF such that cc (GIC-*E*_{xI}) = 0.85 and cc (GIC-*E*_{xII}) = 0.87. The model parameters are the same as used in the calculations for MMB except for the depth of the upper layer of the two-layer model being 15 km. Figure 12 shows an SC event with time scales of 1–10 min, where the window for the moving average is 30s. The correlation coefficients are better than those of the DP2 event such that cc (GIC-*E*_{xI}) = 0.93 and cc (GIC-*E*_{xII}) = 0.95. The correlation coefficients of the GIC with *B*_{x}/*E*_{yII} are not so good; cc = 0.54/0.14 and 0.27/0.51 for the DP2 and SC events, respectively. It is remarkable that the GIC at SYG is strongly dependent on *B*_{y}/*E*_{x}, similarly to the GIC at MMB. Furthermore, there is no big difference between the one- and two-layer models, suggesting us to use the simple one-layer model to estimate the GIC at SYG during the past major storms. Using the models constructed in the present study, we would be able to predict the GIC during space weather disturbances with the aid of the global simulations. Ebihara et al. (2014) successfully reproduced ground magnetic disturbances due to the equatorial electrojet driven by the penetration electric fields during substorms. Furthermore, Tanaka et al. (2020) reproduced magnetic disturbances due to field-aligned currents as well as the ionospheric currents during the SC and substorm.

**FIGURE 11**. **(A)** *B*_{x} and *B*_{y} observed at the Kakioka (KAK) magnetic observatory and GIC observed at the Shin-Yamaguchi (SYG) substation of the Chugoku Electric Power Company during the DP2 fluctuation event with periods of 60–80 min in the early morning (16-20 UT, 01-05 MLT). The GIC data is smoothed by applying the moving average over 10 min. **(B)** *E*_{x} and *E*_{y} calculated in one- and two-layer models. The parameters in the frames are the same as in Figure 1 except that the depth of the upper layer of the two-layer model is 15 km.

**FIGURE 12**. **(A)** *B*_{x} and *B*_{y} observed at KAK in the morning (2220 UT, 0720 MLT) and GIC at SYG during the SC event (T = 1–10 min) with the same parameters as in Figure 11, except that the GIC data is smoothed over 30s. **(B)** IEFs in the same format as in Figure 1.

The power transmission line in Hokkaido is directed southwestward (Watari et al., 2009), which would predict that the GIC is affected equally by both *B*_{y}/*E*_{x} at SYG, where the power line and coastline are in the east-west direction. Two possible mechanisms may explain the strong _{0} mode waves in the Earth-ionosphere waveguide (Watari et al., 2009; Brändlein et al., 2012). The TM_{0} mode wave transmits the _{0} mode propagates at the speed of light and explains the simultaneous occurrence of the PI of SC (Araki, 1977) and DP2 fluctuations (Kikuchi et al., 1996) at high latitude and equator. In Figure 13, we show the equatorial electrojet (EEJ) defined as difference in *B*_{x} between Yap, Micronesia (YAP, 0.5° GML), and Okinawa, Japan (OKI, 17.0° GML) (Kikuchi et al., 1996) together with *B*_{x} (dots) and *B*_{y} (solid) at MMB, KAK, and OKI. It is remarkable that the EEJ is well correlated with *B*_{y} at MMB, KAK, and OKI, of which amplitude decreases as the latitude decreases. The latitudinal features may indicate that the Pedersen currents responsible for *B*_{y} at middle latitudes flow into the equatorial ionosphere. Since the TM_{0} mode waves induce ionospheric currents and ground surface currents (Kikuchi, 2014), it would be reasonable to attribute *B*_{y} and the GIC to the TM_{0} mode waves. It should be noted, however, that the TM_{0} mode wave scenario may not be valid on the nightside, since ground magnetic fields are caused by magnetospheric currents in addition to the ionospheric currents during substorms (Ritter et al., 2008). Among these currents, the field-aligned currents transport the electromagnetic energy from the magnetosphere to the polar ionosphere. Therefore, a question arises, what kind of propagation mode transports the electromagnetic energy from the foot of the field-aligned currents or directly from the magnetosphere to the power transmission line at middle latitudes on the nightside? This will be a challenging issue of the magnetosphereionosphere coupling at middle latitudes.

**FIGURE 13**. Bx (dotted lines) and By (solid lines) recorded during the SC event (Figure 2) at Memambetsu (MMB, 35.7°GML), Kakioka (KAK, 27.8°GML), Okinawa (OKI, 17.0°GML), and the magnetic deflection caused by the equatorial electrojet (EEJ) defined as the difference between Bx (YAP, 0.5°GML) and Bx (OKI). All the stations are in the same local time zone (0630 MLT).

The other possible mechanism is the effects of the geometry such as the direction of power lines and coastlines and of the 3-D structures of Earth’s conductivities (Fujii et al., 2015; Goto, 2015; Nakamura et al., 2018). Ivannikova et al. (2018) found that much of Great Britain was affected by coastal effects owing to the strong conductivity gradient between the land and the ocean. The coastline effects on the GIC are also significant in Hokkaido as deduced from the model calculations (Nakamura et al., 2018). Furthermore, Fujii et al. (2015) clarified that the MT response at Memambetsu shows that *B*_{y} affects the induction in x-direction more strongly than *B*_{x} does in y-direction. The MT-deduced anisotropy is explained by means of the spatial inhomogeneity of the Earth’s conductivity. Thus, both effects of the coastline and inhomogeneous distribution of the Earth’s conductivity should have affected the anisotropic response of the GIC to the surface magnetic field. We would need to take into account the inhomogeneous conductivity distribution even in a thin layer model (e.g., McKirdy and Weaver, 1984). However, the horizontally uniform models employed in the present study well explain the GIC-*B*_{y}/*E*_{x} correlations. The consistency between the MT and GIC results and the inconsistency between the nonuniform and uniform models remain a question to be addressed in future studies.

## Conclusion

1) We have shown that the GIC at Memambetsu in Hokkaido (35.7° GML) is linearly correlated with the y-component geomagnetic field,

2) The induced electric field in the one-layer model with the semi-infinite conductor (

3) We constructed the two-layer model with higher conductivity in the upper layer (

4) The GIC at Shin-Yamaguchi, Japan (25.3° GML) is well correlated with *B*_{y}/*E*_{xII} similarly to the GIC at MMB, such that cc = 0.87 and 0.95 for the DP2 and SC events, respectively.

5) The strong _{0} mode in the Earth-ionosphere waveguide, which carries

## Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

## Author Contributions

TK built the one- and two-layer models and wrote the whole sections of the manuscript. YE contributed to creating the GIC database and to the calculation of the IEF in the models. KKH performed space weather event studies with magnetometer data and contributed to establishing the data acquisition system from SYG substation. KK installed the GIC meter and calibrated the data at SYG. S-IW contributed to recording the GIC at MMB. All authors contributed to manuscript revision, read, and approved the submitted version.

## Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

## Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

## Acknowledgments

The measurement of the GIC at Memambetsu substation of the Hokkaido Electric Power Co., Inc., was carried out under contract with the National Institute of Information and Communications Technology (NICT) and Institute for Sun-Earth Environmental Research (ISEE), Nagoya University. This contract is subject to the data sharing restrictions defined under the Memorandum of Understanding signed by the four organizations, including the NICT (S-IW) and Nagoya University (TK). We would like to thank Mr. Yuji Watanabe, Research and Development Department, the Hokkaido Electric Power Co., Inc., for supporting the GIC measurement at Memambetsu substation. The measurement of the GIC at Shin-Yamaguchi substation of the Chugoku Electric Power Co., Inc. was carried out under contract with the National Institute of Technology/Tokuyama College (TCT) and Kibi International University (KIUI). This contract is subject to the data sharing restrictions defined under the Memorandum of Understanding signed by the three organizations, including the TCT (KK) and KIUI (K.KH). We would like to thank Mr. K. Fujii at the Chugoku Electric Power Co., Inc., for supporting the GIC measurement at the Shin-Yamaguchi substation. Those who are interested in the data may contact with any one of TK at ISEE (kikuchi@isee.nagoya-u.ac.jp), S-IW at NICT (watari@nict.go.jp), and K.KH (hashi@kiui.ac.jp). The magnetometer data at Memambetsu and Kakioka are provided by the Kakioka Magnetic Observatory of the Japan Meteorological Agency (www.kakioka-jma.go.jp). The magnetometer data at Yap and Okinawa are from the Space Weather Magnetometer Network of the NICT. This study is supported by the grants-in-aid for Scientific Research (15H05815, 20H01960) of Japan Society for the Promotion of Science (JSPS), Electric Technology Research Foundation of Chugoku, and Wesco Scientific Promotion Foundation. The works of T.K. are supported by the joint research programs of the Institute for Space-Earth Environmental Research, Nagoya University and the Research Institute for Sustainable Humanosphere, Kyoto University.

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Keywords: geomagnetically induced current (GIC), middle latitude, polar-equatorial ionospheric currents, TM0 mode in the earth-ionosphere waveguide, induced electric field in the two-layer conductivity model, geomagnetic by dependence of GIC

Citation: Kikuchi T, Ebihara Y, Hashimoto KK, Kitamura K and Watari S-I (2021) Reproducibility of the Geomagnetically Induced Currents at Middle Latitudes During Space Weather Disturbances. *Front. Astron. Space Sci.* 8:759431. doi: 10.3389/fspas.2021.759431

Received: 16 August 2021; Accepted: 02 September 2021;

Published: 11 October 2021.

Edited by:

Toshi Nishimura, Boston University, United StatesReviewed by:

Larry Lyons, UCLA Atmospheric and Oceanic Sciences, United StatesHermann Lühr, German Research Centre for Geosciences, Germany

Copyright © 2021 Kikuchi, Ebihara, Hashimoto, Kitamura and Watari. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Takashi Kikuchi, kikuchi@isee.nagoya-u.ac.jp