Electric Mode Excitation in the Atmosphere by Magnetospheric Impulses and ULF Waves

Variations of vertical atmospheric electric field E z have been attributed mainly to meteorological processes. On the other hand, the theory of electromagnetic waves in the atmosphere, between the bottom ionosphere and earth’s surface, predicts two modes, magnetic H (TE) and electric E (TH) modes, where the E-mode has a vertical electric field component, E z . Past attempts to find signatures of ULF (periods from fractions to tens of minutes) disturbances in E z gave contradictory results. Recently, study of ULF disturbances of atmospheric electric field became feasible thanks to project GLOCAEM, which united stations with 1 sec measurements of potential gradient. These data enable us to address the long-standing problem of the coupling between atmospheric electricity and space weather disturbances at ULF time scales. Also, we have reexamined results of earlier balloon-born electric field and ground magnetic field measurements in Antarctica. Transmission of storm sudden commencement (SSC) impulses to lower latitudes was often interpreted as excitation of the electric TH0 mode, instantly propagating along the ionosphere–ground waveguide. According to this theoretical estimate, even a weak magnetic signature of the E-mode ∼1 nT must be accompanied by a burst of E z well exceeding the atmospheric potential gradient. We have examined simultaneous records of magnetometers and electric field-mills during >50 SSC events in 2007–2019 in search for signatures of E-mode. However, the observed E z disturbance never exceeded background fluctuations ∼10 V/m, much less than expected for the TH0 mode. We constructed a model of the electromagnetic ULF response to an oscillating magnetospheric field-aligned current incident onto the realistic ionosphere and atmosphere. The model is based on numerical solution of the full-wave equations in the atmospheric-ionospheric collisional plasma, using parameters that were reconstructed using the IRI model. We have calculated the vertical and horizontal distributions of magnetic and electric fields of both H- and E-modes excited by magnetospheric field-aligned currents. The model predicts that the excitation rate of the E-mode by magnetospheric disturbances is low, so only a weak E z response with a magnitude of ∼several V/m will be produced by ∼100 nT geomagnetic disturbance. However, at balloon heights (∼30 km), electric field of the E-mode becomes dominating. Predicted amplitudes of horizontal electric field in the atmosphere induced by Pc5 pulsations and travelling convection vortices, about tens of mV/m, are in good agreement with balloon electric field and ground magnetometer observations.

E-mode, or by mode conversion owing to crust conductivity inhomogeneities. Direct measurements of the vertical electric field in the atmosphere seemingly indicated the possibility of the E-mode existence in the Pc3 (Chetaev et al., 1975) and Pc1 (Chetaev et al., 1977) frequency bands.
On the other hand, Anisimov et al. (1993) found no systematic pulsations in atmospheric E z field coherent with geomagnetic Pc3 pulsations at middle latitude. Rare events with quasiperiodic variations of E z were possibly the result of advection by wind of spatially inhomogeneous aero electric structures. At high latitude, the coherence between E z fluctuations and simultaneous geomagnetic pulsations was low, though they both sometimes demonstrated periodic variations in the same period range 5-30 min (Kleimenova et al., 1996).
The problem is further complicated by the sporadic occurrence on the ground of periodic long-lasting variations of E z owing to small-scale meteorological processes in the ULF band. Upon the upward transmission, the near-surface electric field noise attenuates exponentially and becomes negligible at the typical balloon heights (∼30 km). The electric field as observed by balloon platform is actually a local ohmic response to current, because a balloon is drifting with the wind, so space charge structures are not moving past balloon. Therefore, the balloon experiments are more promising than the ground observations for the study of magnetospheric effects in atmospheric electric field.
The ideal observational conditions in Antarctica (more than 30% days at the surface and >90% of the days at balloon altitude match the "fair weather" condition) enabled Bering et al. (1987) to address the long-standing problem of coupling between atmospheric electricity and space weather disturbances at ULF time scales using the coordinated balloon-born electric and ground magnetic observations. Several electric and magnetic field events were recorded during the 1985-86 Balloon Campaign at South Pole Station (Bering et al., 1988, Bering et al., 1990Lin et al., 1995). However, no detailed theoretical analysis of these events was performed, so in Simultaneous Geomagnetic and Ez Variations During Storm Sudden Commencement Events, we will reexamine the results of the early balloon campaigns.
Another remaining controversy is related to the possibility of excitation of the electric TH o mode (fundamental mode of the atmosphere-ground waveguide) by a magnetic storm sudden commencement (SSC). Kikuchi and Araki (1979) interpreted the propagation of SSC impulse from polar to low latitudes as "instantaneous" propagation of electromagnetic disturbance in TH 0 mode in the ionosphere-ground waveguide. This E-mode should carry a significant E z disturbance, which can be detected by a sensor with a sufficient sampling rate (Yumoto et al., 1997). However, this predicted feature of SSC impulse was never validated.
In contrast to ubiquity of geomagnetic high-sampling observations, until recently there was no regular monitoring of the atmospheric electric field with a high time resolution. The previously mentioned results on occurrence of ULF pulsations in E z field near the earth's surface were obtained from short-term observational campaigns, and these data were mostly lost completely, so the results cannot be verified. Recently, the study of short-period disturbances of the atmospheric electric field became feasible thanks to the project GLOCAEM (GLObal Coordination of Atmospheric Electricity Measurements), which united the high-resolution (up to 1 sec) measurements of potential gradient worldwide (Nicoll et al., 2019). The GloCAEM atmospheric electricity database for potential gradient measurements provided insights into a number of meteorological processes. Here, this database is used to examine the influence of geomagnetic disturbances on atmospheric electric field and to resolve a controversy about the possibility of the E-mode excitation by SSC. Also, we reexamine the results of coordinated balloon-born electric and ground magnetic observations in Antarctica.
To interpret the results of the SSC observations and earlier balloon experiments in Antarctica, we have developed a numerical model of electromagnetic ULF response to the incidence of oscillating magnetospheric field-aligned currents onto a realistic ionosphere-atmosphere system.

DATABASE OF GEOMAGNETIC AND ATMOSPHERIC MEASUREMENTS
To examine the impact of an interplanetary shock on the atmospheric electric field E z as well, we used the list of observed SSC provided by International Index Service (http:// isgi.unistra.fr and http://www.obsebre.es). The occurrence of IP shocks can also be seen in the plasma pressure p from the 1 min OMNI database (https://omniweb.gsfc.nasa.gov). We have examined all SSC events during the period 2007-2019.
As a source of information on disturbances of atmospheric electric field, we used the data provided by the project GloCAEM (GloCAEM.wordpress.com), which provides a portal to freely access potential gradient data from 17 sites worldwide. From available long-term 1 sec observations of atmospheric potential gradient (E z ), we have chosen data from the following sites: Available 1 sec data from some stations (e.g., Nycenk and Tripura) are low-quality, with too much interference, and have been omitted.
For magnetic field variations, we use the 1 min data from the INTERMAGNET array (https://intermagnet.github.io) from the following stations: near-equatorial stations MBO and AAE; midlatitude European stations ESK, LER, BFE, and CLF in the same region as atmospheric electricity sites. An SSC is a global phenomenon of a planetary scale, thus very close colocation of magnetometer and electric field sensor is not a crucial necessity. The map with location of selected stations is shown in Figure 1.
An ideal place for monitoring the fine characteristics of atmospheric electricity is the Antarctic plateau, because of the lack of anthropogenic influences, weak and stable winds, and lack of low-altitude clouds. A large database of 10 sec atmospheric E z and J z observations with high-sensitive field-mill and current collector has been collected at South Pole, Vostok, and Concordia stations (Byrne et al., 1991;Few et al., 1992;Burns at al., 1998). With the use of these data, relationships between variations of the atmospheric electricity and IMF parameters (Frank-Kamenetsky et al., 1999), and the ionospheric electric potential (Corney et al., 2003) were found. The Antarctic atmospheric electricity data are available via website (http://globalcircuit.phys.uh.edu). From available 10 sec magnetometer data from South Pole observatory and atmospheric electric field and current measurements during the period 1991-1993, we have analyzed 18 SSC events.
The balloon experimenters have stored their data and made them available online (https://uh.edu/research/spg/data.html). Payloads at an altitude of ∼32 km carried 3-axis double probe electric field detectors and provided 15-s averaged 3-axis electric field data. We have re-analyzed the results of the 1985-86 Balloon Campaign at South Pole Station (Bering et al., 1987;.

ESTIMATE OF E Z PERTURBATIONS ACCOMPANYING STORM SUDDEN COMMENCEMENT EVENTS
Among a large variety of MHD disturbances in the near-earth environment, special attention has been paid to the study of SSC's caused by interaction of an interplanetary shock with the magnetosphere (Araki, 1977). The impulsive impact of a shock can bring a significant amount of energy and momentum into the magnetosphere in a very short time (Curto et al., 2007). Despite the seeming simplicity of such impact, the complexity of geomagnetic and plasma phenomena stimulated by an interplanetary shock turns out to be surprisingly large . SSC transmission from high to low latitudes was often associated with the electric mode in the ionosphere-ground waveguide, instantly propagating along the earth's surface (Kikuchi and Araki, 1979). Among possible electric modes in the atmospheric waveguide, the fundamental TH 0 mode without a cutoff frequency is excited most effectively by a magnetospheric Alfven wave. Distinctive features of TH 0 mode are the propagation velocity just somewhat less than the light speed, and weak attenuation, which is due to the geometrical factor, not due to dissipation in the ionosphere (Kikuchi, 2014). Therefore, it seems that the TH 0 mode may contribute to geomagnetic response far from the MHD disturbance incident on the ionosphere (Kikuchi and Hashimoto, 2016). This notion about the TH 0 mode has been applied to interpret prompt SSC transmission from auroral to low latitudes (Kikuchi, 1986;Chi et al., 2001).
However, in the original papers on the TH o mode, the excitation rate of this mode by magnetospheric sources was not considered. Simple scaling shows that a vertical current J z penetrating into the atmosphere resulting from the magnetospheric field-aligned current J (M) Z with a transverse scale L is determined by the ratio between the resistance of the ionospheric E-layer (which is inversely proportional to the height-integrated Pedersen conductance Σ P ) and the resistance of the atmospheric column between the ground and height of the ionospheric conductive layer: In the atmosphere with exponential height-increasing conductivity σ A (z) σ 0 exp(z/α) and negligible displacement current ω ≪ σ 0 /ε 0 (that is for frequencies less than ∼1 Hz), the parameter L p is L p Σ P /(σ 0 α) . For typical values Σ P 20 S, Σ 0 2*10 −14 S/m, and α 10 km L p ∼10 4 km. This simple estimate shows that a somewhat significant part of the magnetospheric current would penetrate to the low-conductive atmosphere only for extremely large-scale disturbances. Thus, SSC seems to be a very promising source of E-mode excitation, because the scale of an SSC-associated source is the distance between the dawn and dusk ionospheric vortices, which is about several thousand km.
Let us estimate the expected magnitude of the vertical electric component E z of the TH 0 mode. From the subsystem of Maxwell's equations for the E-mode, one can obtain the relationship between the components E z and B y of a wave propagating with the horizontal wave vector k ≡ k x : Here, the dielectric permittivity is ε A 1 + iσ A /ε 0 ω, and k 0 ω/c is the vacuum wave number. Assuming that kxR −1 E , Eq. 2 yields in the case ω ≪ σ 0 /ε 0 : From the relationship (Eq. 3), it follows that a TH 0 mode with magnetic component B y ∼1 nT in the atmosphere with σ 0 10 −13 S/m must be accompanied by a spike of atmospheric electric field E z at the earth's surface with amplitude ∼10 3 V/m. Thus, even a weak magnetic signature of the E-mode must be accompanied by a burst of E z exceeding the atmospheric potential gradient. More rigorous treatment of the problem of magnetospheric field-aligned current interaction with the multilayered ionosphere-atmosphere-ground system will be provided in Modeling of E-Mode Excitation by Magnetospheric FAC. Frontiers in Earth Science | www.frontiersin.org January 2021 | Volume 8 | Article 619227 5

SIMULTANEOUS GEOMAGNETIC AND E Z VARIATIONS DURING STORM SUDDEN COMMENCEMENT EVENTS
We compare the above theoretical estimate with simultaneous observations of the atmospheric E z field and geomagnetic variations (X-component). We have identified >50 events with simultaneous variations of E z and ΔX. We examine the time intervals in the ±10 min vicinity of SSC events. The plots in Figure 2 present examples, showing vertical electric field E z (mV/ m) from available stations and magnetic field ΔX (nT) component from selected stations. The data on the solar wind dynamic pressure has too many missing values for these events and are not shown. The moment of each SSC is marked by vertical lines in Figure 2.
In a majority of the events, no response of E z on SSC was seen. The lack of E z response imposes a limit on a possible amplitude of an expected electric mode-it is at least less than sensor sensitivity and background noise level. In none of >50 SSC events during 2007-2019 recorded by magnetometers and atmospheric electricity stations from the GLOCAEM array or Antarctica was a similar disturbance noticed.
However, in some events, a burst of E z during an SSC can be seen. Figure 2 presents several promising events. Let us exclude for a moment the possibility that the geomagnetic and E z disturbances were just mere coincidences. In any case, the amplitudes of E z disturbance occurring simultaneously with SSC do not exceed ∼10 V/m. A similar negative result was obtained using E z and J z observations at the South Pole station (not shown). Therefore, SSC cannot be exciting or associated with the TH 0 mode.

MODELING OF E-MODE EXCITATION BY MAGNETOSPHERIC FAC
Basic features of electric field transmission from the ionosphere into the near-earth atmosphere in the DC approximation (when the time scale is larger than the relaxation time τ > ε 0 /σ 0 ∼ 20 min) can be understood in a simple 1D model (Park, 1976). This model predicts that a potential difference Φ between the ionosphere and ground supports E z varying with altitude z as follows: Here, Σ A is the total conductance of the atmospheric column Typical values are Σ A x10 − 17 S/m 2 , σ 0 ∼ 10 −14 S/m, and Φ ∼ 250 kV. This relationship shows that a modification of the atmospheric conductivity profile σ A (z) by precipitation of high-energy solar particles (Kokorowski et al., 2006) or emanation of radioactive gas (Harrison et al., 2010) can modify E z (z) structure.
Penetration of nonsteady field, e.g., in the ULF band, is different and seldom studied. We have elaborated a model of the electromagnetic ULF response to an incidence of oscillating magnetospheric azimuthally symmetric FAC field-aligned current onto the realistic ionosphere and atmosphere. A similar multilayer model of the ionosphere-atmosphere-ground system has been used to examine the transmission of Pc1 waves through the ionosphere to the ground (Fedorov et al., 2018). The geomagnetic field B 0 at high latitudes may be assumed to be vertical. The problem is azimuthally symmetric, so a cylindrical coordinate system {z, ρ, ϕ} is used, with ρ 0 in the axis of the current tube.
The model is based on a numerical solution of the full-wave equations in the realistic ionosphere. At the ground-atmosphere interface, the impedance boundary condition is imposed E ϕ /B ρ E ρ /B ϕ Z g /μ, where Z g is the surface impedance. The ground conductivity is assumed to be σ g 10 −4 S/m. The parameters of the ionospheric collisional plasma were reconstructed using the IRI model (http://irimodel.org). The IRI parameters were chosen to correspond to day 2009, 06/21, 02 UT (premidnight) at auroral latitude (geographic latitude 56.5°a nd latitude 280.8°). According to the IRI model, the ionospheric conductances would be Σ P 0.95 S and Σ H 1.40 S.
The vertical profile of atmospheric conductivity is modeled by exponential dependence σ A (z) σ 0 exp(z/α) that merges the IRIpredicted conductivity at z 80 km. The choice of a more realistic conductivity profile will not change the results noticeably. The complex atmospheric conductivity that includes displacement current is given by σ(z) σ A (z) − iεε 0 ω (where ε 0 is the vacuum permittivity). Figure 3 shows the altitude dependence of the absolute magnitude of the complex conductivity (black line). The magnitude of the displacement current for frequencies from 2 mHz to 1 Hz is denoted by vertical lines. Evidently, at low altitudes, σ(z) is determined by the displacement current, while at higher z, it is determined by the conductivity current. The height where ωε 0 ε σ A (z) is denoted z z* (ω).
We have calculated both the vertical and horizontal distributions of magnetic and electric field components, including the vertical electric field in the atmosphere. The 6component electromagnetic field is excited by an incident Alfven wave (that is, oscillatory field-aligned current) with horizontal radius R 350 km. The amplitudes of all field components are normalized in such a way as to have the unit magnetic disturbance on the ground B ρ (z 0) 1 nT for all frequencies in the region of spatial maximum ρ ρ max . The magnetic mode in the atmosphere is excited by ionospheric Hall currents. These eddy currents produce a magnetic response in the atmosphere in the radial direction, that is, in the B ρ component. The electric mode in the atmosphere is associated with vertical current. This current produces a magnetic disturbance in the azimuthal direction, that is, in the B ϕ component. Thus, B ρ and E ϕ components are associated with H-mode, while B ϕ and E ρ components are associated with the E-mode.
The radial distribution of the amplitudes of the magnetic components on the ground for various frequencies is shown in Figure 4. The maximum of B ρ (ρ) is reached at ρ max R/ 2 √ x280 km (Figure 4, upper panel). The distribution of B ϕ (ρ) component is rather similar (Figure 4, middle panel). This component is associated with the E-mode in the atmosphere, and it is about four orders of magnitude weaker than the radial component, associated with the H-mode. The occurrence of the vertical magnetic component B z is due to inhomogeneity of an initial field, and its magnitude is determined by the ratio between the skin-depth and horizontal wave scale (Pilipenko et al., 1998). In contrast to horizontal components, the vertical component B z (ρ) has spatial maximum beneath the current center ρ 0 (Figure 4, bottom panel). The radial distribution of the electric component amplitudes on the ground for various frequencies is shown in Figure 5. The electric field of the H-mode is revealed in the E ϕ component, whereas the E-mode has E ρ and E z components. The distribution of horizontal electric components is similar to that of horizontal magnetic components ( Figure 5, upper and middle panels). However, the vertical electric component E z , associated with the E-mode, has maximum beneath the source at ρ 0 ( Figure 5, bottom panel). Amplitude of E ρ component, ∼3 10 −5 mV/m, is about four orders of magnitude less than amplitude of E ϕ component, ∼0.2 mV/m. As expected for the  electric field structure near the surface of a conductor, the normal to the surface electric field component E z , ∼80 mV/m is much larger than the transverse component. The altitude profile of the horizontal magnetic components at the distance ρ max is presented in Figure 6. The steep variation at z∼90 km is related to a π/2 rotation of the polarization ellipse in the F-layer. The B ρ component is nearly the same at all altitudes in the atmosphere. The B ϕ component is many orders of magnitude less than the B ρ component. The vertical magnetic component B z is comparable in amplitude with the B ρ component and just weakly increases with altitude.
The altitude profiles of the horizontal electric field components at ρ max and vertical component E z (z) at ρ 0 are presented in Figure 7. The E ϕ (z) component only weakly depends on altitude for low frequencies, but for higher frequencies, it grows with altitude up to the E-layer, as expected from Faraday's law z z E ϕ iωB ρ . The altitude dependence of the E ρ (z) component changes drastically at height z z*, where the Ohmic current equals the displacement current. This component is nearly constant in the more conductive upper atmosphere (z > z*), but it drops in the less conductive lower atmosphere (z < z*). For the vertical electric component, the modeling results can be understood, remembering that the altitude distribution of E z (z) is proportional to the total complex conductivity Σ (z). The E z perturbation at higher altitudes, z > z*, decays exponentially E z (z) ∝ σ A (z) − 1 , whereas at lower altitudes, z < z*, E z (z) is nearly constant. In the ionosphere (>80 km), the E z component vanishes owing to the high field-aligned conductivity of the ionospheric plasma.
The relative magnitude of the atmospheric electric field disturbances owing to magnetospheric ULF variations may be seen in Figure 8. This figure compares the altitude structure of all three electric field components. At the ground, the horizontal components drop to very low magnitudes prescribed by the boundary impedance relationship. On the ground, the electric field of H-mode is dominating, E ρ << E ϕ . However, because E ρ increases fast until z ∼ z*, at the balloon height (∼30 km), the electric field of the E-mode becomes much larger, E ρ >> E ϕ .  This behavior can be comprehended from the following consideration. At the earth's surface, electric E (g) and magnetic B (g) components of the E-mode are about five orders of magnitude less than those of the H-mode. Magnetic components of both modes slowly vary with altitude: B ϕ is practically constant till ∼40 km and B ρ increases about 1.5 times only till 80 km. The behavior of electric components is more complicated. From Faraday's law, it follows that the electric field of the H-mode varies with altitude as ϕ . So, this electric field component is nearly constant throughout the atmosphere. The electric field of the E-mode strongly varies with altitude As a result, the ratio of electric fields of both modes varies with altitude as ϕ . Therefore, starting from ground values B (g) ϕ 1.1p10 − 6 nT, E (g) ϕ 2.5p10 − 6 V/m, for k 10 −3 1/km, and T 500 s, this ratio will grow linearly with altitude as E ρ (z)/E ϕ (z) 3.2z (km). Thus, at balloon heights, electric field of the E-mode becomes much larger than that of the H-mode, whereas, on the other hand, the magnetic field of the E-mode (B ϕ ) is much less than that of the H-mode (B ρ ) in the entire atmosphere (up to the E-layer).

OBSERVATIONS OF E Z PERTURBATIONS DURING TRAVELLING CONVECTION VORTICE AND PC3-5 EVENTS IN ANTARCTICA
Responses of the atmospheric electric field associated with impulsive and wave magnetospheric disturbances were observed during the balloon campaigns. The reported events include travelling convection vortices (TCVs) and Pc5 pulsations.
TCVs in the high latitude ionosphere are revealed on the ground as magnetic impulsive events with duration ∼5-10 min. These localized daytime disturbances are thought to be responses to transients in the solar wind or magnetosheath. A survey of the campaign data looked for unipolar magnetic pulses above background in the vertical component B Z on the ground and electric field perturbations ≥10 mV/m at balloon altitude (Lin et al., 1995). From total of 112 events found, electric field responses were observed for 90% of the events with the average E z amplitude ∼15 mV/m.
For example, the TCV event on January 3, 1986, was recorded by both the South Pole magnetometer and the balloon electric field sensor (Bering et al., 1990). This TCV was estimated to have a radius ∼350 km and moved antisunward along the oval at a speed of ∼4 km/s. The magnetometer observed a unipolar impulse in the magnetic vertical B z component of ∼80 nT and a bipolar impulse in the horizontal B x component of ∼100 nT. The accompanying atmospheric electric field pulse was less than 10 mV/m in the E z component (at the noise level), and ∼40 mV/ m in the eastward E y and ∼25 mV/m in the poleward E x components. In another event on Jan. 14, 1986, the TCV impulse amplitudes were ∼20 nT in the horizontal magnetic and ∼15 mV/m in the electric fields. The spike in the vertical E z field reached ∼40 mV/m.
As an example of Pc5 pulsations, the event on July 9, 1975, may be presented (Maclennan et al., 1978). During this event coincident magnetic field, transverse electric field and electron precipitation fluctuations with 5 min period were measured around ∼06 LT by ground magnetometer and balloon-borne double-probe and scintillation counter. The balloon reached a ceiling altitude of ∼35 km. The experiment recorded magnetic variations with a peak-to-peak amplitude in the B x component of ∼6 nT and in the B y component of ∼8 nT, which were coherent with horizontal electric field variations with peak-to-peak amplitudes in the N-S component E x of ∼20 mV/m and in the E-W component E y of ∼15 mV/m. Thus, the normalized transverse electric field response to TCV magnetic pulses is E ⊥ /B ⊥ ∼ (0.4-0.8) (mV/m)/nT and to Pc5 waves is E ⊥ /B ⊥ ∼ 2.5 (mV/m)/nT. The normalized response of vertical electric field to TCV magnetic pulses is E Z /B ⊥ ∼ 2 (mV/ m)/nT. The expected model magnitude of an atmospheric electric field disturbance may be estimated from Figure 5 for a 1 nT magnetic disturbance. The horizontal electric field disturbance at typical balloon altitude (32 km) is about 1.5 mV/m, depending on frequency. Thus, for a typical ground magnetic amplitude (20 nT), the balloon measurements should reveal an E perturbation of about 30 mV/m. This value is in a good agreement with the results of balloon observations discussed above (e.g., Bering et al., 1990). At the same time, the inductive electric field produced by the H-mode E ϕ at balloon height would be ∼1 mV/m only.
Amplitudes of the vertical and horizontal components become comparable at an altitude of ∼30 km. For the ground magnetic disturbance with B 1 nT and f ∼ 10 mHz, the predicted vertical electric field disturbance is ∼0.02 V/m. Thus, for intense ULF disturbances of the geomagnetic field ∼100 nT, the disturbance of FIGURE 8 | The altitudinal structure of all three electric field components E ρ (z), E ϕ (z), and E z (z) (in V/m).
Frontiers in Earth Science | www.frontiersin.org January 2021 | Volume 8 | Article 619227 the ground level atmospheric field must be ∼2 V/m. This value is small, and it can be detected by modern electric field sensors only under extremely quiet weather conditions.

APPARENT IMPEDANCES OF H-AND E-MODES
Simultaneous measurements of the wave electric and magnetic components gives one the possibility to determine the apparent wave impedance in order to obtain additional information about the wave mode. This method was applied by Pilipenko et al. (2012) to the radar-measured electric field and ground geomagnetic field of Pc5 waves and by Bering et al. (1998) to the analysis of coordinated balloon-born electric and ground magnetometer measurements. More importantly, a preliminary knowledge of the atmosphere-ionosphere impedance gives one the possibility to estimate the wave electric field amplitude in the ionosphere from ground magnetometer observations.
Here, we first provide simple analytical estimates and then support them with numerical modeling. For the H-mode excited by a toroidal Alfvenic-type magnetospheric disturbance, the ratio between the dominant components of the electric field in the ionosphere, E x , and ground magnetic response, B x , follows from the thin ionosphere theory : For the E-mode, the relationship between electric field in the ionosphere and ground magnetic disturbance was derived by Hughes, (1974). Here, we present a similar relationship for a wave infinite in the E-W direction (k y 0) and localized in N-S direction (k ≡ k x ). The ratio between the meridional electric field E x and the azimuthal component of the magnetic field B y on the ground is given by This ratio is altitude-dependent and does not depend on the ionospheric conductivity. At altitudes z > z p , the ratio coincides with the equation from Hughes, (1974) (transformed into SI units): Liu and Berkey, (1994) and Yizengaw et al. (2018) used the relationship between ionospheric electric field and magnetic field fluctuations from Hughes, (1974) to estimate the amplitude of the ionospheric electric field fluctuations driven by geomagnetic pulsations. However, the relationships they have used were incorrect choices. Moreover, it is wrong to model ULF pulsations as an E-mode.
The numerically calculated apparent impedances for both electric (E) and magnetic (H) modes (that is, the ratio E (z 120 km)/B (z 0) is shown in Figure 9. For the H-mode, the ratio E ρ /B ρ ∼ 0.6 (mV/m)/nT. This value is very close to the theoretical estimate (4) for Σ H ∼1.4 S. For the E-mode, the ratio E ρ /B ϕ is frequency dependent, slowly decreasing from ∼10 2 (V/m)/nT at f ∼ 3 mHz to ∼10 (V/m)/nT at f ∼ 1 Hz. Therefore, the E-mode impedance is at least four to five orders of magnitude larger that the impedance of the H-mode. Interpretation of ULF waves as E-mode would provide unrealistically high magnitudes of the wave electric field in the ionosphere.
An attempt to compare Pc1-3 pulsations using the South Pole search-coil magnetometer and balloon E-field data was made by Bering et al. (1998). While magnetic component was clearly observed as narrow-band emissions with power spectral densities (PSDs) P (B) f ∼ 0.1 (nT) 2 /Hz in Pc1 band and ∼9 (nT) 2 /Hz in Pc3 band, the balloon-borne detector observed broadband emission without prominent features in the electric field spectra. During these events, the noise power spectral densities (PSDs) in the Pc1 and Pc3 bands were P f ∼ 2 10 3 and ∼4 10 2 (mV/m) 2 /Hz, correspondingly. According to the modeling results, E/B ∼ 2 (mV/m)/nT at f 0.01-0.3 Hz (Figure 7), so at balloon heights, the PSD of the electric component could be P f (E/B) 2 ∼0.4 (mV/m) 2 /Hz in the Pc1 band and ∼30 (mV/m) 2 /Hz in Pc3 band. Thus, the PSD of theoretically possible electric components of geomagnetic Pc1 and Pc3 pulsations was below the noise level.

DISCUSSION
The conclusion in Estimate of E z Perturbations Accompanying Storm Sudden Commencement Events about the occurrence of large E z in the ULF electric mode was made earlier in Zybin et al. (1974) from other considerations. The ULF field in the atmosphere can be locally approximated as an inhomogeneous plane wave with a horizontal wave vector k. In this approximation, the vertical component E z in the field of Pc3-5 pulsations must appear. The expected magnitude of E z must be coupled with magnetic component magnitude as follows: For the commonly observed horizonal velocity of Pc3-5 pulsations ω/k ∼ 20 km/s, pulsations with a magnetic component amplitude B ⊥ 1 nT should be accompanied by disturbances of E z ∼60 V/m. To put it another way, the E z component in the air can be estimated from the continuity of vertical current at the interface earth's crust-air E (air) . According to this estimate, the amplitude components of E z in the air should be a few tens of V/m according to borehole observations of J z for σ g ∼ 10 −4 S/m and ω∼0.01 s −1 .
Our search for an E z signature in disturbances from magnetospheric sources has given negative results. Even for the most promising source-large-scale intense SSC impulses, observations show that the excitation of the E-mode is negligible. Therefore, the assumption of the directional analysis (Chetaev et al., 1975;Chetaev et al., 1977;Chetaev, 1985) on the occurrence of the E-mode in the incident ULF wave field is not supported by observations. Nonetheless, the mathematical formalism developed in the frameworks of the directional analysis may be applied for MTS in the ELF band (e.g., Schumann resonance).
Our numerical modeling has resulted in a rather paradoxical conclusion. Excitation of the E-mode by magnetospheric sources is very weak, and this mode practically does not contribute into the ULF wave magnetic field. The E-mode contribution into the horizontal telluric field produced by ULF pulsations is also negligible. However, in the atmosphere, at the balloon heights, the electric field of this mode becomes dominant. Thus, an adequate interpretation of coordinated balloon-ground observations of Pc5 waves and TCVs is possible only with account of multimode structure of ULF disturbance in the atmosphere comprising both H-and E-modes. The important aspect of this problem is the polarization structure of H-and E-modes (Nenovski, 1999). The pertinent theoretical modeling and comparison with data from coordinated balloon-ground observations will be considered elsewhere.
At the same time, periodic fluctuations of the atmospheric electric field E z in the ULF range that are not associated with geomagnetic disturbances are quite common. These fluctuations may confuse and mislead a researcher upon a search of simultaneous geomagnetic and atmospheric electricity pulsations. Periodic fluctuations of the atmospheric potential gradient and vertical atmospheric current J z in the range of Pc4-5 frequencies were observed by Yerg and Johnson, (1974) and in the Pc1 and Pc3 bands by Anisimov et al. (1984). These fluctuations were not coherent with geomagnetic pulsations, so authors suggested that they may be caused by nonmagnetospheric sources, e.g., infrasound emissions from distant meteorological sources. Pc5 pulsations of atmospheric electric field were observed near local midnight under very clear weather by balloon campaign (altitude ∼32 km) (Liao et al., 1994). Both transverse and vertical electric field components of pulsations had amplitudes of 20-30 mV/m, but no similar signal was observed in magnetometer or riometer data. Narrow-band wave packets in the Pc1 band in both horizontal and vertical components of the atmospheric electric field without a ground magnetic response were detected during the 1985-86 South Pole Balloon Campaign . The driving mechanisms of such "electrostatic" ULF pulsations are very speculative and have not been established.
The model implicitly assumes that a single cylindrical FAC is spread along the ionosphere out to infinity. In realistic magnetosphere-ionosphere disturbances, coupled incident and return FACs of opposite polarity are formed at various distances from each other, from about ten thousand km in SSC events to few hundred km in TCV or Pc5 events. If the geometry of the magnetosphere-ionosphere current system is known, the modeled electromagnetic fields due to each isolated FAC are to be summed up.
We have considered a simple geometry with the plane ionosphere and ground and vertical geomagnetic field B 0 . This assumption is well justified for the consideration of local structure of electromagnetic disturbance at distances less than 10 3 km from an incident FAC. At larger distances upon propagation to low latitudes, additional factors become noticeable: ionosphere/ground curvature, inclination of geomagnetic field, and lateral inhomogeneity of ionospheric parameters. However, the magnetic field decreases with distance as ∼r −2 , so at large distances, the response would be too weak to observe. Probably, there is no need to advance theory to interpret very weak signatures at large distances from a source.

CONCLUSION
We have addressed the long-standing problem of coupling between atmospheric electricity and space weather disturbances at ULF time scales (from fractions minutes to tens of mins). The generation of ULF impulses and noises by atmospheric electric discharges is a more or less well-known aspect of the problem (see Pilipenko, 2012). The inverse aspect, the influence of magnetospheric magnetic disturbances on the atmospheric electric field is much less studied.
The GloCAEM atmospheric electricity field-mill measurements with 1 sec cadence have been used to examine the influence of geomagnetic SSC disturbances on atmospheric electricity. The predicted mechanism of SSC transmission by the electric-type TH 0 mode along the earth-ionosphere waveguide was not confirmed. Observations with field-mills and current collectors in Antarctica also have not found any signature of the E-mode accompanying SSC magnetic pulses. Therefore, the model of prompt transmission of disturbances from auroral latitudes to low latitudes by the atmospheric TH 0 mode is not supported by observations and should be rejected.
We have advanced the theory of ULF disturbance transmission though the ionosphere and atmosphere to the ground by considering the possible role of the electric mode. The constructed model of electromagnetic ULF response to an incidence of oscillating magnetospheric field-aligned current onto the realistic ionosphere is based on a numerical solution of the full-wave equations in the atmospheric-ionospheric collisional plasma whose parameters were reconstructed using the IRI model and a realistic vertical profile of atmospheric conductivity. The modeling strictly proved that excitation of the electric mode is weak and its contribution into the field of ULF waves on the ground is very small. In a most favorable situation, only a weak E z disturbance with a magnitude of ∼several V/m could be produced by a large-scale intense (∼100 nT) geomagnetic disturbance. At the same time, the predicted amplitudes of electric field at balloon heights, ∼few tens of mV/m, induced by Pc5 pulsations and travelling convection vortices are in good agreement with coordinated balloon-ground magnetometer observations. Therefore, E-mode excitation by magnetospheric ULF disturbances cannot be completely ignored, because an adequate interpretation of balloon observations is possible only on the basis of a model comprising both H-and E-modes.

DATA AVAILABILITY STATEMENT
The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: http://www.wdcb.ru/ arctic_antarctic/antarctic_magn_3.ru.html.

AUTHOR CONTRIBUTIONS
VP performed theoretical analysis, EF did numerical modeling, VM-B analyzed data, and EB provided observational data.