Disturbances in the Doppler frequency shift of ionospheric signal and in telluric current caused by the atmospheric waves from an explosive eruption of Hunga Tonga volcano on January 15, 2022

On January 15, 2022, in the day of the Hunga Tonga volcano explosive eruption, the barometer located at the territory of the Tien Shan mountain station registered a short time anomalous pulse of the atmosphere pressure, as illustrated by Figure 2. As it follows from this plot, the peak amplitude of pressure growth above the preceding level of undisturbed slow variation was about (1.3$-$1.4) hPa, and the whole effect lasted about (25$-$30) min. The start of the atmosphere pressure pulse was detected at the moment of 16:00:55 UTC, nearly 12 h after the Hunga Tonga volcano explosion.

Similarly, anomalous short-time pulses of the atmosphere pressure were detected in the same day of the Hunga Tonga volcanic event by the barometric equipment installed in the various points of the globe. A number of the atmospheric pressure time series registered at that time, including the record of the Tien Shan station, are presented in the upper panel of Figure 3. Except the Tien Shan station data, the information for these plots was obtained from an open access database [25]. It is seen, that everywhere the detected pulses of the atmosphere pressure had similar shape and duration, which varied only slightly between the observation points.

In the bottom panel of Figure 3 the moments of the atmosphere pressure pulses are plotted in dependence on the distance between the observation point and the Hunga Tonga volcano. The distances for the latter plot were defined on the basis of the geographical coordinates of corresponding points by the Garmin MapSource program. With account to these distances and the time delays of the pressure pulses it was calculated the average propagation velocity of the atmosphere disturbance, which values are listed in Table 1. As it follows from the data presented in Figure 3 and Table 1, the maximum velocity was observed in the nearest registration points, i. e. in Auckland and Brisbane, and only starting since the distances above $\sim$$10^{4}$ km the atmosphere pressure pulse was propagating in the SE–NW direction with a practically constant speed of 0.306 km$\cdot$s^-1.

Positive anomalies of the atmosphere pressure which were moving with the velocity of $\sim$0.3 km$\cdot$s^-1 from SE to NW over the territory of Japan and lasted in total about 20 min were also reported in [6]. According to [26], generally such pulses of atmospheric pressure are brought by a Lamb wave which propagates with the speed of sound ($\sim$0.3 km$\cdot$s^-1) along the surface of the Earth.

It should be noted that Barcelona is situated only at a $\sim$2100 km distance from the antipode point relative to the Hunga Tonga volcano. This may be the reason why the atmosphere pressure pulse plotted for this station in Figure 3 has a maximally complicated shape with two peaks and double duration, which features can be explained by successive registration of the direct and antipodal Lamb waves moving from the volcano explosion point.

The moment of the atmosphere pressure peak observation at the Tien Shan station, 16:00:55 UTC, agrees well with the general trend of the world data, and corresponds to the propagation speed of a surface Lamb wave from the Hunga Tonga volcano explosion. This agreement permits to identify the observed anomaly of atmospheric pressure as an effect also connected with the Hunga Tonga volcanic event.

The Doppler frequency shift of ionospheric signal at the Radio polygon “Orbita” is registered on the two radio paths, Beijing—Radio polygon “Orbita” and Kuwait—Radio polygon “Orbita”. The optimal radio frequencies for the day- and night time are chosen in accordance with the Short Wave Radio Frequencies BBC Catalog [23]. The geometric disposition of both paths relative to location of the Hunga Tonga volcano is illustrated by a chart in Figure 1.

Continuous monitoring of Doppler frequency in the day of the Hunga Tonga volcano explosion, January 15, 2022, made it possible to reveal two disturbances in the ionosphere, which are illustrated by the plots in Figure 4.

The upper plot of Figure 4 demonstrates a set of superimposed time series of the Doppler frequency shift of ionospheric signal which were obtained at the radio path Beijing—Radio polygon “Orbita” on the dates of 13, 14, 16, and 17 January, i. e. both immediately on the eve, and a few days after the considered volcanic event. It is seen in this plot, that the undisturbed daily records of Doppler data do not differ considerably between the days, and generally overlap within the limits $\pm$1 Hz.

In contrast to the regular background oscillations observed in the preceding days, on January 15, 2022 it was detected a considerable negative disturbance of Doppler frequency with an amplitude of about 2 Hz and duration of 1073 s, which is shown in the middle plot of Figure 4. This disturbance appears at the time of 14:35:21 UTC, i. e. 37236 s (10.3 h) after the explosion moment of the Hunga Tonga volcano. With account of the distance between the volcano and the reflection point of radio waves at the Beijing—Radio polygon “Orbita” radio path, 11393 km, the propagation velocity of the atmospheric disturbance in the ionosphere can be calculated as 0.3059 km$\cdot$s^-1. As it was discussed above, practically same value, 0.3056 km$\cdot$s^-1, was obtained at the Tien Shan mountain station for the speed of the pulse of atmosphere pressure which corresponded to the propagation of the Lamb wave from the volcano explosion (see Table 1).

The observed time correlation is an evidence, that the Lamb wave propagating over the whole thickness of the atmosphere had initiated disturbances in the ionosphere as well, which revealed themselves in the record of the Doppler frequency shift. As additional argument in favour of this conclusion the ICON-MIGHTI and Swarm satellite observations [27] can be mentioned of the penetration of Lamb waves at the heights of (90–300) km into the ionosphere.

The second anomaly in the Doppler frequency shift of ionospheric signal found on January 15, 2022 was registered at the time of 19:35:21 UTC, i. e. 55241 s (15.3 h) after the Hunga Tonga volcano explosion, when the Doppler sounding equipment had just switched into operation with the Kuwait—Radio polygon “Orbita” radio path. The corresponding time series of Doppler data is presented in the bottom plot of Figure 4. It is seen there a disturbance with a maximum frequency shift of 1.84 Hz and a 1270 s duration, followed by a sequence of undulating perturbations with much lesser amplitudes and the quasi-periods of 1223 s, 1146 s, and 1053 s. As known, similar periodicity of 1000 s order can be observed by propagation of acoustic-gravity waves in the ionosphere [28].

In supposition that the reason of the ionospheric effect detected at 19:35:21 UTC is also connected with the Hunga Tonga volcano explosion, and with account to the 14367 km distance from the volcano to the radio waves reflection point at the radio path used, a calculation analogous to above gives the distribution speed of the disturbance 0.2602 km$\cdot$s^-1. This estimate corresponds well to the velocity of acoustic-gravity waves [5].

The characteristics of the two anomalous effects found during the day January 15, 2022 in the records of the Doppler frequency shift of ionospheric signal are summed up in Table 2.

Thus, the data obtained at the Radio polygon “Orbita” permit to connect the revealed ionosphere disturbances with successive propagation of the Lamb and acoustic-gravity waves generated by the explosion of the Hunga Tonga volcano. At the same time, the detected effects demonstrate the effectiveness of the applied method of Doppler sounding on inclined radio path for revealing ionospheric disturbances of volcanic origin at a distance of more than $10^{4}$ km.

As it follows from the previous section, powerful atmosphere disturbances, distributing after the explosion of the Hunga Tonga volcano as Lamb waves over the entire atmosphere thickness, initiated perturbations in the ionosphere as well. Resulting modulation of the electric currents in the ionosphere causes geomagnetic effects which may be registered at the ground level in variation of the telluric current. This consideration was the reason for searching for anomalies in the monitoring data of telluric current after the Hunga Tonga explosion event.

In Figure 5 the time series of the atmosphere pressure and of the intensity of telluric current recorded at the Tien Shan station on January 15, 2022 are matched against each other. As it follows from this figure, at the moment of 16:00:55 UTC an appreciable (6$-$10) $\mu$V decrease appears in the record of telluric current, almost simultaneously with arrival of the atmosphere pressure pulse, which propagated with the 0.3056 km$\cdot$s^-1 speed from the Hunga Tonga volcano point. After the bay-like dip feature in the record it was observed an increase of the telluric current amplitude.

It is worth to note that the decrease of the current lasted about 1800 s, which is quite comparable with the length of the barometric pressure pulse. The total duration of the whole period of telluric current variations, both of the negative dip and of the subsequent rise, was $\sim$4900 s.

Another noticeable disturbance in the record of telluric current starts at 18:04:05 UTC, as it is also seen in Figure 5. This moment corresponds to the arrival time of the acoustic-gravitation wave from the Hunga Tonga volcano which was moving with the speed of 0.260 km$\cdot$s^-1 (see Table 2). The second period of the telluric current disturbances lasted about 6800 s.

The described time correlations may be a reason to suppose an electromagnetic nature of the detected disturbances, at which the modulation of the electric currents in the ionosphere by atmospheric waves may result in the variation of the telluric current measured at the ground level.

In Figure 6 the time history considered above of the Doppler frequency shift of ionospheric signal at the Beijing—Radio polygon “Orbita” radio path is superimposed with the record of the atmosphere pressure, as it was written in the date of Hunga Tonga explosion at the Tien Shan mountain station. The barometric data series in this plot is shifted along the horizontal axis to the time of $-$1.50 h, in correspondence with the propagation speed of the Lamb acoustic wave from the Hunga Tonga explosion, 0.3056 km$\cdot$s^-1 (see Table 1), and the distance difference of 1560 km between the Hunga Tonga volcano and the Tien Shan station, from the one side, and between the volcano and the reflection point of radio waves on the Beijing—Radio polygon “Orbita” radio path, from another.

As it follows from Figure 6, the duration of the period of anomalous Doppler frequency shift is reasonably close to that of the atmosphere pressure pulse, and the start moments of both effects practically coincide with each other. The distribution speed of the two anomalous effects also seems to be practically identical, about 0.306 km$\cdot$s^-1, as it was discussed in the previous paragraphs. These experimental facts mean that both anomalies originate from the same acoustic disturbance which had arose at a height of about 100 km and was propagating with the velocity of the surface Lamb wave. In turn, the specific features of these phenomena permit to estimate the order of energy which was transferred into the atmosphere at the considered explosion event.

Since the average energy of an air molecule is $\frac{3}{2}kT$, the energy density of the atmosphere equals to $\frac{3}{2}nkT$, where $n$ is the concentration of molecules, $T$—temperature, and $k$—the Boltzmann’s constant. The barometric pressure $p$ is connected with the molecules concentration by an equation of state $p=nkT$. As a result, the energy density can be expressed through the atmosphere pressure as

The total energy $\Delta E$ transmitted to the mass of atmosphere by the Hunga Tonga eruption can be found as a product of the disturbed energy density, $\Delta\varepsilon=\frac{3}{2}\Delta p$, to the effective spatial volume of the disturbance region $V_{eff}$:

Here, $r_{\oplus}$ is the radius of the Earth; $r$—the distance to the eruption point; $2\pi r_{\oplus}\sin(\frac{r}{r_{\oplus}})$ is the length of the circumference of the disturbance front on the spherical Earth’s surface, $\tau$ and $c_{s}$ are, correspondingly, the time duration of the disturbance and the sound speed; and $H$ is the height of the homogeneous atmosphere, in which the surface Lamb wave concentrates. Finally, a simple expression for the transferred energy $\Delta E$ looks as

According to the measurements data presented above, at the Tien Shan mountain station ($r=12948\cdot 10^{3}$ m) the average amplitude of the pulse of atmospheric pressure was $\Delta p\approx 0.65$ hPa, the pressure disturbance lasted $\tau\approx 1000$ s and had the propagation speed $c_{s}=306$ m$\cdot$s^-1. Putting these values together into Equation (3), and taking into account that $1$ hPa $=100$ Pa [ J$\cdot$m^-3 ], $r_{\oplus}=6371\cdot 10^{3}$ m, $H=8\cdot 10^{3}$ m, and $4.184\cdot 10^{15}$ J $=1$ Mt${}_{\text{TNT}}$, the next rough estimate follows for the energy released into the atmosphere by the Hunga Tonga explosive eruption, as expressed in the megatons of TNT equivalent: