Figure 2 shows the series of dTEC maps over Japan from 0600 to 1500 UT [1500 to 2400 Japan Standard Time (JST)]. (A movie of the time evolution of the dTEC maps with 5-min time step is included in Additional file 1). It can be seen that there are traveling ionospheric disturbances (TIDs) with two different characteristics. At 0700 UT, ionospheric disturbances of dTEC amplitude of about \(\pm 0.5\) TECU appeared from the east. The amplitude is comparable to those of typical TIDs over the mid-latitude region. The wave front was aligned in the NNE–SSW direction. To estimate the propagation velocity and wavelength more quantitatively, keograms of dTEC (time–distance plot of dTEC) were used to estimate the TID parameters. It helps reducing the effects of the geographical distributions of the GEONET stations which are constrained by the shape of the Japanese archipelago. Figure 3b shows the keograms of dTEC from 0800 to 1100 UT along the lines in Fig. 3a. From the apparent velocity in the northward and westward direction from (37\(^\circ\) N, 142\(^\circ\) E), propagation velocity was estimated as 250 m \(\text {s}^{-1}\) in the direction − 69\(^\circ\) counter-clockwise from the north (WNW). According to the keogram in the direction of the propagation velocity, the wavelength was estimated as about 400 km. After 1000 UT, the speed seemed to slow down. Similar ionospheric disturbances were observed until 1100 UT. After 1100 UT, another ionospheric disturbances with dTEC amplitude of more than \(\pm 1.0\) TECU appeared. The amplitude is stronger than the first TID, but is still within the range of amplitudes of typical TIDs in the mid-latitude region. Figure 3d shows the keograms of dTEC along the lines in Fig. 3c from 1000 to 1300 UT. In the same way as the first TID, the propagation velocity is estimated as 270 m \(\text {s}^{-1}\) in the direction − 53\(^\circ\) counter-clockwise from the north (NW). According to the keogram along the direction of the propagation velocity from (33\(^\circ\) N, 135\(^\circ\) E), the wavelength is estimated as about 800 km. The wavelengths of the first and second TIDs are within the range of the medium-scale traveling ionospheric disturbance (MSTID).
Figure 4 shows the series of ROTI maps over Japan from 0600 to 1500 UT [1500 to 2400 Japan Standard Time (JST)]. (A movie of the time evolution of ROTI maps with 5-min time step is included in Additional file 2). The distributions of IPPs may be slightly different from those of dTEC maps, because ROTI needs only 5 min before the value is obtained, while it takes 1 h for dTEC. The ROTI structures were matched with the dTEC structures of the first TID. In contrast, the second TIDs which started to be observed from 1100 UT did not accompany ROTI enhancement structures corresponding to the dTEC structure. ROTI enhancements are observed in a limited region.
Figure 5 shows the location of Hunga Tonga-Hunga Ha’apai in the azimuthal equidistant map with its center at Tokyo (35.69\(^\circ\) N, 139.78\(^\circ\) E), Japan. The surface distance between Tokyo and Hunga Tonga-Hunga Ha’apai is about 7800 km. Hunga Tonga-Hunga Ha’apai is in the azimuth direction of 135\(^\circ\) clockwise from the north center of Japan.
For the TIDs started to be observed around 0700 UT which is about 3 h after the eruption of Hunga Tonga-Hunga Ha’apai, the arrival is too early, if they are caused by the atmospheric acoustic wave, because it would take roughly about 7 h. They might be caused by the atmospheric shock waves which propagates faster than the acoustic wave. Afraimovich et al. (2001) showed that atmospheric waves with phase velocity of 1100–1300 m \(\text {s}^{-1}\) were generated by earthquakes. They might also be caused by acoustic waves propagating in the thermosphere where the acoustic velocity is higher than the lower atmosphere. However, the propagation velocity of the TIDs was not so fast as the mean velocity estimated by the time difference from the eruption to the arrival. Another possibility is that the TIDs associated with electric field in the conjugate hemisphere might be mapped over Japan. The magnetic conjugate points of Japan is located over Australia which is located to the west of Hunga Tonga-Hunga Ha’apai. For example, the conjugate point of this TID (37\(^\circ\) N, 142\(^\circ\) E) is (21.03\(^\circ\) S, 140.46\(^\circ\) E). It is about 4600 km from Hunga Tonga-Hunga Ha’apai which is in the azimuth angle of 98\(^\circ\) clockwise from the north. If the atmospheric waves induce oscillating electric field which could be generated by the E region dynamo process because it was in the daytime and are mapped over Japan, the shorter arrival time and propagation time could be explained.
Other sources which are not related to the eruption cannot be excluded by this analysis only. In the daytime in the winter in the northern hemisphere, TIDs associated with atmospheric gravity waves. However, their typical propagation direction is northward and different from what is observed for the first TID (Otsuka et al. 2021). It should be noted that the TID activity on the previous day (14 January 2022) was low and no clear TIDs were observed. TIDs are also induced by geomagnetic activity. Indeed, it was in a recovery phase of a moderate magnetic storm commenced on 14 January 2022. The Kp index on 15 January 2022 was not high (2–4\(^+\)). TIDs associated with magnetic storms are usually associated with heating of the thermosphere in the auroral region and propagate equatorward. Therefore, the first TID is not likely to be associated with geomagnetic activities. To understand the cause of this TIDs, observations between Hunga Tonga-Hunga Ha’apai and Japan are necessary. There are some GNSS stations in the Pacific Ocean by International GNSS Service (IGS). Although the number of stations are limited, data from IGS stations between Tonga and Japan would help understanding the propagation mechanisms. The first TID is rich in irregularities, as seen in ROTI maps, though it is still in daytime. Usually, the daytime TIDs caused by atmospheric gravity waves do not accompany ionospheric irregularities. It is unusual for daytime TIDs to accompany irregularities. This indicates that the atmospheric waves, if it is the cause of the TID, included turbulence which could generate turbulent structure of the ionospheric plasma. If the TID was associated with the electric field mapped from the magnetic conjugate points, the irregularities could be caused by electrodynamic plasma instability processes.
The second TIDs started to be observed after 1100 UT which is about 7 h after the eruption may be associated with the atmospheric acoustic waves. The propagation direction is consistent with the direction of Hunga Tonga-Hunga Ha’apai from Japan. It should be noted that surface pressure changes are observed around 1130 UT along the pacific coast of Japan as mentioned above. One of the interesting phenomena associated with the eruption was the abnormal enhancement of the tide level at the coast of Japan, while it was not so much at the Pacific islands. One of the potential mechanism is the effects of atmospheric waves on the sea surface, but evidences are limited. The observed TIDs with two different characteristics may add some information to understand the mechanisms of the abnormal tide level enhancement.
The ionospheric irregularities represented by ROTI are distributed not all over the second TIDs, but in a limited region as it can be seen ROTI map at 1130 UT. Ionospheric irregularities did not exist all over the TIDs, but exist in the limited region centered around (37\(^\circ\) N, 135\(^\circ\) E) with width of \(\pm 4^\circ\) in latitude and longitude. In the nighttime, MSTIDs which are associated with the Perkins-type plasma instability accompanies ionospheric irregularities, but have same structures as MSTIDs. In the case of the current study, a region of ROTI enhancement appeared at the eastern edge of the coverage around 1000 UT and moved westward were distributed in the area where the two observed TIDs intersect each other. Two atmospheric waves interacted to generate small-scale waves and hence the ionospheric plasma structure becomes irregular. Other sources are not related to the eruption. As mentioned above, a moderate magnetic storm was going on. The observed structure of the region of ROTI enhancement looks similar to the storm-induced plasma stream observed in the low to mid-latitude region during magnetic storms (Maruyama et al. 2013), though it is usually observed strong geomagnetic storms. More studies are necessary to distinguish the effects of eruption from the magnetic storm.
From the viewpoint of GNSS applications, spatial variations of ionospheric TEC associated with the TIDs could degrade GNSS applications based on the differential GNSS technique. Even with the variation of ± 1 TECU, precise positioning systems which utilize carrier-phase measurements may be impacted, because the ionospheric delay of 1 TECU at the GPS L1 frequency is 0.16 m and comparable to the wavelength of the signals at the frequency, 0.19 m. The amplitude of the TIDs are within the range of those of typical MSTIDs, but the observed TIDs are associated with ROTI enhancements. Ionospheric irregularities which causes fluctuation of TEC represented by ROTI could further degrade performance of GNSS-based precise positioning systems by making differential GNSS difficult and signal tracking difficult. Real-time and wide-area monitoring of the ionospheric disturbances would be useful for accurate, stable, and reliable operations of GNSS-based systems.