Atmospheric Modes Excited by the 2021 August Eruption of the Fukutoku-okanoba Volcano, Izu-bonin Arc, Observed as Harmonic Oscillations of QZSS Total Electron Conte

Continuous Plinian eruptions of volcanoes often excite atmospheric resonant oscillations with several distinct periods of a few minutes. We detected such harmonic oscillations excited by the 2021 August eruption of the Fukutoku-Okanoba volcano, a submarine volcano in the Izu-Bonin arc, in ionospheric total electron content (TEC) observed from global navigation satellite system (GNSS) stations deployed on three nearby islands, Chichijima, Hahajima, and Iwojima. Continuous records with the geostationary satellite of Quasi-Zenith Satellite System (QZSS) presented four frequency peaks of such atmospheric modes. The harmonic TEC oscillations, started at ~5:16 UT, exhibited an unprecedented large amplitude but decayed in a few hours. upward propagation of atmospheric acoustic waves and ionospheric electron density anomalies made by the passage of the wave. Red and blue parts show the positive and negative electron density anomalies (arbitrary unit) in the north-south vertical section. We assumed a simple N-shaped pulse with a period of 4 minutes. Geomagnetic eld (Inclination: 34.5º, Declination -3.0º, at a point ~300 km above Fukutoku-Okanoba, shown as B) makes north-south asymmetry. Details of the simulation are in Kundu et al. (2021). In (b) we compare slant TEC signatures to be obtained by observing a satellite in the northern/southern skies, with elevation 45º, from the southern/northern points Ps/Pn (gray curves), and those assuming the geometry of 0603-J07 (red curve). (c) Line-of-sight from


Introduction
With arrays of continuous global navigation satellite system (GNSS) stations, we can continuously monitor the Earth's ionosphere in terms of total electron content (TEC), an integrated number of electrons along line-of-sights connecting satellites and receivers. GNSS-TEC observations enabled us to detect ionospheric responses to large volcanic eruptions worldwide during the last two decades. Such responses have two distinct types, (Type-1) harmonic oscillations of TEC (e.g. Nakashima et al. 2016), and (Type-2) short impulsive pulses of TEC changes (e.g. Heki 2006). Type-1 disturbances are caused by continuous Plinian eruptions and often lasts for hours. Type-2 occurs 8-10 minutes after a Vulcanian explosion of a volcano as a single N-shaped change of TEC. Both types propagate outward with a speed of 0.8-1.0 km/s, the acoustic wave velocity in the ionospheric F region. Cahyadi et al. (2020) and Cahyadi et al. (2021) compiled the recent cases of such Type-1 and Type-2 disturbances, respectively. Type-1 cases have never been found in Japan except the 2009 eruption signal of the Sarychev Peak Volcano, Russia, from stations in northern Japan (Shestakov et al. 2021).
Global Positioning System (GPS) has been the main GNSS used to study ionospheric TEC. GPS satellites employ orbits with periods of a half sidereal day and can stay within the view of a ground station only for periods shorter than 4-5 hours. On the other hand, Quasi-Zenith Satellite System (QZSS), the Japanese satellite system for positioning, is composed of three satellites with quasi-zenith orbits (J01, J02, J03) and one geostationary orbit satellite (J07). These satellites stay longer within the view of a station (~8 and 24 hours a day for J01-03 and J07, respectively). This offers a rare opportunity to observe the TEC oscillation caused by a Plinian volcanic eruption lasting for hours without disruptions of data. In this study, we take this advantage in discussing the frequency content and temporal decay of the oscillation caused by a recent case of Type-1 ionospheric disturbance by a volcanic eruption in Japan.
Ionospheric response to the 2021 August eruption of the Fukutoku-Okanoba volcano The 2021 Plinian eruption Fukutoku-Okanoba is a submarine volcano located ~5 km NNE of Kita-iwojima Island (uninhabited) in the Izu-Bonin arc, located ~1,000 km south of Tokyo, Japan (Fig. 1). Its submarine eruptions in 1904-1905, 1914, and 1986 resulted in formation of a tiny island, which disappeared within a few years by collapse and marine erosion.
The latest volcanic activity started in 2020 February, when the sea water of this area changed its color to yellow-green. A strong eruption with Volcanic Explosivity Index (VEI) 4 started on August 13, 2021. According to Japan Meteorological Agency (JMA), the eruption column as high as ~16,000 m lasted from August 13, 00 UT to August 14, 19 UT (JMA, 2021).
Formation of an island with a diameter of ~1 km was con rmed on August 15, but this new island has been shrinking day by day. The 2021 eruption is one of the largest eruptions in Japan in terms of the total mass of the ejecta. A few months later, huge amount of oating pumice reached the coast of the Ryukyu Islands, southwestern Japan, hindering shing and ferry navigation in that region.

Eruption signatures in GNSS-TEC
We use GNSS raw data les from GEONET (GNSS Earth Observation Network) run by Geospatial Information Authority (GSI), Japan. Within ~300 km from the Fukutoku-Okanoba volcano, there are ve GEONET stations on three inhabited islands, P217 and 2007 on Chihijima, 0603 on Hahajima, and 0604 and 0605 on Iwojima (Fig. 1b). Although the two stations in Iwojima track only GPS satellites, the three other stations track GLONASS, Galileo, and QZSS in addition to GPS. Figure. 1c-f shows sub-ionospheric point (SIP) trajectories of these four GNSS as viewed from 0603, Hahajima. SIP trajectories of the QZSS satellites are much shorter than other GNSS, and the SIP of J07 hardly moves. This indicates that these satellites are nearly xed in the sky when viewed from the ground station.
We converted the L1 and L2 carriers into total electron contents (TEC) (we also try L5 as discussed later in this article). Basic procedures in the GNSS-TEC studies follow Heki (2021). Figure. 2 compares the TEC time series 4:30-7:30 UT obtained using the QZSS geostationary satellite (J07) from the 0603 station over ve consecutive days, August 11-15, 2021. One can see that TEC oscillation started at ~5:20 UT on August 13, the day the Plinian eruption started. This is a typical ionospheric signature of Plinian volcanic eruptions (Cahyadi et al., 2020). Such oscillations are not seen on other days.
In Figure. 3a, we selected stations 2007, 0603, 0605 representing the three islands, Chichijima, Hahajima, and Iwojima, respectively, and showed slant TEC time series on Aug. 13, 2021, using various GNSS satellites with SIP located close to the volcano. Those observed at P217 and 0604 are not shown because they are very similar to those at 2007 and 0605 stations, respectively. In Figure. 3b, we modi ed the time axis correcting for the travel time of the acoustic wave from the volcano to the ionospheric penetration points of line-of-sights assuming 0.8 km/s propagation velocity. We can see that the phases of TEC oscillations are largely coherent among different satellite-station pairs and that the atmospheric oscillation started at around 5:16 right above the volcano.
Outward propagation of ionospheric disturbances from the volcano can be con rmed also in Figure. 4, where we plot the disturbance observed by various station-satellite pairs in colors as a function of time (horizontal axis) and distance from the volcano (vertical axis). There, we can recognize peaks align along lines with a slope corresponding to the acoustic wave speed (0.8 km/s).

Discussion And Conclusion
Frequency spectrum of the TEC oscillations Time-variable amplitudes of the TEC oscillation ( Fig. 3) suggests the existence of multiple frequency peaks. Long continuous TEC records enabled by QZSS are suitable for studying their frequency spectra. Figure. 5a shows the time series of slant TEC of J07 observed at three stations (0603 on Hahajima, 2007 and P217 on Chichijima) in 5:00-9:30 UT. A positive pulse at ~8:50 UT observed at 2007 and P217 would possibly be a sporadic-E irregularity (e.g., Maeda and Heki, 2015) irrelevant to the volcanic eruption. We select the 4-hours data 5:20-9:20 and estimated their frequency components using the Blackman-Tukey method (Fig. 5b).
They show four frequency peaks at about 3.7, 4.4, 4.8, and 5.4 mHz, with the 4.8 mHz peak somewhat weaker than the other three. They correspond to periods of about 270, 227, 208, and 185 seconds, respectively. The rst two are the atmospheric resonance frequencies detected by seismometers after the 1991 eruption of the Pinatubo volcano (e.g., Kanamori and Mori, 1992). They also coincide with the two modes with abnormally large amplitudes in the background free oscillation of the Earth (Nishida et al., 2000). The higher two frequencies are also overtones of the atmospheric resonant oscillation (Watada and Kanamori, 2010). Identi cation of these four peaks would have been di cult with short arcs of conventional GNSS like GPS.
Temporal decay of the TEC oscillations Next, we analyze how such TEC oscillation decayed in time. Figure. 6a compares time series in two sequential 3-hours periods (5:20-8:20 and 8:20-11:20) and two spectrograms made using the initial two hours of these time windows. Strong atmospheric mode peaks in the earlier time disappear in the later time (Fig. 6b). Figure 6c shows gradual decay of the three peak frequency intensities. Because the time corresponds to local afternoon (5:20 UT is 14:20 in local time), background TEC also decays. However, the decay of the oscillation exceeds that in the background TEC calculated with a global ionospheric map (Mannucci et al., 1998) suggesting that the atmospheric resonance would have decayed substantially within 3 hours (Fig. 6c).

Comparison of 3 different combinations of L1, L2, and L5
The QZSS satellites transmit microwave signals in three different frequencies L1 (~1.575 GHz), L2 (~1.228 GHz), and L5 (~1.176 GHz). So far, we have been combining L1 and L2 phases to calculate TEC, but the three frequencies allow us to compare three different combinations (L1-L2, L1-L5, and L2-L5) for TEC. Let f h and f l be the higher and lower frequencies of the two bands to be combined, then we multiply their phase differences (expressed in lengths) with the factor f h 2 f l 2 /(f h 2 -f l 2 ) to obtain TEC. This factor becomes smaller (TEC data become less noisy) if the two frequencies are more different. The actual values of this factor are 7. 76, 9.52, and 42.08 for the L1-L5, L1-L2, and L2-L5 combinations, i.e., the L1-L5/L2-L5 combinations would have the smallest/largest noises.  TEC oscillation amplitude Cahyadi et al. (2020) compared the TEC oscillation amplitudes relative to the background vertical TEC from three cases and suggested that they might be proportional to the mass eruption rate (MER). The motions of electrons in the ionospheric F region are constrained in the direction of the ambient geomagnetic elds. This causes the directivity of ionospheric disturbances. They appear strongly on the equator side of the volcano, i.e., stronger disturbances emerge on the southern side in northern hemisphere (e.g., Heki, 2006;Kundu et al., 2021), and northern side in southern hemisphere (Nakashima et al., 2016). Figure 8a shows how such north-south asymmetry occurs using numerical simulation of upward propagation of atmospheric acoustic waves following Kundu et al. (2021). There, hypothetical line-ofsight with elevation angle 45º from two points assumed 270 km due south (Ps) and due north (Pn) are given with white lines. In Figure 8b,c, we compare slant TEC changes as viewed from the points Pn and Ps. Their amplitude differs by a factor of ~4, and the amplitude observed at 0603 using J07, calculated real azimuth and elevation of J07 from 0603 (red curve in Fig. 8b), is similar to the point Pn case. The current 0603-J07 slant TEC peak-to-peak amplitude of ~0.23 TECU becomes ~0.19 TECU in vertical TEC by multiplying with the cosine of the incidence angle of line-of-sight ( ~33º) with the F region ionosphere. This corresponds to ~0.76% of the background vertical TEC, ~25 TECU according to the GIM.
This relative TEC oscillation amplitude in the 2021 Fukutoku-Okanoba eruption is comparable to those associated with the 2015 Calbuco and 2010 Merapi eruptions (Cahyadi et al., 2020). However, we would have observed four times as strong oscillation if we had a GNSS station to the south of the volcano (Fig. 8). If we consider this factor 4 difference, the TEC oscillation amplitude of the 2021 Fukutoku-Okanoba eruption may reach ~3% of the background vertical TEC, which exceeds the value for the 2014 Kelud eruption (Nakashima et al., 2016;Cahyadi et al. 2020). Then, the MER at the peak time (~5:20 UT) of the TEC oscillation may have been as large as 5 x 10 7 kg s −1 . This is consistent with the total amount of ejecta in this eruption inferred as 3-10 x 10 11 kg (GSJ, 2021).

Conclusions
We summarize this study as follows.
1. The 2021 August eruption of the Fukutoku-Okanoba submarine volcano caused typical ionospheric signatures associated with Plinian eruptions.
2. Atmospheric modes in four different frequencies are observed and the TEC oscillation decayed within three hours.
3. QZSS has two bene ts for ionospheric studies, i.e., long continuous records suitable for frequency spectrum analyses, and three different microwave carriers that enable separation of intensities of true ionospheric scintillation signals from receiver noises.     (a) High pass ltered slant TEC time series at three stations observed using J07, the QZSS geostationary satellite, at three GNSS stations 0603, 2007, and P217 (Fig. 1b). Frequency components of the four hours data 5:20-9:20 UT (shown with a dashed line) obtained using the Blackman-Tukey method are shown in (b). We see three strong peaks (3.7, 4.4, and 5.4 mHz) and one weak peak (4.8 mHz) for the TEC data at all the three stations (color corresponds to those in (a)).  Three curves correspond to period 1 (5:20-6:20), period 2 (6:20-7:20) and period 3 (7:20-8:20). (c) Receiver noises s rx remain nearly constant, while ionospheric scintillation s ion decays rapidly with time. The receiver noise s rx is scaled with the frequency factor for the L1-L2 combination.

Figure 8
Numerical simulation of the upward propagation of atmospheric acoustic waves and ionospheric electron density anomalies made by the passage of the wave. Red and blue parts show the positive and negative electron density anomalies (arbitrary unit) in the north-south vertical section. We assumed a simple N-shaped pulse with a period of 4 minutes. Geomagnetic eld (Inclination: 34.5º, Declination -3.0º, at a point ~300 km above Fukutoku-Okanoba, shown as B) makes north-south asymmetry. Details of the simulation are described in Kundu et al. (2021). In (b) we compare slant TEC signatures to be obtained by observing a satellite in the northern/southern skies, with elevation 45º, from the southern/northern points Ps/Pn (gray curves), and those assuming the geometry of 0603-J07 (red curve). (c) Line-of-sight from