The ionospheric condition during the TC Usagi was analyzed in terms of scintillation index S4, occurrence rate of cycle slips, and TECR. Firstly, the variations of Kp, Dst, and F10.7 (Rostoker 1972) indices during the Usagi were studied because the strong geomagnetic and solar activities can also induce the ionospheric disturbance (Moeketsi et al. 2007; Brunini and Azpilicueta 2010; Guo et al. 2017). For a quiet geomagnetic condition, the Kp index should be smaller than 3 (Mungufeni et al. 2016), and the Dst index should be larger than − 20 nT (Gulyaeva and Arikan 2017). For a relatively quiet solar condition, the F10.7 index should be smaller than 150 sfu (Tapping 2013). According to the variations of the indices as shown in Fig. 4, there were no strong geomagnetic or solar activities during the 2013 TC Usagi. The Kp index varies below 3 with the mean of 1.3 during the period from 13 September to 12 October. The variation of Dst index confirms that the geomagnetic condition was quiet during the Usagi with the average value of − 7.8 nT, which is much larger than − 20 nT. As for the solar condition, the F10.7 index is very stable with the mean of 108.3 sfu, which indicates a relatively quiet solar condition.
Furthermore, we also investigated two other solar-related indices, i.e., X-ray flux and electron flux, to further confirm the solar condition. The data were retrieved from the National Oceanic and Atmospheric Administration (NOAA)/National Aeronautics and Space Administration (NASA) Geostationary Operational Environmental Satellite (GOES) 15 satellite. The results are shown in Fig. 5. The X-ray flux measured at the wavelength of 0.1–0.8 nm varied stably without significant increases during the TC period including the TC landfall day. There were no intensive solar X-ray flares of X-class (X-radiation flux larger than 10–4 W/m2 for wavelength between 0.1 and 0.8 nm) or M-class (X-radiation flux between 10–5 W/m2 and 10–4 W/m2) during the TC period (16 to 24 September), while the recorded solar X-ray flares of Class C (X-radiation flux between 10–6 W/m2 and 10–5 W/m2) were too weak (their flux were lower than 4 × 10–6 W/m2) to cause significant disturbances in the ionosphere. Figure 5c shows the variation of E2 electron fluxes from 13 September 2013 and 11 October 2013. During this TC period, as denoted by the period of two vertical red dashed lines, it started to increase on 19 September and kept a high value larger than 1000 cm−2 s−1 sr−1 between 20 and 24 September, which would affect the operation of spacecraft systems (Forsyth et al. 2020). However, the reason for this high electron flux cannot be easily attributed to the solar radiations and geomagnetic activities, because other indices, including Kp, Dst, F10.7, X-ray flux, and solar X-ray flare counts, clearly indicate a quiet geomagnetic and solar conditions during the TC period. Thus such an electron flux increase is very likely attributed to the TC event.
Scintillation index S
4
The electron density irregularities in the ionosphere can cause rapid amplitude and phase fluctuations, under some conditions, even the loss of lock of GPS signals. Such irregularities are called ionospheric amplitude and phase scintillations (Čokrlić and Galas 2013). Here, we just analyzed the amplitude scintillations during the period of the Usagi due to the strong correlation with the phase scintillations (Mushini et al. 2012). The amplitude scintillation can be described as the index of S4. The formula of S4 can be written as (Van Dierendonck et al. 1993):
$${S}_{4}=\sqrt{\frac{\langle {SI}^{2}\rangle -{\langle SI\rangle }^{2}}{{\langle SI\rangle }^{2}}},$$
(1)
where SI denotes the GPS signal intensity. 〈∙〉 represents the mean operation within the interval of interest, i.e., 60 s used in this study.
The ionospheric scintillation index S4 was calculated based on the data from the ISMR station, and the GPS data observed above 30° elevation angle were considered to reduce the multipath effects (Yang and Liu 2016b). As S4 > 0.3 always indicates nonignorable scintillation activity (Muella et al. 2008), the number of scintillations with S4 > 0.3 from 14 September to 12 October 2013 is shown in Fig. 6. It is noteworthy that there was no significant increase of scintillations during the period of the Usagi, even on the landfall day of 22 September 2013. However, a sudden increase of scintillations was observed on 24 September 2013, the second day after the Usagi made landfall. The number of scintillations reached up to 508. Then, the count of scintillation events returned to normal levels on 26, 27, and 28 September 2013. Again, a slight increase of 185 and 100 scintillation events showed on September 29 and October 1, respectively. The number of scintillations returns to normal level afterwards except October 4.
Cycle slips
The electron density irregularities in the ionosphere can also interrupt the propagation of the GPS signals, known as cycle slips on the carrier phase measurements (Brunini and Azpilicueta 2010). Although other factors, i.e., (1) low signal–noise ratio (SNR) and multipath; (2) surrounding obstructions; (3) high dynamic state of the receiver; (4) failure in the receiver software can trigger the occurrence of cycle slips (Wang et al. 2016), the ionospheric disturbance is the major factor for the occurrence of cycle slips in this study because of the well-performed GPS receivers and carefully-selected locations of the Hong Kong SatRef network stations (Chan and Li 2007).
The sophisticated cycle slip detection algorithm based on the TECR and Melbourne–Wübbena wide lane (MWWL) observations was applied in this study (Liu 2011). The algorithm was validated under the active ionospheric condition (Cai et al. 2013). Figure 7 shows the total cycle slips for the HKOH, HKPC, and HKST stations on each day during the period from 14 September to 12 October 2013. The variation of the number of cycle slips on the GPS L1 and L2 signals shares the same pattern as the change of the scintillations. During the TC period, the occurrence rate of cycle slips on each day shows a stable variation. However, a sudden increase of cycle slips can be observed on 24 September 2013, the second day after the Usagi made landfall. The total number of cycle slips reaches up to ~ 400. Then, the number of cycle slips on September 27 falls back to a normal level. Again, the number of cycle slips bounces back on September 29 and October 1 with the value of ~ 300 and ~ 200. Afterwards, the number of cycle slips returns to a normal level.
TECR
The scintillations always indicate the electron density irregularities in the ionosphere. However, it is difficult to derive the electron density directly from the GPS measurements. Fortunately, the TECR along the satellite–receiver line-of-sight (LOS) can be derived to study the variation of the TEC in the ionosphere. Considering the large noise on the pseudorange measurements, the carrier phase measurements are used to calculate the TECR in this study. The TECR can be calculated by differentiating the TEC values between two consecutive epochs. It can be written as (Liu 2011):
$$\text{TECR}=\frac{TEC\left(k\right)-TEC(k-1)}{\Delta t},$$
(2)
where Δt is the sample interval, in the unit of seconds.
$${\text{TEC}}\left(k\right)=\frac{{f}_{1}^{2}\{\left[{\lambda }_{1} \varphi_{1}\left(k\right)-{\lambda }_{2}{\varphi}_{2}\left(k\right)\right]-\left[{\lambda }_{1}{N}_{1}-{\lambda }_{2}{N}_{2}\right]-{b}_{r}-{b}^{s}\}}{40.3\times {10}^{16}(\gamma -1)},$$
(3)
where \({\varphi}_{1}\)(k) and \({\varphi}_{2}\)(k), in the unit of cycles, are the carrier phase measurements of the two frequencies \({f}_{1}\) and \({f}_{2}\), respectively, at the epoch k; \({\lambda }_{1}\) and \({\lambda }_{2}\) are the wavelength of the frequencies \({f}_{1}\) and \({f}_{2}\), respectively, in unit of m/cycle; \({N}_{1}\) and \({N}_{2}\), in unit of cycles, are the ambiguities for the frequencies \({f}_{1}\) and \({f}_{2}\), respectively, which are often constants in a continuous arc; \({b}_{r}\) and \({b}^{s}\), in unit of meters, are the inter-frequency biases of the receiver r and the satellite s, respectively, which can also be regarded as constants in a continuous arc; \(\gamma ={f}_{1}^{2}/{f}_{2}^{2}\) is the ratio of the squared frequencies. Cycle slip detection and repair is needed before the TECR computation in order to make sure a continuous observation arc is obtained.
Figure 8 shows the variation of the TECR derived from the HKPC station in terms of mean and standard deviation (STD) for each GPS satellite during the period from 14 September to 12 October 2013. The variation of the mean value of the TECR is stable, changing within approximately ± 0.005 TECU/sec as shown in Fig. 8a. However, the change of the STD of the TECR shows a different way for each GPS satellite as shown in Fig. 8b. It is clear to see the TECR of GPS pseudorandom noise (PRN) 29 and GPS PRN 24 satellites has a relatively large standard deviation. It is suspected that the electron structure in the ionosphere along the LOS for GPS PRN 29 and GPS PRN 24 experienced an abnormal change. In addition, a sudden increase of the STD of the TECR for some GPS satellites can be observed on 24, 25, 29, and 30 September and 1 October 2013.
Figure 9 demonstrates the daily STD of the TECR for the HKOH, HKPC, and HKST stations during the period from 14 September to 12 October 2013. The STD of the TECR was averaged over the STD of the TECR of all the GPS satellites for each day. The change of the STD of the TECR for the HKOH, HKPC, and HKST stations is consistent with each other. It is worth noting that the change pattern of the STD of the TECR is the same as the change pattern of the scintillations and cycle slips. A stable period can be observed during the Usagi with an average value of ~ 0.008 TECU/sec. Then, the STD of the TECR suddenly increases to ~ 0.016 TECU/sec on 24 September 2013. After 2 days’ decrease, the STD of the TECR comes back to the normal value of ~ 0.007 TECU/s. Again, it bounces back on September 29 with the value of ~ 0.013 TECU/s. Afterwards, the STD of the TECR returns to a normal level.
The connection between the TC and ionospheric disturbances
The ionospheric disturbance occurred in the context of the clear geomagnetic and solar condition. It is suspected that the strong convection like TCs generates the AGWs, especially during the landfall period when the strong convection interacted with rough terrains, strengthening the AGWs power to propagate to the ionospheric layer (Chen et al. 2016; Chou et al. 2017; Kong et al. 2017).
Our findings show that the strong ionospheric disturbances occurred on the second day after the TC made landfall near Hong Kong. Moreover, the ionospheric disturbances often presented during the period from 12:00 UT (20:00 LT) to 18:00 UT (02:00 LT), which will be provided in the following section. It shows that the AGWs cannot trigger the ionospheric disturbances, i.e., scintillations, immediately. The reason is that the electron density in the ionosphere is relatively stable before sunset. After sunset, steep gradients of the electron above Hong Kong were generated from the eastward electric field (Song et al. 2017; Lou et al. 2019). The two factors, upward AGWs and steep gradients of the electron, jointly produced a more unpredictable electron distribution in the ionosphere. Consequently, strong ionospheric disturbances were triggered between 12:00 UT (20:00 LT) and 18:00 UT (02:00 LT) on 24 September 2013, the second day after the TC made landfall. Previous studies have shown that ionospheric disturbances occurred with one to four days delay after other TCs. Yang and Liu (2016a) found the ionospheric irregularities above Hong Kong on the second day after the 2012 TC Tembin made landfall over the southern coast of Taiwan. The ionospheric anomaly on the fourth day after the 2013 TC Haiyan made landfall over the eastern coast of Philippines was observed by Li et al. (2017). In Australia, the ionospheric disturbances occurred on the second day after the 2011 TC Yasi and the 2018 TC Marcus made landfall over the eastern and northern coast of Australia, respectively (Ke et al. 2019). Similar results were obtained for hurricanes near America, the ionospheric disturbances were observed 2 days delay after the 2005 Hurricane Katrina and Rita made landfall over the northern Gulf coast and the Texas/Louisiana border, and one day delay after the 2005 Hurricane Wilma made landfall near the northeastern Yucatan Peninsula (Polyakova and Perevalova 2011).
Furthermore, our findings show that there were strong ionospheric disturbances on 29 September and 1 October in terms of S4, number of cycle slips, and TECR. The disturbances were probably caused by the other TC, i.e., the TC 2013 Wutip. It passed by the south of Xisha Islands on 29 September with the intensity of Severe Typhoon and made landfall over the coast of central Vietnam on 30 September 2013 with the intensity of severe tropical storm. Compared with the TC Usagi, the TC Wutip had a weaker intensity. Therefore, the number of scintillations and cycle slips, and the value of TECR showed a lower level.