This study is organized as follows: Section 2.1 presents the observations and analysis of FORMOSAT‐5 induced circular waves. Section 2.2 shows the comparison of rocket‐induced TIDs from previous events. Section 2.3 discusses the generation mechanism of circular SAWs. Section 2.4 briefly presents the rocket‐induced ionospheric plasma hole signature. A summary is given in section 3 .

Here we apply the two‐dimensional GPS‐TEC observations over the continental United States (CONUS) to evaluate the ionospheric response to the launch of FORMOSAT‐5. Prominent circular SAWs and an ionospheric plasma hole were observed over the western CONUS‐Pacific region after the launch. Despite the frequent reports of rocket‐induced V‐shape SAWs, there has been no prior report of circular SAWs triggered by rocket launches. The unique orbit insertion of FORMOSAT‐5 with a lofted rocket trajectory may account for the unusual circular SAWs.

Recently, the first independently developed Earth remote sensing satellite, Formosa satellite‐5 (FORMOSAT‐5), of Taiwan's National Space Organization was successfully launched by the SpaceX Falcon 9 v1.2 rocket into the low Earth orbit (LEO) from the Space Launch Complex 4 East (SLC‐4E) at Vandenberg Air Force Base in California on 24 August 2017. FORMOSAT‐5 operates in a sun synchronous orbit at nearly 720 km altitude with 98.28° inclination angle. It carries the remote sensing instruments for providing multispectral and panchromatic imaging capabilities and the Advanced Ionospheric Probe for monitoring the ionospheric irregularities and earthquake precursors (Chen et al., 2017 ; Liu & Chao, 2017 ).

Over the past few decades, rapid developments in space technology have enabled human exploration beyond the Earth's orbit. With the large number of space vehicles carrying payloads into orbits, space weather effects linked to human activity have become an important issue. Since the 1960s, several studies have reported that rocket launches could cause changes to the adjacent space environment. For example, exhaust plumes generated from the shuttle or rocket launches resulted in ionospheric electron density depletions via chemical recombination process along the ascending trajectories (e.g., Booker, 1961 ; Furuya & Heki, 2008 ; Mendillo et al., 2008 ; Mendillo, Hawkins, & Klobuchar, 1975 ; Park et al., 2016 ). Theoretical studies and numerical model simulations on the effect of plume‐released reactive molecules in the ionosphere have been conducted (Bernhardt et al., 1975 ; Mendillo & Forbes, 1978 ). The passage of rocket‐triggered traveling ionospheric disturbances (TIDs) associated with the shock acoustic waves (SAWs) were investigated and simulated (Arendt, 1971 ; Afraimovich, Kosogorov, & Plotnikov, 2002 ; Calais & Minster, 1996 ; Donn et al., 1968 ; Noble, 1990 ; Kakinami et al., 2013 ; Lin et al., 2014 , Lin, Chen, et al., 2017 ). Kakinami et al. ( 2013 ) observed the V‐shape SAWs in GPS total electron content (TEC) triggered by a missile launch from North Korea on 12 December 2012 by using the dense regional GPS networks in Japan, Korea, and Taiwan. The V‐shape waves had horizontal phase velocities of 1.8–2.6 km/s, which were much faster than the speed of acoustic waves reported by previous studies. Ding et al. ( 2014 ) also observed the long‐distance propagation of V‐shape SAWs on both sides of the rocket trajectory during the launch of the Shenzhou 10 spacecraft in China on 11 June 2013. These rocket events often generated V‐shape signatures while the rockets flew horizontally in the ionosphere. Lin, Shen, et al. ( 2017 ) first reported the concentric traveling ionospheric disturbances (CTIDs) in GPS‐TEC associated with the concentric gravity waves (CGWs) induced by the Falcon 9 rocket. The CGWs originated from the mesopause region after the ignition of the second‐stage rocket and propagated into the ionosphere as a manifestation of CTIDs. These human‐made space environment changes could introduce additional errors to the precision of positioning, navigation, reconnaissance systems and radio communication applications.

The ionosphere consists of a great number of electrically charged particles in the Earth's upper atmosphere that can affect radio wave propagation. It is strongly influenced by disturbances like solar flares, geomagnetic storms, and solar eclipses (e.g., Afraimovich et al., 1998 ; Blanc & Richmond, 1980 ; Chimonas & Hines, 1970 ; Liu et al., 2004 , 2013 ; Lin, Liu, et al., 2012 ; Lin, Richmond, Liu, et al., 2005 ; Lin, Richmond, Heelis, et al., 2005 ; Liu, Tsai, et al., 2006 ; Mannucci et al., 2005 ; Tanaka, 1986 ; Tsai & Liu, 1999 ). Global‐scale lower atmospheric activities also contribute to significant global ionospheric variations (e.g., Immel et al., 2006 ; Goncharenko et al., 2010 ; Lin, Liu, et al., 2012 ; Lin, Lin, et al., 2012 ). Recent studies indicate that the ionosphere could also be influenced by geophysical and meteorological events on Earth, such as earthquakes, tsunamis, volcano eruptions, typhoons, and tornados (e.g., Azeem et al., 2015 ; Chou, Lin, Yue, Chang, et al., 2017 ; Chou, Lin, Yue, Tsai, et al., 2017 ; Dautermann et al., 2009 ; Liu, Chen, et al., 2011 ; Liu, Lin, et al., 2006 ; Liu & Sun, 2011 ; Nishioka et al., 2013 ; Sun et al., 2016 ). These natural sources can create disturbance waves that interact with the ionized and neutral particles, thus possibly introducing errors into the positioning and navigation for the Global Navigation Satellite Systems.

2 Observations and Discussions

2.1 FORMOSAT‐5 Induced Circular SAWs According to the SpaceX Launch Report (http://www.spacex.com/sites/spacex/files/formosat5presskit.pdf), the Falcon 9 v1.2 rocket lifted off at 18:51:00 UT and deployed FORMOSAT‐5 to a roughly 720 km altitude approximately 11 min after the launch. Clear ionospheric perturbations were detected from ground‐based GPS networks in the U.S. after the rocket launch. We derived the vertical TEC by using the 30 s sampling GPS observational data in Receiver Independent Exchange (RINEX) format from Scripps Orbit and Permanent Array Center (http://sopac.ucsd.edu/) to study the ionospheric perturbations. The ionospheric pierce point altitude (i.e., the altitude of slant‐to‐vertical TEC conversion) is adjusted to 300 km, and cutoff elevation angle is set as 20° to avoid multipath errors. Then we applied a fifth‐order Butterworth band‐pass filter to extract the characteristics of SAWs associated with the rocket launch. It is common to study the ionospheric perturbation using the Butterworth band‐pass filter (e.g., Bowling et al., 2013; Calais & Minster, 1995, 1996; Chen et al., 2011; Komjathy et al., 2012; Lin, Shen, et al., 2017; Yang et al., 2012). Using this type of filtering technique allows us to extract the wave perturbations within an expected range of wave periods and eliminate the long period and high amplitude TEC variations due to the daily solar activity or satellite motion. In this study, the filtered TECs with cutoff periods of 4–15 min are applied to study the TIDs corresponding to the acoustic wave. These cutoff periods are compared to those used in previous studies of rocket‐induced TIDs using GPS observations (Calais & Minster, 1996; Ding et al., 2014; Lin, Shen, et al., 2017). Figure 1 reveals the time sequence maps of Butterworth band‐pass filtered TECs (4–15 min) during 19:00:00–19:18:30 UT on 24 August 2017, which shows pronounced ionospheric perturbations with a circular shape off the west coast of California. The circular waves initially appeared ~5 min after the rocket launch, and the crest and trough of circular waves quickly emanated outward with a radius of about 750 km (~1,770,000 km2) for ~20 min. These circular waves had amplitudes exceeding 0.4 TECu (1 TECu = 1016 el/m2), which corresponds to approximately 3% of the background TEC (~12 TECu), and gradually diminished by 19:18:30 UT. The origin of circular waves located right above the rocket trajectory (magenta line) suggests that the circular ripples were triggered by the rocket launch. Figure 1 Open in figure viewer PowerPoint Two‐dimensional TEC maps derived from ground‐based GPS observations with the Butterworth band‐pass filtering (4–15 min) indicating the concentric shock acoustic waves triggered by the launch of SpaceX Falcon 9 rocket on 24 August 2017. The Falcon 9 v1.2 rocket lifted off at 18:51:00 UT, and its trajectory and launch site are indicated by the overplotted magenta dash line and white triangle. To better understand the characteristics of circular wave disturbances, the band‐pass filtered TEC data within 120–122°W and 33–38°N are organized and plotted as a function of latitude versus time after the rocket launch. Thus, we can roughly estimate the horizontal velocities, periods, and wavelengths of circular waves, with a similar approach used in earlier studies (Chou, Lin, Yue, Chang, et al., 2017; Kotake et al., 2007). Figure 2 illustrates the various propagation velocities of circular waves that can be estimated by the slopes of slant dashed lines. The results show that the circular waves have horizontal phase velocities of ~629.15–726.02 m/s, periods of ~10.28 ± 1 min, and horizontal wavelengths of ~390–450 km. Afraimovich et al. (2002) reported the velocities of SAWs ranging from 600 to –1,100 m/s, which are close to the acoustic velocities in the upper atmosphere depending on corresponding atmospheric conditions. The horizontal phase velocities of circular waves exceeding 600 m/s in this study are most likely related to the SAWs instead of atmospheric CGWs. Figure 2 Open in figure viewer PowerPoint The time‐latitude‐filtered TEC (Butterworth band‐pass filter) map in 120°–122°W longitudes and 33°–38°N latitudes. The red line and slant dash lines denote the second stage engine start and propagation velocities of ionospheric disturbances, respectively. 1974 (1) γ = 7/5 is the ratio of specific heat and R = 8.3145 J mol−1 K−1 is the molar gas constant. The molecular weight M and neutral temperature T are obtained from the NRLMSISE‐00 empirical neutral atmosphere model (Picone et al., 2002 ω a ) and buoyancy frequency ( ω b ) can be expressed as follows: (2) (3) To verify the characteristics of circular waves, we calculate the theoretical acoustic velocity, acoustic cutoff, and buoyancy periods in the ideal gas (Yeh & Liu,). The theoretical equation for acoustic velocity is expressed as follows:where= 7/5 is the ratio of specific heat and= 8.3145 J molis the molar gas constant. The molecular weightand neutral temperatureare obtained from the NRLMSISE‐00 empirical neutral atmosphere model (Picone et al.,) for the conditions on 24 August 2017 at 120°W, 35°N. Then the acoustic velocity can be computed as shown in Figure 3 a. The acoustic cutoff frequency () and buoyancy frequency () can be expressed as follows: Figure 3 Open in figure viewer PowerPoint The vertical profile of (a) acoustic wave velocity and (b) acoustic cutoff and buoyancy periods calculated from the NRLMSISE‐00 model at 120°W, 35°N on 24 August. The dash lines indicate that the acoustic wave velocity, acoustic cutoff, and buoyancy periods are 826.61 m/s, 13.62 min, and 15.02 min at 300 km altitude, respectively. where H and g are the scale height and gravitational acceleration. The acoustic cutoff period (T a = 2π/ω a ) and buoyancy period (T b = 2π/ω b ) have the height profiles given by Figure 3b. We note that the theoretical acoustic velocity, acoustic cutoff, and buoyancy periods at 300 km altitude are about 826.5 m/s, 13.6 min, and 15 min, respectively. The SAW velocity is essentially close to the acoustic velocity in the ionosphere. The observed wave periods (~10.28 ± 1 min) fall into the acoustic mode, but the horizontal phase velocities (~629.15–726.02 m/s) are slower than the theoretical result. The slower horizontal phase velocity might be due to the limited observational geometry of 2‐D TEC map where only the horizontal component of phase velocity can be derived. If the rocket flight has a vertical component, as do the SAWs induced by it, the vertical component of the phase velocity may not be detectable. Consequently, the actual SAW velocity might be greater than that measured from the TEC maps. On the other hand, the short period implies that the impulsive circular waves are most likely related to the rocket‐induced SAWs instead of atmospheric CGWs, since it is impossible for a gravity wave to have period shorter than the buoyancy period. If the rocket moved faster than the sound speed, a “bow shock wave” formed by acoustic waves appears along the rocket trajectory, and the shock wave immediately decays into the acoustic mode (e.g., Ding et al., 2014; Kakinami et al., 2013; Lin et al., 2014). Similar bow shocks and stern waves were also observed during the solar eclipses (Liu, Sun, et al., 2011; Sun et al., 2018; Zhang et al., 2017).

2.2 Comparison of Rocket‐Induced Ionospheric Disturbances in Other Events 2.2.1 Rocket‐Induced V‐Shape SAWs To further compare the properties of rocket‐induced SAWs generated in other events, a series of rocket‐induced SAWs in time rate change (time derivative) of TEC (rTEC) from launches of the North Korea Taepodong‐2, China Chang'e 2, SpaceX Falcon 9 JASON‐3, and North Korea Kwangmyongsong‐4 mission are shown in Figure 4. General information on these rocket launches are listed in Table 1 (including the launch date, time, sites, and shape of SAWs). These rocket‐induced pronounced ionospheric SAWs had amplitudes of over 0.3 TECu that are comparable to the FORMOSAT‐5 induced SAWs (0.4 TECu). However, they mainly resulted in the V‐shape signature that is very different from the circular SAWs reported in this study. Figure 4 Open in figure viewer PowerPoint Snapshots of time rate change (time derivative) of TEC (rTEC) indicating the rocket‐induced shock acoustic waves from (a) North Korea Taepodong‐2, (b) China Chang'e 2, (c) SpaceX Falcon 9 Jason‐3, and (d) North Korea Kwangmyongsong‐4 missions. Table 1. General Information of Rocket Launches Mission Launch date Launch time Launch site Shape of SAWs North Korea Taepodong‐2 5 April 2009 02:30:00 UT Musudanri V shape China Chang'e 2 1 October 2010 10:59:00 UT Xichang LC‐2 V shape SpaceX Falcon 9 JASON‐3 17 January 2016 18:42:18 UT Vandenberg Air Force Base V shape North Korea Kwangmyongsong‐4 7 February 2016 00:30:00 UT Sohae Space Center V shape SpaceX Falcon 9 FORMOSAT‐5 24 August 2017 18:51:00 UT Vandenberg Air Force Base Circular shape Various wave periods and horizontal phase velocities of rocket‐induced SAWs are reported in previous literature by Calais and Minster (1996), Bowling et al. (2013), Ding et al. (2014), Lin et al. (2014), Lin, Shen, et al. (2017), and Lin, Chen, et al. (2017). The wave period (~10.28 min) in this study is longer than the previous events listed in Table 2, but it is still within the acoustic cutoff period shown in Figure 3b. Li et al. (1994) reported the space shuttle excited SAWs with periods of ~50–150 s at 105–110 km altitude. Ding et al. (2014) and Lin, Shen, et al. (2017) reported the rocket‐induced SAWs with periods of ~9 min in the ionosphere. These studies suggest that the SAW period corresponds to the altitude reached by the rocket, since the acoustic cutoff period varies with altitude. Detailed characteristics of the rocket‐induced SAWs are listed in Table 2. Table 2. Detail Characteristics of Rocket‐Induced SAWs Mission Amplitude (TECu) Velocity (m/s) Period (min) Technique North Korea Taepodong‐2 (Lin et al., 2014 ~0.2 ~831–1296 1.7–10 GPS China Chang'e 2 ~0.2–0.3 ~897–904 ~4–10 GPS SpaceX Falcon 9 JASON‐3 (Lin, Shen, et al., 2017 ~0.4–0.5 ~808–990 ~8–9 GPS North Korea Kwangmyongsong‐4 (Lin, Chen, et al., 2017 ~0.3–0.5 ~873–997 6–12 GPS SpaceX Falcon 9 FORMOSAT‐5 ~0.4 ~629–726 ~10.28 GPS Lin, Shen, et al. (2017) reported that the V‐shape SAWs appeared simultaneously when the rocket reached 200 km approximately 5 min after the rocket liftoff. In this study, we observed that the circular waves emerged in the TEC maps approximately 5 min after rocket liftoff according to the SpaceX report. This coincidence indicates that the SAWs were simultaneously excited while the rocket was passing through the ionosphere. 2.2.2 Rocket‐Induced Circular Waves Lin, Shen, et al. (2017) reported remarkable patterns of V‐shape SAWs and CTIDs in the ionosphere during the JASON‐3 launch by the Falcon 9 v1.1 rocket from Vandenberg Air Force Base at 18:43:18 UT on 17 January 2016. The CTIDs continuously emanated outward with a number of wavefronts (crests and troughs) following the V‐shape SAWs for almost 1 h with horizontal phase velocities of 241–617 m/s, periods of 10.5–12.7 min, and horizontal wavelength of ~200–400 km. The characteristics of CTIDs in Lin, Shen, et al. (2017) agree well with the gravity wave dispersion relation, suggesting the CTIDs are related to the atmospheric CGWs. We select the JASON‐3 mission for comparative study since the rocket type, launch location, and local time are similar to the FORMOSAT‐5 mission. Most importantly, they both triggered circular waves in the ionosphere. At first glance, the observed circular waves in this study have some similarities to the observations of CTIDs induced by the JASON‐3 launch, but they also have some differences. For example, the FORMOSAT‐5 launch simultaneously produced a single impulsive circular wavefront (a single crest and a trough) instead of multiple circular wavefronts produced by the JASON‐3 launch based on TEC maps. The presence of CGWs always has several simultaneous wavefronts in the middle and upper atmosphere (Miller et al., 2015). This implies that the single impulsive wave of FORMOSAT‐5 launch was unlikely related to CGWs. It is more likely a SAW since the single impulsive wave pattern is similar to other previous reports of rocket‐induced SAWs. Further, the circular waves induced by the FORMOSAT‐5 launch lasted for ~20 min, which is much shorter than the 1 h duration of the circular waves manifested by the CGWs of the JASON‐3 launch. The circular waves driven by the JASON‐3 CGWs appeared ~16–40 min after the rocket liftoff, since it took tens of minutes for the CGWs to propagate from the mesosphere to the ionosphere (Lin, Shen, et al., 2017). The rapid appearance of circular waves in the ionosphere (~5 min after the Falcon 9 rocket liftoff) suggests that the CGWs were not the candidate source responsible for the waves associated with the FORMOSAT‐5 launch. Furthermore, the FORMOSAT‐5 induced circular waves have higher horizontal phase velocities, horizontal wavelengths, and shorter wave periods than the CTIDs induced by the JASON‐3 launch.

2.3 The Generation Mechanism for Circular SAWs The possible mechanism of FORMOSAT‐5 induced circular SAWs is most likely related to the flight trajectory of rocket. We further compare the rocket's trajectory of JASON‐3 with FORMOSAT‐5 mission. Figure 5 shows the trajectories and velocities representing the JASON‐3 (blue line) and FORMOSAT‐5 (red line) launches, respectively, based on the launch reports and videos released by SpaceX. The Falcon 9 rockets for both missions reached supersonic speed approximately ~1 min after the rocket launch and continuously accelerated to over 2 km/s above 200 km altitudes (Figure 5a). For the FORMOSAT‐5 mission, the first stage fired for 2 min and 28 s accompanied with the first and second stage separation near 90 km altitude, then the second stage kept going on a single 6 min and 30 s burn, reaching about 720 km altitude nearly vertically (Figure 5b) in supersonic flight to deploy the FORMOSAT‐5 satellite with 98.28° inclination angle. The first stage rocket reached the maximum altitude of 247 km, which is the highest altitude reached by a Falcon 9 booster so far. In contrast to the FORMOSAT‐5 launch, the stage separation of JASON‐3 launch occurred in the mesopause, and the second stage accelerated horizontally at about 200 km altitude (see Figure 5b) to reach an elliptical orbit of ~66.038° orbital inclination angle, while deployment and the circularization maneuver were implemented at apogee using satellite's onboard thrusters. There are substantial differences in the rockets' trajectories for the two missions, partly because the targeted orbits of the two missions are at different inclination and altitude. This suggests that a rocket flying vertically in the ionosphere could act as a point source to induce the circular waves, while a rocket with a horizontal flight trajectory could excite the V‐shape waves along the horizontal projection of the flight trajectory as the schematic diagrams shown in Figures 6a and 6b. Furthermore, the horizontal phase velocities of circular waves and actual SAWs are functions of the cosine angle as illustrated in Figure 6c, which depicts the vertical flight of rocket‐generated SAWs in the ionosphere. The blue and green arrows indicate the velocities of actual SAWs (V bow ) and observed circular SAWs (V cir ). The relationship between V bow and V cir is given by V cir = V bow cos(θ), where θ is the included angle. This can explain the slower observed velocity compared to the theoretical acoustic velocity (826.5 m/s). For example, when the rocket reached 300 km altitude, the downrange distance from the launch site is ~180 km. Then the elevation angle of the rocket can be estimated as ~60°. The included angle should be less than or equal to 60°. If we assume the included angle to be 40°, the actual SAW velocities can be estimated as ~821–948 m/s, which are similar to previous observations of rocket‐induced SAWs. Figure 5 Open in figure viewer PowerPoint The Falcon 9 rocket's (a) velocities and (b) trajectories for the FORMOSAT‐5 (red) and JASON‐3 (blue) missions on 24 August 2017 and 17 January 2016, respectively. Figure 6 Open in figure viewer PowerPoint V bow ) and horizontal circular SAWs (V cir ) velocities is also shown in Figure Cartoon illustration representing the circular and V‐shape ionospheric disturbances triggered respectively by different orbit insertions of (a) FORMOSAT‐5 and (b) JASON‐3. The cosine angle relationship of actual SAWs () and horizontal circular SAWs () velocities is also shown in Figure 6 c. The differences between the JASON‐3 and FORMOSAT‐5 induced circular waves may prompt the question regarding why the FORMOSAT‐5 launch did not trigger CGWs. The absence may be related to the background wind conditions that affect the upward propagation of CGWs. Yue et al. (2009) suggested that the weak background wind is a necessary condition for the CGWs propagating upward from the lower atmosphere to the middle and upper atmospheres without wind filtering. According to the Horizontal Wind Model 2014 (Drob et al., 2015), the meridional and zonal winds had maximum speeds of ~20 m/s and ~40 m/s (with altitude ranges of 25–300 km) during the FORMOSAT‐5 launch. The background winds are not expected to influence the propagation of CGWs to the ionosphere because the rocket‐induced CGWs have higher horizontal phase velocities of 241–617 m/s that could reach the ionosphere from their source without much filtering (Lin, Shen, et al., 2017). Thus, we suspect that the generation of CGWs may be related to the flight trajectory of the rockets. For the launch of JASON‐3, the rocket flew below 200 km altitude and gradually maneuvered from vertical to horizontal at ~200 km altitude for ~6 min after the liftoff, whereas the steep ascent of FORMOSAT‐5 allowed it to stay in the middle and lower atmosphere only briefly (see Figure 5b). In fact, the atmosphere is a dissipative medium for the gravity waves especially above the mesopause region. The CGWs generated at sufficiently high altitudes are all subject to various dissipation processes such as molecular diffusion, thermal conduction, ion drag, nonlinear saturation, and other processes (Richmond, 1978; Vadas & Fritts, 2005). This implies that the rocket's dwell time below 200 km may enhance the effect of localized heating on the excitation of CGWs, and the brief stay of a rapidly moving rocket passing through the atmosphere would make the excitation of CGWs inefficient owing to the larger dissipation process at higher altitudes. In general, future investigation on the impact of flight trajectory and background atmospheric condition to the generation of CGWs and circular SAWs using theoretical modeling is still necessary.