Numerical Modeling and GNSS Observations of Ionospheric Depletions Due To a Small‐Lift Launch Vehicle

Space launches produce ionospheric disturbances which can be observed through measurements such as Global Navigation Satellite System signal delays. Here we report observations and numerical simulations of the ionospheric depletion due to a Small‐Lift Launch Vehicle. The case examined was the launch of a Rocket Lab Electron at 22:30 UTC on 22 March 2021. Despite the very small launch vehicle, ground stations in the Chatham Islands measured decreases in slant total electron content for navigation satellite signals following the launch. Global Ionosphere Thermosphere Model results indicated ionospheric depletions which were comparable with these measurements. Measurements indicated a maximum decrease of 2.7 TECU in vertical total electron content, compared with a simulated decrease of 2.6 TECU. Advection of the exhaust plume due to its initial velocity and subsequent effects of neutral winds are identified as some remaining challenges for this form of modeling.

. Recently there has been interest in the effect of depletions on high frequency radio propagation (Gong et al., 2022;Li et al., 2022;Ma et al., 2021).
In this study, we investigate ionospheric depletions due to the launch of a Rocket Lab Electron launch vehicle.This three-stage partially recoverable Small-Lift Launch Vehicle (SLLV) has a wet mass of 13,000 kg and carries payloads of up to 300 kg to low-Earth orbit (Rocket Lab, 2022).Both stages use an RP-1/liquid oxygen propellant mixture.Observations of ionospheric depletions were first made for the launch of the Vanguard SLV-4 rocket, a comparably sized SLLV (Booker, 1961).However, subsequent studies of ionospheric depletions have focused overwhelmingly on much larger launch vehicles.Ionospheric effects of such small launch vehicles as the Electron have not previously been simulated numerically or observed in GNSS data.
The launch (mission name "They Go Up So Fast") occurred at 22:30 UTC on 22 March 2021, corresponding to 11:15 Chatham Standard Time (CHAST).Rocket Lab Launch Complex 1 was the launch site, located at 39.262°S, 177.865°E (on the Māhia Peninsula, New Zealand).The launch vehicle carried 7 small satellites to target altitudes between 450 and 550 km and 45.0° inclination.Sections 2 and 3 respectively outline the numerical ionosphere-thermosphere system modeling and GNSS observation methods applied to the "They Go Up So Fast" launch case.Results of these investigations are detailed in Section 4 and further discussed in Section 5.

Numerical Modeling
A numerical simulation of the ionospheric depletion due to the rocket launch was performed using GITM (Ridley et al., 2006), adopting the methods outlined by Bowden et al. (2020).This simulation covered an 8-hr period from 22:30 UTC on 22 March to 06:30 UTC on 23 March.The chosen domain spanned 50°S-30°S in latitude, 170°E-155°W in longitude, and 100-536.67 km in altitude.This domain was covered by a regular 108 × 144 grid horizontally and 50 grid points vertically.These altitudes corresponded to the thermosphere (in the neutral atmosphere) and E-and F-regions (in the ionosphere).The simulation was run both with and without rocket exhaust gasses being added.The electron density integrated along the line-of-sight, or slant total electron content (STEC), was computed for GNSS satellites based on azimuth and elevation data from the source described in Section 3. Output was taken at 300 s intervals.
The rocket trajectory was estimated based on the target orbit, altitude, and speed data.Rocket Lab provide speed and altitude data in their launch video (Rocket Lab, 2021).The inferred rocket trajectory for the first and second stage firing is plotted in Figure 1.These data indicated that passage through the simulation domain coincided with the second stage firing.The total mass flow rate during the second stage firing was estimated based on a nominal thrust of T = 25.8 kN and specific impulse of I sp = 343 s using    =  ∕(0) (Rocket Lab, 2022), yielding a mass flow rate of    = 273.6 kg.s −1 .This was divided between H 2 O and CO 2 assuming complete combustion, giving flow rates of 7.95 × 10 25 molecules.s−1 and 7.34 × 10 25 molecules.s−1 respectively.The rocket chemical source was added at points along the trajectory for 520 s following launch (approximately corresponding to second stage cut-off at approximately 320 km altitude).These were added following 300 s delay during which diffusion was modeled using the approximate expression derived analytically by Bernhardt (1976), avoiding excessive concentration gradients which cause problems for the GITM numerical solver (Bowden et al., 2020).

GNSS Observations
Changes in Total Electron Content (TEC) following the launch were measured from the Chatham Islands reference station (CHTI), located at 43.735°S, 176.617°E, 75.764 m altitude.Slant TEC (STEC) data for the CHTI station were obtained from the Madrigal Coupling, Energetics and Dynamics of Atmospheric Regions Program (CEDAR) database.These were available for both GPS (here numbered 1 to 31) and GLONASS (numbered 32 to 55) satellites.Data also included estimated pierce point locations, which are plotted in Figure 2, and azimuth and elevation data.Data were recorded at 30 s intervals, though the time series was interspersed with brief gaps in availability.To approximate vertical TEC (VTEC), STEC data were multiplied by  sin() , where α was the elevation angle of the satellite measured at the ground station.This quantity will be referred to here as pseudo-VTEC (PVTEC).The quantity varies much less strongly with elevation than STEC and therefore allows ionospheric depletions to be identified more easily when data are plotted.Nevertheless, PVTEC can be computed directly from measured STEC and satellite position data, by contrast with VTEC, which also requires assumptions about ionospheric altitude profile and horizontal variation.Assumptions commonly used to compute VTEC may be less accurate in the case of ionospheric depletions.
The trajectory of the rocket passed to the north of the islands and is shown in Figure 2. In the 90 min following launch, satellite 15, satellite 29, and satellite 55 pierce points were identified as crossing the rocket ground track and selected for further study.As shown in Figure 3, the crossing occurred earliest for satellite 15, followed by satellite 55, and then satellite 29.
To provide comparison with an undisturbed ionosphere, data at a time offset of 1 day (i.e., at the same time of day for 23 March) were also considered.Levels of solar activity were similarly low for both days, with observed Penticton F 10.7 solar flux index of 80 SFU and 79 SFU on the launch and following day respectively (Tapping, 2013).There were no flares of Class C or greater on either day.Geomagnetic activity was also low on both days, with the Potsdam K p index not exceeding 3+ on either day (Matzka et al., 2021).As the orbital period of GNSS satellites is half a sidereal day, the ground track of each GPS satellite approximately repeats from one day to the next.By contrast, the ratio of the orbital period of GLONASS satellites to a sidereal day is approximately 8/17.Because 8 GLONASS satellites orbit in each plane, a satellite will approximately repeat the ground track traced by the preceding satellite the previous day.Thus, data for satellite 55 on the launch day could be compared with those for satellite 48 the following day.The great-circle distance between the pierce point for satellite 55 on launch day and satellite 48 the following day does not exceed 0.73° for 22:30 to 00:00 UTC.
TEC data from the OWMG reference station, located at 44.024°S, 176.369°E, 21.620 m altitude, were also analyzed.The features of these data were very similar to those of the nearby CHTI station, supporting the same conclusions but not providing additional information.Therefore, OWMG station data are not presented here.

Results
The initial expansion and subsequent decay of the simulated ionospheric depletion is shown in Figure 4. Simulated undisturbed ionospheric profiles (i.e., without addition of rocket exhaust) directly above the GNSS station are shown in Figure 5. Shortly after launch, the VTEC depletion was highly elongated and was aligned with the rocket ground track.At later times the depletion expanded perpendicular to the ground track while the magnitude at its center decreased.Comparing simulations with and without rocket exhaust, the largest VTEC depletion was 3.46 TECU, occurring at 23:30 UTC.The background VTEC in the simulation increases and becomes more spatially uniform as local time progresses from late morning to mid afternoon (11:15-14:45 CHAST).For satellite 55 observations, the pierce point crossed the ground track at approximately 23:10 UTC. Figure 7 shows that this crossing approximately coincided with a minimum in PVTEC for the GITM simulation.However, the real GNSS observations indicate that the minimum occurred earlier, at 23:02 UTC.The simulated maximum depletion was 2.6 TECU while the observed maximum (based on the difference between the 1 day offset and post-launch data) was 2.7 TECU.The depletion in the simulated quantity was apparent (>1% of maximum value) in the GITM simulations between 22:45 and 23:45 UTC.Significant differences between the real GNSS data and those offset by 1 day were observed for approximately the same time period.
In the case of satellite 29, the ground track crossing occurred at approximately 23:40 UTC.However, the minimum in PVTEC for the GITM simulation occurred earlier at 23:20 UTC.Observed values of this quantity had a minimum at 23:14 UTC.The maximum depletion based on the simulations  was 0.9 TECU, while the maximum depletion based on observations (determined as above) was 2.6 TECU.The depletion appeared in simulated data from 23:00 UTC onwards (at >1% of maximum value) and significant differences between real GNSS data and those offset by 1 day appeared at approximately this time.
Global evolution of the depletion is illustrated by plotting changes in the total numbers of exhaust molecules and electrons in Figure 9.We define −ΔN e ,  ΔCO 2 , and  ΔH 2 O as the respective differences in the number of electrons, CO 2 molecules, and H 2 O molecules due to the addition of rocket exhaust.Only electrons and molecules above 200 km are considered, as significant ionospheric depletions are limited to this region and GITM introduces unrealistic changes in concentrations near the lower boundary at 100 km (Bowden et al., 2020). ΔCO 2 , and  ΔH 2 O both decreased rapidly from their initial value after deposition by the rocket.This resulted in a maximum in ΔN e of approximately 8.2 × 10 27 at 00:05 UTC on 23 March.Subsequently, ΔN e decayed with a characteristic time of τ ≈ 2-3 hr  ( ) . This quantity can be taken to represent the recovery time of the ionosphere following a depletion.
Simulated changes in the number of exhaust molecules and electrons across different altitudes resulting from addition of rocket exhaust are shown in Figure 10.We define −λ e ,  CO 2 , and  H 2 O as the respective differences in the number of electrons, CO 2 molecules, and H 2 O molecules per unit altitude due to the addition of rocket exhaust.Both CO 2 and H 2 O concentration increases were initially peaked around 270 km altitude before falling to lower altitudes.Electron concentration decreases were initially concentrated around similar altitudes, before they diffused to higher altitudes over subsequent hours.These decreases tended to persist for longer times at higher altitudes.

Discussion and Conclusions
The observations and simulations presented in Section 4 showed that ionospheric effects of even comparatively small launch vehicles such as the Electron are detectable through GNSS observations.Both real and simulated measurements evidenced ionospheric depletions larger than the uncertainty for these measurements.These results suggest that observations from GNSS ground stations are sufficiently sensitive to detect most space launch vehicles as they pass through F-region altitudes.Numerical simulations could be used in future to provide data for a classification scheme to determine when launches occur using GNSS observations.
Our method provides better agreement with observations of the magnitude of TEC depletion in the current case than it did for the Falcon 9 launch of FORMOSAT-5 which was investigated previously (Bowden et al., 2020).This can be attributed to the shallower angle of ascent for the case presented in this paper.Consequently, the vertical component of initial plume velocity was lower in the Electron case and therefore ignoring the consequent vertical advection of CO 2 and H 2 O molecules in the simulations is more realistic.Lower altitudes corresponded to decreased thermosphere residence times for the molecules.Moreover, ionosphere production rates increase with decreasing altitude in the F-region.Together these effects result in a shorter-lived ionospheric depletion (comparing Figure 9 with Figure 10b in Bowden et al. (2020)).In future, satellite-based GNSS radio occultation may provide opportunities to study the evolution in the depletion at higher altitudes more directly.
Advection of rocket exhaust due to its initial velocity in the horizontal direction may have been important in the Electron case.This may help explain why the depletion appeared to have been underestimated by GITM for the  10.1029/2023SW003563 6 of 8 satellite 29 observations but not those for satellite 55. Figure 2 shows that the pierce point for the former satellite passed closer to the launch site.The Electron I sp value corresponded to an exhaust velocity of v e = 3,360 m.s −1 .
The launch vehicle was estimated to reach this speed approximately 297 s after launch when located at 40.88°S, 177.31°W.Prior to this time, exhaust would have had an initial velocity opposite that of the launch vehicle (in an Earth Centered Earth-fixed reference frame).
The launch of an Electron SLLV better approximates our model of initial plume expansion as a series of point releases than those of larger launch vehicles.Plume dimensions are reduced for smaller launch vehicles, with an approximate analytical treatment indicating length and maximum radius are each proportional to  √  where T is thrust (Jarvinen et al., 1966).Moreover, forces exerted by smaller launch vehicles on the background ionosphere and thermosphere are expected to affect the background state less.Resulting disturbances such as the "snow-plow effect," wherein the plume directly displaces the ionosphere, are thus minimized.
For smaller launch vehicles initial high concentrations of exhaust gasses are less likely to saturate the ionosphere, reducing electron and ion concentrations to very low levels thereby inhibiting these gasses further contribution to the depletion.Therefore, in such cases, numerical models will be less sensitive to the treatment of the early expansion of the plume.It will also limit the opportunity exhaust gasses have to diffuse to higher altitudes where they can give rise to long-lived ionospheric depletions.Figure 9 shows that time that exhaust gasses spent within the thermosphere in the simulation was short compared with that for which the depletion existed (  ΔCO 2 and  ΔH 2 O declined below 10% of peak levels 95 and 65 min after launch respectively) for the Electron launch.The exhaust gasses declined more rapidly in simulations for this case than for either Falcon 9 launch examined by Bowden et al. (2020) (see Figure 10 in the reference).
The minima in PVTEC observations of satellites 55 and 29 occurred earlier than their pierce points crossed the satellite track.Therefore, the depletion appears to have been pushed southwards toward the CHTI ground station due to advection of rocket exhaust gasses by thermospheric winds.GITM estimated that minima occurred later, suggesting the model may have underestimated the southward component of these winds.Alternatively, the depletion may have been concentrated at higher altitudes than in the simulation.Figure 10 shows significant upward diffusion of the depletion over time in the simulated results, though this cannot be directly compared with the TEC data available.Additional data from GNSS occultation measurements may help discriminate between the effects of horizontal advection and vertical diffusion, though is beyond the scope of the present study.
The regional GITM simulations in this study did not include global-scale convection, which affects neutral wind and ion drift velocities.Open boundary conditions at the upper and lower bounds for latitude and longitude were applied in these simulations, which produces unrealistic results for longer simulations.Figure 4 shows that latitudinal variation in TEC outside of the depletion decreases significantly over time.The boundary condition issue could be rectified in future by using global GITM runs with local grid refinement, a capability for investigating multi-scale phenomena described by Zhao et al. (2020).
The GITM simulation undertaken here did not capture the atmospheric wave generation which can result in traveling ionospheric disturbances (TIDs) during rocket launches.Addition of gasses to the simulation following diffusion from a point source neglected the generation of shock acoustic and gravity waves through their expansion.Nevertheless, the typical amplitudes and periods of TIDs associated with these waves are significantly smaller than the magnitude and lifetime of the depletions observed here (Afraimovich et al., 2013).Therefore, TIDs are not expected to have significantly impacted the observations detailed above.It has been shown that ionospheric depletions were observed following the launch of an Electron SLLV.Observations and GITM simulations of STEC changes due to these depletions were comparable in magnitude and duration, demonstrating the promise of general circulation models (GCMs) such as GITM for modeling these anthropogenic impacts upon the ionosphere.Simulations indicated that exhaust gasses were short-lived compared with the resulting ionospheric depletion, unlike the FORMOSAT-5 launch case previously examined by Bowden et al. (2020).Evidence was found in GNSS observations for southward advection of the ionospheric depletion, which was not accounted for in the regional GITM simulation.These findings will inform future GCM development for simulating interactions between rockets and the ionosphere.

Data Availability Statement
MAPGPS TEC and satellite line-of-sight data were obtained through the Madrigal CEDAR Database, accessible via the World Wide Web (Rideout & Coster, 2006).The version of GITM including effects of rocket exhaust which was used in this work is available through Zenodo (Bowden, 2023b).GITM input files and processed TEC data are available through Zenodo (Bowden, 2023a).This repository also includes Python scripts used in preparing the data.

Figure 1 .
Figure 1.Altitude (blue) and distance along the ground track (orange) as functions of time for the Electron rocket trajectory.
Figures 6-8 compare the GITM output with GNSS measurements taken at the CHTI ground station.In each case, GITM output is shown with and without rocket exhaust gasses while GITM simulation results are shown on the day of launch and following day.Evidence of a depletion in  STEC × sin() was found for GNSS data following the launch in each case.The depletion appears earliest for satellite 15, followed by satellite 55, and then satellite 29.

Figure 2 .
Figure 2. Pierce points for Total Electron Content measurements from the Chatham Islands Global Navigation Satellite System ground station (CHTI) between 21:40 and 24:00 UTC.Markers are plotted at 10 min intervals The estimated rocket ground track while the first and second stages were firing is indicated by the thick black line.

Figure 3 .
Figure 3. Similar to Figure 2, zoomed in around pierce point crossings of the ground track.

Figure 4 .
Figure 4. Vertical TEC (VTEC) maps from the Global Ionosphere Thermosphere Model (GITM) simulation of the Electron launch at 22:30 UTC on 22 March 2021.Red contour lines occur at intervals of 1 TECU ≡ 10 16 electrons.m−2 .Estimated ionospheric pierce points for satellites 15, 55, and 29 are overlayed.An animation of VTEC simulated using GITM is available in Movie S1 provided online.

Figure 5 .
Figure 5. Undisturbed electron density profiles for 22:40 UTC on 22 March (solid blue line) and 0:00 UTC on 23 March (dashed orange line) at the CHTI station from Global Ionosphere Thermosphere Model.

Figure 6 .
Figure6.Pseudo-VTEC measured at the CHTI ground station for Global Navigation Satellite System (GNSS) satellite 15.Simulated results from Global Ionosphere Thermosphere Model with (black line) and without (red line) the addition of rocket exhaust are shown for a 90-min period following the launch.GNSS measurements from the satellite (blue lines) and comparable measurements from the next day (green lines) are also provided.Measured value (thick line) and upper and lower bounds (thin lines) are plotted for the GNSS measurements.Estimated distance from the pierce point to the ground track is also indicated (thin orange line, right axis).

Figure 7 .
Figure 7. Similar to Figure 6 for Global Navigation Satellite System satellite 55 (black, red, and blue lines) and satellite 48 (green lines).

Figure 8 .
Figure 8. Similar to Figure 6 for Global Navigation Satellite System satellite 29.

Figure 9 .
Figure 9. Changes in the total number of electrons and exhaust molecules above 200 km altitude in the Global Ionosphere Thermosphere Model simulation due to the rocket.ΔN e (solid line),  ΔCO 2 (dashed line), and  ΔH 2 O (dash-dotted line) are shown.

Figure 10 .
Figure 10.Altitude distribution of changes in the number of (a) electrons, (b) CO 2 molecules, and (c) H 2 O molecules over time.