The Ionospheric Effects of the 2022 Hunga Tonga Volcano Eruption and the Associated Impacts on GPS Precise Point Positioning Across the Australian Region

The Hunga Tonga Volcano eruption launched a myriad of atmospheric waves that have been observed to travel around the world several times. These waves generated traveling ionospheric disturbances (TIDs) in the ionosphere, which are known to adversely impact radio applications such as Global Navigation Satellite Systems (GNSS). One such GNSS application is Precise Point Positioning (PPP), which can achieve cm‐level accuracy using a single receiver, following a typical convergence time of 30 min to 1 hr. A network of ionosondes located throughout the Australian region were used in combination with GNSS receivers to explore the impacts of the Hunga Tonga Volcano eruption on the ionosphere and what subsequent impacts they had on PPP. It is shown that PPP accuracy was not significantly impacted by the arrival of the TIDs and Spread‐F, provided that PPP convergence had already been achieved. However, when the PPP algorithm was initiated from a cold start either shortly before or after the TID arrivals, the convergence times were significantly longer. GNSS stations in northeastern Australia experienced increases in convergence time of more than 5 hr. Further analysis reveals increased convergence times to be caused by a super equatorial plasma bubble (EPB), the largest observed over Australia to date. The EPB structure was found to be ∼42 TECU deep and ∼300 km across, traveling eastwards at 30 m/s. The Hunga Tonga Volcano eruption serves as an excellent example of how ionospheric variability can impact real‐world applications and the challenges associated with modeling the ionosphere to support GNSS.

which is some 10,000 km away from Tonga (Matoza et al., 2022). Not surprisingly, the eruption caused a myriad of waves in the atmosphere and ionosphere Astafyeva et al., 2022;Ghent & Crowell, 2022;Hong et al., 2022;Themens et al., 2022;Wright et al., 2022) that were observed to encircle the Earth multiple times (Matoza et al., 2022;Pradipta et al., 2023;. Waves in the ionosphere can be remotely detected using Global Navigation Satellite System (GNSS) signals in terms of the delay that the ionospheric plasma imparts upon the signals. The phase difference that is measured is related to the total electron content (TEC) between the GNSS satellite and the receiver, with the majority of the TEC contribution coming from the ionosphere (Yizengaw et al., 2008). An expansive network of ground-based GNSS receivers therefore make it possible to geographically map ionospheric TEC around the world (Mannucci et al., 1998) and track the propagation of any ionospheric waves (e.g., Borries et al., 2009;Kotake et al., 2006;Lay et al., 2018;Otsuka et al., 2002;Pradipta et al., 2016;Tsugawa et al., 2011;H. Yang et al., 2017). To date, a range of ionospheric effects associated with the Hunga Tonga Volcano event have been published, and many of these studies have utilized the International GNSS Service network of receivers (Johnston et al., 2017). Themens et al. (2022) and S.-R. Zhang et al. (2022) reported both large-scale and medium-scale traveling ionospheric disturbances (TIDs) propagating away from the volcano location. S.-R. Zhang et al. (2022) showed evidence of these TIDs continuing to propagate around the world for at least 4 days. Harding et al. (2022) and Le et al. (2022) observed changes to the equatorial electrojet that were caused by variations in the ionospheric dynamo as a result of the eruption. Aa et al. (2022) reported a localized ionospheric plasma depletion in the vicinity of the volcano and increased equatorial plasma bubble (EPB) activity in the Asia-Oceania low-latitude region, which has been further supported by recent modeling efforts (Huba et al., 2022). Evidence of "super EPBs" has been reported spanning across Chinese (Sun et al., 2022) and Japanese/Australian (Rajesh et al., 2022) longitude sectors following the eruption. Aa et al. (2022) also reported propagating ionospheric irregularities that exhibited a phase speed that matched the prevailing Lamb mode at ∼315 m/s. GNSS Precise Point Positioning (PPP) is an advanced positioning technique that uses dual frequency observations made by a single receiver to achieve cm-level positioning accuracy Leick et al., 2015;Teunissen & Montenbruck, 2017;Zumberge et al., 1997). Over the previous few decades, the dominant method for achieving cm-level accuracy has been relative positioning, in which a nearby accurately located reference station is used to determine the precise position of a "rover" receiver (e.g., Hofmann-Wellenhof et al., 2007;Leick et al., 2015;Odijk, 2002;Teunissen & Montenbruck, 2017). Utilizing a nearby reference station makes it possible to eliminate spatially correlated GNSS observation errors, such as the tropospheric and ionospheric delays imposed on the GNSS signals. Unsurprisingly, this precise positioning capability has now found its way into many applications across several major industries, including mining, agriculture and construction (e.g., Choy et al., 2017;Pérez-Ruiz et al., 2015;Rao et al., 2022;Woodgate et al., 2017). Over recent years, PPP is fast becoming the new global standard for cm-level positioning applications due to its ability to model and account for GNSS observation errors without the need for a nearby reference station. However, the most significant drawback that is limiting the widespread uptake of PPP is the rather long convergence times, which are typically on the order of 10s of mins to hours (Bisnath & Gao, 2009;Choy et al., 2017;Van Bree et al., 2009). As a result, researchers have been investigating methods to significantly reduce PPP convergence times (e.g., Banville et al., 2014;Collins & Bisnath, 2011;Collins et al., 2012;Duong, 2020;Geng & Bock, 2013;Li et al., 2015;H. Zhang et al., 2013). Given the significant influence of the ionosphere on GNSS signals, space weather poses a potential vulnerability to the PPP technique and its anticipated widespread up-take. As such, researchers have also been investigating the impact of solar and geomagnetic activity on PPP (e.g., Luo et al., 2018Luo et al., , 2022Poniatowski & Nykiel, 2020;Z. Yang et al., 2020;Zha et al., 2021).
The Hunga Tonga Volcano eruption provides a unique opportunity to uncover new fundamental knowledge of the physics of atmosphere-ionosphere coupling. In addition, given the adverse influence of ionospheric variability on GNSS, this event can also provide insights into the impact of such ionospheric disturbances across broader society, particularly in industries that rely heavily on precise GNSS positioning. In this study, the impact of the Tonga volcano eruption on Global Positioning System (GPS) PPP across the Australian region is explored. Supporting this analysis are the data collected by ionosondes throughout the region that show both TID and Spread-F activity in the wake of the volcano eruption. The PPP accuracy throughout the day of the eruption is explored, followed by an analysis of the PPP convergence times from stations located throughout the region. Finally, ionospheric observations using GPS receivers across the region are used to investigate the physical mechanisms causing the disruptions identified in this study.

Data
In this analysis, the Australian Bureau of Meteorology Space Weather Services' ionosonde data are used. Figure 1 shows the locations of the ionosonde stations (black triangles) and Tonga volcano (red cross . Each ionosonde generates ionograms by sweeping through radio frequencies between 2 and 22 MHz, transmitting and receiving ionospheric echoes that indicate the electron density for a given virtual height determined by time-of-flight. In this analysis, the ionosonde data were used to indicate the presence of TIDs and spread-F traces. The ionosonde data complement the primary data set used in this study, namely the GPS receiver data. GPS Continuously Operating Reference Station (CORS) data from stations located across Australia, spanning into the Southeast Asian region and across the South Pacific, were used in this analysis. While previous works have employed such GPS CORS data to analyze ionospheric TEC fluctuations caused by the eruption, this study focuses on the impact of this eruption on the GPS application of PPP.
The Geoscience Australia's Ginan system was used for performing the PPP calculations (https://geoscienceaustralia.github.io/ginan/). PPP is a high-accuracy positioning method used to correct errors in GNSS positioning based on the robust modeling and estimations of systematic errors in the GNSS signals. The source code and a detailed technical description of Ginan can be found on Geoscience Australia's GitHub website (https://geoscienceaustralia.github.io/ginan/page.html?p=science.index). The specific Ginan setup used in this analysis closely follows the Ginan PPP example "Ex11", in which the PPP is performed in "static mode" using the ionosphere-free combination (https://geoscienceaustralia.github.io/ginan/codeDocs/Pea_8Configuration_8Examples.html).
The carrier-phase measurements between the GPS satellites and receivers were used to calculate the TEC along the signal path (i.e., the slant TEC, sTEC) following similar methodology to Le Huy et al. (2016) and T. Dao et al. (2020). The possible jumps in the sTEC values estimated from the carrier-phase measurements due to cycle slips were eliminated by comparing them against the sTEC estimated from the pseudo-range measurements that were smoothed by a fourth-degree polynomial approximation, as done by Le Huy et al. (2016) and T. Dao et al. (2020). A change in the carrier-phase sTEC of more than 5 TECU was taken to indicate an instrumental data jump/spike; in such instances, the change in the carrier-phase sTEC was substituted by the change in the smoothed pseudo-range sTEC. The sTEC was then compared with the Center of Orbit Determination in Europe Global model to determine the total delay of device (including biases), using elevation angles above 30° to remove multipath effects. Finally, the resulting sTEC was converted to the vertical total electron content (VTEC) observed at the pierce point of the ionosphere by using a single-layer model (Klobuchar, 1986) and an assumed altitude of 400 km. While physical VTEC is positive by definition, sometimes the bias calculations (particularly when ionospheric irregularities are present) may result in negative values. The presence of scintillation-causing small-scale ionospheric irregularities can be detected using the rate of TEC index (ROTI), which is defined as the 5-min standard deviation in the rate of change in the sTEC for each satellite-to-ground link (Pi et al., 1997).

Results
This analysis begins with an overview of the ionospheric conditions before and after the arrival of the disturbances caused by the volcano eruption using the ionosonde network in Figure 1. First, it is worth mentioning that a moderate geomagnetic storm occurred in the late hours of 14 January, with Dst reaching −91 nT and Kp reaching 6- . A useful way to analyze temporal changes in ionograms is by representing the data in a format similar to a "range-time-intensity" plot (Carter et al., 2018;Currie et al., 2021;Pradipta et al., 2015). Instead of using total power, Pradipta et al. (2015) integrated over the dBm amplitudes across all sounding frequencies, effectively creating a sum of digitized echoes. This methodology was adopted for the present study. Figure 2 shows these range-time-intensity-style plots for the ionosondes during 14-15 January 2022; the panels are ordered by the station great circle distance to Tonga, closest to farthest. The colors indicate the number of echoes received across all frequencies in each virtual height bin (10 kms). The presence of TIDs and spread-F traces in the ionograms are indicated at the bottom of each plot by the pink dots and salmon bars, respectively; these have been determined by visual inspection of the ionograms by R. Pradipta and P. Wilkinson. In Figure 2, the TIDs present as sharp descending traces and the presence of Spread F is indicated by vertically thick echoing regions. Figure 2 shows a range of ionospheric conditions across 14 and 15 January; for example, sporadic E features at virtual heights of 100 km are present for all stations at various times and F region traces that display typical altitude changes with time. TID signatures are also clear in the data on 15 January for all stations, beginning at approx. 4:30 UT at Niue (top panel) and at approx. 10 UT at Cocos Keeling Islands, with the other stations showing the TID signatures at times in between. All stations-with the exception of Darwin, which was suffering some intermittent hardware issues during this period-show the presence of spread-F traces in the hours following the TIDs, and in all cases, the spread-F traces are persistent for a number of hours. In particular, the TID activity at Norfolk Island begins shortly before 6 UT, with Spread-F present from 09:15 UT until 13:30 UT. Thus, the occurrence of spread-F traces measured by the Norfolk Island ionosonde span local times (LT) 21:15-01:30. At Townsville, the TIDs are first observed close to 7 UT (17 LT) and bring with them batches of Spread-F. The Spread-F then intensifies close to 11:24 UT (21:24 LT) and remains strong until 15 UT (1:00 LT), before finally ceasing at 17:30 UT (03:30 LT).
Next, the GPS data from receivers close to the Norfolk Island and Townsville ionosonde stations are examined as initial examples of the features and trends present throughout the GPS data. Figure 3 shows the observed vertical TEC (VTEC, upper panels) and the ROTI (lower panels) observed by the Norfolk Island (NORF, left) and Townsville (TOW2, right) GPS receivers on 15 January 2022. The VTEC data for both stations show the presence of TIDs that disrupt the diurnal pattern starting at ∼6 and 7 UT for NORF and TOW2, respectively, in good agreement with the ionosonde observations in Figure 2. In the NORF data, the TIDs are observed in the individual satellite traces as rather small-amplitude wave structures compared to the variations over the 24-hr period. Slight differences in the timings of these structures (or phase progression) for different satellite links are due to the geographical spread of the ionospheric pierce points and the motion of the TIDs over the station. In the TOW2 data, the TIDs are much clearer as strong changes in VTEC for specific satellite links at different times. The phase progression of the VTEC structures overhead are much clearer in the TOW2 data. The lower panels reveal the times in which increased ROTI values were observed. For Norfolk Island ( Figure 3c) ROTI increases shortly after the TIDs arrive and then decreases back to low levels by 9 UT. Townsville also observed increased ROTI values once the main TIDs arrived and remained high until ∼15 UT once the strong Spread-F ceases, cf. Figure 2.
Next, we illustrate how the Ginan PPP software achieves convergence, as defined here by a 3-D position error of less than 10 cm. Figure 4 shows six examples of PPP convergence on 15 January 2022 using data collected by the NORF (top row) and TOW2 (bottom row) receivers. Each panel represents a "cold start" of the PPP algorithm starting at a different time; 02:30, 04:30, and 06:30 UT, as indicated in the subfigure titles. The positioning error was calculated as the difference between the PPP estimations and the known geodetic station locations. The position errors in the X, Y, and Z directions, as well as the full 3-D position, are shown in each panel. The 10.1029/2023SW003476 5 of 19 10 cm position error threshold is indicated by the dash-dot line, and zero error is indicated by the dashed line. Also displayed in each panel is the time it took for the 3-D position error to reach below 10 cm, indicated by the vertical dotted line; that is, the convergence time.
Given the TID and subsequent Spread-F activity shown in the ionosonde data in Figure 2, one might expect that PPP errors for nearby GPS receivers would noticeably increase during these periods. However, Figure 4a shows that despite the onset of TIDs at approx. 6 UT for the NORF station, the position error remained below the 10-cm threshold. The same is true in Figure 4d for the TOW2 station, for which the onset of TIDs was approx. 7 UT. While Figure 4b shows that the NORF station position error increased following the commencement of Spread-F close to 9 UT, it remained well below 10 cm. Interestingly, despite the commencement of rather strong Spread-F at 11:24 UT at TOW2, Figure 4f shows no significant increase in the position error. This is likely the result of running the PPP algorithm in "static mode." From these results, one can conclude that the static-mode PPP algorithm was robust enough to remain at cm-level accuracy for these stations throughout the turbulent ionospheric conditions caused by the Tonga eruption, provided that convergence had already been achieved. The PPP convergence time is a complicated parameter that is dependent on the number and geometry of available satellites, and the ability of the algorithm to model and account for the signal errors including the atmospheric components caused by the ionosphere and troposphere (e.g., Choy et al., 2017;Kouba et al., 2017;Leick et al., 2015;Teunissen & Montenbruck, 2017;Zumberge et al., 1997). To further explore the possible impact of the disturbed ionosphere on the PPP convergence time, a numerical experiment was performed using the GPS CORS across the Australian region. The Ginan software was used to perform the PPP processing using data from staggered start times throughout 13-15 January 2022, in 30-min steps. In other words, the experiment simulated a series of "cold starts" of the PPP algorithm every 30-min during 13-15 January 2022. At each time and for each station, the time it took for the PPP algorithm to achieve convergence was recorded. Figure 5 shows how the convergence time for the NORF (a) and TOW2 (b) stations varied throughout 13-15 January. For 13 and 14 January, convergence times for both stations were typically on the order of 30 min to 2.5 hr, and appear to follow a similar diurnal variation for each station. On 15 January, however, the convergence times are typically 2-4.5 hr, with some times showing significant differences compared to the 13 and 14 January values; particularly close to 6 UT for NORF and between 6 and 12 UT for TOW2. For NORF, the maximum increase in convergence time on 15 January (relative to 14 January) was almost 3 hr at 6 UT. For TOW2, the maximum increase in convergence time was 3.6 hr at 10:30 UT.
In order to investigate what impact, if any, the disturbed ionosphere had on GPS PPP convergence time across the region, a reliable baseline was needed. At first glance of Figure 5, it appears that simply choosing the PPP convergence time from the day prior as the baseline is a good option. However, some GPS stations showed significant  differences between the diurnal variations in the convergence times between 13 and 14 January; not shown here. In these cases, it is possible that the differences could be explained by a difference in the handling of the tropospheric delays by the algorithm, as the geomagnetic activity level was quiet and the satellite geometry was very similar. Therefore, in order to exclude times and GPS stations' data for which the chosen baseline of 14 January was not reliable, a simple selection criterion was used. Namely, if the convergence time for a given moment in the day of 14 January was different compared to 13 January by more than 1 hr, then that time was considered as a "null" data point. Otherwise, the difference between the convergence time on 15 January and 14 January for that time of day was taken as the change in convergence time due to the disturbed ionosphere on the day of the Tonga volcano eruption, ΔT C . Figure 6 shows how the change in convergence time varied throughout 15 January for GPS stations colocated with the ionosondes in Figure 1, with two additional stations at farther distances; Makassar and Jakata in Indonesia. The size and color of the dots indicates the change in convergence time, ΔT C . Also plotted is the line of best fit that describes the propagation of the TIDs as detected by the ionosondes from Pradipta et al. (2023). In addition, the detection of Spread-F traces in nearby/co-located ionosonde data is shown by the dotted lines.
First, it is worth mentioning that prior to the arrival of the TIDs, some GPS stations in Figure 6 show some isolated increases in the convergence time on 15 January compared to 14 January. Makassar, Christmas Island, Canberra and Perth all show isolated increases in the convergence time on the order of 2 hr before any ionospheric disturbances from the eruption arrive. However, most of the stations in Figure 6 show significant and lasting convergence time increases after the TIDs arrive at their respective locations. There are the exceptions of Canberra, Exmouth, and Perth that do not observe any clear convergence time increases. Interestingly, some GPS stations show convergence time increases the moment the TIDs arrive, for example, Norfolk Island and Jakarta, whereas others observe their largest increases some hours later, for instance Darwin and Townsville. In the Townsville ionosonde data shown in Figure 2, it was noted that spread-F traces accompanied the arrival of TIDs at 7 UT (17 LT), with strong spread-F traces observed during 11:24-15:00 UT (21:15-01:00 LT). It is interesting to note that the largest ΔT C increases for the TOW2/Townsville GPS station occurred for the algorithm start time of 10:30 UT (20:30 LT), consistent with the beginning of the 3.5-hr period of strong Spread-F activity detected by the Townsville ionosonde. Finally, it is also worth noting that the magnitude of the ΔT C increases vary between  Figure 1, and two additional stations located at Makassar and Jakarta. The size of the circles also indicates the ΔT C value. For reference, the trend line representing the propagation of the ionospheric disturbances as identified in the ionosonde data in Figure 2 is shown. Due to some stations' data overlapping in the plot, Townsville, Makassar, and Christmas Island data points are shown with black outlines. The presence of Spread-F signatures in the ionograms measured by co-located/nearby ionosondes is also indicated by the horizontal dotted lines. the stations, from an increase of 2 hr observed at the Cocos Keeling Islands to an increase of 3.6 hr observed at Townsville and 3.8 hr at Jakarta.
To further explore the impact of the disturbed ionosphere on the GPS PPP convergence time across the region, Figure 7 shows ΔT C for all of the GPS stations each hour between 6 UT and 15 UT on 15 January. At 6 and 7 UT, it can be seen that ΔT C values were mostly close to 0; some stations across South Eastern Australia show some elevated values at 6 UT, but most reduce to 0 by 7 UT. At 6 UT, the Norfolk Island station-located to the southwest of Tonga approximately halfway to Australia-is already showing elevated convergence times, as also shown in Figure 6. By 8 UT, some stations on Australia's northeastern coast are showing some elevated convergence times, which further increase at 9 UT. At this time, several stations show convergence time increases of more than 5 hr. At 10 UT, the convergence time increases in the far-north Australian region begin to decline as stations further south begin to show increases that reach 4 hr for some stations. The ΔT C values are still elevated at 11 UT in the east Australian region, but some stations farther north and to the west are showing values close to 5 hr. At 12 UT, the elevated ΔT C values across Australia's north and across Southeast Asia remain at 3-4 hr as the eastern Australian stations approach 0. There is a slight increase in ΔT C across Australia's northeast once again at 13 UT to more than 3 hr, before almost all stations across the region approach ΔT C = 0 by 15 UT. An interactive map showing these data is included in Movie S1.
In an effort to diagnose the physical phenomena that may be responsible for these impacts on PPP convergence, ionospheric observations made by these GPS stations are examined next. Figure 8 is the similar to Figure 6, but the data points are colored according to the maximum ROTI value detected for each GPS station in each 30-min interval. Similar to the increased convergence times in Figure 6, the ROTI values for most stations show a marked increase following the arrival of the TIDs from the volcano. Some stations observed increased ROTI values some time after the primary TID arrivals, such as Norfolk Island, Townsville and Darwin. The Perth and Exmouth stations generally show very low ROTI values, as does the Canberra station; although at 08:30 UT, Canberra shows one elevated ROTI value. The agreement between the ROTI results in Figure 8 and the convergence time results in Figure 6 suggests a strong link between the two.
To explore the potential link between ROTI and PPP convergence time, Figure 9 is similar to Figure 7 but shows the 30-min maximum ROTI value for each GPS receiver; the full interactive map is available in Movie S2. These maps show a lot of similar trends to those in Figure 7, particularly the increased ROTI values over the northern Australian region compared to the south, and the increased values going into the Southeast Asian region. However, there is one notable difference between Figures 7 and 9; namely panel (d) that corresponds to 9 UT. While the change in convergence times were low throughout South Eastern Australia, the ROTI values in Figure 9 show that ROTI was actually quite high across this region. While the wave of increased ROTI clearly sweeps across northern Australia, the increased ROTI across southern parts of the country disappeared in place and did not make it to Western Australia.
Finally, VTEC observations made by the GPS stations are presented. Figure 10 is a series of maps of the 15-min averaged VTEC (i.e., 〈VTEC〉) for a select group of GPS stations at latitudes between 24°S and 10°S and longitudes between 128°E and 152°E (geographic). Each point represents the ionospheric pierce point (IPP) assuming an altitude of 400 km. A full interactive animation of this data sequence is included in Movie S3. Figure 10a shows the presence of a deep 〈VTEC〉 valley over eastern of Papua New Guinea at 9 UT; a dashed black line indicates the approximate location of the depletion throughout the time sequence. By 09:30 UT (Figure 10b) it appears as though the 〈VTEC〉 valley/depletion extends south to the Townsville station, and remains almost in place for the remaining times plotted. The shape of the 〈VTEC〉 depletion is quite pronounced in Figure 10e (11 UT) as a thin dark blue feature with an approximate north-south alignment. Within this depletion, values as low as 6 TECU were observed, and were as high as 48 TECU only 300 km to the west.
To track and measure the propagation of this 〈VTEC〉 depletion feature, Figure 11 shows the same data from Figure 10, but it is restricted to spanning latitudes 17°S-14°S and longitudes 140°E−155°E; that is, the blue box in Figure 10c. The depletion noted in Figure 10 is quite clear in Figure 11, along with some other 〈VTEC〉 variations during this interval. Figure 11 also includes a manually plotted trendline that highlights the propagation of the most pronounced depletion with longitude; y = 0.942x + 135.78. A noteworthy observation is that this ionospheric depletion is propagating to the east, albeit rather slowly. As the trendline indicates, the depletion is propagating eastwards with a speed of ∼0.9°/h, or equivalently ∼30 m/s (assuming 111 km/°).

Discussion
In the results above, the ionospheric variability resulting from the Hunga Tonga Volcano eruption across the Australian region was presented, followed by an investigation of the associated impact on PPP accuracy and convergence time. It was found that positioning accuracy did not appear to be adversely impacted in the wake of the eruption. Although, an experiment simulating "cold starts" to the PPP algorithm showed that convergence times were affected by the variable ionosphere in the wake of the eruption. Using the PPP convergence times from 13 to 14 January as a baseline, it was found that stations across northern Australia and Southeast Asia experienced significant convergence time increases on 15 January, with some stations experiencing increases of more than 5 hr. It was revealed that the stations experiencing the largest convergence time increases measured extended periods of enhanced ROTI values. Examination of the 15-min averaged VTEC data then revealed the presence of a significant depletion that extended from Papua New Guinea into central eastern Queensland. A close examination of this depletion revealed that it was propagating eastwards with a velocity of ∼30 m/s. PPP accuracy is at the core of PPP as a useable application. As such, previous works that have studied the impact of adverse ionospheric conditions on positioning focus on the solution accuracy, and this has typically been done using "kinematic" mode. For instance, Poniatowski and Nykiel (2020) reported the degradation of PPP accuracy across central Europe during the 2015 St. Patrick's Day storm, with root mean square errors of 0.58, 0.37, and 0.26 m in the vertical, north and east directions, respectively. Z. Yang et al. (2020) also investigated the impact of the 2015 St. Patrick's Day storm on PPP accuracy, but their analysis included stations located around the world. They found that intense auroral activity played a significant role in degrading the PPP solutions, with ∼70% of high-latitude stations suffering position errors of greater than 1 m. Importantly, the most severe degradations in position accuracy were found to coincide with intense ionospheric irregularities, as determined by the GPS ROTI parameter. Z. Yang et al. (2020) also attributed some observed position accuracy degradation in low latitudes to large-scale TIDs-∼1 TECU in amplitude-that were generated by the storm. In the present study, the PPP errors during the passage of the TIDs from the volcano eruption-and the subsequent Spread-F activity-appeared to be smaller compared to that reported by Z. Yang et al. (2020), despite the larger amplitude of the initial TIDs for this event, ∼3 TECU (S.-R. Zhang et al., 2022). A similar analysis of the 2017 September geomagnetic storms also revealed a strong relationship between enhanced ROTI and degraded PPP accuracy (Zakharenkova & Cherniak, 2021). In their analysis, it was found that the 3-D errors rose to several meters due to the presence of small-scale ionospheric irregularities. The lower errors in the present study can be understood by the fact that "static mode" was used in the positioning algorithm; that is, the range of potential receiver velocities passed to the filter via the "process noise" parameter was set to zero. Interestingly, the positioning errors in this study remained lower than 10 cm, provided that the solution had already converged. One exception is shown in Figure 5c, where the arrival of TIDs at NORF delayed the convergence by ∼2 hr. While Figure 5 only shows a few examples for two stations, their results largely reflect the results of the other stations considered in this analysis. How these results compare with various kinematic-mode PPP experiments (i.e., applying nonzero "process noise") would be an insightful investigation for future work. Given the rather minimal impact of the volcano eruption on static-mode PPP accuracy across the Australian region, the focus of this study shifted to the potential impact on the PPP convergence time, which is a key limiting factor in the widespread use of PPP (Choy et al., 2017). Here, the investigation into the PPP convergence time made use of an experiment in which "cold starts" to the positioning algorithm were performed every 30 min during 15 January 2022. Perhaps the most significant finding in this study is that the change in convergence time-that is, the difference between the 15th and 14th-reached 5 hr or higher for some stations. Interestingly, these convergence time increases were consistently observed over northern Australia, and were largely absent across central and southern Australia, cf. Figures 6 and 7.
At first glance, the ionosonde data showed several inconsistencies with the PPP convergence time results. All ionosonde stations observed clear TIDs associated with the volcano eruption, followed by some period of  Spread-F activity in the ionograms. As reported by Pradipta et al. (2023), the propagation of the disturbances in these ionosonde data agrees well with other studies that have investigated the TID propagation using GPS TEC data (e.g., Themens et al., 2022;. As observed by most ionosonde stations, the TIDs gave way to Spread-F activity, but in some cases there was a significant delay between the arrival of the TIDs and the onset of Spread-F. For example, the Townsville station TVL5F, Figure 2d, showed Spread-F activity commencing some 3 hr after the initial TIDs passed, and the Learmonth station showed Spread-F commencing more than 6 hr after the TID passage. The intensity of the Spread-F also widely varied across the stations. Stations like Canberra, Townsville and Cocos Keeling Islands observed quite strong and prolonged Spread-F, whereas one of the stations closest to the eruption, Norfolk Island, and another among the farthest away, Perth, observed relatively weak Spread-F activity. To better understand the differences in the detection of Spread-F across the Australian region, it helps to be reminded about what the presence of TID signatures and Spread-F in the ionograms indicates about the ionospheric plasma. The TID signatures highlighted in Figure 2 that are characterized by descending traces are clear signatures of large-scale TIDs, on the order of 100s of kms (e.g., Cervera & Harris, 2014;Pederick et al., 2017). While Spread-F observed at low latitudes is typically associated with EPBs generated by the Generalized Rayleigh-Taylor instability during the post-sunset to local midnight hours (Burke et al., 2004;Carter et al., 2014Carter et al., , 2020Kelley et al., 2006;Sultan, 1996, and references therein), mid-latitude Spread-F is generally considered to be due to the Perkins instability (e.g., Kelley & Fukao, 1991;Perkins, 1973) or specular reflections from medium-scale TIDs with scales on the order of 10s of kms (e.g., G. Bowman, 1981;G. G. Bowman, 1990;G. G. Bowman & Monro, 1988). Interestingly, the results in Figure 6 do not appear to show a clear and consistent relationship between the presence of large-scale TIDs or medium-scale TIDs/spread F and increased PPP convergence times.
The GPS stations used in this study are not high-rate receivers that enable a detailed analysis into the full spectrum of ionospheric waves (e.g., Carrano et al., 2012;Cervera & Thomas, 2006;van de Kamp & Cannon, 2009). However, given the apparent motion of the GPS satellites above ground-based receivers and assuming typical ionospheric wave phase speeds, the GPS ROTI parameter can provide insight into the presence of ionospheric irregularities on the order of a few kms (e.g., Ma & Maruyama, 2006;Nishioka et al., 2008;Pi et al., 1997;Zou & Wang, 2009). Generally speaking, there is quite good agreement between the impact on the convergence time and enhanced ROTI, by comparing Figures 6 and 8 and comparing Figures 7 and 9. Although, one noted difference was the presence of enhanced ROTI that propagated over southeast Australia and then disappeared. The propagation of this ROTI disturbance agrees well with the propagation of the Lamb wave across the region reported by Aa et al. (2022) (see their Figure 4). From these observations, one can conclude that the large-scale TIDs caused by the eruption had secondary small-scale irregularity generation all the way down to the scale of kms, making them detectable using the ROTI parameter. Although, an open question that arises is why did these secondary waves not continue to propagate across southern Australia? In other words, what caused the small-scale irregularities over southeast Australia at 9 UT in Figure 9d to either no longer be generated-or be more heavily dampedby 10 UT in Figure 9e, when the presence of the Lamb wave in the ROTI data was still clear over northern Australia? The answer either lies in the differences in the effectiveness of the energy cascade from large-scale to small-scale waves, or in the factors that control the damping of small-scale structures between northern and southern Australia. In either case, this is one interesting observation that requires further study and explanation.
In terms of the impact of ionospheric irregularities on the PPP convergence time, these results suggest that increased ROTI-and therefore the presence of small-scale (i.e., km-scale) ionospheric irregularities-tends to prolong PPP convergence times only in the event that the period of increased ROTI lasts for 30 min or longer. This likely explains why stations in Australia's northern region are clearly impacted compared to the stations in southern and central Australia in Figure 7. Therefore, an ongoing challenge for the GPS PPP community is to effectively mitigate the adverse impacts of extended periods of small-scale ionospheric irregularity activity. The next question is by what physical mechanism are these small-scale ionospheric irregularities being generated in order to have such a detrimental impact on GPS PPP? At first glance, the most heavily influenced region in northeastern Australia are too far south for typical EPBs to be an obvious likely candidate. At 400 km above Townsville (i.e., the IPP), the magnetic latitude is 31.5°S, and the magnetic field line from this location maps to the equator at an altitude close to 2100 km; using a combination of the International Geomagnetic Reference Field (IAGA, 2010; Maus et al., 2005) and the Altitude Adjustment Corrected Geomagnetic (AACGM) (Baker & Wing, 1989;Laundal & Richmond, 2017) models. While some observations have been reported of such EPBs in the past (Cherniak & Zakharenkova, 2016;Ma & Maruyama, 2006), disturbances this large are particularly uncommon. Further, EPBs in the Southeast Asian/Australian longitude sector are not commonly observed during the months surrounding the December solstice (e.g., Burke et al., 2004;Carter et al., 2014Carter et al., , 2020E. Dao et al., 2011;Nishioka et al., 2008). However, Aa et al. (2022) and Rajesh et al. (2022) recently reported observations of EPBs in the vicinity of Australia in the hours following the eruption. The detection of strong spread-F traces by the Townsville ionosonde coincides with LTs that are typical of postsunset EPBs; that is, 21-01 LT (see Figure 2). Further, plots of VTEC in Figure 10 in this study agree well with the observations reported by Rajesh et al. (2022) in revealing the presence of a deep depletion over northeastern Australia. Here, we measure that depletion to be 48 TECU on the ridges and 6 TECU in the valley. The propagation of this depletion was determined in this study to be eastwards (Figure 11), on the order of 30 m/s. If this TEC depletion was a signature of TIDs propagating away from the eruption, then the propagation would have been westwards. Moreover, if it were TIDs from Tonga then the propagation would have been expected to much larger than 30 m/s. Such low eastward propagation speeds are typical of the F-region dynamo in the dusk sector, within which EPBs drift following their non-linear growth to the topside F region (e.g., Chapagain et al., 2013;Kelley, 2009, and references therein). Therefore, the LT of the Spread-F observed over Townsville, the VTEC depletion depth of 42 TECU and the associated eastward propagation speed in results presented here strongly indicate that the structure responsible for hours of increased ROTI, and subsequently increased PPP convergence times, in northeastern Australia is an EPB, in agreement with Rajesh et al. (2022).
It can be seen from the full animation of Figure 11 (Movie S3) that data points associated with the depletion over northeastern Australia appeared as far south as 18°S, equivalent to 30°S magnetic latitude with an apex altitude of 1,900 km over the magnetic equator. The authors are unaware of any other previously reported EPB disturbance that has been observed this far south over the Australian continent before, although similar-sized EPBs (referred to as "super bubbles" due to their high altitude) have been reported using dense GPS stations across Japan (Ma & Maruyama, 2006). The EPBs that featured in that study would have also appeared over Australia due to magnetic conjugacy, but the relative sparsity of GPS stations across northern Australia did not allow clear EPB observations. However, the density of GPS stations across northern Australia has improved significantly during the solar cycle since Ma and Maruyama (2006)'s study. It is also worth highlighting that elements of Figures 10 and 11 indicate the presence of TEC depletions farther to the south, but the sparsity of data at these locations makes a clear separation of TID disturbances from EPB-like disturbances difficult for this event. Further, the low density of GPS stations (and therefore, IPPs) across the rest of northern Australia makes a clear determination of whether depletions/EPBs were present difficult in this analysis. However, the impact on PPP convergence times across the rest of northern Australia and southeast Asia shown in Figure 7 strongly suggests the ongoing presence of EPBs throughout the region during this event; a result in good agreement with the observations of Sun et al. (2022) and Aa et al. (2022) (in particular, the ICON plasma density depletions shown to the north of Australia in their Figure 6). Some key insights into how TIDs from the eruption caused unseasonal EPB activity in the western Pacific sector can be gained from recent work by Huba et al. (2022). In Huba et al. (2022)'s modeling analysis, waves launched by the eruption caused significant perturbations in the zonal neutral wind in the equatorial plane, which effectively modified the equatorial upward plasma drift and gave rise to a huge EPB that spanned 30° in longitude (between 140°E and 170°E). Huba et al. (2022) referred to this EPB as a "super EPB" due to its large longitudinal extent. In addition, two very-high-altitude EPBs that reached 4,000 km at ∼155°E and 180° were also generated by their simulation (altitudes well above those that Ma and Maruyama (2006) referred to as "super bubbles" in their study). While the 30°-wide EPB in Huba et al. (2022)'s simulation was not clearly observed in the present study (possibly due to its limited latitudinal extent), the observation of a longitudinally narrow, high-altitude and low-density structure over northeastern Australia is consistent with the very-high-altitude EPBs in Huba et al. (2022)'s study; noting the rather reasonable differences in observed versus modeled location. This structure over northeastern Australia thus fits the definition of a "super bubble" according to Ma and Maruyama (2006) and is in good agreement with the results of Rajesh et al. (2022). The impacts on GPS reported in the present study across the rest of northern Australia indicate that further analysis of this event farther toward the west across southern and southeastern Asia is needed.

Conclusions
The Hunga Tonga Volcano eruption is a unique and complicated event that has provided an unprecedented opportunity to study how the ionosphere couples to the lower atmosphere. In this study, the impact of the eruption-via the ionospheric disturbances that it generated-on GPS PPP was investigated. While static-mode PPP accuracy itself did not appear to be heavily affected, the time taken for convergence to be achieved was found to be significantly impacted. Across northern Australia the impact was particularly clear, with some GPS stations near Townsville reporting increases in convergence time of more than 5 hr. Long convergence times are limiting the widespread use of PPP, so the Hunga Tonga Volcano eruption presents a good opportunity to research the impacts and vulnerabilities of a variable ionosphere on PPP and to learn how to mitigate/account for them.
In this study, it was found that large-and medium-scale TIDs from the eruption were not the cause of convergence time increases, but it was the presence of small-scale ionospheric structures on the order of a few kms, as determined using the ROTI parameter. Further, it was revealed that PPP was robust enough to endure some enhanced ROTI, but not if the duration is longer than ∼30 min. This observation effectively differentiated the impact observed on PPP in northern and southern Australia; northern Australia/southeast Asia experienced extended periods of increased ROTI and subsequently increased convergence times, whereas southern Australia only experienced a short burst of increased ROTI with marginal impact on convergence time.
The results of this study indicate that the ionospheric phenomenon responsible for the presence of small-scale irregularities in southern and northern Australia was different. In southern Australia, the small-scale irregularities were the result of secondary generation from the large-and medium-scale TIDs propagating away from the eruption. The enhanced ROTI region propagated to the west in a manner consistent with the Lamb waves previously reported. These small-scale structures were rather promptly damped and did not propagate far beyond southeastern Australia. In northern Australia, the extended periods of enhanced ROTI were found to be due to the presence of at least one "super bubble" that was observed as far south as ∼30°S magnetic latitude, with an estimated apex altitude of ∼1,900 km above the magnetic equator; this is the same "super EPB" recently reported by Rajesh et al. (2022). The VTEC data revealed that the EPB was ∼42 TECU deep and ∼300 km across in longitude. Further, it was shown that the EPB traveled eastwards at ∼30 m/s, consistent with the F-region dynamo speed and direction. This super bubble is the largest/most southward-reaching EPB observed over the Australian continent; only recently made possible due to GPS station deployments in the region.
The Hunga Tonga Volcano eruption stands as an excellent example of how ionospheric variability can adversely influence satellite-based precise positioning that is increasingly heavily relied upon across many industries and sectors around the world.

Data Availability Statement
The Bureau of Meteorology Space Weather Services' World Data Centre provides ionosonde data via their website; https://www.sws.bom.gov.au/World Data Centre. Geoscience Australia provides GNSS data for all of the stations used in this analysis via their Global Navigation Satellite System Data Centre; https://gnss.ga.gov.au/. Geoscience Australia's Ginan platform is also accessible via their github repository; https://geoscienceaustralia. github.io/ginan/. The higher level analysis products, particularly the PPP convergence times that were calculated using Ginan, are available on the Zenodo data repository .