Tomographic Imaging of a Large Scale TID during the Halloween Storm of 2003

The most intense ionospheric storm observed in recent times occurred between 29-31 October 2003. The disturbances to the high-latitude regions set off several Large-Scale Travelling Ionospheric Disturbances (LSTIDs), wavelike perturbations in the ionospheric electron density. This paper investigates one particular Travelling Ionospheric Disturbance (TID) on 31 October 2003 using North American Global Positioning System (GPS) receiver network data and a tomographic imaging technique. The TID has an estimated period of 30 min, an estimated horizontal wavelength of 700 km and propagates South5 Westward over North America. The tomographic reconstruction of the wave is validated using a simulation of the observations and with independent observations from ionosondes and the CHAMP Planar Langmuir Probe. The results are discussed in the context of the magnetic and ionospheric conditions that may have contributed to the launch of the wave. Large-scale TIDs are challenging to study over large regions of the Earth, and the GPS network here is shown to offer a unique perspective on the spatial and temporal variation of the TID. The experimental results are backed up by simulations that show a denser network 10 of receivers, as is available in more recent years, would produce improved accuracy in the TID imaging.

and 30 October 2003 (e.g. Mannucci et al., 2005;Horvath and Lovell, 2010). The planetary K-index (Kp) peaked at 9 on 29 and 25 30 October 2003, and 8 on 31 October. Kp remained above 4 throughout 31 October, which, although still disturbed, constituted the recovery phase corresponding to the second sudden onset. The Auroral Electrojet index (AE) reached a maximum of 1827 nT at 06:31 UTC on 31 October, which is plotted in Figure 1. Change in AE is related to auroral ionospheric current activity, which has been correlated with the appearance of TIDs at mid-latitudes (Hajkowicz, 1991;Hunsucker, 1982;Hocke and Schlegel, 1996;Lewis et al., 1996). These TIDs are thought to be launched by Joule heating of the atmosphere caused by 30 increased ionospheric currents. High variability in AE occurred several times throughout 31 October, as seen in Figure 1. This variability in AE provides evidence for a potential TID generation mechanism being present. LSTIDs during the first two days of the October 2003 ionospheric storms have been studied extensively (e.g. Afraimovich et al., 2006;Ding et al., 2007;Perevalova et al., 2008;Valladares et al., 2009;Borries et al., 2009;Horvath and Lovell, 2010).
This study focuses on the less intense third day of the storms, 31 October 2003, and specifically on a high-amplitude TID 35 observed over North America in the local morning hours (16-20 UTC).
Section 2 covers the data instrumentation used for the study of the TID, and shows examples of the GNSS slant TEC (sTEC) observed. In section 3.1, observations from different instruments and techniques -GPS tomography, an ionosonde and a spaceborne Planar Langmuir Probe (PLP) are compared. To investigate the effects of using a sparse network of GPS receivers, an additional tomographic inversion using simulated data is performed in section 4. Section 5 contains a short discussion on the 40 results and generation of the TID and final conclusions.

Data and instrumentation
The primary data used in this study were sTEC measurements derived from phase delay observations by a network of groundbased dual-frequency GPS receivers. In addition to the GPS sTEC used to image the TID, independent ionosonde data and measurements from the Challenging Minisatellite Payload (CHAMP) PLP were used to confirm the presence of a TID.

GPS TEC
The GPS receiver network is shown in Figure 2 and includes 40 stations in North America (listed in Table A1) which are part of the International GNSS Service (IGS) and UNAVCO networks.
Slant TEC values were calculated using the geometry-free combination. It should be noted that MIDAS (section 2.1.1) uses time-differenced sTEC measurements, so satellite-and receiver biases which change slowly over time have no effect on the 50 accuracy of the inversion (Mitchell and Spencer, 2003).   perturbations (e.g. Wan et al., 1997;Hernández-Pajares et al., 2006;Penney and Jackson-Booth, 2015). Bolmgren et al. (2020) showed, using simulations, that MIDAS has the capacity to correctly image LSTIDs without explicitly taking this effect into account.

MIDAS
Computerised ionospheric tomography is a method that can estimate the 2D or 3D ionospheric electron density over an area 60 using integrated electron density measurements, such as TEC. In general, ionospheric tomography can be described as solving an inverse problem formulated by the relationship between the geometry, the observations and the discretised electron density distribution. For a historical review of different methods of ionospheric tomography see Bust and Mitchell (2008).
In this study, the electron density was imaged using the Multi-Instrument Data Analysis Software (MIDAS) tomography algorithm (Mitchell and Spencer, 2003). MIDAS uses differential phase observations from a network of ground-based geodetic 65 GNSS receivers and solves for an estimate of the ionospheric electron density. Empirical Orthogonal Functions (EOFs) are used as a change of basis in the height dimension; this constrains the problem by decreasing the degrees of freedom and by providing a basic structure to the variation of electron density with height. MIDAS has previously been tested as a TID imaging algorithm using a simulation approach in Bolmgren et al. (2020), which established that the algorith can successfully reproduce LSTIDs using GNSS data. In this study we will show that this is possible with real data even in relatively challenging conditions. 70

Ionosondes
The first scientific observations of TIDs were made using ionosondes (Munro, 1948). Ionosondes are ground based radio instruments that characterise the bottomside electron density of the ionosphere. Ionosondes work by generating signal pulses that sweep through a span of frequencies. The pulses reflected back to the Earth from close to the zenith are used to estimate the height distribution of the plasma frequency, which is proportional to the square root of the electron density, directly above the 75 ionosonde. The highest plasma frequency is usually found in the F2 layer, and is denoted foF2. Since electromagnetic waves with frequencies above foF2 pass through the ionosphere, ionosondes provide no information on the electron density above the height of the F2 layer (referred to as hmF2).
MIDAS EOFs, while measurements from the Dyess ionosonde are used in Section 3.2.

CHAMP Planar Langmuir Probe
The CHAMP satellite was active for ten years between 2000 and 2010, and was equipped with atmospheric and ionospheric observation instruments. CHAMP has a near circular polar orbit and had an altitude around 390 km at the time of the storm, which usually would be in the topside of the ionospheric F layer. This study makes use of electron density data from the 85 CHAMP PLP, a planar langmuir probe which was used to measure in-situ electron temperature as well as electron density in the front of the spacecraft every 15 s. Details on the CHAMP PLP can be found in McNamara et al. (2007).

Results
Sections 3.1, 3.2 and 3.3 present the results in terms of the tomographic GPS inversion, foF2 and hmF2 from the Dyess ionosonde, and CHAMP PLP in-situ electron density respectively. longitude and height respectively, and time steps of 10 minutes. Two EOFs were generated using a set of Chapman profiles (Chapman, 1931), adjusted to fit the vertical profiles observed by the Millstone Hill ionosonde.    Using consecutive tomographic images from MIDAS, the TID parameters were estimated as follows: horizontal wavelength λ h ≈ 700 km, phase velocity v ph ≈ 390 m/s, and direction of travel ≈ 195 • S-W . The period T was estimated as T = λ h /v ph ≈ 30 min. These parameters would qualify the TID as medium scale, following the definitions in Hunsucker (1982).
However, considering the high amplitude, geomagnetic conditions and equatorward direction of travel we will consider it a LSTID.

Ionosonde observations
The Dyess ionosonde is located within the area that was visibly affected by the TID in the MIDAS images. There is an indication of a periodical signature in the F2 layer critical frequency (foF2) with a 30 min period between 18:00 and 19:30 UTC, which may be related to the TID visible in the GPS data. However, the 15 min sampling makes it impossible to detect potential shorter perturbations. In Figure 6, foF2 and hmF2 from the Dyess ionosonde are plotted against the equivalent parameters calculated

CHAMP PLP observations
The CHAMP satellite had one north-to-south pass over North America between 17:00 UTC and 19:00 on 31 October 2003,

Method verification by simulation
The Dyess ionosonde and CHAMP PLP electron density both suggest the presence of a TID, but the wave-like features observed by these instruments are not clearly translated onto the same spatial and temporal coordinates in the MIDAS inversion To investigate the effect of data-coverage and geometry used for the tomographic inversion, simulated TEC from a model ionosphere was inverted with MIDAS under the same geometric conditions (satellite geometry and receiver coverage) as the original inversion. Any discrepancies between the model and simulated inversion results can be used to identify where there may be issues in the results presented in Section 3.1. A second inversion of the simulated data, using a denser, fictional network is used to identify the effect of receiver geometry.
The TID parameters estimated in section 3.1 were used together with the Hooke (1968) TID model and the International 140 Reference Ionosphere, IRI2016 (Bilitza et al., 2017), to generate a model ionosphere with TID, through which sTEC measurements were integrated (following Bolmgren et al. (2020)). A single frame of the model ionosphere is shown in Figure   8a).
The resulting inversion shows that the while the reconstruction with the regular network ( Figure 8b) is able to conserve the main morphology of the TID, it does not correctly replicate the perturbations of the wave East of 105 • W and South of 30 • N.

145
In addition, the wavefronts in Figure 8b) appear skewed when compared to the model in Figure 8a). In all panels of Figure 8, a 1 h running mean was subtracted from each voxel post-inversion to minimise the background ionosphere and to better see the TEC perturbations caused by the modelled TID.
The wave is more accurately reproduced if a denser network of GPS receivers than was available in 2003 is used. Figure 8c) shows the improved simulation result, which uses a larger number of receivers. The simulated receiver network is marked by 150 points in the same sub-figure. This inversion more accurately reproduces the perturbations in Figure 8a), including the direction of the wavefronts.

Discussion and Conclusions
In this paper, we have used GPS tomography to reconstruct the ionospheric electron density over North America for 31 October 2003, the third day of the Halloween storm of 2003, and to identify a LSTID. The presence of a large-scale TID was evidenced 155 by other instrumentation. A potential discrepancy in the TID morphology was observed between the measurements of two other instruments and the large-scale MIDAS reconstructions, in particular in that the TID was captured by the Dyess ionosonde and CHAMP PLP. However, this was identified to be the result of poor receiver coverage available for the MIDAS inversion and was studied through a computer end-to-end simulation, as discussed in Section 5. The receiver network used has an approximate receiver density of 1 per 10 deg 2 , compared to approximately 6 per 10 deg 2 for the denser synthetic network shown in Figure   160 8c).
The observed TID had an estimated phase velocity of 390 m/s, an estimated period of 30 min, horizontal wavelength of 700 km and a southwesterly direction, suggesting a source in the auroral region. The high variability in AE occurring between 11:00 UTC and 14:00 UTC (Figure 1) may indicate a possible time of launch of the observed LSTID, if it were launched by Joule heating resulting from variations in the auroral electrojets. Another possible source mechanism may have been heating 165 by auroral particle precipitation. The auroral oval was centered at latitude 63 • N at this time with the region experiencing strong energetic particle precipitation at 14:30 UTC, as estimated by OVATION (Newell et al., 2002) as shown in Figure 9. The highest levels of precipitation around the presumed launch time of the LSTID ocurred between 08:00-10:00 Magnetic Local Time (MLT), which coincides with northern North America at the presumed launch time of the LSTID (11:00-14:00 UTC) and with the increased levels of AE activity around the same time. However, further analysis of additional datasets would be needed 170 to obtain a detailed understanding of the generation mechanisms responsible for this LSTID. Since TIDs are effectively relative changes in the background electron density, the enhanced storm density likely contributed to the high perturbation amplitudes. The work discussed in this paper is built on that of Bolmgren et al. (2020), where MIDAS was demonstrated to be capable to image certain TIDs, and has shown that the tomographic algorithm is capable of imaging LSTIDs with relatively small spatial dimensions, provided that a sufficiently dense ground receiver network is available.   Supported by NERC grant number NE/P006450/1. The authors thank the UML DIDBase (http://umlcar.uml.edu/DIDBase) for providing the data from the Dyess and Millstone Hill ionosonde stations. We thank the IGS (http://www.igs.org/) and UNAVCO (https://www.unavco.org/) for providing the The GPS RINEX files, and the WDC for Geomagnetism, Kyoto (http://wdc.kugi.kyotou.ac.jp/wdc/Sec3.html) for providing the AE index data.