Ionospheric total electron content (TEC) data has been used to study ULF waves in the ionosphere for decades. Davies and Hartmann (1976) found small (<0.1%) TEC fluctuations during magnetically quiet days which were associated with micropulsations observed on the ground and in the magnetosphere. Skone (2009) analyzed the statistical relationship between Pc3 pulsations and GPS Vertical TEC (VTEC) variations and found that the variations of magnetic Pc3 pulsations and ionospheric VTEC variations are similar. Watson et al. (2015Watson et al. ( , 2016) ) reported TEC variations related to Pc4 and Pc5-6 ULF waves, with the Pc5-6 waves showing large peak-to-peak amplitudes of 2-7 TECU. In addition to VTEC fluctuations, the ionospheric scintillations are also found to be related to Pc1 and Pc5 pulsations (Francia et al., 2020;Yizengaw et al., 2018). Previous studies have shown that the TEC technique is sensitive enough to detect ionospheric response to ULF waves.

Due to the ionospheric screening effects (Hughes & Southwood, 1976) and radar sampling biases (Shi, Ruohoniemi, et al., 2018), high-m ULF waves are difficult to detect on the ground. In-situ space-based measurements are sparse and often inadequate for obtaining wave spatial distributions. Taking advantage of widely distributed GPS receivers, TEC observations can provide a great opportunity to investigate the spatial distribution, propagation, and time evolution of high-m ULF waves. Coordinated geophysical measurements from GOES, SuperDARN, GPS and ground magnetometers are used in this study to examine high-m ULF wave properties. Using VTEC measurements from 10 GPS receivers, we analyze the temporal evolution and 2D spatial structure of ULF waves in the ionosphere.

High-m ULF waves were observed on January 24-26, 2016 during the recovery phase of a moderate geomagnetic storm (minimum Dst = -95 nT, Figure 1a). An overview of the event and the instrument locations is presented in Figure 1. A substorm indicated by the AE index enhancement occurred on January 24, 2016 from 18 to 20 UT (Figure 1b). The substorm onset was associated with a southward excursion of the IMF Bz component (Figure 1c) at ∼18 UT. The AE index peaked at a maximum value of ∼1,000 nT at ∼19:00 UT followed by a solar wind dynamic pressure enhancement that peaked at ∼20:00 UT (Figure 1d). Figure 1e shows the distribution of multi-instruments in the altitude-adjusted corrected geomagnetic coordinates (Shepherd, 2014) at 00:00 UT on January 25, 2016. Note that the GPS receiver FSIC, the ground magnetometer FSIM, and the PGR radar are close to the footprint of GOES-15.

TEC data used in this study are derived from 1 Hz GPS carrier phase observations. Slant TEC was converted to vertical TEC based on the zenith angle of GPS signals at their pierce points. The cut off angle is 25° and the altitude of ionospheric pierce points (IPP) is 450 km. GPS satellites are identified by their pseudo random noise (PRN) number. The magnetic field data from GOES-13 and GOES-15 are sampled at 0.512 s and are expressed in local mean-field-aligned (MFA) coordinates. The mean magnetic field data are obtained by a 30-minute running average. The three magnetic components in MFA coordinates are B r (outward, perpendicular to the mean magnetic field), B Φ (eastward, perpendicular to the mean magnetic field), and B ∕∕ (parallel to the mean magnetic field). Magnetic perturbations in the B ∕∕ direction (∆B ∕∕ ) are derived by subtracting the 30-minute averaged mean magnetic field. Thus, the signal components below 0.55 mHz are filtered out. Line-of-sight (LOS) plasma velocity observations from the SuperDARN Prince George (PGR) radar are used to detect the ionospheric response to the ULF waves. Ground magnetic field data with 2 Hz sampling rate are also detrended by subtracting a 30-minute running average. A continuous wavelet transform (CWT) (Foufoula-Georgiou and Kumar, 2014) is used to obtain the power spectral density (PSD) of the various data sets. wavelet coherence (WTC) and cross wavelet transform (XWT) (Grinsted et al., 2004) are used to examine the correlation between the ULF signals in the GOES and GPS VTEC measurements.

As shown in Figure 1e, the FSIC GPS receiver, SuperDARN PGR radar camping beam, and FSIM ground magnetometer are all located close to the GOES-15 footprint. We take advantage of this to validate the ULF wave signatures in GPS VTEC and to investigate the different responses of the magnetosphere, ionosphere and geomagnetic field to high-m ULF waves. Figure 2 shows the time series and PSD from various space-and ground-based instruments. As seen from Figure 2a, sinusoidal waveforms appeared in B Φ and B r (larger amplitude in the mode) during the period 22:15-24:00 UT. Figure 2b shows the dominant frequency of the monochromatic signal in B r is ∼10 mHz. The time series and PSD of SuperDARN PGR radar observations also showed similar wave signatures at the same frequency (Figures 2c and 2d). order Butterworth bandpass filter (5-20 mHz) and shown in Figure 2f. VTEC disturbances with 0.1 TECU peak-to-peak amplitudes were registered in both PRN 03 and PRN 23. Figures 2g and 2h display the PSDs of PRN 03 and PRN 23 detrended VTEC. Significant narrowband power around 10 mHz can be seen during 21:50-22:40 UT in the PRN 03 data and during 21:40-23:00 UT in the PRN 23 data. High-m waves are usually localized in L-shell. Depending on the orbit of GOES-15 and GPS satellites, the ULF waves observed by GOES-15 and GPS receivers were sporadic. The time delay in the appearance of the narrowband waves in FSIC VTEC (Figures 2g and 2h) and those in GOES-15 observations (Figures 2a and 2b) is attributed to waves observed at different regions rather than the same wave packet propagated from one location to another. Figures 2i and 2j give the WTC and XWT results of GOES-15 B r and PRN 23 detrended TEC. The 5% significance level against the red noise is shown as thick contours in Figure 2i. High coherence and significant common power during the time period of 22:20-23:00 UT suggest that FSIC PRN 23 observed the same ULF waves as GOES-15.

Figure 2k shows perturbations in the geographic downward (Z), eastward (E), and northward (N) components of the magnetic field observed at the FSIM station. No sinusoidal signatures appeared in the three FSIM magnetic perturbations and the PSD of the FSIM eastward (poloidal component) did not show any of the narrowband power around 10 mHz seen in the GOES B r (Figure 2b) and VTEC data (Figures 2g and 2h). This indicates that the high-m poloidal wave signals observed by the GOES satellite, SuperDARN radar and FSIC receiver were high-m mode and thus not observed by the FSIM ground magnetometer because they were screened by the ionosphere.

Figures 2i and 2j has shown that the detrended VTEC data has high coherence and significant common power with the high-m ULF wave signatures seen in the GOES B r data. We now further investigate the magnetic latitude (MLAT) and universal time (UT) distribution of these ULF waves by examining the WTC and XWT results of GOES-15 B r and VTEC data at FSIC using 32 separate GPS satellites. The peak power of XWT results below 20 mHz and corresponding WTC results are filtered by WTC > 0.7 and XWT > 15 (see Text S1 and Figure S1 in Supporting Information for details). The results are provided in Figure 3 which shows the high-m ULF wave distribution in GOES-15 B r and GPS TEC from January 24 to January 26 in 2016 and their relationship with ionospheric scintillation. Figure 3a gives the PSD below 20 mHz from the GOES-15 B r data. The distributions of the filtered wave signatures according to the stated criteria are shown in Figures 3b-3d. In Figures 3b-3e, the red (black) vertical lines indicate local noon (midnight) time, the green (blue) vertical lines indicate local dawn (dusk) time.

Panel 3a shows ∼10 mHz ULF waves were observed from local noon to dusk on January 24 and monochromatic ULF waves were observed across the dayside on January 25 and 26. The wave frequency decreased from around 10 mHz for the first time GOES-15 passed through the wave active region to around 6 mHz during the third pass. The WTC (Figure 3b) and XWT (Figure 3c) analyses of the FSIC TEC data and GOES-15 B r data show that the ULF wave signatures in TEC data have high coherence and significant common power with those observed by GOES-15. The ULF wave signatures are primarily distributed between ∼62° and ∼68° MLAT on the dayside. Figure 3d shows the frequency distribution color-coded as a function of MLAT and UT. Similar frequency-time evolution of the waves can be seen in the GOES-15 B r and VTEC data, that is, both have a general decreasing trend with time. Similar WTC and XWT analyses applied to the TEC data from the SANC GPS receiver and GOES-13 B r data (see Figure 1e for locations) produced similar results (not shown).

Besides analyzing the MLAT and UT time distribution of high-m ULF waves in GPS VTEC, we also checked the correlation between the waves and ionospheric scintillation using the phase sigma (the standard deviation of the detrended carrier phase) and S4 (standard deviation of the received signal power normalized to average signal power) indices. Figure 3e shows the phase sigma index MLAT versus UT distribution while Figure 3f shows the phase sigma value versus the elevation angle distribution. The mean values of selected phase sigma and all phase sigma are 0.0165 and 0.0182 rad, respectively, and median values of the two data sets are 0.170 and 0.180 rad, respectively. This suggests the high-m ULF waves during this particular event had little contribution to ionospheric phase scintillation. We also checked the S4 index (not shown), and not surprisingly, we found no clear correlation between the ULF wave occurrence and ionospheric amplitude scintillation.

To investigate the temporal evolution and 2D spatial structures of the high-m ULF waves in the ionosphere, VTEC measurements from all 10 GPS receivers (red asterisks) shown in Figure 1e are processed. ULF wave signatures are automatically identified using full width at half maximum (Takahashi & Ukhorskiy, 2007), continuity and standard deviation filters (see Text S2 and Figures S2-S8 in Supporting Information for details). Figure 4 shows the MLAT and MLT distributions of the integrated high-m ULF wave PSD in the VTEC and GOES B r component on January 25, 2016. Figures 4a-4d show time evolution of ULF wave signatures in GPS VTEC data over 4 successive 6-hour time intervals. The wave signatures appeared near dusk with relatively stronger power but as the GPS receivers rotate with Earth into the nightside, the wave signatures tended to gradually disappear. When the GPS receivers moved into the dayside, the wave signatures were observed again in VTEC observations and they were mainly constrained to local noon. Note that in Figure 4b, ULF wave signatures observed from 06 to 12 UT were significantly reduced compared with the other UT intervals, even with GPS satellite paths covering the morning sector. The IMF variations shown in Figure 1c during this time interval made it difficult to distinguish the narrowband wave signatures from broadband waves and other ionospheric disturbances in GPS VTEC (one example is shown in Figure S5 in Supporting Information).

Figures 4e and 4f show the high-m ULF wave signatures in VTEC as well as GOES-13 and GOES-15 B r components on January 25, 2016. For visualization purposes, the magnetic latitudes of the GOES-15 footprints were moved 10° equatorward. The blue and red numbers indicate the UTs of the GOES-13 and GOES-15 observations, respectively. Figure 4e shows the ULF waves were visible in the TEC data on the dayside and in the post-dusk sector. The power in the afternoon sector was relatively larger than at other MLTs. Note that there are wave signatures identified around 80° MLAT. These are probably outliers associated with ionospheric disturbances rather than ULF waves driven by drift-bounce resonance (Watson, Jayachandran, & MacDougall, 2016). In Figure 4f, ULF wave signatures from GOES satellites observations occurred mainly on the dayside. Due to the limitations in spatial coverage, GOES-13 measurements started at 00:00 UT of January 25, 2016 from the post dusk sector and did not show the wave signatures around 18:00 MLT. Based on the widely distributed GPS receivers, the VTEC measurements give a more complete 2D spatial distribution as well as the time evolution of the high-m ULF waves than the GOES satellites measurements.

The MLAT-MLT distribution of ULF waves and its temporal evolution are critical constraints needed for understanding the role of wave-particle interactions in ring current and radiation belt dynamics (Oimatsu et al., 2018;Zong et al., 2009). However, because of the limited high time resolution measurements from coherent and incoherent scatter radars as well as sparse satellite in-situ observations, it is difficult to determine the spatial and temporal distribution of ULF waves in a single event. In this study, by taking advantage of the widely distributed GPS VTEC observations, which cover from ∼50° MLAT to near the magnetic pole, we obtained the global high-m ULF wave spatial distribution (Figure 4e) during a single event. In addition, VTEC observations which cover more than 200° in geomagnetic longitude also provide constraints of the wave distribution in MLT. Using data from 10 GPS receivers we also examined the temporal evolution of the 2D spatial structure of the ULF wave PSD (Figures 4a-4d). For future work, the onset time of this kind of long-lasting ULF wave observed during the recovery phase of geomagnetic storms (Table 1 in Shi, Baker, et al., 2018) can be identified and the 2D spatial distribution of ULF waves during the wave onset can also be obtained using multi-point GPS TEC data. This information can be used to further investigate the driver of ULF waves, which is difficult to obtain using satellite observations alone (Archer et al., 2018). The altitude of the IPP is assumed to be 450 km. It is still unknown at what altitude range the ULF modulation of TEC occurs. The distribution range will expand (decrease) with the increase (decrease) of the assumed IPP altitude. Shi, Baker, et al. (2018) estimated the m value (-258, westward propagating) of this ULF event using the drift-bounce resonance theory. Watson, Jayachandran, Singer, et al. (2016) also observed high-m mode Pc4 ULF waves in TEC data. By applying a multi-satellite triangulation technique, the m value was estimated to be -240 to -310 and -20 to -40 in the former and latter periods of a 16-minute time interval, respectively. However, these waves were detected by ground magnetometers and GOES satellites with an estimated m value of -35 to -60. This study presents the first GPS TEC observations of high-m ULF waves that were screened by the ionosphere and not detected by ground magnetometers. Note that Pc5 waves were present in GPS TEC (Figures 2g and 2h), ground magnetometer (Figures 2g-2i), and GOES observations (Figure 3a). These are low-m toroidal waves which have been investigated in Shi et al. (2020) and are beyond the scope of this study.

When very high-frequency radio signals pass through plasma irregularities in the ionosphere, random fluctuations will occur in their parameters such as phase, amplitude, and propagating direction. This effect is referred to as ionospheric scintillation (Jiao et al., 2013). In addition to TEC disturbances, ULF waves have also been found to contribute to ionospheric scintillations (Francia et al., 2020;Yizengaw et al., 2018). However, as shown in Figures 3e and 3f, no significant variation in phase sigma index and S4 index (not shown) were observed during the wave activity that occurred during this event, which suggests high-m ULF waves made little contribution to ionospheric scintillation. Pilipenko et al. (2014) proposed several possible mechanisms for how ULF waves might produce TEC modulation, including periodic particle precipitation, plasma compression by reflected fast mode waves, ion heating, field-aligned plasma transport, etc. The VTEC fluctuations related to high-m ULF waves in this study may be caused by plasma transport in field-aligned current due to Alfvén waves (Pilipenko et al., 2014). The modification of the recombination coefficient induced by ion heating may be also responsible for the VTEC modulations (Baddeley et al., 2017;Kozyreva et al., 2020). Consideration of physical mechanisms for generating ULF wave signatures in TEC data is left to future study.

Multi-instrument observations from space and the ground have been used to investigate high-m ULF wave signatures during the recovery phase of the geomagnetic storm that occurred from January 24 to 26, 2016. GPS VTEC data captured ULF wave signatures similar to those seen in GOES B r data and SuperDARN LOS velocity observations. The high-m poloidal wave perturbations were screened by the ionosphere and not detected by ground magnetometers. WTC and XTW results showed the detrended GPS VTEC data had high coherence and significant common power with the GOES-15 B r data. The ULF wave signatures in VTEC data showed similar temporal distribution and frequency time evolution to GOES-15 B r data. By comparing the MLAT and UT distribution of the phase sigma index of FSIC with the ULF wave occurrence, we found the high-m ULF waves during this event made little contribution to ionospheric scintillation. An automatic identification procedure is developed to detect ULF signatures in GPS VTEC data. Based on measurements from 10 GPS receivers on January 25, 2016, the time evolution and 2D spatial structures of high-m ULF waves in the ionosphere were revealed for the first time. The high-m ULF wave signatures in the GPS VTEC data were mainly observed on the dayside and continue into the post dusk sector over MLATS from ∼64° to ∼71°. The abundance of GPS VTEC measurements is an excellent resource that can be further exploited to provide new insights into the ionospheric response to ULF waves including their temporal and spatial characteristics.