We have investigated the propagation of large-scale traveling ionospheric disturbances (LSTIDs) during the super magnetic storm of 29–30 October 2003. Two-dimensional total electron content (TEC) perturbation maps over North America were built using TEC data provided by the American GPS network and the International GNSS Service. Three LSTID events were observed in the range of 30°N–50°N, 60°W–110°W during this period. The first two LSTIDs occurred consecutively during 0620–0800 UT on 29 October at the local time of midnight, right after the onset of the big substorm; the third one was found at noon during the expansion phase of another substorm on 30 October. The phase fronts of these LSTIDs passed over the United States and traveled southwestward to the distance of ∼2000 km with the maximum front width of ∼4000 km and the duration of less than 2 hours. The maximum amplitude of TEC perturbations attained 3 total electron content units (TECUs). The results differ from the former observation of Afraimovich and Voeykov (2004) and Afraimovich et al. (2006), who reported a solitary LSTID propagating southwestward over the United States with the amplitudes of up to 14 TECU on 30 October 2003. We have checked the magnetic H component observed at the geomagnetic observatories in North America and found it is most likely that the auroral westward electrojet was the cause of the LSTIDs on 29 October. The source region for these TIDs was likely to be located several hundred kilometers north of 50°N. Cross-spectral analysis was conducted to obtain the global propagation characteristics of LSTIDs during this superstorm. Equatorward LSTIDs were found in all the three sectors of North America, Europe, and Asia, showing high correlation with the occurrence of auroral substorms.
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 The excitation and propagation of large-scale traveling ionospheric disturbances (LSTIDs) has been widely studied over decades. LSTIDs, with horizontal velocities between 400 and 1000 m/s and periods in the range of 30 min to 3 hours, are most likely to be ionospheric manifestations of atmospheric gravity waves (AGWs) launched by high-latitude sources such as Joule heating, Lorentz forces, or intense particle precipitations [Hunsucker, 1982]. These LSTIDs are frequently detected at middle and high latitudes during the period of auroral substorms.
 Ground-based GPS network provides a powerful tool to monitor large-scale traveling ionospheric disturbances continuously in a wide range. In order to get propagation characteristics of LSTIDs from the observation of network GPS total electron content (TEC), scientists used the two-dimensional TEC mapping method and the method of cross-spectral analysis. Ho et al.  originally collected TEC data observed by more than 60 worldwide GPS stations to generate global ionospheric disturbance maps and discovered an equatorward propagating LSTID during a magnetic storm. Afraimovich et al. [1998, 2002] developed a method for determining the large-scale TIDs' parameters based on calculations of spatial and temporal gradients of TEC measured at three spaced GPS receivers. He found LSTIDs excited in the auroral region traveled equatorward to the distance of more than 2000 km with the velocity of ∼300 m/s and the front width of 3700 km. Wan et al. [1997, 1998a, 1998b] demonstrated that when estimating the velocities and periods of TIDs from GPS TEC, they could remove the errors caused by the movement of GPS satellites by Galileo transformation. Using TEC data from more than 1000 GPS receivers in Japan, Saito and Fukao  derived high-resolution two-dimensional maps of TEC perturbations, which clearly showed the temporal resolution and spatial structure of the medium-scale TIDs. Tsugawa et al. [2003, 2004] used GPS network data of Japan to statistically study the large-scale TID propagation characteristics. They found clear correlation of LSTID occurrence rate with Kp index.
 Recently, there were a few studies focusing on two-dimensional structures of LSTIDs over North America sector. In North America, the International GNSS Service (IGS) and the American GPS network provide TEC data from about 500 GPS receivers, which cover the wide area with geographic latitude in the range of 25°N–55°N and longitude of 60°W–130°W. Using these data, Afraimovich et al. [2000a] studied the propagation of LSTIDs and noticed a southwestward LSTID in the range of geographic latitudes 50°N–60°N with the front width of no less than 7500 km. Nicolls et al.  used similar TEC data set to map the structures of TEC perturbations over North America during the geomagnetic storm of 1–2 October 2002. He found an equatorward TID propagating at the phase velocity of 600 m/s with the maximum amplitude of 2 TECU (total electron content units). Afraimovich and Voeykov  and Afraimovich et al.  studied the LSTID over North America occurring during the super geomagnetic storm on 30 October 2003. They found a solitary LSTID propagated southwestward with the amplitude of up to 40%. The location of its source was between 50°N and 60°N in the northeast region of the United States.
 In this paper, we present our studies on the two dimensional structures of LSTIDs occurring over North America during the super geomagnetic storm on 29–30 October 2003. We have developed a method of obtaining two-dimensional TEC perturbation maps and calculated the propagation parameters of LSTIDs. We also discussed the possible source region of these LSTIDs.
2. Data and Method
 IGS and the American GPS network provide GPS TEC data from more than 900 dual-frequency GPS receivers (in year 2003) all around the world [Beutler et al., 1999]. The data are available on the Web site of ftp://garner.ucsd.edu. Figure 1 shows the geographic locations of GPS receivers in North American sector in the range of 25°N–55°N and 60°W–130°W, corresponding to the geomagnetic latitudes of about 35°N–65°N. There are about 500 GPS receivers in this area. Each GPS receiver generates RINEX files recording carrier phase delays and group delays. We converted the RINEX files into TEC files in the form of slant TEC time series with 30-s resolution.
2.2. Filtering Method and Generation of Two-Dimensional TEC Perturbation Maps
 The relation between the original observed slant TEC and the vertical TEC is
where STEC refers to the slant TEC time series observed by any GPS receiver-satellite pair. VTEC is the corresponding vertical TEC time series. Here, ele is the elevation angle for the line of sight path from a GPS receiver to the ionospheric pierce point. Brs is the instrumental biases.
 Assume that the vertical TEC series (VTEC) observed by any GPS receiver-satellite pair consist of two parts: VTEC0 which represents the background trends of vertical TEC, and VTECw which reflects the TEC perturbations caused by TIDs. We have
The background trend VTEC0 can be expressed as
where lat and LT are the geographical latitude and local time, respectively. C0, C1, and C2 are the fitting coefficients. LT0 is the local time when the maximum of elevation angle ele for the TEC series of a satellite-receiver pair reaches and lat0 is the latitude of the ionospheric pierce point at time LT0.
 As the ionospheric pierce point moves from time to time, background trends VTEC0 are mainly characterized by diurnal, latitudinal, and longitudinal variations. We ignore the longitudinal effects on TEC series. The TEC series observed by any receiver-satellite pair have a typical longitudinal range of less than 10°. Compared to temporal and latitudinal effects, the longitudinal variations of TEC within this range are much weaker, except for the TEC variations during the time of sunset or sunrise [Foster and Rideout, 2005]. Our later results will show the TIDs are observed at midnight or at noon.
 Storm-time TEC is influenced by the poleward expansion of the equatorial ionization anomaly, the TEC enhancement at mid and low latitudes and the ionization depletion in midlatitude trough region. On the basis of TEC observed by CHAMP satellite, Mannucci et al.  reported that during the storm of 30 October 2003, the equatorial ionization anomaly crest over North America appeared at the geomagnetic latitude of 17°, i.e., the geographical latitude of 28°. Foster and Rideout  found that TEC gradients over the central US exceeded 60 TECU per degree latitude during the same storm. Through the observation of scintillation from geostationary satellites, Basu et al.  found nearly simultaneous formation of ionospheric plasma density structures at middle and equatorial latitudes during the period of this storm. Through the observation of the Millstone Hill radar, Foster and Vo  noticed remarkable electronic density trough formed at the geomagnetic latitude of 52° during the storm of 12 April 2001.
 Despite the effects on the background TEC mentioned above, we express the temporal and latitudinal variation of the vertical TEC as one order function of local time and latitude. The TEC time series observed by any GPS receiver-satellite pair have the typical time duration of 3–5 hours and latitudinal range of less than 8°. Because the time duration is relatively short and latitudinal range is limited, we choose one order fitting method, as it is sufficient to remove background trends in these short time series without introducing artificial perturbations as higher-order polynomials could do. Generally, complex designation of filtering method may lead to the missing of TIDs' information that is contained in original slant TEC series. Similar methods of excluding the linear trends of background TEC were conducted by many authors [Afraimovich et al., 2002; Nicolls et al., 2004; Tsugawa et al., 2004]. These authors detrended the vertical TEC by subtracting a running average of the TEC series with a time window. Wan et al. [1997, 1998a] and Afraimovich et al. [1998, 2000a] alternatively removed the background trend with polynomial fits. We have tried these methods and found our method yields relatively clear TEC perturbation structures in our case.
For the given time series of STEC, we calculate the fitting coefficients C0, C1, C2 and Brs by least square method. Then we get the temporal variation of VTECw through equation (4). An example of the filtered TEC time series is given in Figure 2a. We have calculated the VTECw series observed by all of the satellite-receiver pairs during 29–31 October 2003.
 We include in our study the slant TEC data with the elevation higher than 30°. TEC series with elevation lower than 30° is disregarded to avoid the errors when we convert slant TEC to vertical TEC. The lower elevation limit of 30° was also chosen by Afraimovich et al. [2000a], who suggested that most reliable TID structures and dynamics correspond to high values of the elevation angle. Saito and Fukao  and Tsugawa et al.  alternatively used slant TEC with the elevation angle greater than 60° in their study of TIDs over Japan. The adoption of higher elevation results in more precise TID local structures in TEC maps, while it narrows the horizontal observation range of GPS receivers. This is not a problem in the study of LSTIDs over Japan, as there is a dense distribution of GPS receivers in Japanese GPS network (GEONET). However, it is necessary for us to set lower elevation limit and improve the TEC filtering method, since we only have the data from about 500 GPS receivers in North America.
 The method of creating two-dimensional TEC perturbation maps is similar to that of Tsugawa et al.  and Nicolls et al. . We divide the area in the range of 25°N–55°N and 60°W–130°W into small pixels with the size of 0.5° latitude × 0.5° longitude. The TEC perturbation value at each pixel at the local time of LT is an average of VTECw for all the GPS satellite-receiver paths whose ionospheric pierce points cross this pixel during the time LT − 60 to LT + 60 s at the height of 350 km. The height of 350 km is an average of F-layer peak height predicted by IRI model. An example of the TEC perturbation map is presented in Figure 2b. Figure 2b shows clear structures of TEC perturbations during the passage of TIDs. We obtained the sequence of two-dimensional TEC perturbation maps every 150 s.
 We then apply the two-dimensional nonuniform polyfits to obtain the value of TEC perturbations for those pixels over which there is no ionospheric pierce points crossing at the time. It is seen from Figure 2b that there are a lot of pixels that contain no TEC perturbation value. We choose the data in the region of 30°N–50°N and 70°W–110°W to apply nonuniform polyfits, for the ionospheric pierce points in this range are relatively well distributed compared to those in other regions. An example of the TEC perturbation map processed through nonuniform polyfits is shown in Figure 2c. On the basis of the sequence of two-dimensional TEC perturbation maps such as Figure 2c, we obtain the temporal variation of TEC perturbation amplitudes at some certain pixels in the region of 30°N–50°N and 70°W–110°W, which will be shown later.
 If there were TIDs passing by, the TEC maps such as Figure 2b would show perturbation structures. At the same time, the time series of TEC perturbations at different pixels would show obvious phase differences. This indicates the movement of the perturbation structures. We then measure the phase differences by calculating the time delay among the peaks of the amplitude time series.
2.3. Determination of Propagation Parameters of TIDs
 Our next step is to determine the propagation parameters of TIDs, following the visual examination of TEC perturbation maps and the measurement of time delay for the peaks amplitude among the perturbation series at different pixels. The geometry of calculating TIDs' propagation parameters is plotted in Figure 2d. Considering three observation points A, B, and C, we have got the time delay for the TID's peak amplitude to move from point A to point B and C. The observation points hereafter refer to the points at the center of the corresponding fixed pixels. Assume that the TIDs' front moves along the spherical surface of the Earth and crosses point A, B, and C with the speed of v and the propagation azimuth of α. The azimuth hereafter is measured from north toward the east along the horizon. The propagation velocity of the phase front satisfies
where δt1 and δt2 are the time intervals it takes for the phase front to move from point A to point B and C, respectively, along the spherical surface of the Earth. Here δl1 is the spherical distance between A and B, δl2 is the spherical distance between A and C, and β1 and β2 are the azimuth of spherical paths AB and AC.
 The propagation azimuth of LSTIDs can be deduced from equation (5) as follows:
We choose different observation points of A, B, and C to calculate v and a. Then we take the average value of v and a as the propagation velocity and azimuth for the observed LSTIDs.
3. Observation of LSTIDs During 29–30 October 2003
3.1. Geomagnetic Activity
 The super geomagnetic storm during 29–30 October 2003 was originally caused by two consecutive, extremely huge Sun flare events [Skoug et al., 2004; Zhao et al., 2005]. The flare events drove coronal mass ejections (CMEs), which arrived at the Earth and caused the geomagnetic storms. Figure 3 shows the time dependence of the Kp index, the Dst index, the GSE z component of the magnetic field of interplanetary magnetic field (IMF), and the AE index during this period. Bz of IMF was measured from the ACE satellite. The magnetic field B of the IMF increased rapidly at two shocks on 29 October and 30 October. The direction of Bz component turned to south at the two shocks. It was moderately southward or northward during the two shocks. Major geomagnetic storms occurred, as indicated by Dst variations, with two sudden commencements at 0612 UT on 29 October and 1627 UT on 30 October. The AE variations show intense substorm activities on 29 and 30 October, with the peak value of AE values exceeding 4500 nT.
3.2. Events of 29 October TID
 We observed three TID events over North America during the period of 29–30 October. The first two LSTIDs occurred consecutively between 0620 and 0800 UT on 29 October during the local time of midnight, shortly after the onset of the big substorm. The third one started at 1850 UT at noon on 30 October and lasted for about 1 hour. The occurring time for the TIDs is basically concurrent with the time when the two shocks arrived at the Earth.
Figure 4 presents the sequence of two-dimensional maps of TEC perturbations during the period of 0620–0800 UT on 29 October. Clear band-like structures are seen. A negative TEC perturbation band appeared at 0620 UT in the northeast area of the United States, and a positive band appeared at the same time to the south of the negative region. A phase front can be clearly seen, which was the border between the negative region and the positive region. Twenty minutes later, another phase front formed, which was characterized by the north border of the negative band in the northeast area of the United States at 0640 UT. The phase fronts passed over the United States and traveled southwestward to the distance of ∼2000 km, with the duration of 1 hour and 40 min and the front width of ∼4000 km. The perturbation structures gradually disappeared in the maps after 0800 UT. We plot the change of phase fronts in Figure 5. It can be seen from Figure 5 that the two phase fronts traveled to different orientations, denoting the change of propagating direction for these TID structures.
 The amplitudes of TEC perturbations have a maximum of 2 TECU (1 TECU = 1016 eletrons/m2). Nicolls et al.  applied mapping technique to the same data set to study TEC perturbations over US during the geomagnetic storm of 1–2 October 2002 and found a TID propagating at 600 m/s with the maximum amplitude of 2 TECU. The amplitude of the TID reported by Nicolls et al.  is similar to ours. Tsugawa et al.  statistically analyzed the TEC perturbations caused by LSTIDs over Japan and found that the amplitudes were in the range of 1.3 ± 0.7 TECU, which is in agreement with our results.
Figure 6 shows the temporal dependence of TEC perturbations at certain fixed observation points. We set the observation points along the latitude of 40°N and along the meridian of 90°W, respectively. It shows the TEC perturbation series at different observation points are similar in shape and shifted with time. On the basis of these perturbation series, we plotted in Figure 7 the time at which the maxima and minima of the amplitudes appeared. It can be seen that the time delays between the amplitude minimum and the second amplitude maximum nearly remain constant, while the time delays between the first amplitude maximum and the amplitude minimum change obviously. Thus the two kinds of fronts in Figure 5 differ not only in moving direction but also in moving velocity. This indicates that there are two consecutive LSTID events rather than one LSTID event.
 The calculations based on equation (6) and (7) reveal that the first TID propagated with the azimuth of 217° and the horizontal phase velocity of 270 m/s, and the second TID propagated with the azimuth of 191° at 500 m/s. The period of the two consecutive TIDs, though it cannot be precisely determined, is close to 1.2 hour, as calculated by doubling the peak-to-trough time intervals shown in Figure 7. As shown in Figure 7, only one or two perturbation peaks can be found during 0620–0800 UT. Hence our observation does not include a whole cycle of the perturbations for both the first and the second TIDs. Similar observation of LSTIDs through TEC mapping technique was conducted by Tsugawa et al. , who also found two consecutive LSTIDs over Japan with the duration of 2 hours and phase velocities of more than 500 m/s during the 23 September 1999 storm. The period of the LSTIDs in the work of Tsugawa et al.  cannot be precisely measured, either. Afraimovich et al. [2000b] believed that the LSTIDs detected by GPS arrays are more likely to correspond to solitary waves than to periodic processes. This was also reported by Hunsucker .
 Long-distance traveling of slow-speed TID over North America was also reported by Afraimovich et al. [2000a], who studied the TIDs over North America and Russia through applying cross-spectral analysis to GPS TEC array data and found TIDs propagating equatorward to the distance of ∼3000 km, with mean velocity of 300 m/s. The north edge of the detected region for both studies of Afraimovich et al. [2000a] and ours is at the geomagnetic latitudes of 61°N. This location is very close to the auroral oval where there exists possible auroral source, especially at the local time of midnight. The observation of slow velocity TID near this region is consistent with the simulation results of transfer function for the excitation of gravity waves [Mayr et al., 1990], which indicate that relatively small-scale TID is likely to be found near the source.
3.3. Event of 30 October TID
 The third TID event was observed to start at 1850 UT (i.e., 1250 LT) on 30 October, as shown in Figure 8. This TID occurred during the expansion phase of the auroral substorm, which occurred 2 hours after the second IMF shock arrived at the Earth. The phase front of the third TID moved more quickly than the first two. The TID propagated from northeast to southwest of America to the distance of ∼3000 km during 1850 and 2000 UT with the front width of ∼1500 km. The horizontal phase velocity, period, and propagation azimuth were measured to be 738 m/s, 1.1 hours, and 224°.
 The maximum of the perturbation amplitudes of the third LSTID attained 3 TECU. The amplitude was obviously larger than those of the first two TIDs. It was also larger than the amplitude of TID obtained by Nicolls et al. . We noticed that both the TID observed by Nicolls et al.  and the first two TIDs in our study occurred during the local time of midnight, while the third TID event in our study was observed at local noon. It seemed that the maximum amplitudes of these TIDs were roughly proportional to the background TEC, since the background TEC was larger at noon during the passage of the third TID and its maximum amplitude was larger than those of the first two.
Afraimovich and Voeykov  and Afraimovich et al.  first investigated the LSTIDs during the geomagnetic storm on 30 October 2003 through longitudinal chains of GPS receivers. They filtered out the TEC time series with a running time window of 60 min. By comparing the detrended TEC time series observed by GPS receiver chains, they found a solitary LSTID propagated southwestward to the distance of 4500 km over US during 1930–2015 UT on 30 October 2003. The LSTID caused TEC perturbations with the relative amplitude of up to 40% and the absolute amplitude of 5–14 TECU. Using the SADM-GPS method [Afraimovich et al., 1998], they found the LSTID propagated at the phase velocity of 1400 m/s. Afraimovich and Voeykov  estimated the location of the source of the disturbance and found it was between 50°N and 60°N in the northeast region of the United States.
 It is thought that during auroral substorms, auroral sources such as Joule heating, Lorentz forces or intense particle precipitations [Hunsucker, 1982] generated atmospheric gravity waves, which in turn cause LSTIDs at middle and high latitudes. Both the third LSTID in our study and the solitary LSTID in the work of Afraimovich and Voeykov  were found during the expansion phase of the substorm. The substorm occurred with the onset at about 1830 UT on 30 October after the second shock arrived at the Earth. It is possible that during the substorm, the auroral source generated a variety of gravity waves with different velocities, frequencies, and amplitudes. The gravity waves propagated equatorward and subsequently caused a variety of LSTIDs. As different processing method is sensitive to LSTIDs with different amplitudes and velocities, it is reasonable to suggest that both the third LSTID in our study and the solitary LSTID in the work of Afraimovich and Voeykov  were excited almost simultaneously and were observed by Afraimovich and Voeykov  and us, respectively. Sun et al.  and L. F. Sun et al. (manuscript in preparation, 2007) built the three-dimensional transfer function model to study the excitation of gravity waves and their propagation at ionospheric height. Their study revealed that the source in the form of a unit impulse could excite a series of harmonic gravity waves with a certain frequency range rather than one monochromatic wave.
3.4. Discussion of TIDs' Source Region
 All the three TIDs were observed during the auroral substorms at the geomagnetic latitudes of 41°N–61°N. This strongly implies the TIDs are closely related to auroral sources.
 We used the magnetic field data to investigate the possible source region of LSTIDs over North America. The magnetic field data used here were from 12 geomagnetic observatories located in North America, which belongs to Geological Survey of Canada. The geomagnetic data are available on the Web site http://www.intermagnet.org. We also chose one European observatory and one Asian observatory. The locations and codes of all the fourteen geomagnetic observatories were plotted in Figure 9. Also plotted in Figure 9 were the locations of 6 GPS arrays, each of which consists of three GPS receivers, whose data will be used later in next section to study the propagation of TIDs through cross-spectral analysis.
Figure 10 presents the temporal variation of magnetic field H component observed by all the 14 geomagnetic observatories during 0500–1000 UT on 29 October (Figure 10a) and during 1800–2200 UT on 30 October (Figure 10b). After the onset of the substorm at 0612 UT on 29 October, the values of magnetic field H component at YKC, FCC, IQA, PBQ, GDH, and NAQ began decreasing during 0612–0620 UT. The decreases of H component values at these observatories exceeded −2000 nT. Four of these observatories, namely YKC, IQA, GDH, and NAQ, are located between the geographic latitude of 60°N and 70°N. The other two, namely FCC (59°N, 94°W) and PBQ (55°N, 78°W), are more close to the north edge of the region where TIDs were observed (50°N). The geomagnetic latitudes of these stations are roughly calculated as the geographic latitudes plus 11 degrees. The variations of H component values at the observatories between the latitudes of 45°N–50°N (namely NEW, OTT, and STJ) are not noticeable. This denotes the south edge of auroral oval at the local time of midnight is between 50°N and 60°N (i.e., between the geomagnetic latitudes of 61°N and 71°N) in North America.
 The first TID, which propagated at 270 m/s, was observed about 10 min after the decrease of H component at YKC, FCC, IQA, PBQ, GDH, and NAQ. As the north edge of the region where TID was observed was 50°N, the source region for this slow-velocity TID should be located within 200 km to the north of 50°N (i.e., the geomagnetic latitudes of 61°N). There are two geomagnetic observatories (MEA and PBQ) between 55°N and 50°N. However, the decrease of H component was not obvious at MEA. Thus the source region may lie to the south of PBQ. The region near PBQ is in the northeast of North America. This is consistent with the southwestward propagating direction of the first TID.
 In order to get more information of the location of source region, we estimated the elevation of the gravity waves corresponding to the observed TIDs through
The elevation of a gravity wave refers to the angle between the wave vector and the local horizon, kz and kh are the vertical and horizontal wave number of the gravity wave, ωa and ωb are the Brunt-Väsälä frequency and sound cutoff frequency, respectively, and c is the sound speed. The dispersion equation of gravity waves is used in equation (8) [Ding et al., 2003]. Here, ω is the intrinsic frequency of the gravity waves, which is related to the observed frequency ω′ by
where is the gravity wave vector and is the thermospheric wind vector. The thermospheric wind always exceeds 100 m/s, as calculated by HWM93 wind model. thermospheric wind speed to the direction of thermospheric wind speed to the direction of is in the range of ±100 m/s. We use this unreal wind speed value to estimate the biases that may arise when we include wind in calculating the elevation of gravity waves.
 The elevations for the atmospheric gravity waves corresponding to the first two TIDs are 76° ± 5° and 70° ± 4°, respectively. As the observation height of GPS TEC is about 350 km, the source region may locate below 300 km height to the distance of a few hundred kilometers north of 50°N. The source region for the second TID are likely to locate between 50°N and 55°N (i.e., the geomagnetic latitudes of 61°N–66°N) near the observatory of PBQ (55°N, 78°W).
 Moreover, the second TID was related to the second decrease of H component at PBQ at 0640 UT. The magnetic H component decreased twice between 0600 and 08:00 UT on 29 October at PBQ with the first decrease at 0612 UT and the second one at 0640 UT. The decrease at 0640 UT was much weaker in other observatories. The phase front of the second TID moved at the velocity of 500 m/s after 0640 UT on 29 October, as shown in Figure 4. If the TID had been caused by the decrease of H component at 0612 UT, it should have taken 28 min for the TID to propagate to the distance of ∼800 km from the source region to 50°N. However, this propagation distance does not agree with the elevation angle of 70°, as mentioned above.
 It is most likely that the westward electrojet, which is always detected near the auroral oval at midnight-dawn sector, is the cause for the TIDs observed on 29 October. We checked the variation of magnetic field X and Y component at the observatory of PBQ and found the significant decrease of H component during 0612–0700 UT was mainly caused by the decrease of X component. As magnetic field X component is northward in Canada, the decrease of the X component indicates the enhancement of westward electric current. This subsequently excited atmospheric gravity waves (AGWs) and LSTIDs through the enhancements of Lorentz force (J × B) or Joule heating (J × E) [Hunsucker, 1982].
 The change of the first and the second TIDs' propagation direction during 0620–0800 UT on 29 October may indicate the movement of auroral source region along auroral oval. Tsugawa et al.  also reported two consecutive TIDs over Japan during the storm of 22 September 1999. However, as the longitudinal range is limited in the work of Tsugawa et al. , and Japan is far away from auroral region, the difference of the azimuths for two TIDs is not as obvious as those shown in Figure 5. Hajkowicz [1991, 1990] suggested “the AGW source is neither a point nor a line but circular or oval… It is generated in the wake of an auroral surge moving with supersonic velocities along the ovals [Hajkowicz, 1991, 1990; Hocke and Schlegel, 1996].” However, in this stage, we have no direct evidence to demonstrate the movement of the source region.
 The third TID was observed at 1850 on 30 October during the expansion phase of the substorm which occurred with the onset at about 1830 UT. The elevation for the atmospheric gravity wave corresponding to the third TID was 60° ± 10°. Because the TID was observed at local noon, the variation of magnetic H component seems not as obvious as that of 29 October. However, we could still find the decrease of H component to the extent of −1000 nT at around 1840 at the observatories of BLC (64°N,96°W), FCC (59°N, 94°W), PBQ (55°N, 78°W), and NAQ (61°N, 45°W). Because of the high elevation angle of the third TID, the source region is within several hundred kilometers north of 50°N in North America.
 The source of the third TID remains unknown. Shiokawa et al.  suggested that the electrodynamic instability in the ionosphere could cause southwestward medium-scale TID. However, there is still no evidence to show that electrodynamic instability can cause large-scale TID. Huang et al.  suggested the midlatitude ionospheric disturbances could be caused by the penetration of magnetic electric fields that were controlled or modulated by the oscillations in the IMF or solar wind pressure. However, quasiperiodic turning of IMF z component was not found during 1850–2000 on 30 October, as shown in Figure 3, and the temporal variation of magnetic H component appeared to be steady during that time at the observatories between 30°N and 50°N.
4. Propagation of LSTIDs in North America, Europe, and Asia: Cross-Spectral Results
 In order to get more information of the LSTIDs during 29–30 October 2003, we chose the small local network of GPS arrays in North America, East Asia, and Europe and applied the multichannel maximum-entropy method to get the TIDs' parameters. In each sector we chose two GPS arrays, each of which consists of three GPS receivers. The horizontal distance among these receivers in each array is no more than 300 km. Figure 9 plots the location of the chosen GPS arrays. The geographical latitudes and longitudes of the GPS sites and their codes are listed in Table 1.
Table 1. Location and Codes of GPS Receivers, Whose TEC Observation Data Were Used in Cross-Spectral Analysis to Evaluate TID Parameters
 Multichannel maximum-entropy method was evaluated by Strand . It is a statistical spectral analysis technique, which permits to enhance the resolution and signal/noise ratio of any measure on a given system. Owing to this priority, multichannel maximum-entropy method was used by authors to determine TID propagation parameters [Wan et al., 1998a; Ma et al., 1998]. The adoption of this method on GPS TEC array data was developed by Wan et al. . First, a running time window with 2-hour duration was applied to the original slant TEC time series at intervals of 2 min. This generated a sequence of shorter time series with duration of 2 hours. Two-hour length time window was chosen, since the typical period of LSTID measured by GPS TEC is in the range of 80 ± 29 min as reported from the statistical results of Tsugawa et al. . Thus a time series of 2 hours is long enough to contain at least one cycle of such disturbance. Next, background trends were removed from these 2-hour time series using residues obtained from polynomial fits. At last, the three-channel maximum entropy method was carried out on these 2-hour time series. This generated the time series of TID's parameters such as frequency, phase speed, and propagation azimuth. If a steady TID field were passing by, the temporal variation of TID's parameters would remain steady for the duration of that field.
 The cross-spectral analysis results are shown in Figure 11 (for 29 October events) and Figure 12 (for 30 October events). On 29 October, obvious TID event was found during 0620–0800 UT at midlatitude of North America (Figure 11a) propagating at about 500 m/s, whose velocity and period were consistent with those of the second TID event we found through TEC mapping. The TID reached the south of Florida (26°N) at about 0800 UT (Figure 11b). During 0800–0900 UT, we found southeastward propagating TIDs at the middle and high latitude of Europe (Figures 11c and 11d) and southward TIDs at around 0830 UT (1630 LT) at middle and low latitude of Asia (Figures 11e and 11f). The LSTIDs propagated in Europe and Asia at velocities ranging from 500 m/s to 1000 m/s, with the periods of about 1 hour. Compared to the LSTID in North America, they were similar in periods but different in phase velocities.
 On 30 October, we observed the LSTID propagating southwestward at ∼700 m/s and ∼1 hour in North America during 1825–1920 UT (Figures 12a and 12b). This was the third LSTID we found through TEC mapping. Southwestward LSTIDs were also observed in Europe (Figures 12c and 12d) and Asia (Figures 12e and 12f) with periods and phase velocities in the range of 0.5–1.8 hours and 300–1000 m/s, respectively. The results show the complexity of the global propagation of LSTIDs, since they are significantly influenced by the features of auroral source and the variation of thermosphere wind [Yeh and Webb, 1972; Afraimovich et al., 2005].
 We have built two-dimensional TEC maps to study the propagation of large-scale traveling ionospheric disturbances (LSTIDs) over North America during the magnetic storm on 29–30 October 2003. Spatial resolution for the TEC maps is 0.5° latitude × 0.5° longitude and temporal resolution is 150 s. We also adopted cross-spectral analysis to study the propagation of LSTIDs in North America, Europe, and Asia. The results are summarized as follows:
 1. Three LSTID events were observed over North America in the range of 30°N–50°N, 60°W–110°W during the period of 29–30 October 2003. The phase fronts of these TIDs passed over the United States and traveled southwestward to the distance of ∼2000 km. The maximum of front width reached ∼4000 km, and the duration was 1 to 2 hours. Two consecutive LSTIDs were observed during 0620–0800 UT on 29 October around the local time of midnight. The first TID propagated at 270 m/s with the azimuth of 217°. The second TID switched to the azimuth of 191° and propagated at 500 m/s. The two consecutive TIDs had the maximum amplitude of 2 TECU. The third one was found at noon at 1850 UT on 30 October with the maximum amplitude of 3 TECU. The phase velocity, period, and propagation azimuth of the third TID event were measured to be 738 m/s, 1.1 hour, and 224°.
 2. It is most likely that the auroral westward electrojet is the cause for the TIDs on 29 October. The two consecutive LSTIDs on 29 October were observed a few minutes after the onset of the auroral substorm around the local time of midnight. Significant decreases of magnetic H component were found during this period between 50°N and 70°N. The decrease of magnetic H component was mainly caused by the decrease of X component. The value of H component at the geomagnetic observatory of PBQ (55°N, 78°W) dropped twice at 0612 UT and at 0640 UT. The dropping time agreed well with the emerging time of the two consecutive LSTIDs. Thus the source region for these two TID events were likely to locate between 50°N and 55°N near the observatory of PBQ (55°N, 78°W). The change of direction for the first two LSTIDs may imply the moving of source region along auroral oval. The third TID event was found during the expansion phase of the substorm on 30 October, with the source region within several hundred kilometers north of 50°N.
 3. Cross-spectral analysis was conducted to investigate the global propagation of LSTIDs during 29–30 October. Equatorward LSTIDs were observed in all the three regions during the period of substorms, with their periods and velocities in the range of 0.5–1.8 hours and 300–1000 m/s, respectively. The appearance of these LSTIDs showed high correlation with the occurrence of auroral substorms on 29–30 October 2003.
 We acknowledge the Scripps Orbit and Permanent Array Center (SOPAC) and IGS for providing GPS network data on the Internet. We thank Geological Survey of Canada for providing geomagnetic observation data over North America. We also thank the geomagnetic observatories of Abisko and Irkutsk for providing geomagnetic data. This work was supported by the KIP Pilot Project (KZCX-YW-123) of Chinese Academy of Science, the National Natural Science Foundation of China (grants 40304011 and 40636032), and the National Important basic Research Project (2006CB806306). We thank the State Key Laboratory of Space Weather, Chinese Academy of Sciences for its support.
 Zuyin Pu thanks the reviewers for their assistance in evaluating this paper.