3.1. March 08, 2008
 Figures 1a–1c show three 2D contour plots of GPS VTEC in geomagnetic coordinates over Alaska on March 08, 2008. In Figures 1a–1c, the GPS VTEC data have been averaged for 15 min and then interpolated. Five ground magnetometers used are also denoted. On this day, a substorm occurred at ∼1140 UT based on ground magnetometer signatures. The three contour plots reveal the GPS VTEC distribution during quiet time, right after onset and during expansion phase. The trough can be easily identified as a belt with purplish color. Figures 1a and 1b show that the trough extended over several degrees in latitude and that its boundaries were very irregular, though roughly aligned with latitude. Comparing them with the trough location in Figure 1c, one can clearly see that the poleward wall of the trough moved from ∼64° mlat to ∼59° mlat, ∼5° equatorward within an hour, and the width of the trough became only a couple of degrees. During this interval, the region between 60° and 65° mlat experienced significant electron density variations. In certain locations, the TEC value reached ∼7 TECU (1 TECU = 1016 electrons m−2), compared with less than 1 TECU in the trough.
Figure 1. (a–c) Contour plots of GPS VTEC over Alaska at three selected times, i.e., 0900–0915 UT (quiet time), 1145–1200 UT (right after onset), and 1245–1300 UT (during expansion phase) on March 08, 2008. Magnetometers used in the study are denoted. Magenta line in each panel indicates longitude −96°, from which the GPS VTEC data are chosen to produce the time series plots. Time series of GPS VTEC at −96° mlon and magnetograms from three magnetometers at the same longitude for (d) a quiet day, March 07, 2008 and (e) a disturbed day, March 08, 2008.
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 Figures 1d and 1e show time series of the GPS VTEC at ∼−96° geomagnetic longitude (mlon), i.e., magenta lines in Figures 1a–1c, and magnetograms from three ground magnetometers at the same MLT on March 7, 2008, a quiet day, and March 8, 2008, the disturbed day, respectively. For a given time, data points at the same latitude and within 3° centered at this mlon are averaged. The latitudinal coverage is from 50° to 75° mlat, much wider than that of the ISR FOV used previously for studying the trough and thus allows full coverage of the trough throughout the nightside under low and moderate geomagnetic conditions. Magenta dots represent minimum of the trough and black squares denote the solar terminator, where the solar zenith angle equals 90°. Magenta line indicates substorm onset time. The magnetic midnight for this meridian is ∼1110 UT.
 In Figure 1d, the GPS VTEC data for March 07, 2008, a quiet day, is shown for comparison. A persistent trough can be seen, which lasted for more than 10 hours. It appeared around the dusk terminator above 70° mlat and disappeared near the dawn terminator. This is consistent with earlier observations that the trough is most frequently observed when the solar zenith angle exceeds 90° [Moffett and Quegan, 1983]. The width of the trough was about several degrees during the whole period. Poleward of the trough, i.e., in the auroral zone, the VTEC data were very irregular.
 In Figure 1e, on March 08, 2008, during the first half of the day, the trough was quite similar to that during the quiet day. The trough minimum moved from ∼73° mlat to ∼64° mlat from 03 to 07 UT with an average speed of 2° per hour and then remained at ∼63° ± 1° mlat for ∼4 hours until the initiation of the substorm activity. However, dramatic differences are introduced by the substorm. After the onset, the trough minimum moved rapidly equatorward at ∼4°–5° mlat per hour. Zherebtsov et al.  reported similar rapid equatorward motion of the poleward wall of the trough using vertical-incident sounding stations. In Figure 1e, the trough width started to shrink right after the onset and almost disappeared due to the continuous equatorward expansion of the auroral oval between ∼1315 UT and ∼1400 UT.
 The recovery phase of the substorm initiated at ∼1400 UT, when the large negative H perturbations started to increase, and terminated at ∼1600 UT, when they returned back to the pre-onset value. During this interval, the trough reappeared and shifted to higher latitude. However, the trough became shallower and its minimum value was three times of that before the onset. Collis and Haggstrom  reported that such poleward motion was not observed by the EISCAT radar. As can be seen in this case, the trough only moved back to ∼62° mlat, which would be below the limited latitudinal coverage of EISCAT. Other substorm activity occurred later this day between 17 to 21 UT, while the trough at this MLT was already terminated due to sunlight.
 Figure 2a shows POES-18 spacecraft observations from 1246:34 UT to 1254:40 UT. From top to bottom, shown are the energy flux, characteristic energy, height-integrated Pedersen and Hall conductances. The conductance due to electron and proton precipitations are calculated based on empirical formula given by Robinson et al.  and Galand and Richmond , respectively. The spacecraft trajectory is also shown on the top right. Red asterisks represent when the footprint of the spacecraft was within the auroral oval. The equatorward boundary of the auroral oval was located at ∼60° mlat, consistent with the poleward boundary of the trough shown in Figures 1c and 1e, and suggests that the energetic electron precipitation was responsible for the formation of the trough's poleward boundary at this time. At 1252:30 UT, the TEC value of the trough minimum was ∼1 TECU, and the Hall and Pedersen conductances at the trough minimum were only a couple tenths of a Siemen. Figure 2b shows the auroral keograms from ASIs at Fort Yukon and Gakona, which further confirm that the VTEC enhancement and equatorward propagation were associated with energetic electron precipitation. These observations suggest that in the post-midnight sector, energetic electron precipitation can be responsible for the formation of the trough poleward boundary and thus shed light on the dynamics of the inner edge of plasma sheet.
Figure 2. (a) Energy fluxes and characteristic energies of precipitating particles observed by POES-18 from 1246:34 UT to 1254:40 UT on March 08, 2008. Height-integrated Pedersen and Hall conductances are also shown. Trajectory of POES-18 is shown in the top right panel. Red asterisks denote that the spacecraft was in the auroral zone. (b) Auroral keograms from 08 to 15 UT on March 08, 2008. Grey line indicates onset time. Y-axis is the image pixel numbers with 128 representing the zenith above the imager. (c) Comparison between the observed location of the trough minimum (black dots) and model predictions.
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 Figure 2c compares the observed trough minimum locations with model predictions. Models used include Werner and Prölss  (blue/red for model A/B), Ben'kova et al.  (green), and Best et al.  (magenta). The first model used the AE6 index and the other two used Kp. In general, observation and model predictions agree well with each other before the substorm activity reaches the peak. However, the agreement is relatively poor during the recovery phase. In addition, models parameterized by Kp clearly cannot capture the rapid motion of the trough during substorms.
3.2. More Events
 Figure 3a shows the time series of GPS VTEC and magnetograms on Oct. 12, 2007, in the same format as Figure 1d and 1e. On this day, a substorm onset occurred right over Fort Yukon at ∼1119:42 UT and has been studied in detail by Zou et al. . The mid-latitude trough initiated right after the dusk terminator and disappeared at the dawn terminator. Similar to the previous event, right after onset, the VTEC in the mid-latitude trough increased and the mid-latitude trough reappeared during the recovery phase. PFISR was running a world day mode on this day and the electron density observations from two northward looking beams are shown in Figure 3b. These beams are at ∼−96° mlon meridian and are organized from higher to lower latitudes. For each beam, the electron density is shown as a function of altitude (left Y axis) and magnetic latitude (right Y axis). Two vertical red dashed lines indicate the transition between the regular dense dayside ionosphere and the mid-latitude trough. The E-region coverage of PFISR is also shown as two horizontal dashed lines in Figure 3a. As can be seen, the PFISR observations agree with the GPS VTEC data very well in terms of the beginning and ending of the trough at this meridian, further confirming the validity of the GPS VTEC measurement. The electron density enhancement associated with enhanced particle precipitation is also evident in the PFISR data between ∼1120 UT to ∼1300 UT.
Figure 3. (a) Time series of GPS VTEC and magnetograms for October 12, 2007, in the same format as Figures 1d and 1e. (b) Electron density profiles from two northward looking beams of PFISR as a function of UT are shown.
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 In the work by Zou et al. , the Reimei satellite observed an extremely low latitude polar cap boundary at ∼67.7° mlat at ∼1119:41 UT, i.e., ∼1 min before the onset, based on the sudden drop of the fluxes of precipitating energetic particles. The location of the polar cap boundary is consistent with that shown in the GPS VTEC data in Figure 3a, where the GPS VTEC increased significantly from higher to lower latitude at ∼68°. Therefore, during the growth phase of this substorm (∼10–1119 UT), the low VTEC region extending from >75° to ∼68° was in the polar cap. This example indicates that GPS VTEC, when data are sufficient, can reveal the poleward boundary of the auroral oval as well as trough features.
 The behavior of the mid-latitude trough shown in the above two events are quite common in our database, although there are great day-to-day variations. In Figure 4, we show time series of GPS VTEC for four more days (March 02, July 13, August 19, September 04 and all of them in 2008). The trough signatures are observed for all four days, including two days in summer. In general, the duration of the trough is shorter during summer than that during winter or equinox because of longer exposure in sunlight. The trough observed on July 13, 2008 was one of the deepest among the events we studied. In Figure 4, each vertical line indicates a substorm event. When the onset occurred close to the chosen meridian, the enhanced VTEC associated with auroral equatorward boundary started to move equatorward after the onset, and the trough became narrower or even disappeared. A delay of TEC enhancement was observed if the onset was not near the chosen meridian, such as the first event on August 19, 2008 in Figure 4c. THEMIS GBO data show that the onset location occurred east of this meridian and the TEC started to increase when the auroral bulge reached this meridian. This observation suggests that a local index, e.g., the local AL index constructed using a chain of magnetometers at the same meridian [Kauristie et al., 1996; Weygand et al., 2008], is probably better than the global AE index, to characterize the trough location. Similar to the events described in detail, when the auroral activity retreated to higher latitude, the trough reappeared and its poleward wall moved to higher latitudes. The only exception is the event at ∼12 UT on July 13, 2008. Because the chosen meridian was already in sunlight when the recovery phase initiated.