Large-scale traveling ionospheric disturbances (LSTIDs) during the geomagnetic storm on 22 September 1999 were studied using total electron content (TEC) data from the GPS Earth Observation Network (GEONET) in Japan, International GPS Service (IGS), and Continuously Operating Reference Stations (CORS) in the United States. The damping rates of the LSTIDs were precisely derived in several local time sectors and were found to depend on values of the background TEC. This indicates that the dominant physical mechanism of the LSTIDs' damping is the ion-drag effect by the background ionosphere. The high-resolution TEC data from GEONET revealed that two successive LSTIDs were damped significantly as they traveled equatorward in the dawn sector. The ratio of the perturbation component of TEC to the background component (ΔI/I0) decreased exponentially with the damping rate of 0.89/1000 km and 0.77/1000 km. We studied also the amplitude of ΔI/I0 at high latitudes using IGS data and found that the damping rates of LSTIDs at high latitudes tended to be smaller than those at midlatitudes. Global TEC observations during this geomagnetic storm by the IGS and CORS networks detected that several LSTIDs propagated also equatorward in the afternoon sector and in the night sector. The LSTIDs in the afternoon sector were most damped with the damping rate of 1.04/1000 km, which corresponds to the e-folding length of 961 km. The damping rate of LSTIDs in the night sector was found to be small. The LSTIDs had a tendency to be damped rapidly in the regions where background TEC was large. This dependence of the damping rate on latitude and local time indicates that this intense damping of LSTIDs was caused mainly by the ion-drag effect that is proportional to the ion collision frequency. The relation between the damping rates and the background TEC derived from the observation are consistent with those estimated with a theoretical calculation of the gravity wave damping by the ion-drag effect. The worldwide distribution of GPS receivers enabled us to estimate the longitudinal extent of these LSTIDs. The zonal width of LSTIDs in the dawn sector was narrower than 45° in longitude (2,900 km) around 55°N and wider than 20° in longitude (1,800 km) around 40°N. These widths were narrower than those reported in previous studies.
 Many investigations have been devoted to the study of large-scale traveling ionospheric disturbances (LSTIDs), and the progress of these studies is summarized in several review papers [e.g., Hunsucker, 1982; Hocke and Schlegel, 1996]. LSTIDs, which have a period of 30–120 minutes and longer than 1,000 km wavelength, are generally recognized as ionospheric manifestations of the propagation of atmospheric gravity waves (AGWs) that are generated by the energy input from the magnetosphere to the auroral ionosphere. The generation and propagation of LSTIDs is believed to play an important role in the transport of energy from the magnetosphere to the low-latitude ionosphere.
 Although LSTIDs have been studied for three decades [e.g., George, 1968; Davis and da Rosa, 1969], some fundamental questions remain unsolved. Where and how are they generated in the auroral zone? How and how far do they travel to low-latitude regions? How wide in longitude are their wavefronts? There have been many attempts to solve these questions with ionosonde networks [Maeda and Handa, 1980; Hajkowicz and Hunsucker, 1987], HF radars [Bristow et al., 1994], and incoherent scatter radars [Rice et al., 1988; Oliver et al., 1997]. However, the sparseness of the observatories have restricted the resolution of the observations. Several assumptions are necessary to interpret the data, such as the neglect of the temporal variations of their structures.
 In recent years, the dual-frequency radio beacon of the Global Positioning System (GPS) has been applied to study the dynamics of the ionosphere. Global coverage of the GPS receiver networks can provide global maps of total electron content (TEC) and be used in studies of LSTIDs [Ho et al., 1996, 1998]. Afraimovich et al. [2000a] derived the parameters of LSTIDs, such as the phase velocity, the propagation direction, and the zonal width, from sets of three GPS receivers.
 We investigated spatial structure and temporal evolution in order to acquire precise observational results about damping rates and zonal widths of LSTIDs. In this study, we analyzed LSTIDs occurring in a geomagnetic storm on 22 September 1999 using the GPS data of GPS Earth Observation Network (GEONET) in Japan, International GPS Service (IGS), and Continuously Operating Reference Stations (CORS) in the United States. Several LSTIDs were observed during this storm all over the world.
2. Observations of LSTIDs on 22 September 1999
2.1. Geomagnetic Activity
 A strong geomagnetic storm commenced on 22 September 1999. Variations of the AE, Dst, and Kp indices on 22 and 23 September are presented in Figures 1a, 1b, and 1c, respectively. The AE index is a proxy of the intensity of the auroral electrojet, although the AE values presented in Figure 1a are tentative values. It began to increase at 2000 UT on 22 September and reached its maximum, 1,877 nT, at 2127 UT. The variation of the Dst index, a proxy of intensity of the geomagnetic storm activity, indicated that a large storm began at 2000 UT and reached its maximum of amplitude, 184 nT. The Kp index was 8 at 2100 UT. It is inferred from variations of these indices that a strong magnetic storm commenced at 2000 UT on 22 September 1999, and its main phase continued through 2300 UT.
 LSTIDs are well known to be related to geomagnetic activity at high latitudes [Davis, 1971; Hajkowicz and Hunsucker, 1987]. Williams et al.  reported that it took about one hour for LSTIDs to pass over the United Kingdom, 50°N of geomagnetic latitude, after an auroral event. In general, LSTIDs have been reported to travel from auroral regions to equatorial regions with propagation velocities of 200–600 m/s, as summarized in Table 1 after Table 4 of Afraimovich et al. [2000b]. From these observational results, it is expected that LSTIDs take 2–3 hours to reach Japan, 30°N of geomagnetic latitude, after auroral events. Indeed, no clear LSTID was detected at midlatitudes by the GPS observation during this storm before 2000 UT on 22 September and after 0200 UT on 23 September 1999.
Table 1. Observational Method, Propagation Direction, and Propagation Velocity of LSTIDs in Previous Research
 GEONET is a dense, wide-area GPS network in Japan, which consists of more than 1,000 GPS receivers and provides GPS data every 30 seconds. High-resolution TEC maps over Japan have been derived with GEONET data since 1997 [Saito et al., 1998, 2001, 2002]. Figure 2 shows a time sequence of two-dimensional maps of TEC perturbations between 2230 UT on 22 September 1999 and 0050 UT on the subsequent day with a 20-minute interval. Each map covers the area from 124°E to 148°E longitude and from 24°N to 48°N latitude. The size of each pixel is 0.15° latitude × 0.15° longitude. The TEC values for each pixel is an average of perturbations for all satellite-receiver paths which crossed the pixel at 300 km altitude that is the F-region peak height predicted by the IRI90 model. The ionospheric altitude only affects the location of piercing point of satellite-receiver path. The piercing point for the 60° elevation angle varies horizontally about 30 km when the ionospheric altitude varies vertically 50 km from 300 km. The horizontal deviation that is caused by the vertical deviation of the ionospheric altitude is much smaller than the horizontal scale of LSTIDs that is larger than 1000 km. Therefore, we believe that the result is robust on this assumption. The perturbation components of TEC values were derived by subtracting the large-scale trend of the TEC values that is a 60-minute running average. The data derived from paths with low elevation angle are uncertain because of errors on conversion from slant to vertical TEC, and include cycle slips. Therefore, data from elevation angles lower than 60° were not included in this procedure.
 Two consecutive TEC enhancements are seen to stretch zonally and travel over Japan to an almost southward direction between 2230 and 0030 UT in Figure 2. The two-dimensional maps reveal that the wavelength of these enhancements was about 1,800 km and their propagation directions was about 10° east from south. Judging from these parameters, these large-scale structures are identified as LSTIDs [Hunsucker, 1982; Hocke and Schlegel, 1996].
 Medium-Scale TIDs (MSTIDs) are clearly seen to overlap the LSTIDs around 36°N latitude at 2250 UT and around 34°N at 0030 UT. Such MSTIDs, which have wavelengths of a few hundred kilometers and wavefronts stretching from northwest to southeast, are often observed during the summer nighttime and winter daytime over Japan regardless of geomagnetic activity [Saito et al., 2001, 2002]. The MSTIDs propagated to the southwest direction in about a tenth of the LSTIDs' velocity.
 To investigate the temporal evolution of LSTID in detail, we analyzed the TEC variations along the Horizontal Distance axis (HD axis), which is perpendicular to the wavefronts of the LSTIDs. This HD axis, which is shown in Figure 3, is defined from the point of reference (136°E, 44.5°N) to direct 10° east of south and pass through the center of GEONET. Because the enhancement of TEC caused by the LSTIDs is considered isotropic along the wavefronts, we averaged the TEC values along the lines orthogonal to HD axis to increase the spatial resolution of TEC along the HD axis. The wavefront of MSTIDs overlapping the LSTIDs was not orthogonal to the HD axis.
 Several cycles of TEC variations due to MSTIDs were included in this integration range and a integral number of MSTIDs' wavelengths were cancelled. The decimal component of MSTIDs' cycles was averaged orthogonal to the HD axis and smeared out, while the LSTIDs' amplitude was averaged in phase and not reduced by this averaging.Temporal variations of the absolute TEC, I, the background TEC, I0, and the ratio of the perturbation component of TEC to I0, ΔI/I0, are displayed in Figures 4a, 4b, and 4c, respectively. I values were derived with a technique in which a weighted least squares fitting is used to determine unknown instrumental biases, assuming that hourly TEC average is uniform within an area covered by a GPS receiver. This technique developed by Otsuka et al.  can produce absolute values of TEC in the accuracy of 3 × 1016electrons/m2 without interpolation between TEC measurements.
I0 values were determined with a 60-minute running average of absolute TEC at each point along the HD axis. This period of running average was selected according to the typical periods of LSTIDs, 30–90 minutes [Sharadze et al., 1986; Rice et al., 1988; Shibata and Schlegel, 1993]. The I0 values do not have TEC variations whose temporal scale is shorter than 120 minutes as shown in Figure 4b. The 60-minute running average of I values would be adequate to derive the background TEC because LSTIDs during the geomagnetic storm on 22 September 1999 had periods of 30–60 minutes. ΔI was given by subtracting I0 from I, that is ΔI = I − I0.
 The I values at any latitude are seen to begin increasing at sunrise, around 0600 LT (2100 UT), and keep increasing for about three hours, as seen in Figure 1a. The enhancements of I are larger at low-latitudes than those at high latitudes because of the solar zenith angle. The I values started to decrease at 0830 LT (2330 UT) at high latitudes. I0 shows a similar variation as seen in Figure 4b. In Figure 4c, it is clearly seen that one LSTID travels southward between 0730 and 0830 LT (2230 and 2330 UT), and another LSTID from 0830 and 0930 LT (2330 and 0030 UT). The amplitudes of the LSTIDs, which are defined by ΔI/I0, decreased as they traveled to the south. These decreases indicate that the LSTIDs were damped significantly as they traveled equatorward.
 However, the ΔI/I0 values of the second LSTID started to increase at 0900 LT (2400 UT) at 1,000 km HD. This increase was coincident with the beginning of TEC depletion that was seen for several hours at any latitude in the dawn sector. This rapid decrease of I would cause the I0 to be too low. The too low I0 gives a too large ΔI. We believed that the enhancement of ΔI/I0 of the second LSTID at low-latitudes is caused by this rapid decrease of TEC and does not represent exactly the characteristics of the LSTID. We neglect this peculiar increase of ΔI/I0 in this study.
 Spatial and temporal variations of the peaks of these LSTIDs were studied in detail to investigate the damping rate and the velocity of these two LSTIDs. Spatial variations of the maximum amplitudes of ΔI/I0, and temporal variations of locations of the peaks for these LSTIDs are plotted in Figures 5a and 5b, respectively. These peak values and least-square fitted lines are represented by open triangles and a solid line for the first LSTID, and by crosses and a broken line for the second LSTID, respectively. The ΔI/I0 values fluctuates in a cycle with 0.1 amplitudes and 200–400 km horizontal wavelengths. Although these small fluctuations would be caused by MSTIDs, ΔI/I0 values decrease at the rate of 1/1000 km. The least-square fitting lines of ΔI/I0 values represent well a tendency of the LSTIDs and are not effected by the small scale fluctuations caused by MSTIDs. Both LSTIDs were damped as they propagated southward (from low to high HD), as seen in Figure 5a. Their damping rate, γ, is defined by ΔI/I0 ∝ exp (−γx), where x is the horizontal distance given in 1,000 km. γ is represented by the gradients of the lines in Figure 5a. The damping rates of these two LSTIDs were 0.89/1000 km and 0.77/1000 km for the first and the second LSTID, respectively. The propagation velocities were 522 m/s and 573 m/s for the first and the second LSTID, respectively, as shown in Figure 5b. They are within the range of the propagation velocities reported in previous studies, which is shown in Table 1. The difference between the two velocities indicates that the two LSTIDs were multiple LSTIDs rather than multiple cycles of a single LSTID. We regarded the LSTIDs during the storm on 22 September 1999 as independent events in this study.
2.3. Global Observations
 The observations by GEONET in Japan revealed that two LSTIDs propagated southward with large damping rates. We investigated the source region, the spatial scale, the propagation, and the damping of LSTIDs in three sectors: the dawn sector in the West Pacific (100°E–150°E), the afternoon sector in North America (90°W–130°W), and the night sector in Europe (10°E–20°E), using TEC observations from three GPS networks, GEONET, IGS, and CORS. Geomagnetic field data from four stations in the auroral zone were also used. The locations of the observatories are shown in Figure 6.
2.3.1. Dawn Sector in the West Pacific
 The temporal variation of the geomagnetic field H component at Tixie (tixi), which were observed by the CPMN Group [Yumoto and the CPMN Group, 2001], is displayed in Figure 7a. The average of H component of the five quietest days for this month is subtracted from the data to show the activity of the auroral electrojet.
 The H component values began to decrease at 0600 LT (2100 UT) and reached −1,151 nT at 0650 LT (2150 UT). The perturbation component of TEC observed at ten GPS stations in the dawn sector in the West Pacific (100°E–150°E) is displayed in Figure 7b. These stations are tixi, Yakutsk (yakz), Magadan (mag0), Irkutsk (irkt), Yuzhno-Sakhalinsk (yssk), Suwon-shi (suwn), and Taejon (daej) of IGS, and 0520, 0022, and 0544 of GEONET. Several lines for each station were derived from satellite-receiver paths whose elevation angles were larger than 60°. These paths pierced the ionosphere within 170 km from each station at 300 km altitude, the F-region peak height predicted by the IRI95 model.
 The two LSTIDs were detected by yssk station and the stations at lower latitudes from 0730 to 0900 LT (from 2230 to 2400 UT), as shown in Figure 7b. No TEC enhancement of LSTIDs was detected at irkt and mag0, though two or three satellite were in the field of view with different aspect angles. The amplitude of the LSTIDs was interpreted to be too small to be detected by GPS observations at irkt and mag0. These stations are located at about 20° in longitude far from the center of the GPS chain. Therefore the zonal widths of these LSTIDs are estimated to be narrower than the distance between irkt and mag0, 2,900 km, at 60°N latitude. A single enhancement of TEC was observed at yakz at 0650 LT (2150 UT). Intense fluctuations appeared in the perturbation component of TEC at tixi. The geomagnetic latitude of tixi is 61°N. These fluctuations would be caused by the ionization of particle precipitations and make the identification of the LSTIDs at tixi difficult.
 Two LSTIDs were detected at the four IGS stations, yakz, yssk, suwn, and daej, in the dawn sector, in addition to the GEONET stations.
 We calculated the ΔI/I0 values at each station for satellite-receiver paths whose elevation angles larger than 60° and derived the maximum amplitude of the LSTIDs for each satellite-receiver path. Then, these maximum amplitudes was averaged to determine the maximum amplitude of the LSTIDs for the station. Figure 8a displays the maximum amplitude of the ΔI/I0 at yssk, suwn and daej with respect to the HD values shown in Figure 3. The times when the peaks of the LSTIDs passed over these stations are shown in Figure 8b. These peak values are represented by solid triangles and circles for the first and second LSTID, respectively. Error bars overplotted on the symbols represent standard deviations. Auto-regression lines derived with GEONET data, which are displayed in Figures 5a and 5b, are also shown in Figures 8a and 8b, respectively.
 In Figure 8a, the ΔI/I0 values for yssk, suwn, and daej stations lie quite well on the auto-regression lines. The passage time of the two LSTIDs at yssk, suwn, and daej lay also quite well on the auto-regression lines of Figure 8b. The two LSTIDs detected at these three GPS stations were identified with the two LSTIDs detected in Japan. The amplitudes and the traveling time of LSTIDs observed at Korean stations, Suwon-shi and Taejon, are consistent with those from GEONET stations in Japan. Considering the distribution of these GPS stations, the zonal widths of these LSTIDs are estimated to be at least 1,800 km at 30°N latitude.
 Only one TEC enhancement was identified at the yakz station, as seen in Figure 7b. The time of the TEC enhancement at yakz was well on the line for the first LSTID, as seen in Figure 8b. Thus the single TEC enhancement detected at yakz is identified with the first LSTID detected in Japan. The value of ΔI/I0 at yakz is lower than the auto-regression line for the first LSTID in Figure 8a. The ratio of the perturbation component of TEC to the background at high latitudes is smaller than that expected from the extrapolation of the observation over Japan.
2.3.2. Afternoon Sector in North America
 The temporal variation of the geomagnetic field H component at Yellowknife (yell) and Fort Churchill (chur), which are operated by CANOPUS Project, are displayed in Figures 9a and 9b, respectively, in the same format as Figure 7a. The H component values at yell began decreasing at 1230 LT (2030 UT) and reached −652 nT at 1350 LT (2150 UT). The values at chur increased to 361 nT at 1350 LT (2020 UT) and began decreasing to −410 nT at 1520 LT (2150 UT). The perturbation components of TEC observed at seven stations along 125°W and at six stations along 100°W in the afternoon sector are displayed in Figures 9c and 9d, respectively, in the same format as Figure 7b. The seven stations along 125°W are Pacific Beach (pabh), Fort Stevens (fts1), Newport (newp), Cape Blanco (cabl), Cape Mendocino (cme1), Mt. Hamilton (mhcb), and Vandenberg (van1), and the six stations along 100°W are Neligh (nlgn), Fairbury (fbyn), Hillsboro (hbrk), Purcell (prco), Palestine (patt), and Aransas Pass (arp3) of CORS from north to south.
 One LSTID appeared and propagated southward as observed at the higher-latitude stations than mhcb around 1300 LT (2100 UT) in Figure 9c. It was rapidly damped and became undetectable because it was immersed in noise between the cme1 and mhcb stations.
 We derived maximum amplitudes of ΔI/I0 values of this LSTID at each station in the same way as in the dawn sector. These values are plotted by solid triangles, and the auto-regression line is represented by a solid line in Figure 10a. The number of GPS stations in this sector was not sufficient to derive the precise direction of the LSTID propagation. Therefore the propagation direction of the LSTID was assumed to be along the geographic meridional line. The damping rate of this LSTID was estimated at 1.04/1000 km.
 Three LSTIDs were detected between 1400 and 1630 LT (2030 and 2300 UT) in Figure 9d. The maximum amplitudes for the first, second, and third LSTIDs were represented by solid triangles, circles, and squares, respectively, in Figure 10b in the same format as Figure 10a. The auto-regression lines are represented by a solid line, a broken line, and a dotted line for the first, second, and third LSTID, respectively. The damping rates of the LSTIDs were 0.71/1000 km, 0.69/1000 km, and 0.72/1000 km, respectively.
2.3.3. Night Sector in Europe
 The temporal variation of the geomagnetic field H component at Abisko (absk), one of the IMAGE magnetometer arrays, is displayed in Figure 11a in the same format as Figure 7a. The values of the H component began decreasing at 2200 LT (2100 UT) and reached −1,254 nT at 2250 LT (2150 UT). The perturbation component of TEC observed at five European stations (10°E–20°E) in the night sector are displayed in Figure 11b in the same format as Figure 7b. These stations are Onsala (onsa), Potsdam (pots), Graz (graz), and Matera (mate) from north to south. Intense fluctuations of TEC, which would be caused by particle precipitation, make it not possible to detect any LSTIDs at the Onsala station.
 Two consecutive LSTIDs appeared and propagated southward over the lower-latitude stations than the pots station from 2230 to 2400 LT (from 2130 to 2300 UT).
 The maximum amplitudes for the first and second LSTIDs are represented by solid triangles and circles, respectively, in Figure 12 in the same format as Figure 10a. The auto-regression lines are represented by a solid line and a broken line for the first and second LSTID, respectively. The damping rates of the LSTIDs were −0.26/1000 km and 0.37/1000 km, respectively. The first LSTID had the minus damping rate, which signifies that its amplitude increased as it traveled to the low latitudes.
3.1. Damping of LSTIDs
 Several LSTIDs were detected by GPS receiver networks at midlatitudes on 22–23 September 1999. The LSTIDs propagated equatorward and were damped with different rates at different local times. In the dawn sector, two LSTIDs propagated south-southeastward between 0730 and 0930 LT and were damped at the rate of 0.89/1000 km and 0.77/1000 km for the first and second LSTID, respectively. In the afternoon sector, several LSTIDs were detected by two GPS chains along 125°W and 100°W in geographic longitude. One LSTID, which was observed along 125°W, was damped at the rate of 1.04/1000 km around 1300 LT. This damping rate corresponds to 961 km of the e-folding length and was the largest during this storm. Three LSTIDs were observed along 100°W between 1400 and 1630 LT. Their damping rates were 0.71/1000 km, 0.69/1000 km, and 0.72/1000 km for the first, second, and third LSTID, respectively. In the night sector, two LSTIDs traveled equatorward between 2230 and 2400 LT and were damped at the rate of −0.26/1000 km and 0.37/1000 km for the first and second LSTID, respectively. The damping rates of the LSTIDs on 22–23 September 1999 were the largest in the afternoon sector and the smallest in the night sector. It is incomprehensible that the first LSTID in the night sector had the minus damping rate, which signifies that its amplitude increased as it traveled to the low latitudes. There would not be any energy input causing such increase of the LSTIDs' amplitude in the ionosphere at the midlatitudes. Though a possibility that it was caused by some effects due to penetrating and/or dynamo electric fields and background neutral winds is left, it is beyond the present analysis mainly using GPS data. Therefore we neglect this minus damping rate in this study.
 The damping rates of the LSTIDs detected in the dawn, afternoon, and night sectors are shown in Figure 13 against the background TEC, I0, as solid diamonds, circles, and triangles, respectively. Because the background TEC, I0, was not constant in each sector, the average values of I0 were used. The auto-regression line of these observational values except for the minus value is shown as a solid line in Figure 13. It has a correlation coefficient of 0.61. The damping rates of the LSTIDs on 22–23 September 1999 increased by 0.1/1000 km as the background TEC increased by 10 × 1016 electrons/m2.
 LSTIDs are generally interpreted to be the manifestations of disturbances caused by AGWs which are generated in the auroral region and propagate equatorward [e.g., Georges and Hooke, 1970]. While neutral particles move freely across the geomagnetic field line, ions gyrate around a field line and have difficulty in crossing the field line. This difference between the mobility of neutral particles and that of ions restricts the motion of neutral particles in AGWs by the neutral-ion collision. This mechanism is called the ion-drag effect and was initially proposed by Hines . Liu and Yeh  discussed theoretically the damping rate of AGWs by the ion-drag effect. The damping of LSTIDs caused by the ion-drag effect was discussed by Hajkowicz , who studied the global occurrence distribution of LSTIDs using a network of fifteen ionosondes. In the cited reference, the correlation between AE values and uplifts of the ionospheric height at midlatitudes during geomagnetic storms were larger at the night-time than in the daytime. This local-time dependence of the correlation was attributed to the enhanced ion-drag in the daytime.
 We estimated the damping of AGWs by the ion-drag effect using the formulation of Liu and Yeh  based on the linear theory of AGWs, which was initially developed by Hines . The procedure of this theory includes the neutral-ion collision term in the equation of motion as follows;
where ρ, p, and v are the density, the pressure, and the velocity of neutrals, respectively, vi is the velocity of ions, ρp is the density of plasma particles, and g is the gravitational acceleration. The neutral-ion collision frequency, νni, was given by the following equation [Chapman, 1956];
where A is the mean molecular weight of neutrals and ions. It is assumed that ions are restricted to be moved along the geomagnetic field line by neutral particles. The continuity equation, the equation of motion, and the equation of state are linearly solved on the assumption that perturbation components of ρ, p, and v vary as f(z)exp i(ωt − k · x). The wave number vector, k, is in general complex, indicating the presence of damping, and is dependent on the AGWs' frequency (ω), the neutral-ion collision frequency (νni), the direction of the geomagnetic field line, the propagation direction of AGWs, and the equilibrium component of ρ and p. The imaginary part of the horizontal wave number should be compared with the observational damping rate, which was obtained with respect to horizontal distance.
 In the estimation, ω values and the propagation directions of AGWs were calculated using the dispersion relation of Hines  with observational values of the horizontal velocity and the wavelength of LSTIDs on 22–23 September 1999. The equilibrium components of ρ and p, and A values were derived with the MSIS model at 300 km altitude, the F-region peak height [Hedin, 1991]. The inclination and declination angles of the geomagnetic field at 300 km altitude for the center of each GPS chain was calculated using the IGRF2000 model. ρp values were derived from dividing the observational value of I0 by the 250 km thickness of the thin-shell ionosphere. Therefore ρp values were treated as constant in the procedure. Because the precise propagation directions, velocities, and wavelengths of the LSTIDs in the afternoon and night sectors were not derived, those LSTIDs were assumed to propagate exactly southward with 550 m/s horizontal velocities and 1,800 km wavelengths. We checked the dependency of the theoretical damping rate on the physical parameters such as the ionospheric thickness, the horizontal velocity and the wavelength of LSTIDs, and the inclination and declination angles of the geomagnetic filed. The theoretical damping rate 0–20% varied in the dawn sector when each parameter varied in conceivable errors on the condition that the other parameters were constant. The result was summarized in Table 2. It was found that the theoretical damping rate were most dependent on the ionospheric thickness in this procedure.
Table 2. Variations of the Theoretical Damping Rates With Respect to the Variations of Physical Parameters in the Dawn Sectora
Variation of Parameter
Variation of Damping Rate
The background TEC in the sector was 40 × 1016 electrons/m2. dI, LH, VH, Bi, and Bd represent ionospheric thickness, horizontal wavelength, horizontal velocity, and inclination and declination angles of the geomagnetic field, respectively. Each parameter was varied in conceivable errors on the condition that the other parameters were constant.
250 ± 50 km
1800 ± 300 km
573 ± 100 m/s
54.3 ± 5°
−17.1 ± 2°
 The theoretical damping rates of AGWs with 200 km, 250 km, and 300 km of the ionospheric thickness are shown in Figure 13 as open diamonds, triangles, and squares, respectively. The damping rates from observations have a similar tendency against background TEC to those derived in the linear theory. This fact indicates that the ion-drag effect is mainly responsible for the damping of LSTIDs. The observational values are more consistent with the theoretical values with 200 km ionospheric thickness than 250 km. This indicates that the F-peak of the ionosphere was tapered by the atmospheric gravity waves [Hooke, 1968]. The 200 km thickness, however, seems to be a little thinner than the profile of the actual ionosphere. With TEC of 40 × 1016 electrons/m2 and 200 km ionospheric thickness, the electron density becomes 2 × 106 electrons/m3, which is up to double of that at F-peak of the IRI95 model. Though the 250–300 km ionospheric thickness was more suitable for the IRI95 model than the 200 km thickness, the damping rates of the theoretical model tend to be smaller than those of the observation. The effect of the background electric field and neutral wind, which were neglected in the procedure, would contribute for increasing the damping rate of the theoretical model. Northward drift of plasma increase the effect of the ion-drag in the equation (1) for the southward propagating AGWs. The northward drift of plasma is generated by eastward electric field and/or northward wind. A computational simulation could include the contribution of the electric field, background wind, and non-linear effect. It is beyond the scope of this paper.
 In the dawn sector, the LSTIDs that were detected by GEONET in Japan were also detected at higher-latitude stations, Yakutsk (yakz), and Yuzhno-Sakhalinsk (yssk), as shown in Figure 7. The LSTIDs' amplitudes, ΔI/I0 values, at these stations were smaller than that expected by the extrapolations from the observation over Japan as shown in Figure 8a. This indicates that the LSTIDs propagate with smaller damping rates at high latitudes than at midlatitudes. This small damping rate is not caused by large inclination angle of the geomagnetic field at high latitudes than that at midlatitudes because the damping rate tends to increase as the inclination angle of the geomagnetic field increases as shown in Table 2. The ion-drag effect was considered to be weak at high latitudes because the background TEC was smaller than that at low latitudes.
3.2. Zonal Width of LSTIDs
 The widely distributed GPS receivers are effective to ascertain the width of the wavefronts of LSTIDs. All of the GEONET receivers observed two LSTIDs on 22–23 September 1999 over Japan, which are located between 128°E and 148°E in longitude, and between 28°N and 48°N in latitude. As shown in Figures 8a and 8b, these LSTIDs were also detected at Suwon-shi (suwn) and Taejon (daej) stations in Korea, which are located around 127°E in longitude and 37°N in latitude. These indicate that the zonal width of their wavefronts were wider than 20° in longitude (1,800 km) around 40°N. On the other hand, no LSTID appeared over Irkutsk (irkt) [52°N, 104°E] and Magadan (mag0) [60°N, 150°E], as displayed in Figure 7. The zonal width of their wavefronts is estimated to be narrower than 45° in longitude (2,900 km) around 55°N. Two GPS chains along 100°W and 125°W in North America detected several LSTIDs. The separation between these chains is about 2,000 km. The chain along 100°W detected three LSTIDs, as shown in Figure 9d, while the chain along 125°W detected only one LSTID as shown in Figure 9c. Considering the traveling time of the LSTIDs, the first LSTIDs of both GPS chains were considered identical. They had a zonal width larger than 2,000 km. However, the second and third LSTID, which were observed along 100°W, were not detected along 125°W. Although it is not possible to determine the zonal width of LSTIDs using two GPS chains, these LSTIDs did not stretch in longitude to cover the whole of North America.
 These zonal widths of the LSTIDs on 22–23 September 1999 were much narrower than those reported in previous work. Ho et al.  studied the global evolution of the ionospheric storm on 26 November 1994 using a worldwide GPS network of IGS. In this event, the dayside LSTIDs were found to travel over the North Atlantic and stretch to about 8,000 km in longitude at 40°N latitude. However no GPS station in the North Atlantic was used in this study. It would be difficult to determine the precise zonal width of these LSTIDs in this event. Several previous observations assumed that LSTIDs have large zonal widths [e.g., Hajkowicz and Hunsucker, 1987; Rice et al., 1988]. It is difficult for sparse observational network, such as ionosondes and radars, to detect LSTIDs with small zonal widths. Therefore, only the LSTIDs that have large zonal widths, have been studied. We found using a dense GPS network that the zonal width of the LSTIDs was not always globally stretched, but localized zonally, narrower than 2,900 km around 55°N on 22–23 September 1999.
 Why do the LSTIDs have such narrow zonal widths? This would be caused by the zonal scale of the AGWs' source region. Large-scale gravity waves are statistically generated in the auroral zone by the Joule heating of the auroral electrojet and the heating by the particle precipitation from the magnetosphere during geomagnetic storms [Davis, 1971]. The energy injected into the auroral zone from the magnetosphere would not be uniform, but must be localized during storms. The ultraviolet imager of the POLAR satellite provided evidence that the injected energy is localized [Lummerzheim et al., 1997; Brittnacher et al., 1997]. AGWs would be generated in these localized regions.
3.3. Source of LSTIDs
 Though two consecutive LSTIDs were detected by the GPS stations at lower latitudes than Yuzhno-Sakhalinsk (yssk) in the dawn sector, the second LSTID was not observed at Yakutsk (yakz). This LSTID had a horizontal wavelength of 1,800 km and a horizontal phase velocity of 573 m/s. Using the dispersion relation of atmospheric gravity waves proposed by Hines , the vertical wavelength of AGWs that generated this LSTID was estimated at 690 km. The wave vector of this AGWs was directed 21° from downward. The inclination of the geomagnetic field at yakz is about 77° at the altitude of 300 km. Considering the angle between the AGWs and the geomagnetic field at yakz, the AGWs propagating southward generates a large displacement of plasma in the ionosphere along a geomagnetic field line. On the other hand, the oscillation of the AGWs propagating northward is nearly perpendicular to the geomagnetic field and generates a small displacement of plasma. It is difficult for the AGWs propagating eastward or westward to generate a plasma displacement because the horizontal component of the geomagnetic field is directed northward. The AGW that caused the second LSTID in the dawn sector would propagate poleward or not pass over yakz. This AGW would be generated at a lower latitude than yakz, 52°N in geomagnetic latitude.
3.4. Propagation Velocity of LSTIDs
 Propagation velocities of LSTIDs were accurately determined by the dense GPS networks. The two LSTIDs over Japan traveled toward 10° east from south. The directions of LSTIDs were reported to somewhat shift clockwise from south caused by Coriolis force effect [Maeda and Handa, 1980; Afraimovich et al., 2000a]. The observational result for 22–23 September 1999 is not consistent with this refunding. More observations of LSTIDs in the other local time sectors are necessary to unravel the propagation mechanism of LSTIDs.
 The velocities of the LSTIDs in the dawn sector on 22–23 September 1999 were 522 m/s and 573 m/s, which is consistent with previous studies summarized in Table 1. Most of the high velocities in Table 1 were estimated from the time difference of the height variations of the F-region detected by a pair of Ionosondes on a certain meridional line [Hajkowicz and Hunsucker, 1987]. These velocities were the meridional component of LSTIDs velocities and would have been too high for LSTIDs that did not propagate along a meridional line. This possibility of the overestimation was pointed out by Afraimovich et al. [2000a], who calculated the propagation velocities of LSTIDs using GPS networks. The mean velocity of LSTIDs reported by Afraimovich et al. [2000a] was 300 m/s, or smaller than the velocities derived in this study by 200–300 m/s. This small value of the propagation velocity was determined by averaging the velocities derived from the GPS data from several groups of three stations along the same meridional lines. These velocities scattered between 0 m/s and 700 m/s, and their deviation was very large. Small velocities would be those of Medium-Scale TIDs (MSTIDs), which are often detected by GEONET during the night-time in summer and in the daytime in winter even in a geomagnetically quiet period, and have a lower velocity than the LSTIDs [Saito et al., 1998, 2001, 2002]. These small propagation velocities of the MSTIDs would cause a small average velocity reported by Afraimovich et al. [2000a]. The LSTIDs in the dawn sector on 22–23 September 1999 was overlapped by MSTIDs, as shown in Figure 2. The two-dimensional TEC maps derived by GEONET can help to identify the effect of these MSTIDs and provide accurate propagation velocities of the LSTIDs.
 The LSTIDs during the geomagnetic storm on 22 September 1999 were studied using three GPS networks, GEONET, IGS, and CORS. The high-resolution TEC data from the GPS networks provided on accurate damping rate, propagation direction, and velocity of LSTIDs. The damping rates of the LSTIDs were the largest, 1.04/1000 km, which corresponds to 961 km of the e-folding length, in the afternoon sector, and the smallest in the night sector. The damping rates of the LSTIDs were also larger at midlatitudes than at high latitudes. The LSTIDs had a tendency to be damped rapidly in the regions where background TEC was large. This indicates that the damping of LSTIDs is caused by the ion-drag effect. The relation between the damping rates and the background TEC derived from the observation is consistent with that derived from a theoretical calculation of the gravity wave damping by the ion-drag effect. The zonal width of the LSTIDs was narrower than 2,900 km around 55°N and wider than 1,800 km around 40°N in the dawn sector. These zonal widths were much narrower than those reported in previous studies. Such narrow zonal widths would be related to the configuration of the source region in the auroral zone.
 We acknowledge Geographical Survey Institute (GEONET), Japan, International GPS Service (IGS), and the U.S. National Geodetic Survey (CORS) for providing the GPS data. The Tixie data were provided by the CPMN Group (Kyushu Univ., STEL of Nagoya Univ., IKFIA Institute at Yakutsk, Russia, etc.). The CANOPUS instrument array, constructed, maintained and operated by the Canadian Space Agency, provided the data used in this study. We thank the institutes who maintain the IMAGE magnetometer array. This work was supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology of Japan (#12554016).
 Arthur Richmond thanks E. L. Afraimovich and another reviewer for their assistance in evaluating this paper.