Large-scale traveling ionospheric disturbances (LSTIDs) were statistically studied using total electron content (TEC) data from the GPS Earth observation network (GEONET) in Japan during 45 months from April 1999 to December 2002. One hundred fifty-four LSTIDs propagating southward were identified with time sequences of two-dimensional TEC maps. Fifty LSTIDs were observed in 2000, 45 in 2001, and 38 in 2002. Their occurrence rate (occurrence probability of one LSTID per 3 hours) increased as Kp value increased, that is, 1% at Kp = 4 and 75% at Kp = 9. The disturbed-time LSTIDs were frequently observed over Japan in spring and autumn, which is consistent with the seasonal dependence of the geomagnetic disturbances. On the other hand, the number of LSTIDs under quiet conditions, Kp ≤ 3, reached 43, that is, 28% of all the LSTIDs. The wave parameters, such as the damping rate, horizontal velocity and direction, and period of the clear 58 LSTIDs were precisely determined. The amplitude of the quiet-time LSTIDs decreased during their passage over Japan for every event, while that of the disturbed-time LSTIDs not only decreased but also increased. The LSTIDs can be classified from these observational results into the following three types: the disturbed-time damping LSTIDs (DD-LSTIDs), the disturbed-time growing LSTIDs (DG-LSTIDs), and the quiet-time damping LSTIDs (QD-LSTIDs). The occurrence number of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs was 35 (60%), 11 (19%), and 12 (21%), respectively. The mean horizontal velocity, period, wavelength, and propagation direction of all LSTIDs were 475 ± 171 m/s, 80 ± 29 min, 2131 ± 863 km, and 3 ± 19° east from south, respectively. Both the growth and decrease rates of the LSTIDs were correlated with their propagation velocities. An examination of the relation between the damping rates and the vertical propagation direction, θ, of atmospheric gravity waves (AGWs) which was derived from the horizontal velocity and the period of LSTIDs using the AGWs' dispersion relation, revealed that their damping and growth rates showed a clear correlation with θ. This correlation is due to the ion-drag effect, which is directly dependent on the angle between AGWs' propagation directions and the geomagnetic field. Considering the inclination of the geomagnetic field over Japan, both the damping and growing LSTIDs could be explained by the upward and downward propagating AGWs, respectively. The QD-LSTIDs had smaller θ which resulted from slower velocities and longer periods than those for the disturbed-time LSTIDs. These different characteristics would reflect those of the source mechanisms of the three types of LSTIDs.
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 Large-scale traveling ionospheric disturbances (LSTIDs) have been investigated for more than 3 decades [e.g., George, 1968; Davis and da Rosa, 1969] and the progress of these studies is summarized in several review papers [e.g., Hunsucker, 1982; Hocke and Schlegel, 1996]. LSTIDs have a horizontal scale of more than 1000 km and a period of 30–180 min [Hunsucker, 1982]. They are generally recognized as ionospheric manifestations of the passage of atmospheric gravity waves (AGWs) that are generated at high latitudes by the energy input from the magnetosphere to the auroral ionosphere. Research into the generation and propagation of LSTIDs can clarify a part of the energy flow from the magnetosphere to the low-latitude ionosphere.
 Although many publications have been devoted to the study of LSTIDs using ionosonde networks [Maeda and Handa, 1980; Hajkowicz and Hunsucker, 1987; Hajkowicz, 1990, 1991, 1999], HF radars [Bristow et al., 1994], and incoherent scatter radars [Rice et al., 1988], the fundamental mechanisms of their generation and propagation are still in dispute. The sparseness of the ionospheric observatories has restricted the spatial resolution of observational data. Therefore several assumptions such as the neglect of the spatial and temporal variations of their structures had to be made to interpret the data.
 The recently developed imaging technique using the multipoint GPS network has been applied to study the dynamics of the ionosphere [e.g., Saito et al., 1998, 2002; Afraimovich et al., 2000a, 2002]. Global coverage and continuous operation of GPS networks can provide global maps of total electron content (TEC) that are used to study the LSTIDs [Ho et al., 1996, 1998]. Shiokawa et al.  investigated prominent LSTIDs during a geomagnetic storm using both 630-nm airglow images and GPS data from the GPS Earth observation network (GEONET) in Japan. Information on damping rates of LSTIDs was obtained using several GPS networks [Tsugawa et al., 2003]. Time sequences of two-dimensional TEC maps make it possible to clearly identify LSTIDs and reveal precise spatial structures and temporal evolutions of LSTIDs.
 In this study we statistically studied the occurrence of 154 LSTIDs and the damping rate, propagation velocity, and period of 54 LSTIDs observed by GEONET during 45 months from April 1999 to December 2002. We discuss the occurrence and propagation mechanisms of the LSTIDs.
2. Data and Method of Analysis
2.1. GEONET-TEC Data
 GEONET is a dense and wide-area GPS network in Japan, operated by the Geographical Survey Institute, Japan. The GPS array consists of about 1000 GPS receivers and provides GPS data at every 30 s. High-resolution TEC maps over Japan have been derived from the GEONET data since 1997 [Saito et al., 1998, 2001, 2002]. Time sequences of two-dimensional maps of TEC perturbations provide a powerful tool to identify LSTIDs, as shown by Tsugawa et al. . We made such time sequences of TEC maps with a 10-min interval through all the days from April 1999 to December 2002. 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 value for each pixel is an average of perturbations for all satellite receiver paths which cross the pixel at 300 km altitudes, the F region peak height, predicted by the IRI model. The perturbation components of TEC values were derived by subtracting the large-scale trend of the TEC values that is a 60-min running average. The data derived from satellite receiver paths with low elevation angle have large errors because of conversion from slant to vertical TEC and cycle slips. Therefore the data from low elevation angles between 0° and 30° were not included in this procedure.
2.2. Derivation of the Parameters of LSTIDs
 We first inspected all the time sequences of TEC maps and identified 156 LSTIDs. These LSTIDs were defined as TEC enhancements, which were larger than 0.2 TECU (1 TECU = 1016 electrons/m2), extending horizontally for longer than 1000 km and propagating over Japan within ∼3 hours. These criteria of detecting LSTIDs were determined by the definition of LSTIDs denoted by Hunsucker . All the LSTIDs were propagating toward the equator except for two events: the westward LSTIDs on 12 November 2000 and the northward on 5 May 2001. LSTIDs are generally believed to be generated in the high latitudes during a geomagnetic storm [e.g., Davis, 1971] and propagate equatorward with velocities of 200–800 m/s [Afraimovich et al., 2000b]. Although it is interesting to investigate these two LSTIDs not propagating southward, they were neglected in this paper to focus on clarification of general characteristics of LSTIDs propagating southward.
 In order to derive the precise propagation directions, horizontal velocities, and damping rates of the LSTIDs, we used the following procedure consisting of three steps as summarized in Figure 1. The first step was finding the maximum value of perturbation component of TEC on each meridional line in a TEC map that is derived from the data for each GPS satellite during the passage of each LSTID with 0.15° spatial resolution. There could be differences in the locations of the maximum values for different satellites because of the assumption that the ionosphere is a thin layer at 300 km altitude. The data from every pixels were spatially averaged with the next three pixels (∼100 km) in each TEC map to reduce estimation errors caused by small-scale perturbations of TEC. To identify the peak of the LSTIDs, we neglected the data for the meridional line on which the number of valid pixels is smaller than 30% of the number of all pixels on the line. The locations of the maximum values derived from this method are plotted as asterisks in Figure 1a.
 The second step was obtaining the least squares fitted line of the locations of the maximum values. The fitted line was identified with the horizontal wavefront of the LSTIDs represented by the solid line in Figure 1a. We neglected the fitted line if the number of the maximum values represented by asterisks was smaller than 30% of the number of all pixels on a zonal line. The horizontal distance axis along the propagation direction of the LSTIDs was defined to be perpendicular to the wavefront of the LSTIDs. This axis is defined from the point of reference (44.5°N, 136°E) and shown as the solid arrow in Figure 1a. The propagation direction α was determined from the satellite data which had the minimum standard deviation in fitting the wavefront of the LSTIDs. The direction α is measured clockwise from north, as shown in Figure 1a.
 The third step was determining the parameters of the LSTIDs. Because the enhancements of TEC caused by the LSTIDs are considered isotropic along the wavefronts, the TEC values were averaged along the line orthogonal to the horizontal distance axis to increase the spatial coverage and resolution of the data and to reduce the TEC variations due to medium-scale TIDs (MSTIDs) overlapping the LSTIDs. As seen in Figure 1, the MSTIDs often make locations of the maximum values ΔImax deviate from the wavefront of LSTIDs. 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]. Several cycles of TEC variations due to MSTIDs were included in this integration range and an integral number of MSTIDs' wavelengths was cancelled. The decimal component of MSTIDs' cycles was averaged orthogonal to the horizontal distance axis and smeared out, while the LSTIDs' amplitude was averaged in phase and not reduced by this averaging.
 Locations of the maximum values ΔImax and the minimum ΔImin of the LSTIDs in Figure 1a on the horizontal distance axis are plotted as large and small triangles, respectively, in Figure 1b. The horizontal propagation velocities VH (m/s) of the LSTIDs were derived from the gradient of the least squares fitted lines of the maximum values by the solid line in Figure 1b. The period, T (min), of the LSTIDs was determined by twice average of the time lag between the maximum and minimum value at each horizontal distance.
 Spatial variations of the LSTIDs' amplitudes are plotted as triangles in Figure 1c. The amplitudes were defined as ∣ΔImax − ΔImin∣/I0, where background TEC I0 was determined with a 60-min running average of the absolute TEC at each point along the horizontal distance axis. The absolute TEC values were derived with a technique in which a weighted least squares fitting is used to determine unknown instrumental biases, assuming that the hourly TEC average is uniform within the area covered by a GPS receiver [Otsuka et al., 2002]. This technique can derive absolute values of TEC with the accuracy of ∼3 TECU in the daytime and ∼1 TECU in the nighttime. It is noted that these accuracies concern only I0 values, not ΔI values which have the accuracy less than 0.1 TECU.
 The spatial damping rate δ′(m−1) of the LSTIDs was derived from the gradient of the least squares fitted line in Figure 1c. Because the magnitude of their damping would be related to the impulse (force multiplied by its duration) of forces such as the ion-drag, it would be more reasonable to discuss on the damping rate against time, not against distance. We obtained the temporal damping rate δ(h−1) of the LSTIDs by multiplying the spatial damping rate δ′ by VH, that is δ = 3600 δ′VH. This derivation of δ would be reasonable because the horizontal velocity and period of all the LSTIDs observed by GEONET were able to be regarded as almost constant during their propagation over Japan.
 The average amplitude ΔI of all LSTIDs was 1.3 ± 0.7 TECU; therefore the ambiguity of ΔI is less than 10%. Because the background TEC I0 was generally ∼10 TECU in the nighttime and ∼80 TECU in the daytime, the ambiguity of I0 is also less than 10%. As a result of the above estimation of the ambiguities, the relative amplitudes ΔI/I0 is enough reliable to estimate their spatial gradient, that is, the damping rate δ′. Using the above procedure, we obtained the wave parameters of 58 LSTIDs, which had large amplitudes and exhibited clear characteristics.
3.1. Occurrence of LSTIDs
 One hundred fifty-four LSTIDs propagating southward were observed by GEONET in Japan from April 1999 to December 2002. Of the 154 LSTIDs, 50 LSTIDs were observed in 2000, 45 in 2001, and 38 in 2002. The occurrence rate ξ (%/3 hours) and the number NA of the LSTIDs according to the Kp index are shown in Figure 2. The Kp index represents the disturbance of the geomagnetic field in the subauroral region during each 3-hour period. In this study, we used the Kp values 2-hour before the passage of the LSTIDs over Japan in consideration of the time lag between the generation time of LSTIDs in the auroral region (60°–80°N) and the observation time in Japan (30°–45°N). The occurrence rate ξ for the Kp value was defined as the probability that one LSTID appears over Japan during a 3-hour period with the Kp value. The occurrence rate ξ represented by the solid circle in Figure 2 increases as the Kp value increases, that is, 1% at Kp = 4 and 75% at Kp = 9. This indicates that the occurrence of LSTIDs is closely related to geomagnetic activity at high latitudes, as discussed by many researchers in previous studies [e.g., Davis, 1971; Hajkowicz and Hunsucker, 1987]. The number NA of LSTIDs is represented by the histogram in Figure 2. The distribution of NA as a function of Kp differs from that of ξ because the periods with small Kp values are more frequent than those with large Kp values. The number NA under geomagnetically quiet conditions, Kp ≤ 3, was 43, which reaches 28% of all the LSTIDs observed by GEONET. It should be noted that there are many LSTIDs during geomagnetically quiet periods, although there is an ambiguity that the Kp values do not precisely represent the auroral activity because of their low time resolution and the assumption that it takes 2 hours for the LSTIDs to propagate from the source regions to the midlatitudes.
 The seasonal variation of the number of the LSTIDs and the occurrence rate of geomagnetically disturbed days are shown in Figures 3a and 3b, respectively. The number of all the LSTIDs and LSTIDs which occurred when Kp ≥ 4 are represented by the white and shaded histograms in Figure 3a. A geomagnetically disturbed day is defined as a day for which the average of Kp values is larger than 3. The disturbed-time LSTIDs were frequently observed over Japan in spring and autumn. This is consistent with the seasonal dependence of geomagnetically disturbed days. The quiet-time LSTIDs were not seen in summer, though Kp values in summer were comparable to those in winter.
 The local-time dependence of the number of the LSTIDs and the occurrence rate of geomagnetic storms are shown in Figures 4a and 4b, respectively. Here, the geomagnetic storm was defined as the condition that Kp ≥ 4. The disturbed-time LSTIDs were more often observed in the nighttime than in the daytime. The occurrence rate of geomagnetic storms had no significant diurnal variation, as shown in Figure 4b.
3.2. Damping Rate of LSTIDs
Figures 5a, 5b, 5c, and 5d display the scatter plots of the damping rate δ of the clear 58 LSTIDs versus local time, background TEC, horizontal velocity VH, and period T of the LSTIDs, respectively. The observed LSTIDs could be classified into the following three types: the disturbed-time damping LSTIDs (DD-LSTIDs), the disturbed-time growing LSTIDs (DG-LSTIDs), and the quiet-time damping LSTIDs (QD-LSTIDs). These three types are represented by solid circles, crosses, and open circles, respectively, in all the panels of Figure 5. The quiet-time LSTIDs (Kp ≤ 3) had only positive δ. On the other hand, the disturbed-time LSTIDs (Kp ≥ 4) had not only positive but also negative δ. Negative δ means that the amplitude of the LSTIDs increases as they propagate to the equator. The numbers N of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs were 35, 11, and 12, that is, 60%, 19%, and 21% of the clear 58 LSTIDs, respectively. The solid and broken lines in Figures 5b, 5c, and 5d are autoregression lines of the positive and negative δ, respectively.
 The damping rates δ of the disturbed-time LSTIDs were scattered in the nighttime between −3 and 3 h−1 as shown in Figure 5a, while they had low and positive values in the daytime. The damping rates δ of QD-LSTIDs changed little with local time between 0 and 2 h−1 and were smaller than those of DD-LSTIDs. Figure 5b shows that the positive δ increased slightly against background TEC at the rate of 0.07 h−1 per 10 TECU, though the correlation coefficient was 0.09, while the negative δ clearly increased at the rate of 0.78 h−1 per 10 TECU with the correlation coefficient of 0.58. Figure 5c shows that there was a positive correlation between the horizontal propagation velocities VH and the positive δ. The positive δ increased at the rate of 0.27 h−1 per 100 m/s with the correlation coefficient of 0.54. The negative δ also had a clear negative correlation with VH and decreased −0.34 h−1 per 100 m/s with the correlation coefficient of −0.79.
Figure 5d shows that the positive δ decreased as their periods T increased at the rate of −0.24 h−1 per 30 min with the correlation coefficient of −0.30, while the negative δ increased according to T at the rate of 0.75 h−1 with the correlation coefficient of 0.59.
 Both the growth and decrease rates were best correlated with the horizontal velocity of the LSTIDs among the four parameters shown in Figure 5. The average damping rates of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs were 1.43 ± 0.86, −1.18 ± 0.74, and 0.84 ± 0.49 hour−1, respectively.
3.3. Other Parameters of LSTIDs
Figure 5c shows that the horizontal velocities VH of DD-LSTIDs and DG-LSTIDs were widely distributed between 200 and 800 m/s, while those of the QD-LSTIDs often had relatively small values between 200 and 500 m/s. The average velocities of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs were 487 ± 145, 561 ± 171, and 358 ± 193 m/s, respectively.
Figure 5d shows that the periods of the QD-LSTIDs were long and the most widely distributed between 60 and 180 min. Those of the DD-LSTIDs were also widely distributed between 40 and 140 min. On the other hand, the periods of DG-LSTIDs were between 40 and 100 min. The average periods of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs were 75 ± 22, 63 ± 17, and 111 ± 35 min, respectively.
 The horizontal phase velocities VH against periods T are shown in Figure 6. There were negative correlations between T and VH of all the three types of LSTIDs with the correlation coefficients of 0.44 (DD-LSTIDs), 0.52 (DG-LSTIDs), and 0.23 (QD-LSTIDs). The negative correlation between T and VH indicates that the horizontal wavelengths LH of all the observed LSTIDs were restricted between 1000 km and 3000 km, represented by the dashed curves. The average LH of all the LSTIDs, which was derived by multiplying the average VH and the average T, was 2131 ± 863 km, and is represented by the solid curves in Figure 6. The average horizontal wavelengths of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs were 2108 ± 703, 2021 ± 611, and 2301 ± 1395 km, respectively. The wavelengths of the LSTIDs seem to be little different among the three types.
 The horizontal propagation directions α against local time are shown in Figure 7. The directions α measured clockwise from north were scattered within about ±30° from south, as shown by the left axis of Figure 7. The average of the directions was 177 ± 19°, 3 ± 19° from south, represented by the solid line. The LSTIDs had a tendency to propagate south-southeastward in the prenoon sector. There was no significant difference among the average propagation directions α of 176 ± 19° (DD-LSTIDs), 181 ± 20° (DG-LSTIDs), and 175 ± 20° (QD-LSTIDs).
3.4. Summary of Results
 The fundamental parameters of 58 LSTIDs were successfully obtained out of the 156 LSTIDs detected using the method described in section 2. These LSTIDs could be classified into three types, DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs, according to geomagnetic activity and their damping rates. The average wave parameters of the three types of LSTIDs were summarized in Table 1.
Table 1. Average Wave Parameters of All the LSTIDs, the Disturbed-Time Damping LSTIDs, the Disturbed-Time Growing LSTIDs, and the Quiet-Time Damping LSTIDsa
N, δ, VH, T, LH, α, ΔI, and ΔI/I0, represent the number, damping rate, horizontal velocity, period, horizontal wavelength, propagation direction, amplitude, and relative amplitude to the background of LSTIDs, respectively.
0.81 ± 1.26 h−1
1.43 ± 0.86
−1.18 ± 0.74
0.84 ± 0.49
475 ± 171 m/s
487 ± 145
561 ± 171
358 ± 193
80 ± 29 min
75 ± 22
63 ± 17
111 ± 35
2131 ± 863 km
2108 ± 703
2021 ± 611
2301 ± 1,395
177 ± 19°
176 ± 19
181 ± 20
175 ± 20
1.3 ± 0.7 TECU
1.3 ± 0.7
1.6 ± 0.7
1.0 ± 0.3
2.6 ± 1.3%
2.5 ± 1.3
3.2 ± 1.5
2.5 ± 1.1
 The majority of the observed LSTIDs were DD-LSTIDs, which made up 60% of the 58 LSTIDs. However, the number of DG-LSTIDs and QD-LSTIDs was up to about 20%, not negligible. On the average, DG-LSTIDs had a relatively large velocity and small period, while QD-LSTIDs had a small velocity, large period, and a little large wavelength. The average propagation directions of the three types of LSTIDs were not so much different. The amplitude ΔI of DG-LSTIDs was larger and that of QD-LSTIDs was smaller than that of all LSTIDs. This difference of the average ΔI would be due to the difference of the background TEC I0 because there was little difference between the relative amplitudes ΔI/I0 of the three types of LSTIDs.
4.1. Damping and Growth of LSTIDs
 The most interesting feature of the LSTIDs revealed in this study is that the LSTIDs had not only amplitude decrease but also amplitude increase as shown in Figure 5. It is not negligible that the number of DG-LSTIDs was 11, up to 19% of the 58 LSTIDs, as shown in Table 1. A similar increase in the amplitude of LSTIDs was also reported by Hajkowicz . He investigated the correlation coefficient between the AE index and the associated ionospheric height enhancement observed by ionosonde stations in the East Asian-Australian longitudinal sector and found an anomalous increase in the correlation coefficient between 10° and 25° invariant latitude. Though LSTIDs are considered to be caused by atmospheric gravity waves (AGWs), it is difficult to consider that AGWs grow as they propagate in the midlatitudes because any energy input would not exist there. AGWs would be damped rather than grow because they are subject to the ion-drag effect that is mainly dependent on background plasma density and the angle between the geomagnetic field and their vertical propagation direction [Liu and Yeh, 1969]. Therefore the growth of the LSTIDs is expected to be the result of an apparent increase in TEC during their propagation and not caused by growing AGWs.
 Both positive and negative damping rates of the LSTIDs were most correlated with their propagation velocities, as shown in Figure 5c. The LSTIDs with positive (negative) damping rates had a tendency to be damped (grow) rapidly as their horizontal velocities increased. These horizontal velocities were closely related to their periods, as shown in Figure 6a. These results indicate that the damping rate of LSTIDs is well related to the vertical propagation direction of AGWs, which is derived from the horizontal velocity and the period of LSTIDs using the following AGWs' dispersion relation derived by Hines :
where ω, kx, and kz are the frequency, horizontal wave number, and vertical wave number of AGWs, respectively; C is the sound speed; γ is the ratio of specific heats; and g is the gravitational acceleration. Here ω and kx are derived from the period and horizontal velocity of AGWs, and C and γ are derived from atmospheric parameters. The unknown kz is derived from equation (1) with the other parameters. The vertical propagation direction θ of AGWs is obtained as follows:
 The relation between the damping rates of the observed LSTIDs and θ is shown in Figure 8. Here, θ was defined as a tilt angle of the wave vector of AGWs from the vertical line. In the estimation of θ, we used the observed horizontal velocities and periods of the LSTIDs and the equilibrium components of the atmospheric parameters derived from the MSIS model at 300 km altitude, the F region peak height [Hedin, 1991]. The marks and lines in Figure 8 are the same as in Figure 5. The positive (negative) damping rates increased (decreased) at the rate of 0.35 (−0.47) h−1 per 10° as θ increased with the correlation coefficient of 0.37 (−0.80).
 Theoretically, AGWs with a given θ can propagate both upward and downward with a tilt angle θ. Figures 9a and 9b show that the schematic diagrams of the relation between θ and plasma drift caused by neutral winds in the AGWs propagating upward and downward in the ionosphere over Japan, respectively. The geomagnetic field line at 300 km altitude in the south of Japan (32°N, 136°E) is represented by the thin arrow B in Figure 9. The inclination angle of the geomagnetic field was 45°, as deduced from the IGRF2000 model. The AGWs' phase propagation directions are represented by thick arrows k, and neutral winds in the AGWs and plasma drift are represented by broken arrows and solid arrows in the shaded area, respectively. The plasma was assumed to move only along the field line by the neutral wind through the neutral-ion collisional interaction. Figure 9a illustrates that the neutral winds in upward AGWs become perpendicular to the field line B as θ increases. The ion-drag effect that acts on upward AGWs is proportional to ∣v − vi∣ = v(1 − cos(I + θ)), where v and vi are the velocity of neutrals and ions, respectively, and I is the inclination angle of the geomagnetic field. Therefore the AGWs are more damped through the ion-drag effect as θ increases between 0° and 45° in the south of Japan. On the contrary, the neutral winds in downward AGWs become parallel to the field line B as θ increases, as shown in Figure 9b. Thence the ion-drag effect on downward AGWs is proportional to v(1 − cos(I − θ)) and decreases according to θ.
 Considering the above propagation mechanisms of upward and downward AGWs, the positive correlation between the positive damping rates and θ in Figure 8 indicates that the damping LSTIDs would be caused by upward AGWs, as shown in Figure 9a. On the other hand, the negative correlation between the negative damping rates and θ in Figure 8 indicates that the growing LSTIDs would be caused by downward AGWs, as shown in Figure 9b.
 However, the negative damping rates of the growing LSTIDs cannot be explained only by the damping due to the ion-drag effect on AGWs. To interpret the increasing amplitudes of the growing LSTIDs during their propagation, we need to take into account the apparent increase in TEC. The plasma variation that is caused by the neutral wind in downward AGWs with a constant θ increases as they travel southward because the inclination angle, I, of the geomagnetic field decreases from 60° in the north of Japan (45°N, 136°E) to 45° in the south (32°N, 136°E), as shown in Figure 10. The arrows in Figure 10 represent the same as in Figure 9. The amplitude of the LSTIDs would be found to increase as the downward AGWs travel southward over Japan because the apparent increase of the plasma variation during their propagation overcomes the damping due to the ion-drag effect that has little effect on the downward AGWs.
 The ion-drag effect is also dependent on plasma density. It is necessary to discuss on the dependence of the damping rates on background TEC in addition to θ. The positive damping rates of the LSTIDs increased at the rate of 0.07 h−1 per 10 TECU, though the correlation coefficient was very small, as shown in Figure 5b. Such a dependence was also discussed using global observations of LSTIDs during a geomagnetic storm by Tsugawa et al. . Their research revealed that the positive damping rates increased at the rate of 0.1 (1000 km−1) per 10 TECU, corresponding to 0.2 (h−1) per 10 TECU on the assumption that the horizontal velocity of the LSTIDs was 550 m/s. Although these increasing rates of the damping rates against background TEC indicate that the damping of LSTIDs is also dependent on background TEC, the dependence of the damping rate on background TEC is weaker than that on the vertical propagation direction θ represented by the rate of 0.35 h−1 per 10°.
 The negative damping rates of the LSTIDs against background TEC also increased at a high rate of 0.78 h−1 per 10 TECU and vanished when background TEC is larger than 40 TECU, as shown in Figure 5b. This indicates that the growing LSTIDs are not entirely free from the ion-drag effect but are strongly subject to the effect and grow hardly even if the plasma variation increases during their propagation under the condition that background TEC is large.
 Summarizing this section, the main observational result of this statistical study as shown in Figure 8 revealed that the damping rate of LSTIDs was dependent primarily on the vertical propagation direction θ of the AGWs. This indicates that the damping of LSTIDs depends strongly on θ through the ion-drag effect. The above two models of upward and downward AGWs can explain basically the positive and negative correlations between the damping rate and θ, respectively.
 However, there is a fundamental question whether the large-scale AGWs can really propagate upward in the ionosphere. AGWs are generally believed to be generated in the auroral zone during geomagnetic storms by the Joule heating and/or the Lorentz force of the auroral electrojet [e.g., Davis, 1971]. The flux of the electrojet would be concentrated in the ionospheric E region (80–140 km altitude), where conductivity is maximal in the daytime and still large in the nighttime. Therefore it seems to be difficult to consider that AGWs have a group velocity with a downward tilt from the horizontal in the ionospheric F region (200–500 km altitude) at the midlatitude, as shown in Figure 9a.
 The downward energy propagation (upward phase propagation) of AGWs has been discussed in several papers. Maeda  calculated a numerical solution of the full wave equation for AGWs in an inhomogeneous and viscous atmosphere and revealed that large-scale AGWs undergo significant partial downward reflections caused by increasing kinematic viscosity in the ionosphere, in addition to the total reflection due to the sharp rise of atmospheric temperature near the thermospheric base. There is an observational result on the downward group velocity of traveling atmospheric disturbances during a geomagnetic storm using two ionosondes at midlatitudes [Lee et al., 2002]. To investigate the relation between the damping rate of LSTIDs and the vertical propagation direction of AGWs, it is necessary to observe the vertical variation of the ionospheric parameters such as neutral density, wind, and ion density that cannot be revealed by the present analysis using only GPS data.
4.2. Occurrence of LSTIDs
 The occurrence rate of LSTIDs increased as Kp values increased and reached a maximum of 75% when Kp = 9, as shown in Figure 2. Although it is consistent with the previous studies that the occurrence of the LSTIDs were related to the global geomagnetic activity, there is a remarkable fact that 28% of all the LSTIDs were observed during geomagnetic quiet periods (Kp ≤ 3). Under such quiet conditions, it is difficult to consider that the quiet-time LSTIDs are caused by an enhancement of the auroral electrojet that is generally believed to be their source. These quiet-time LSTIDs (QD-LSTIDs) had only positive damping rates, as shown in Figure 5, and θ of QD-LSTIDs is smaller than the disturbed-time LSTIDs, as shown in Figure 8. It is necessary to consider different generation mechanisms for the disturbed-time LSTIDs and QD-LSTIDs.
 On the disturbed condition that Kp ≥ 4, the occurrence number of the LSTIDs became large in the equinoxes as well as the occurrence rate of the disturbed days, as shown in Figure 3. Such a seasonal variation of geomagnetic activity also appeared in the Dst index and is considered to be caused by the orientation of the terrestrial magnetic dipole relative to the heliospheric topology [O'Brien and McPherron, 2002]. A similar seasonal variation in Figure 3 indicates that the disturbed-time LSTIDs are caused by the energy input into the high latitudes from the magnetosphere during geomagnetic storms.
 The disturbed-time LSTIDs were less often observed over Japan in the daytime than in the nighttime, as shown in the shaded histogram of Figure 4. The occurrence rate of geomagnetic storms (Kp ≥ 4) had no significant dependence on local time or universal time during this period, as shown in Figure 4. The energy input from the magnetosphere during a geomagnetic storm is generally larger in the nightside than in the daytime. The local time variation of occurrence number of the LSTIDs is expected to reflect the local time distribution of the energy input into the high latitudes.
 On the quiet condition that Kp ≤ 3, the occurrence number of the LSTIDs was larger in the daytime than the nighttime, as shown in Figure 4. All the damping rates of the quiet-time LSTIDs were positive, as shown in Figure 5, and the damping rates and θ of QD-LSTIDs were smaller than those of disturbed-time LSTIDs, as shown in Figure 8. These small θ indicate that the horizontal wavelength of the AGWs is exceedingly long compared with their vertical wavelength and their group velocity tends toward an almost horizontal direction. QD-LSTIDs had slower velocities and longer periods than the disturbed-time LSTIDs, as represented by open circles in Figures 5c and 5d, respectively. Because there would be little energy input into the high-latitude ionosphere from the magnetosphere during geomagnetically quiet conditions, the quiet-time LSTIDs would not be caused by the same mechanisms generating the disturbed-time LSTIDs such as the Joule heating and the Lorenz force in the auroral electrojet, which would be caused by a large amount of energy input from the magnetosphere in a short period. The quiet-time LSTIDs would be caused by some mechanism, which have a broad horizontal scale compared with the vertical scale, and a longer timescale than the auroral electrojet. To reveal the mechanism of generation of the quiet-time LSTIDs, we need more observations in the high latitudes and model studies on the generation of AGWs and LSTIDs.
4.3. Other Parameters of LSTIDs
 The horizontal propagation velocity of the LSTIDs was accurately determined by the dense GPS networks, GEONET, as illustrated in Figure 1. Figure 5c shows that QD-LSTIDs have smaller velocities than those of DD-LSTIDs and DG-LSTIDs. In Figure 5d, the periods of DD-LSTIDs are widely distributed between 40 and 140 min and their average was 75 ± 22 min. On the other hand, those of DG-LSTIDs were restricted between 40 and 100 min and their average was 63 ± 17 min. Those of QD-LSTIDs were long, between 60 and 180 min, and their average was 111 ± 35 min. Thus Figures 5c and 5d clarify that there were also different characteristics in the horizontal velocity and period for the three-type LSTIDs which were characterized by their damping rates and the geomagnetic conditions. These different characteristics would reflect the source mechanisms of the LSTIDs. It seems reasonable that the disturbed-time LSTIDs are caused by the energy input into the high-latitude ionosphere in a shorter period than the quiet-time LSTIDs.
 There was no particular tendency in the horizontal wavelengths and propagation directions among the three types of LSTIDs, as shown in Figures 6 and 7, respectively. The characteristics of the LSTIDs such as damping rate, velocity, and period would be independent of their horizontal wavelengths and propagation directions. The propagation directions of the LSTIDs are generally believed to be subject to the Coriolis force effect and somewhat shifted clockwise from the south [Maeda and Handa, 1980; Afraimovich et al., 2000a]. The observational result in this study revealed that the average of the directions of all the observed LSTIDs was 177 ± 19°, anticlockwise from the south. Their horizontal propagation directions would not be affected by the Coriolis force effect. The declination of the geomagnetic field, about −6°, in Japan could affect their propagation directions because the plasma mobility is the largest along the field. This, however, cannot explain the tendency of the anticlockwise shift of the LSTIDs particularly seen between 0500 and 1100 LT. It would be difficult to discuss more elaborately on the characteristics of their propagation direction from this observational result because their standard deviation is so large. More global observations and numerical simulations are needed to clarify the mechanisms determining their directions.
 LSTIDs were statistically studied using the TEC data covering 45 months from April 1999 to December 2002 with the GPS data from GEONET in Japan. One hundred fifty-six LSTIDs were detected using time sequences of TEC two-dimensional maps, and 154 LSTIDs were found to propagate southward. Their occurrence rate (occurrence probability of one LSTID per 3 hours) increased as Kp value increased, that is, 1% at Kp = 4 and 75% at Kp = 9. The disturbed-time LSTIDs were frequently observed over Japan in spring and autumn, which is consistent with the seasonal dependence of the geomagnetic disturbances. However, the number of the LSTIDs under quiet conditions, Kp ≤ 3, reached 43, that is, 28% of all the LSTIDs.
 The amplitude of the quiet-time LSTIDs decreased during their passage over Japan for every event, while that of the disturbed-time LSTIDs not only decreased but also increased. On the basis of these observational results, the LSTIDs can be classified into the following three types: the disturbed-time damping LSTIDs (DD-LSTIDs), the disturbed-time growing LSTIDs (DG-LSTIDs), and the quiet-time damping LSTIDs (QD-LSTIDs). The occurrence number of DD-LSTIDs, DG-LSTIDs, and QD-LSTIDs was 35 (60%), 11 (19%), and 12 (21%), respectively. The mean horizontal velocity, period, wavelength, and propagation direction of all LSTIDs were 475 ± 171 m/s, 80 ± 29 min, 2,131 ± 863 km, and 3 ± 19° east from south, respectively.
 Both positive and negative damping rates of the LSTIDs were most correlated with their propagation velocities. An examination of the relation between the damping rates and the vertical propagation direction, θ, of atmospheric gravity waves (AGWs), which was derived from the horizontal velocity and the period of LSTIDs using the AGWs' dispersion relation, revealed that their damping and growth rates showed a clear correlation with θ. This study revealed that the damping and growth of LSTIDs depends strongly on θ through the ion-drag effect, which is directly dependent on the angle between directions of the AGWs' propagation and the geomagnetic field. Considering the inclination of the geomagnetic field over Japan, both damping and growing LSTIDs could be explained by the upward and downward propagating AGWs, respectively.
 The QD-LSTIDs had smaller θ which resulted from slower velocities and longer periods than the disturbed-time LSTIDs. These different characteristics would reflect those of the source mechanisms of the three types of the LSTIDs.
 This statistical study on LSTIDs using high-resolution GPS data for Japan has revealed several new aspects of LSTIDs. However, there still remain many questions concerning LSTIDs, such as the generation mechanism of quiet-time LSTIDs, the relationship between damping rates of LSTIDs and vertical propagation directions of AGWs, and the mechanisms determining their horizontal wavelengths and propagation directions. More ionospheric and atmospheric observations and global ionospheric model studies will be needed for further investigation.
 The GPS data from GEONET are provided by the Geographical Survey Institute, Japan. We would like to thank S. Maeda, T. Ogawa, and K. Shiokawa for their helpful comments and suggestions. One of the authors (T.T.) is partially supported by a Grant-in-Aid for the 21st Century COE Program (Kyoto University, G3).
 Arthur Richmond thanks E. L. Afraimovich and Lech A. Hajkowicz for their assistance in evaluating this paper.