To investigate gravity wave dynamics in the mesosphere and lower thermosphere (MLT) region, we conducted coordinated observations of mesospheric gravity waves over Japan during the Aeronomy and Dynamics Observation campaign. Two all-sky airglow imagers were used in this campaign to derive a two-dimensional structure of the gravity waves; these imagers were installed at the middle and upper atmosphere (MU) observatory in Shigaraki (34.9°N, 136.1°E) and at the Dynic Astropark Observatory in Taga (35.2°N, 136.3°E). Simultaneous measurements of the horizontal winds and the temperature in the MLT region were provided by the meteor-mode observations of the MU radar at Shigaraki and by a sodium temperature lidar at Uji (34.9°N, 135.8°E), respectively. On 2 October 2008, gravity waves having a horizontal wavelength of ∼170 km, wave period of ∼1 h, and propagating northeastward at ∼50 m s−1 were observed in the airglow keograms. Similar wave structures were observed in the time series of the meteor wind and lidar temperature data; the polarity of these waves varied consistently with the airglow intensity variations according to the linear theory of gravity waves. The phase speeds and momentum fluxes of the gravity waves, estimated from the wind and temperature observations, were also in good agreement with those obtained from the airglow measurements. These results demonstrate, both qualitatively and quantitatively, that an identical gravity wave structure was detected in all the airglow intensities, radar winds, and lidar temperature.
 Atmospheric gravity waves contribute significantly to the wind field and thermal balance in the mesosphere and lower thermosphere (MLT) region because they vertically transport horizontal momentum from the lower atmosphere [Houghton, 1978; Lindzen, 1981; Fritts and Alexander, 2003]. It is considered that a part of the gravity waves propagating upward in the MLT penetrate into the thermosphere/ionosphere and can trigger irregularities there.
 Gravity waves in the MLT have been measured by various ground-based remote sensing techniques such as radars [e.g., Fritts and Vincent, 1987; Tsuda et al., 1990; Fritts et al., 2006], lidars [e.g., Gardner and Voelz, 1987; She et al., 1991; Yang et al., 2006], and airglow imaging [e.g., Taylor et al., 1995; Suzuki et al., 2009a, and references therein]. Radars detect the wave components in wind perturbations and reveal the activities (seasonal, height, and latitudinal variations) and momentum fluxes of the gravity waves. Most waves propagate upward and have fairly large horizontal scales (greater than a few hundred kilometers) [Nakamura et al., 1993]. Lidar techniques have also been used for gravity wave studies for a long time for providing temperature and/or wind profiles with high spatial and temporal resolutions. Radar and lidar observations can provide the vertical structure of gravity waves that transport energy and momentum to the upper atmosphere. Although some studies [Meek et al., 1985; Manson and Meek, 1988] using multiradar systems such as Gravnet provided horizontal scales and phase velocities of gravity waves, direct measurements of the horizontal structures of these waves are difficult.
 Airglow imaging techniques are useful for the investigation of the two-dimensional horizontal characteristics of MLT gravity waves; their horizontal wavelengths and motions can be identified directly and clearly from sequential airglow images. Since Nakamura et al.  first made 18 month long-term imaging observations of midlatitude MLT gravity waves, several studies have reported on their statistical characteristics and seasonal/geographical variations [Nakamura et al., 2003; Walterscheid et al., 1999; Ejiri et al., 2003; Suzuki et al., 2004, 2009a, 2009b]. The observed waves typically had a horizontal wavelength of 20–50 km, an intrinsic phase speed of 30–60 m s−1, and a wave period of less than a few tens of minutes, although their horizontal propagation greatly depended on the season and/or location of the observations. However, intrinsic parameters (i.e., the phase speed and wave period), which are required for determining the vertical structure and calculating the momentum flux of gravity waves, cannot be obtained from airglow observations alone. Therefore, these observations are often accompanied by simultaneous wind measurements.
 Some studies carried out comprehensive airglow, horizontal wind, and temperature observations on a campaign basis. Nielsen et al.  investigated the propagation signatures of short-period gravity waves observed using an airglow imager in northern Scandinavia during the Mountain and Convective Waves Ascending Vertically (MaCWAV) winter campaign. They used two meteor radars and a lidar to derive the intrinsic parameters of the waves observed in the airglow images and discussed their vertical propagation. Recently, Ejiri et al.  reported the dissipation of short-period gravity waves in the Mesospheric Temperature Mapper OH and O2 images associated with the background wind variations observed using a meteor radar. On the basis of the intrinsic wave propagation parameters calculated using the radar winds, they suggested that the critical- and saturation-level interactions of these waves played a significant role in their dissipation. For such the airglow studies of the MLT gravity waves, simultaneous wind and temperature measurements were used as background conditions. Gardner et al.  estimated the momentum flux of gravity waves from OH airglow images; the estimation was accomplished by using the average angular spectra of the airglow intensity variance associated with waves having periods ranging from 4 min to 2 h and horizontal wavelengths ranging from 2.4 to 150 km. They investigated the nightly averaged wave behaviors to compare the obtained momentum fluxes with those measured by the dual-beam technique of sodium wind and temperature lidar measurements.
 One of the difficulties in observing a one-to-one correspondence between the gravity waves detected by airglow imaging and those detected by radar or lidar measurements results from the difference in their observational resolutions; typically, waves in airglow images have significantly smaller spatial and temporal scales compared to those of the radar and lidar observations.
 According to a recent study by Suzuki et al. [2009a], wherein sodium airglow observations were carried out in Canada during two winter seasons, large-scale (long-period) gravity waves were identified in the airglow keograms (time series of the horizontal cross sections of airglow images). They discussed the statistics of these large-scale waves as well as the conventional small-scale (short-period) gravity waves; in the airglow keograms, gravity waves with a horizontal wavelength of 100–400 km, an apparent phase speed of 60–100 m s−1, and an intrinsic period of 30–80 min were predominantly observed, while those of small-scale waves had the corresponding parameters of 20–50 km, 30–60 m s−1, and 5–15 min. Gravity waves having such large spatial and temporal scales match those of the radar and lidar observations, and it is possible to show a one-to-one correspondence among them.
 The Aeronomy and Dynamics Observation (ANDON) campaigns were carried out to elucidate the formation of gravity waves in airglow emissions over Japan and consist of comprehensive measurements of airglow, horizontal winds, and temperature by using two all-sky imagers, the middle and upper atmosphere (MU) radar, and a sodium lidar, respectively. The ANDON campaigns were conducted six times during the new moon periods from October 2008 to August 2009.
 In the present study, our aim is to identify the gravity wave structure deduced from simultaneous measurements of mesospheric airglow intensities, horizontal wind, and temperature that were observed on 2 October 2008 during the ANDON campaign period and to investigate their spatial and temporal characteristics. We also discuss the momentum fluxes estimated from airglow observations and those derived by the wind and temperature measurements. To date, no study has quantitatively examined their difference for the same gravity wave structure.
Figure 1 shows the locations of the stations. Two airglow imagers were used in the ANDON campaign to obtain a two-dimensional structure of the gravity waves. One of the imagers has been operated by Nagoya University as a part of the Optical Mesosphere Thermosphere Imagers (OMTIs) at the MU observatory in Shigaraki (34.9°N, 136.1°E) [Shiokawa et al., 2008, 2009]; the other imager, named ANDON and developed by Kyoto University, was newly installed at the Dynic Astropark Observatory in Taga (35.2°N, 136.3°E). Each imager has a fish-eye lens with a 180° field of view (FOV), interference filters on a wheel, and a cooled CCD camera with 512 × 512 pixels. In this study, we used 557.7 nm and OH airglow images that were obtained simultaneously at both stations. The time resolutions and exposures of the imagers are listed in Table 1. Both imagers recorded airglow emissions with the same exposure (105 s for 557.7 nm and 15 s for OH), but their sequential filter times were different (5.5 min for OMTI and 2.5 min for ANDON).
Table 1. Filter Details for the ANDON and OMTI Imagers
 During the ANDON campaign periods, the MU radar at Shigaraki was operated in meteor-observation mode [Nakamura et al., 1991, 1997], in which meteor winds in the MLT region (80–105 km) spanning the FOVs of the imagers could be detected. Owing to recent developments in the MU radar ultra-multichannel system [e.g., Saito et al., 2008], the signal-to-noise ratio of meteor echoes has been significantly improved; ∼50,000 meteors can be detected per day in an area of 300–400 km diameter over the radar by coherently integrating 25 antenna subarray signals.
 A sodium temperature lidar was operated at Kyoto University in Uji (34.9°N, 135.8°E) from 2005 to 2009, which included the campaign periods. This lidar was originally designed for measuring the temperature in the vicinity of the mesopause region over Syowa Station, Antarctica [Kawahara et al., 2002, 2004]. The lidar uses a two-frequency technique [She et al., 1990] to measure the sodium density and temperature at around 80–105 km. The narrowband laser is tuned alternately to two wavelengths near the sodium D2a (589 nm) peak and bottom. Photon profiles at each wavelength are obtained alternately with an integration time of 2.5 min (1500 shots). Including the switching period of 30 s, the total length of one cycle of observation for the two wavelengths is 6 min.
3. Experimental Results
3.1. Airglow Measurements
 On the night of 2 October 2008, the weather was fairly good, and several wave structures were recognized in the 557.7 nm and OH airglow images at both stations. Small-scale gravity waves having a horizontal wavelength of 20–35 km were actively seen throughout the night (1000–1800 UT, 1900–2700 LT). They propagated northward at first (∼1010–1230 UT), and then the northwestward propagation appeared to be dominant (∼1300–1630 UT). At ∼1630 UT, a clear wavefront structure passed over the imager stations from southwest to northeast. Then, small-scale wave structures (horizontal wavelength of ∼15 km) occupied the airglow images until the end of the airglow observations (∼1800 UT). Ripple signatures were also detected quite frequently in the 557.7 nm images (1042, 1151, and 1515 UT, each lasting for a few tens of minutes). Although the behavior of these small-scale wave structures is interesting, they could not be studied because their spatiotemporal scales are too small to be identified as wind and temperature variations by the radar and lidar observations.
Figure 2 shows the keograms of the 557.7 nm (left) and OH (right) airglow emissions obtained by ANDON at Taga (top) and OMTI at Shigaraki (bottom) for 1000–1800 UT on 2 October 2008. The keograms were made by using the time-difference images mapped onto geographical coordinates with projection heights of 94 and 86 km for the 557.7 nm and OH airglow images, respectively. These projection heights were determined by the triangulation method using the airglow images at the two stations [Kubota et al., 1999; Ejiri et al., 2002]. The horizontal scratches in the keograms are the trajectories of stars. It can be seen that northwestward propagating wave structures with a ∼1 h period enhanced the airglow intensities in the both emissions, in particular, in the interval 1200–1600 UT. Such signatures are more clearly seen in the keograms at Shigaraki compared to those at Taga. The structures that appear at ∼1600 UT are the northeastward propagating wavefront structure (not the wave signatures of interest).
 In the 557.7 nm (OH) emissions, the wave structures had an average horizontal wavelength, λh, of 177.6 km (169.3 km) and apparent wave period, τ, of 60.0 min (58.1 min) propagating along an azimuthal direction (clockwise from north to east) of 320.5° (321.2°) at a phase speed, c, of 49.4 m s−1 (48.6 m s−1). The wave parameters are listed in Table 2. Although these wave structures in each airglow image were inconspicuous compared to the smaller-scale waves, their spatial and temporal scales made them suitable for comparison with the radar and lidar measurements.
Table 2. Wave Parameters Estimated From Airglow Keograms Observed on the Night of 2 October 2008
3.2. Lidar Temperature
Figure 3 (left) shows the contour plot of the MLT temperature obtained by the sodium lidar measurements at Uji for 1000–2000 UT (1900–2900 LT) on the night of 2 October 2008. To investigate the wave structure detected in the airglow keograms, the temperature profiles were calculated by compromising the height resolution (running smoothed over 4 km) in order to increase the temporal resolution (15 min). The errors in the plotted temperature were less than 10 K for the entire plotting range and less than a few Kelvin at the airglow heights (94 and 86 km). Throughout the plotting interval, the ∼1 h period was found to superpose on the downward large-scale structure with a period of greater than 10 h, which may be tide or inertia gravity waves, often resulting in a significant temperature increase of ∼60 K. Figure 3 (right) shows the power spectral densities of the temperature variations at the airglow heights (94 and 86 km), in which the spectra were averaged over a height of ±3 km. The peaks at 54 min at 94 km (Figure 3, top right) and 71 min at 86 km (Figure 3, bottom right), indicated by arrows, are similar to the results obtained from airglow intensities (∼60 min). Note that the power spectral densities show strong oscillation at ∼2 h. It seems that they can also be recognized in the airglow keograms (Figure 2). However, in this paper, we would like to focus on the waves with a ∼60 min wave period, because their airglow signatures are clear compared to the ∼2 h waves in the airglow keograms and easier to make investigations of phases relations (discussed in the next section).
3.3. Meteor Winds by the MU Radar
 Meteor radars generally derive horizontal winds from meteor echoes in the horizontal extent within a radius of ∼150 km. A set of horizontal winds (zonal and meridional directions) is calculated asymptotically by a radial wind velocity of meteor echoes by assuming spatial and temporal homogeneity to a certain extent. By this conventional method, therefore, it is nearly impossible to detect wind variations induced by the waves considered in this study, which have such small horizontal scales (∼170 km).
 Here, we attempted to observe the horizontal wind perturbations along the wave propagation direction by using the radial winds in the area, as shown in Figure 4. The shaded area has a radial range of 80 ± 45 km and an azimuthal range of 320° ± 20°; the azimuthal center corresponds to the propagation direction of the gravity wave observed in the airglow keograms (∼320°). First, the radial wind of each meteor echo was projected onto a horizontal plane by assuming that its vertical component is sufficiently smaller than its horizontal component. Then, the winds were averaged spatially over the entire shaded area with the largest weight at the center. Next, the horizontal winds were weighted-averaged vertically [±4 km, full width at half maximum (FWHM) ∼ 5 km] and temporally (±20 min, at 1 min intervals). The dots in Figure 4 indicate the observed meteor positions in the 70–120 km height region for 1000–2000 UT (1900–2900 LT) on 2 October 2008. Approximately 1000 meteors were detected in the shaded area and used for the calculation of the horizontal winds. The numbers of the meteor echoes were ∼40–60 per 30 min, depending on the time of day, and were likely to increase with time (more frequent in the morning). Such a tendency of the radar echo rate, where the echo number increases toward the morning hours and decreases toward the afternoon hours, is regarded as typical diurnal variation [Nakamura et al., 1997]. Although the echo heights in the area scattered in the 70–110 km range, the mean echo height of 91.4 km is similar to that obtained from the echoes of all arrival directions (90.4 km) and previous meteor mode observations by Nakamura et al.  (89.5 km).
Figure 5 (left) shows the contour plot of the calculated horizontal wind along the azimuthal angle of the wave propagation direction. The positive and negative values correspond to the horizontal winds toward 320° (approximately northwest) and 140° (southeast), respectively. Although the accuracy in estimating the horizontal winds varies with the number of meteor echoes, and hence the UT and height, the standard deviations were fixed as ∼10 m s−1 at 94 km and ∼8 m s−1 at 86 km in the plotted interval. Periodic patterns on a large structure with a downward progression can be observed again in the horizontal wind plots. The power spectral densities of the wind at heights of 94 km and 86 km, in which the spectra were averaged over ±3 km, have clear peaks at 60 min (Figure 5, right); this wave period is also quite similar to that of the wave identified in the keograms of the airglow images (∼60 min). Note that the spectra also have oscillations with a period of ∼2 h, which is similar to that recognized in Figure 3.
 Simultaneous observations using the airglow imagers, MU radar, and sodium lidar on 2 October 2008 showed that the wave structures in airglow intensities, horizontal winds, and temperature have a similar period of ∼60 min. In this section, we discuss the details of the relationship among the wave signatures.
4.1. Phase Relations
 First, we discuss the phase relations between the temperature and horizontal wind and airglow intensity perturbations. One can assume that airglow intensity variations represent the changes in airglow layer heights induced by waves. Higher (lower) airglow intensities correspond to lower (higher) layer height because the airglow intensity increases for lower layer height, where the atmospheric density is higher. At the same time, the temperature of the regions below the mesopause decreases with height. Cho and Shepherd , who carried out spectral airglow temperature imager (SATI) observations in Resolute Bay, Canada, showed such a positive correlation between the airglow temperatures and emission intensities induced by wave perturbations.
Figure 6 shows the phase relations between the temperature and the 557.7 nm (top) and OH (bottom) intensities obtained by the ANDON imager over the lidar station. The airglow intensities were normalized by the average of the entire image counts at each snapshot and smoothed over 5 min intervals. Owing to the contamination by the northeastward propagating wavefront structure that appeared at ∼1600 UT (Figure 2), the airglow intensities after 1530 UT were omitted from the plots. Both the temperature and the airglow variations shown in this figure were applied to a bandpass filter having a bandwidth of 40–80 min. Although the 557.7 nm (OH) intensity variations slightly lag (lead) the temperature variations, the relations at both airglow heights indicate that a temperature increase (decrease) coincides with airglow enhancement (depletion). These relations are consistent with the previous observations and models based on the vertical motions of airglow layers associated with wave perturbations [Cho and Shepherd, 2006]. Cross-correlation analysis revealed that the time lag between the temperature and airglow intensity perturbations was calculated to be 0 min at both airglow heights. Note that the temporal resolution of the temperature measurements were 15 min while the airglow intensities were 5 min running smoothed; thus, the time lag of 0 min implies that the lag between the airglow intensities and temperature variations should be at least less than 15 min. Similar relations were indicated from the airglow measurements of OMTI at Shigaraki; that is, the temperature and airglow intensities varied in phase (not shown).
 On the other hand, the linear theory of gravity waves gives the phase relations between the perturbations of the horizontal wind along a wave vector, k, and that of the temperature as
where u′ are the perturbations of the k-ward horizontal wind, i is the imaginary unit, g (= 9.5 m s−2) is the acceleration of gravity, N is the Brunt-Väisälä frequency, and T′/T is the temperature perturbation. This equation indicates that the phase of the k-ward horizontal wind perturbations lag that of the temperature (and that of the airglow intensity) by 90°.
Figure 7 shows the phase relations between the 40–80 min band-passed components of the k-ward horizontal wind and the airglow intensities in the same way as shown in Figure 6. The time lags between them were calculated to be 15 min at 557.7 nm height and 10 min at OH height; for the wave with a period of 60 min, these time lags correspond to phase differences of 90° and 60°, respectively. The time lags obtained from OMTI were 10 min (phase difference 60°) for the 557.7 nm emission and 5 min (phase difference 30°) for the OH emission.
 Although the time lag between the k-ward horizontal wind and the airglow intensities was somewhat small, the observed phase relations among the airglow, horizontal wind, and temperature perturbations were qualitatively consistent with theoretical relations. Hence, we concluded that the gravity wave structures observed by the airglow imagers, lidar, and radar were identical.
4.2. Phase Speed Estimated From Meteor Winds
 Here, we attempted to estimate the phase speed of the gravity wave from meteor wind measurements by using the method described by Yamamoto et al. . Yamamoto et al.  demonstrated that the eastward phase speed of gravity waves can be determined from the observations recorded by a meteor radar pointing east. They divided the observation range of the radar into five subareas according to the horizontal distances from the radar and estimated the phase speeds from the phase differences of the wind variations observed in the subareas. They used a band-pass filter having a range of 2–12 h for the estimation and obtained that the observed waves predominantly had a wave period ranging from 3.4 to 4.8 h.
Figure 8 shows the summary of the phase speed estimation for the observed wave by adopting a method similar to that described by Yamamoto et al. . We divided the area shown in Figure 4 into three subareas (A, B, and C), as shown in Figure 8c. Each subarea has a width of 30 km in the radial direction and that of 40° in the azimuthal direction. Figure 8a shows the horizontal wind along the wave propagation direction obtained for each subarea. The winds were weighted-averaged over a height of 90 ± 10 km (FWHM ∼ 13 km) because the number of meteor echoes was small in each subarea.
Figure 8b shows the cross-correlation functions for the horizontal winds of Figure 8a after 40–80 min band-pass filtering. The horizontal axis represents the time lag between the winds in each subarea and subarea B. In Figure 8d, the least squares fitting line is plotted to examine the relation between the time lag at maximum correlation and the horizontal distance. This linear relation gives a phase speed of 45.5 m s−1, which agrees quite well with that derived from airglow measurements (∼50 m s−1).
4.3. Momentum Flux Estimations
 Finally, we estimated the vertical flux of the horizontal momentum of the observed gravity wave. The momentum flux per unit mass is defined as the covariance of the horizontal and vertical wind perturbations, denoted as 〈u′w′〉, where w′ is the vertical wind perturbation and the brackets represent a spatiotemporal average. Here, u′ is obtained from the radar winds. Although w′ cannot be measured directly by the observational setup used in this study, it can be estimated by using T′/T [Sato and Dunkerton, 1997; Vincent and Alexander, 2000]. The polarization relation between w′ and T′/T is given as
where (= 2π∣c − u∣/λh) is the intrinsic frequency; can be calculated from the radar winds and using the wave parameters obtained from the airglow observations (listed in Table 1). The value of N is obtained from the lidar temperature measurements as N2 = g(Γd − Γ)/T, where Γd (= 9.46 K m−1) is the adiabatic lapse rate and Γ ( = −∂/∂z) is the local temperature gradient [Nielsen et al., 2006]; iT′/T is derived by the Hilbert transform of T′/T and produced by a 90° phase shift in T′/T [Vincent and Alexander, 2000]. In the work by Vincent and Alexander , wherein the estimations of the gravity wave momentum flux in the stratosphere were made from the radiosonde observations at Cocos Islands (12°S, 97°E), w′ was obtained from the Hilbert transform of the temperature perturbations of the height profiles and the intrinsic frequencies inferred from the hodograph analysis (i.e., the ratio of the major to minor axes of the ellipse of the hodograph corresponds to /f, where f is the Coriolis parameter). In the present study, we used the time series of the temperature perturbations and intrinsic frequency variations to estimate w′ from the simultaneous lidar temperature and radar wind measurements.
Figure 9 (Figure 10) shows the estimation of the momentum flux at 94 km (86 km) in the 1200–1600 UT interval, in which the gravity wave was identified; the 40–80 min band-passed components of the horizontal wind and temperature (Figures 9a and 10a, Figures 9b and 10b, respectively); the intrinsic frequency of the wave (Figures 9c and 10c); the Brunt-Väisälä frequency (Figures 9d and 10d); the estimated vertical wind perturbation from equation (2) (Figures 9e and 10e); and the product of the horizontal and vertical wind perturbations (Figures 9f and 10f). The horizontal winds (Figures 9a and 10a) were calculated in the region of 30 ± 30 km in the radial direction and 320° ± 20° in the azimuthal direction to obtain the variations coincident with the lidar observations; the wavefront elongating in the 50°–230° direction (perpendicular to the k vector pointing 320°) would be located at a distance of ∼30 km from the MU radar along the k vector at the instance when the wavefront passes over the lidar station. The horizontal dashed lines in Figures 9a, 9b, 9e, 9f, 10a, 10b, 10e, and 10f indicate the zero-value lines, and the horizontal dotted lines in Figures 9c and 10c and Figures 9d and 10d indicate, for reference, the intrinsic frequency for the 1h wave period and a typical value of the Brunt-Väisälä frequency of 0.02 s−1, respectively. The momentum fluxes, which were obtained by averaging u′w′ over the plotting interval, were 0.8 m2 s−2 at 94 km and 1.5 m2 s−2 at 86 km.
 Assuming that atmospheric density, ρ, declines with height, z, as e−z/H (where H is the density scale height), the ratio of the magnitude of the momentum flux per unit volume, ρ〈u′w′〉, at 86 km to that at 94 km would be 8:1 (z = 8 km and H = 6 km). The difference in the momentum flux at the two airglow heights (the momentum flux decreases with height) implies a deposition of momentum due to the dissipative gravity wave propagating upward. On the basis of the variances of the radial winds in the mesosphere observed by the MU radar, Tsuda et al.  statistically showed that, in summer, the value of ρ〈u′w′〉 decreased from 1.5 × 10−4 to 0.5 × 10−4 kg m−1 s−2 with an increase in height from 68 to 78 km; however, they measured wave components in a widely spread frequency spectra (wave periods from 5 min to 2 h).
 In the situation that the gravity wave we observed really dissipated significantly in the 8 km height range, a substantial acceleration of the horizontal wind along the wave propagation direction would be induced there. The acceleration associated with momentum flux divergence is expressed as ρ∂u/∂t = −∂(ρ〈u′w′〉)/∂z. With the estimated momentum fluxes at 86 and 94 km, the acceleration was deduced to be 0.8 m s−1 h−1 at the 94 km height. As shown in Figure 5, the k-ward wind (positive contours) in the vicinity of the airglow heights appears to increase in the event interval of 1200–1600 UT; however, the downward large-scale structure also strengthened the k-ward wind simultaneously and, thus, it is difficult to determine the actual contribution of the gravity wave (0.8 m s−1 h−1 acceleration) to the wind field in this event.
4.4. Comparison With the Momentum Fluxes Estimated From Airglow Imaging
where m and k (= 2π/λh) are the vertical and horizontal wave numbers, I′/I is the relative airglow intensity perturbation, and CF is the cancellation factor introduced by Swenson and Liu . CF is a quantitative factor depending on vertical wavelength, λz, and represents the effect that the wave amplitude in the airglow image is reduced due to vertical cancellation through the airglow layer. Recently, Vargas et al.  newly modeled values of CF for emissions of 557.7 nm as well as O2 and OH airglows. Using the linear dispersion relation for a gravity wave [Hines, 1960], m and λz can be calculated as
 The average λz during the period 1200–1600 UT was ∼10 and ∼18 km for the 557.7 nm (94 km) and OH (86 km) emissions, respectively. Consequently, we obtained CF ∼ 1.3 (2.1) for the 557.7 nm (OH) emission from the model by Vargas et al. . We would like to note that the phase difference between the 557.7 nm and OH airglow intensity variations in Figure 6 show the signature of the wave with a vertical wavelength of ∼15 km. This wavelength is consistent with the value calculated earlier from the dispersion relation. However, the phase difference of two airglow emissions in Figure 7 is not clear to determine the vertical wavelength. The temperature and wind profiles also provide a similar vertical wavelength of the waves with a ∼60 min period, which is roughly ∼20 km, although it should be noticed that these profiles were smoothed vertically over 4 and 8 km, respectively.
 For the estimation of I′/I in equation (3), contaminations by background emissions, such as city-light interference and atmospheric continuum emission, need to be removed from the airglow images to obtain the actual airglow emissions. Thus, for the 557.7 nm emissions, we used absolute intensity images [e.g., Shiokawa et al., 2000; Kubota et al., 2001], obtained by using the simultaneous images of the 572.5 nm background emission. However, the ANDON imager had not yet been sufficiently calibrated to obtain absolute intensity images; hence, we used only the OMTI images for this analysis. For the OH images, we used broad-passband filters (Table 1); therefore, it was difficult to calculate the absolute intensity of the OH emission. According to a recent study by Suzuki et al. [2007b], in which the airglow imager and a collocated SATI at Shigaraki were used, the OH images had contamination of 30% caused by background emissions. We incorporated the results of their observational study and used the OH images of OMTI attenuated to a pixel intensity of 30% as the actual OH airglow intensity.
Figure 11 is an example of the image used for the estimation of I′/I. In Figure 11, the 557.7 nm airglow image obtained by OMTI is shown as a geographical image of 512 × 512 km in the absolute intensity of Rayleigh units. The area bounded by the white box is used to calculate I′/I. The box is oriented parallel (X axis, width L = λh) and perpendicular (Y axis, λh/2) to the wave propagation direction (k vector), and it is shifted slightly from the center of the image to attenuate contamination due to the Milky Way for the period of interest (1200–1600 UT).
 To obtain I′/I, we first calculated wave number 1 components of the Fourier series along the k vector as
where Ia(x) are the pixel intensities along the k vector averaged along the shorter side of the box (Y direction); that is, Ia(x) = .
 Time series of the 40–80 min band-passed components of A1 and B1 are shown by the solid and dashed curves, respectively, in Figure 12a. Figure 12b shows the calculated airglow intensity perturbation, /I0(t), where I0(t) is the 1 h running average of the airglow intensity averaged within the box shown in Figure 11. By averaging the intensity perturbation over the period 1200–1600 UT, I′/I in the 557.7 nm emission was estimated to be 2.0%. With the CF derived by Vargas et al. , a momentum flux of 1.0 m2 s−2 is obtained from equation (3). In a similar manner, a momentum flux of 1.3 m2 s−2 is estimated from the OH emission (I′/I = 2.3%) for the same interval. These estimates were slightly smaller than those of previous studies with OH airglow imaging of small-scale (λh < 100 km) gravity waves, wherein the momentum fluxes of 4.9 m2 s−2 at Shigaraki, Japan [Suzuki et al., 2007b], and 2.6 m2 s−2 at Kototabang, Indonesia [Suzuki et al., 2009b], have been obtained.
 These momentum fluxes derived using the airglow intensity perturbations (557.7 nm at 94 km, 1.0 m2 s−2; OH at 86 km, 1.3 m2 s−2) were in very good agreement with those derived from the wind and temperature measurements described in section 4.3 (94 km, 0.8 m2 s−2; 86 km, 1.5 m2 s−2). These results suggest again that the observed variations in airglow intensity, horizontal wind, and temperature had identical gravity wave signatures.
5. Summary and Conclusions
 Simultaneous measurements of mesospheric gravity waves using two all-sky imagers (ANDON and OMTI), the MU radar, and a sodium lidar were carried out during the ANDON campaign. On the basis of the comprehensive data set obtained on 2 October 2008, we have shown, for the first time, the signatures in airglow intensity, horizontal wind, and temperature perturbations, which were probably induced by the same gravity wave. The observational findings of the present study are summarized as follows:
 1. The airglow signatures of the gravity wave in both the 557.7 nm (height 94 km) and OH (height 86 km) emissions had a horizontal wavelength of ∼170 km and wave period of ∼1 h, propagating northwestward at ∼50 m s−1.
 2. The 15 min resolution of the lidar temperature at the two airglow heights showed an oscillation with a period similar to that by airglow.
 3. The k-ward components of the horizontal winds (i.e., winds in the direction of wave propagation, as identified in airglow keograms) were calculated from the radial winds from the meteors in the area, which has a spatial size to enable detection of the wave structure. The k-ward winds also had a quite similar wave period of 60 min at both the airglow heights.
 4. The observed phase relations between the temperature and horizontal wind and airglow perturbations were consistent with theoretical relations; the airglow intensity enhancement (depletion) coincided with the high-temperature (low-temperature) region and was reasonably ahead of the k-ward (anti-k-ward) wind phase.
 5. The phase speed of the gravity wave in the k-ward wind perturbation estimated from the MU radar observations was comparable to the results of those obtained from the airglow data.
 6. The momentum fluxes calculated from the fluctuations in the observed horizontal and vertical winds (the latter being deduced from lidar temperature measurements) were 0.8 and 1.5 m2 s−2 at 94 and 86 km, respectively. These values were in good agreement with those estimated from the technique using the airglow intensity perturbations and the cancellation factor model (1.0 and 1.3 m2 s−2).
 Further comprehensive measurements using the MU radar, lidar, and airglow imager could help to clarify the contributions of gravity waves to MLT dynamics but also the relation of the horizontal extent of instability regions in wind and temperature fields to optical signatures (ripples).
 We gratefully acknowledge S. Takahashi of the Dynic Astropark Observatory for his help in organizing our use of the optical site at Taga during the ANDON campaign. The MU radar belongs to and is operated by the Research Institute for Sustainable Humanosphere, Kyoto University. S.S. is supported as a research fellow of the Japan Society for the Promotion of Science (JSPS). This work was supported by grant-in-aid for JSPS fellows (21-1828) and scientific research (18403011, 20244080, 20403011, 21340141) of the Ministry of Education, Culture, Sports, Science and Technology of Japan. This work was carried out by the joint research program of the Solar-Terrestrial Environment Laboratory, Nagoya University.