Using MF radar data obtained at Tromsø (69.6°N, 19.2°E) for ∼37 months between 1 November 1998 and 8 December 2001, we have examined characteristics of the quasi 2-day wave (Q2DW) in the polar mesosphere in the height range from 70 to 91 km. The activity of the Q2DW is higher in winter months (November–February) than in summer months (May–August) over this height region. The maximum values of the amplitude are ∼25 m s−1 in winter and ∼15 m s−1 in summer. Between 70 and 82 km, the amplitude appears to maximize near winter solstice over the 3 years. The average ratio of meridional to zonal amplitudes is ∼1.1–1.2 over the height region. Thus, there is no significant preference towards either components. The variations of the periods of maximum amplitude are also examined, and periods with 45.2 and 54.9 hours occur more frequently than those with 48.0 and 51.2 hours. However, no clear seasonal trend of the variation of the period is found. In addition, the amplitude is modulated at 4–10 day rate. With simultaneous observational data from the MF radar and the EISCAT UHF radar colocated in Tromsø, we have examined whether or not the Q2DW was able to penetrate to the lower thermosphere for the period of 1–9 July 1999. It is found that the amplitude of the Q2DW with period of 51.2 hours maximized at 95 km height with values of ∼25 m s−1 in both meridional and zonal components. The Q2DW was attenuated above 95 km, but it appears to survive up to 108 km height in the meridional component. Between 85 and 95 km for the meridional component during this 8-day interval, the Q2DW and semidiurnal tide were the strongest among the periodic components.
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 Various processes provide/transfer energy and momentum to the atmosphere in the polar lower thermosphere. It is believed that upward propagating waves significantly affect the atmospheric dynamics there. During geomagnetically active periods, particle precipitation and convective electric fields have significant impact on the lower thermosphere at high latitudes [e.g., Fesen, 1997; Thayer, 1998; Fujii et al., 1998]. In order to understand more deeply how the lower thermosphere responds to geomagnetic disturbances, it is of vital importance to understand the lower thermospheric dynamics at high latitudes during geomagnetically quiet times. In the last decade, understanding of the lower thermosphere has progressed significantly, based on Incoherent Scatter (IS) radar data [Nozawa and Brekke, 1999, and references therein] and satellite data [McLandress et al., 1996a, 1996b] in terms of seasonal variation and solar activity dependencies. Among atmospheric waves (gravity, tidal, and planetary waves) generally propagating from the lower atmosphere, the role of the planetary wave in the lower thermosphere is still very unclear.
 Numerous studies of the mesospheric quasi 16-day wave [e.g., Luo et al., 2000; Forbes et al., 1995] and 2-day wave [e.g., Palo and Avery, 1996] have been conducted in the last two decades. With Saskatoon (52°N, 107°W) MF radar data obtained during the period from 1980 to 1996, Luo et al.  showed that 16-day waves occur in the mesosphere mostly in winter with a maximum at ∼60–65 km height, and cover a large range of altitudes (up to 100 km); in summer, however, the 16-day wave is much weaker and confined to ∼85 km and above. Forbes et al.  confirmed that the 16-day wave observed in the mesosphere is a result of direct upward penetration of the disturbance. In addition, they proposed that there is a ducting channel from the winter hemisphere to the summer hemisphere, which enables Northern Hemisphere observers to find the 16-day wave in summer.
 The preponderance of observational evidence of a recurrent global-scale 2-day oscillation in the middle atmosphere led Salby  to suggest that the disturbance is a manifestation of the third Rossby-gravity normal mode of a windless, isothermal atmosphere; the so-called (3,0) mode in the nomenclature of Longuet-Higgins  [Hagan et al., 1993]. This idea is consistent with numerous observational results at middle/low latitudes. However, Meek et al.  examined the Northern Hemisphere zonal wave number for a striking quasi 2-day wave (Q2DW) “event” or “burst” observed near 90 km altitude in the summer of 1992 seen in data from nine radar sites at latitudes of ∼20°–55°N and concluded that the wave number of that event was 4. They also analyzed a similar event in 1991 for which fewer sites were available and the choice of the wave number between s = 3 and 4 was not clear.
 Another cause of the 2-day wave observed in summer was proposed by Plumb  and Pfister . Based on a one-dimensional stability analysis, Plumb  found that sufficient eastward shear in a solsitital mesospheric westward jet could give rise to instabilities. Pfister  indicated that waves with wave numbers 2–4 and periods near 2 days are strongly trapped at middle and high latitudes (40°–60° latitude) [see also Lieberman, 1999]. For example, Fritts et al.  analyzed wind data observed by MF and meteor radars as well as temperature and wind data from High Resolution Doppler Imager instrument aboard the Upper Atmosphere Research Satellite (UARS). They found apparent wave–mean flow interactions, and then suggested that the 2-day wave could be a transient response to baroclinic instability of the summer hemisphere mesospheric jet. However, their observational results also appear consistent with the study of Salby . Salby and Callaghan  explored the relationship between the Rossby-gravity mode and baroclinic instability of summer easterlies, and suggested that under solstitial conditions the Q2DW receives auxiliary forcing from instability in the summer mesosphere. The forcing alters the mode's growth rate, but it has little effect on its eigenperiod and structure. In this context the Q2DWs observed in the mesosphere can have a variety of sources.
Forbes et al.  examined the relationship between quasi 2-day oscillations in the neutral wind near 90 km altitude, and in the critical plasma frequency (foF2) of the ionospheric F region for the June–September 1992 period. They concluded that there exist ∼0.5–1.0 MHz quasi 2-day oscillations in foF2, which can be credibly connected with quasi 2-day oscillations in mesosphere/lower thermosphere winds, but that the mechanism responsible for the ionospheric response to the quasi 2-day oscillation at lower altitudes remained unknown.
 Early observational reports suggested variability in the magnitude or presence of low and mid latitude Q2DWs with peak occurrences or wave amplitudes during middle to late summer [e.g., Hagan et al., 1993]. In general, the meridional component is larger (by a factor of 2) than the zonal component, and the wave seems to be more prevalent throughout the year at low latitudes. The amplitudes reported for the 2-day wave vary from 0 to 25 m s−1 in the Northern Hemisphere and from 0 to 65 m s−1 in the Southern Hemisphere [e.g., Clark et al., 1994]. The periods reported for the Q2DW vary from 46 to 53 hours. Clark et al.  showed that the 2-day wave amplitude is modulated at a 4–10 day rate, and during these times the wave period is very near 48 hours.
 Similar to the short-time variability of the atmospheric tides in the middle atmosphere [e.g., Teitelbaum and Vial, 1991], the lower thermospheric tide is also characterized by day-to-day variability [e.g., Vial, 1993]. The effect of the planetary wave like wave–wave coupling process would be a cause of the day-to-day variability, but it is not yet understood fully. For example, by using data obtained with the European Incoherent Scatter (EISCAT) [Folkestad et al., 1983; Rishbeth and Williams, 1985] UHF radar for the E region radar and rocket instability study (ERRRIS) campaign, Huuskonen et al.  examined the variability of semidiurnal tides in the lower thermosphere (100–140 km) and concluded that the 2-day wave played a role in modulating the amplitude of semidiurnal tide through the process of non linear wave–wave coupling in the mesosphere. Also, Beard et al.  showed evidence of a nonlinear interaction between the semidiurnal tide and planetary waves of 1.8-day period at the meteor heights (about 85–95 km) based on the Sheffield (53.27°N, 1.35°W) meteor radar data. In this context, for understanding the lower thermospheric dynamics more fully, it is important to examine planetary wave behavior not only in the lower thermosphere but also in the mesosphere.
 It should be pointed out that although numerous reports have been published for the Q2DW observed at middle/low latitudes for three decades, it is very rare for the Q2DW to be observed at high latitudes. In this study, we have examined characteristics of the Q2DW based on MF radar data obtained at Tromsø (69.6°N, 19.2°E). Data analysis is described in the next section, and characteristics of the Q2DW observed at Tromsø are presented in section 3. By using the simultaneous observational data with the EISCAT UHF radar and the Tromsø MF radar, we have examined the importance of the Q2DW in the height range from 70 to 117 km, and present the results in section 4. Discussion is given in section 5, and this work ends with a summary in section 6.
2. Data Analysis
 We have analyzed wind data obtained from 1 November 1998 to 8 December 2001 with the Tromsø MF radar [Hall, 2001] operated under collaboration of the Universities of Saskatchewan, Tromsø and Nagoya. Nozawa et al.  compared wind data obtained with the Tromsø MF radar and the EISCAT UHF radar (they are located at the same site) on a case and statistical basis. They concluded that the wind data obtained above 91 km from the MF radar for summer should be treated with special care: these data can be affected badly due to group retardation. In particular, the group retardation of MF radio waves was found to be significant above 91 km, meaning the differences between virtual and true heights are larger with increasing height. Therefore, we only use the MF wind data obtained between 70 and 91 km in this study. Commonly quoted biases due to receiver saturation do not apply significant to the Tromsø MF radar because its receivers are able to switch gains fast enough that they can be controlled separately for each height gate.
 The time resolution of the MF radar was 5 min until 15 February 1999, 2 min between 16 February 1999 and 20 October 2000, and has been 5 min since then. The Tromsø MF radar receives signals (partially) reflected in the mesosphere and lower thermosphere with thirty-two 3 km gates starting at 40 km, and its analysis is based on the Saskatoon Full Correlation Analysis (FCA) of Spaced Antenna (SA) data [Briggs, 1984; Meek, 1980]. Generally, uncertainties of wind velocities from the MF radar using the FCA method due to the variance associated with gravity waves are estimated to be less than ∼10 m s−1 [see Meek and Manson, 2001]. However, a comprehensive comparison of MF radar, VHF radar and rocket data [Manson et al., 1992] from the Tromsø area revealed a speed bias (reduction) by a factor of ∼1.5 at heights of 80–95 km. Recent adjustments to the MF radar analysis have not led to any increases in the MF radar speeds (Manson and Meek, private communication, 2002).
 We chose a time window of length 8 days (starting at 1200 UT) for deriving Q2DWs whose periods are assumed to be between 45.2 and 54.9 hours in this study, and determine the amplitude and phase every 2 days (thus, the number of intervals is 563 in total). The date for the Q2DW data is the date of the center day of the 8-day window. This window length is appropriate as the amplitudes vary with timescales of ∼4–10 days [e.g., Clark et al., 1994]. To derive wave components, a Lomb-Scargle method [Hocke, 1998] is applied with an over sampling factor of 4.
 In order to investigate if a derived signal is significant, we compare the derived normalized amplitude, where the total variance of the data is chosen as a normalization factor, with significance level. The significance level (s) for a specific value of probability p is obtained from:
where N is the number of data points in the time series [Beard et al., 1999; Horne and Baliunas, 1986]. Thus, significance levels with 99% and 50% are calculated from (1) with p = 0.01 and 0.5, respectively. Only data which exceed a 99% significance level are used in this study except for the event study for the period of 1–9 July 1999. As mentioned by Beard et al. , readers should keep in mind that the significance levels when large deterministic signals are present are at best, rough, overly pessimistic guidelines.
 When we use an 8-day window length with over sampling factor of 4 in the Lomb-Scargle method, the frequency resolution is 2.27 × 10−6 Hz. In contrast, the uncertainty (δω) in the frequency can be given by the following formula [Horne and Baliunas, 1986]:
where σN is a total variance, N is the number of data points, T is the total length of the data (=8 days), and A is the amplitude of the signal. Table 1 summarizes averaged uncertainty in the frequency over the 37 months, its standard deviation, and the ratio of δω to the frequency resolution for meridional and zonal components from 70 to 91 km. The amplitude value is assumed to be 5 m s−1. Although as pointed out by Horne and Baliunas  multiple signals can cause further shifts in detected frequencies, it appears from Table 1 that the frequency resolution is significantly larger than the uncertainty in the frequency for components with amplitude values greater than 5 m s−1.
Table 1. Mean Uncertainty in the Frequency, its Standard Deviation (σ), and the Mean Ratio to the Frequency Resolutiona
Uncertainty (10−6 Hz)
σ (10−6 Hz)
Uncertainty (10−6 Hz)
σ (10−6 Hz)
The frequency resolution is 2.27 × 10−6 Hz.
 Finally, maximum positive (i.e., northward and eastward directions) amplitude will occur at a time (tm) given by:
where Tp is the period of the Q2DW in hours, ϕ is phase value in degrees. A reference date and time of the tm is 0000 UT on the first day of an 8-day window. Local time of Tromsø is 1 hour ahead of UT. Note that the time of maximum positive amplitude (which is a function of both ϕ and Tp) has the opposite sign to the phase. Thus an decreasing phase would correspond to an increasing time of maximum.
3. The Q2DW at Tromsø
Figures 1a and 1b show seasonal variations of meridional and zonal amplitudes, respectively, of the Q2DW over ∼37 months occurring between 5 November 1998 and 3 December 2001 in the height range between 70 and 91 km. The largest amplitude associated with periods of 45.2, 48.0, 51.2, and 54.9 hours is taken as the amplitude of the Q2DW, and illustrated in Figures 1a and 1b. Amplitude values corresponding to significance levels lower than 99% significance level are removed. From Figure 1a, it can be seen that below 82 km the Q2DW amplitude of the meridional component in winter months (November–February) is significantly stronger than that in summer months (May–June) when they are usually below the 99% significance level or less than 5 m s−1. The amplitude appears to maximize near winter solstice between 70 and 82 km every year. A drastic seasonal change occurs at equinox suggesting that the Q2DW activity is divided into two seasons: stronger (∼10 m s−1 on average) between November and February and either weak or nonexistent between May and August. This seasonal trend is also found above 82 km, but the amplitude in summer months increases with increasing altitude. Between 82 and 91 km the Q2DW can be observed over a year with amplitude from ∼4 to ∼25 m s−1, but it rarely exceeds a value of 20 m s−1.
Figure 2a illustrates mean values of the meridional components of the Q2DW amplitudes for winter and summer periods from 70 to 91 km. Owing to a system problem, the data acquisition rate was lower in summer 2001 than at other times, particularly for the lower heights. Thus, data between 70 and 76 km during that time were omitted. There is a slight tendency for the amplitudes in November 1999 to February 2000 to be weaker by ∼10% than during other winter times (except at 79 km). The difference in seasons is more prominent: the amplitude in winter is greater than that in summer over the height region. Winter amplitudes are greater by factor of 3–4 than those in summer at 70 km, and the ratio of the amplitudes is ∼1.4 at 91 km. The ratio tends to decrease with increasing height. The winter amplitude is approximately constant with height and is about 8–12 m s−1 over the height region. In contrast, the amplitude in summer tends to increase with increasing height from ∼3 m s−1 at 70 km to 6–8 m s−1 at 91 km.
 In addition to seasonal variations, short-term variation of the amplitude is also found: the amplitudes do not exhibit smooth variations with time, and burst features can be found over the height region and seasons. For example, an event lasting for a month from the mid-December 1999 to the mid-January 2000 is found over the height region, and its velocity values vary from ∼5 to ∼20 m s−1 at 82 km. Usually, the amplitude appears to be modulated at a 4–10 day rate over the height region, and the modulations appear to occur irregularly.
 Similar features in terms of seasonal variation are also found for the zonal component shown in Figure 1b. At the upper three heights between 85 and 91 km the Q2DW can be found over the whole year. In addition to the seasonal change, the amplitudes of the zonal components appear to vary with time at periods of 4–10 days. It should be noted that an enhancement of the zonal component does not always synchronize with that of the meridional component. At the event for middle of December 1999 to middle of January 2000, no such enhancement can be seen in the zonal component at the upper heights. Figure 2b shows mean values of the zonal component of the Q2DW amplitudes. Similar to the meridional component, the seasonal difference is more prominent than annual difference, but the zonal amplitude in the interval between November 1999 and February 2000 is smaller by ∼20% over the height region than those in other winter times.
 The ratio of meridional to zonal amplitude is examined over the 37 months from 5 November 1999 to 3 December 2001 in the height range between 70 and 91 km. Only data whose values are greater than 5 m s−1 are used. Figure 3 is a histogram of the ratio of meridional to zonal amplitudes of the Q2DW for 3 heights at 70, 79, and 88 km. Filled areas denote an enhanced case where the amplitude values of either or both components exceed a value of 10 m s−1. The average ratio is in the range 1.1–1.2 between 70 and 91 km, and most events fall between 0.57 and its inverse, 1.75. Therefore one component is not stronger than the other. The ratio occasionally becomes greater than 3 or less than 0.33, and usually these events are found in the enhanced case. In the enhanced case, the distribution tends to broaden, indicating that (as noted above) the enhancements of the component amplitudes are not always synchronized with each other. When dividing data into winter and summer, no significant difference can be identified.
 When altitude profiles of the amplitude through the winter months are investigated, it is found that they are variable. Profile shapes can be divided into 3 groups: (1) the amplitude maximizes at around 82–85 km, (2) the amplitude has broad peaks at the middle heights, and (3) the amplitude decreases with increasing height. Altitude profiles where the amplitudes increase with increasing height (at and above 82 km) are also found, but such events occur less frequently in winter months than the other cases mentioned above. Figure 4 shows altitude profiles of the amplitude and corresponding phase for the meridional component with periods of 45.2, 48.0, 51.2, and 54.9 hours for four representative events in winter months. The shapes of amplitude profiles are variable and the altitude where the amplitude maximizes varies with time, but altitude profiles of the corresponding phases are relatively constant with height. This phase behavior is found in most cases. For summer months, in general the amplitude increases with increasing height or is relatively constant over the height range. In most cases, the phase is approximately constant with height or shows small variation, similar to the winter cases.
 Variations of periods of maximum amplitude of the Q2DW for all seasons are examined and the results are illustrated in Figure 5 for both the meridional and zonal components for 3 heights at 70, 79 and 88 km. Data whose amplitudes are greater than 5 m s−1 are used. It should be noted that in this analysis as shown in Figure 4 the peak period is not always prominent. For example, in the event for 29 November 1998 amplitude values at periods of 45.2, 48.0, 51.2, and 54.9 hours are close to each other. Therefore we use a term of “period of maximum amplitude of the Q2DW” rather than “period of the Q2DW.”
 From Figure 5, it can be seen that distributions are similar over the height region and events with periods of 45.2 and 54.9 hours are more prominent than those with 48.0 and 51.2 hours. Those variations in summer and winter are illustrated by open and solid circles, respectively. At and below 79 km in summer the Q2DW is rarely identified, and in winter months events with 45.2 and 54.9 are more prominent than the others. At and above 82 km, shapes in winter months are similar to those between 70 and 82 km, and no clear difference between the seasons is found.
4. Simultaneous Observations of EISCAT and MF Radars
 In contrast to the MF radar observations which, due to total reflection during summer daytime or particle precipitation events, are not considered reliable above 91–100 km [Nozawa et al., 2002], the IS radar can derive wind velocities in the lower thermosphere [e.g., Zhou et al., 1997]. Due to the high operational cost, it is not common for IS radars to make observations of the duration (4 days or longer) necessary for studies of planetary waves. Between 1 and 9 July 1999, the EISCAT UHF radar was operated in a Common Program two (CP-2) mode [Collis, 1995]. We will briefly describe how wind velocities were derived from ion velocity measurements, and then we will present the results from the simultaneous observations.
 In the CP-2 mode the line of sight of the antenna is pointed into four consecutive directions with a dwell time of ∼1 min in each, resulting in a full cycle time of the antenna of 6 min. The CP-2 mode can furnish ion velocity data simultaneously in E and F regions under assumptions of uniformity in space and in time for the duration of each cycle. Owing to the strong coupling between ions and neutrals in the lower thermosphere, one can derive the neutral wind velocity vector (u) using both measured ion velocity (v) in the E region and derived E field (E) from F region ion velocity measurement with the following equation [Rino et al., 1977]:
where B is the Earth's magnetic field, νin is the ion-neutral collision frequency, and Ωi is the ion gyrofrequency. We base our analysis on an International Geomagnetic Reference Field (IGRF) model [IAGA Division I Working Group 1, 1987] and a formula for the ion-neutral collision frequency introduced by Schunk and Walker . The model neutral atmosphere is given by MSIS86 model [Hedin, 1987].
 Although the system noise temperature was higher by a factor of ∼2 than that of usual case [Nozawa et al., 2002], this experiment provides us with a good opportunity to examine the penetration of the Q2DW into the lower thermosphere. It should be pointed out that the EISCAT UHF radar has been operated for ∼20 years, but this experiment is the only case where the EISCAT UHF radar was operated for 8 days consecutively. Figure 6 shows altitude profiles of Q2DW (51.2 hours) amplitudes in the upper two panels and corresponding phases in the lower two panels from 70 to 117 km. MF radar data are used up to 91 km, and at and above 95 km EISCAT radar data are taken following the work of Nozawa et al. . Larger filled diamonds show data values with greater than 99% significance levels, while smaller filled diamonds are for between 50% and 99% significance levels. Open smaller diamonds indicate values less than 50% significance level. Error bars are calculated from the work by Nozawa and Brekke  based on the propagation theory of error [see also Nozawa et al., 2002]. An error value of the neutral wind velocity derived with the EISCAT radar data is calculated from a standard deviation determined by the IS spectrum analysis. For the MF radar data, an error value at each point is assumed to be 10 m s−1 [see Meek and Manson, 2001]. Owing to the high time resolution (2 min) of MF radar data and good data coverage, the derived error bars are much smaller than those for the EISCAT data. By comparing amplitudes with periods of 45.2, 48.0, 51.2, and 54.9 hours over the height range, we found the component with period 51.2 hours to be the strongest, and so was used in the Figure 6 fits. It should be noted that the time of maximum positive amplitude has the opposite sign to the phase.
 The amplitude of the meridional component increases with increasing height from 82 km to 95 km, and maximizes at 95 km. Above 95 km, it tends to decrease with increasing height. Figure 6 suggests that the Q2DW can survive at heights up to 108 km with amplitudes greater than 10 m s−1, although amplitudes are less reliable (between 50 and 99% significance level) in this region. The corresponding time of maximum is almost constant with height between 82 and 95 km at ∼1000 LT on 1 July (and every 51.2 hours from that time: 0° in phase corresponds to 0100 LT on the first day of the 8-day window), suggesting a long vertical wave length (>150 km). On the other hand, for the zonal component, the amplitude also maximizes at 95 km, but this value is only above the 50% significance level. Above 95 km, the amplitude values are not reliable, since they are less than the 50% significance level. The corresponding phase is also almost constant with height between 82 and 91 km at about 0100 LT on 2 July (and every 51.2 hours from that time). In summary, both the meridional and zonal components have their maxima at 95 km and their phase profiles exhibit long vertical wavelengths. In addition a manifestation of the Q2DW's existence up to 108 km has been found.
 In order to examine what other spectral components are dominant in the height region between 82 and 108 km where the Q2DW appears to exist, Figure 7 shows spectra of normalized meridional and zonal amplitudes for 1–9 July 1999. In the figure, significance levels of 99% and 50% are shown with dotted and broken lines, respectively. The semidiurnal tide for both the meridional and zonal components has generally the largest amplitudes over the height region (except for the zonal component at 95 km). The diurnal tide is also significant at and above 105 km and at and below 85 km, and an 8-hour component is found at several heights in both the meridional and zonal components especially above 95 km. It should be noted that the Q2DW component has a comparable amplitude to that of the semidiurnal tide between 85 and 95 km in the meridional component. For the zonal component, the Q2DW is a relatively strong component at 85, 88, and 95 km.
5.1. Origin of the Q2DW Observed in the Polar Mesosphere
 The origin of the Q2DW observed in the mesosphere is still an open question even though numerous studies have been made at middle and low latitude stations over the last 3 decades. In section 3 we have shown that the altitude variation of the phase of the Q2DW observed at Tromsø is, in most cases, small over the 3 years. The altitude profile of the amplitude is variable in the winter, whereas in the summer months it is relatively stable and the amplitude tends to increase or remain constant (at small amplitude) with height. The averaged ratio of the meridional to zonal amplitude is ∼1.1–1.2 in both winter and summer months. Based on his simulation, Salby  showed this ratio is close to 1 at about 70° latitude. If the cause of the Q2DW is an instability at the mesospheric jet [Plumb, 1983], the phase is expected to change significantly with height. Therefore, these results suggest that in summer the Q2DW observed at Tromsø has features more consistent with the Rossby-gravity wave mode as suggested by Salby  than those due to an instability. In winter, the Q2DW appears to propagate from the lower atmosphere, and the phase profiles show longer vertical wavelength, suggesting the observed waves are again likely the Rossby-gravity wave mode. However, its amplitude–height profile is somewhat difficult to interpret. These profiles are probably caused by interaction of the mean wind and tidal waves, although such interactions might change the Q2DW phases if the interactions are strong. Global simulations with realistic background conditions are required to elucidate the observed results.
5.2. Comparison With Results From Midlatitude Stations
 At middle latitudes in the Northern Hemisphere, the activity of the Q2DW is largest in late summer [Clark et al., 1994] and this is explained by ducting from the southern winter hemisphere. Meridional amplitudes are larger by a factor of 1.5 than those of zonal components and the amplitudes are modulated at periods of 4–10 days [Clark et al., 1994]. When comparing the features of the Q2DW between our results and results from middle and low latitudes, some similarities (e.g., modulation of the amplitude) are found, but dissimilarities are also found regarding the Q2DW activity and its period. At Tromsø, which is located at a high latitude, the activity of the Q2DW is stronger in winter than in summer. This is much different from the results from middle and low latitude stations. This could be related to the background wind field in the mesosphere, where the zonal velocity is smaller at high latitudes than at middle latitudes. The vertical propagation of planetary waves through a background wind field was examined by Charney and Drazin  and Dickinson . They concluded that the vertical propagation of stationary planetary waves is only possible in eastward wind regimes when the eastward wind speed is below some upper limit (so-called Charney–Drazin critical speed: uCD). For traveling planetary waves, this idea can be extended if we simply replace “eastward wind” with “eastward wind with respect to the wave” [Forbes, 1995]. The phase speed of the Q2DW for the Rossby-gravity normal mode at 69.6°N is expected to be ∼−27 m s−1 (westward) [Forbes, 1995]. Therefore the vertical propagation is possible under conditions of mean wind speed between ∼−27 m s−1 and uCD. At Tromsø it was observed that the mean wind speed is ∼−40 m s−1 (westward) in summer and ∼40 m s−1 (eastward) in winter [Nozawa et al., 2002]. The presence of the Q2DW in winter suggests that uCD is larger than 40 m s−1. This also suggests that the Q2DW is sensitive to the background wind field, and that the wave does not penetrate into the upper mesosphere from below in summer months. Therefore other mechanisms, such as ducting, could play a role. To confirm this, we need to have global data, in particular, data at middle latitudes from a similar longitude station. It is noted that, based on a study of averaged MF radar data, 87.5–97.5 km, obtained in summer at Mawson (67°S, 63°E), Phillips  found similar results: the typical amplitude was 10–15 m s−1 and the meridional amplitude was slightly stronger (10–15%) than zonal amplitude, though MF radar measurements are less reliable above 91 km in summer at high latitude [see Nozawa et al., 2002].
 Regarding the variation of “the period of maximum amplitude of the Q2DW,” we showed that periods of 45.2 and 54.9 hours are found more frequently than periods of 48.0 and 51.2 hours over the height region. At middle and low latitudes, the period was generally thought to be near 2.1 days in the Northern Hemisphere and nearer 2.0 days in the Southern Hemisphere. For example, Harris and Vincent  based on MF radar data at Christmas Island (2°N, 157°W) between 80 and 100 km over ∼2 years from January 1990 to April 1992 reported that the median periods are between 48 and 52 hours, and wave periods are near 50 hours in July/August and near 48 hours in January/February. However, Thayaparan et al.  based on simultaneous observations at London (43°N, 81°W) and Saskatoon (52°N, 107°W) near 91 km over 2 years in 1993 and 1994 showed that the period of the Q2DW determined is smaller (46–47 hours) than the 51–52 hour period often suggested previously, and that the periods showed variability as a function of time. Clark et al.  also preferred the 48-hour period. Our results do not agree well with these results from middle/low latitude stations. It might suggest a latitudinal difference of the Q2DW period, but we need more coordinated observational data to understand the feature fully.
5.3. Penetration of the Q2DW Into the Lower Thermosphere
 We have examined altitude profiles of the Q2DW over the 37 months from November 1999 to November 2001. We show that in summer months the amplitude tends to increase with increasing height from 82 km; while in winter in most cases the amplitudes may already be large at 70 km, and then tend to maximize at and below 85 km and decrease above. These results would suggest that in summer the Q2DW amplitudes maximize at 91 km or higher and penetrate into the lower thermosphere to some extent. In contrast, in winter months the amplitude of the Q2DW maximizes at and below 85 km and usually decreases above, suggesting the Q2DW does not usually penetrate into the lower thermosphere. Furthermore it can be concluded that the Q2DW is more important in summer than in winter in high latitude lower thermospheric dynamics. However, it should be pointed out that although the Q2DW dissipates in the upper mesosphere, secondary waves caused by nonlinear coupling process between the Q2DW and other waves such as 24 and 12 hour tidal components would penetrate into the lower thermosphere [cf. Beard et al., 1999].
 From simultaneous observational data of the EISCAT UHF radar and MF radar at Tromsø for the period of 1–9 July 1999, we conclude that the Q2DW exists up to 108 km with an amplitude greater than 10 m s−1. Although the EISCAT observational data during the period are of lower quality than usual, this is probably the first observation showing the existence of the Q2DW in the lower thermosphere at high latitude based on wind data.
Zhou et al.  analyzed wind data obtained between 94 and 144 km for 20–30 January 1993 with the Arecibo (18°N, 67°W) IS radar. They derived the Q2DW (with period of 48 hours) amplitude and phase, although the data were mainly obtained during daytime. They showed that the Q2DW dominated the diurnal and semidiurnal tides in the meridional wind between 97 km and 108 km. Furthermore, the Q2DW zonal amplitude maximized at 100 km with values of ∼40 m s−1 and at 108 km with values of ∼40 m s−1 in the meridional. The Q2DW appeared up to 144 km with values greater than 10 m s−1 in both meridional and zonal components. These results are different from the high latitude results presented here. More simultaneous observations in the mesosphere/lower thermosphere are necessary in order to address the subject of penetration of the Q2DW into the lower thermosphere at high latitude as well as to evaluate the role of the Q2DW in the lower thermospheric dynamics.
6. Summary and Conclusions
 In this paper, we have presented the characteristics of the Q2DW observed in Tromsø over ∼37 months from 5 November 1999 to 3 December 2001. It is found that at Tromsø the Q2DW is more prominent in winter months (November–February) than in summer months (May–August). The maximum values of the amplitudes are ∼25 m s−1 in winter and ∼15 m s−1 in summer. Between 70 and 82 km, the Q2DW amplitude exhibits a clear annual variation and maximizes at around the winter solstice. Below 82 km the Q2DW is active only in the winter season, while between 82 and 91 km it is observed over the year but the amplitude in winter is larger than in summer. Amplitude ratios of meridional to zonal amplitude are about 1.1–1.2 over the height region and the seasonal difference of the ratio is small. The amplitude is modulated at periods of 4–10 days in both components, but the modulation is not always synchronized between the zonal and meridional components. In winter the Q2DW amplitude tends to maximize at and below 85 km in most cases, while in summer the amplitude is constant with height or tends to increase with height and maximizes near 95 km. These suggest that the Q2DW can penetrate into the lower thermosphere more frequently in summer than in winter. Variations of the period of the Q2DW between 45.2, 48.0, 51.2, and 51.8 hours are examined. The periods of 45.2 and 51.8 hours occur more frequently by ∼30% than those of 48.0 and 51.2 hours.
 Simultaneous observations with the EISCAT UHF and MF radars at Tromsø for the period from 1 to 9 July 1999 showed the existence of the Q2DW in the height range from 70 to 108 km. The Q2DW amplitude maximizes at 95 km in both meridional and zonal components, and the Q2DW appears to survive up to 108 km in the meridional component. Between 85 and 95 km, it is also found in the meridional component that the Q2DW and semidiurnal tide can be the strongest of the periodic components, including those of the tides.
 S.N. thanks K. Hocke for letting us use his Lomb-Scargle periodogram method routines and T. Nakamura and T. Miyoshi for their informative suggestions. We wish to thank the EISCAT staff. EISCAT is jointly funded by the Particle Physics and Astronomy Research Council (UK), Centre National de la Recherche Scientifique (France), Max-Planck Gesellschaft (Germany), Suomen Akatemia (Finland), National Institute of Polar Research (Japan), Norges Allmennvitenskapelige Forskningsråd (Norway), and Naturvetenskapliga Forskningstrådet (Sweden). This research was financially supported by the Grant-in-Aid for Scientific Research A (12373002), B (11440144), and C (11640441) and by a Center of Excellence (COE) Leadership grant by the Ministry of Education, Science, Sports and Culture, Japan. This research has also been supported by Norges Forskningstråd through grant 129283/431. The Canadian authors recognize the granting council (NSERC) and the University of Saskatchewan (through ISAS).