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 We present periodic variations of the migrating diurnal tide from Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics (TIMED) temperature and wind data from 2002 to 2007 and meteor radar data at Maui (20.75°N, 156.43°W). There are strong quasi-biennial oscillation (QBO) signatures in the amplitude of the diurnal tidal temperature in the tropical region and in the wind near ±20°. The magnitude of the QBO in the diurnal tidal amplitude reaches about 3 K in temperature and about 7 m/s (Northern Hemisphere) and 9 m/s (Southern Hemisphere) in meridional wind. The period of the diurnal tide QBO is around 24–25 months in the mesosphere but is quite variable with altitude in the stratosphere. Throughout the mesosphere, the amplitude of the diurnal tide reaches maximum during March/April of years when the QBO in lower stratospheric wind is in the eastward phase. Because the tide shows amplification only during a limited time of the year, there are not enough data yet to determine whether the tidal variation is truly biennial (24-month period) or is quasi-biennial. The semiannual (SAO) and annual oscillations (AO) in the diurnal tide support previous findings: tidal amplitude is largest around equinoxes (SAO signal) and is larger during the vernal equinox (AO signal). TIMED Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED/SABER) temperature and atmospheric pressure data are used to calculate the balance wind and the tides in horizontal wind. The comparison between the calculations and the wind observed by TIMED Doppler Interferometer (TIDI) and meteor radar indicates qualitative agreement, but there are some differences as well.
 The seasonal cycle of the diurnal tide in the mesopause region and its strong semiannual component are well known. There have also been recurring reports of a biennial or quasi-biennial oscillation (QBO) in the tidal winds. Pronounced variations on seasonal and interannual time scales have been reported in observations from the ground and from satellite. The analysis of long-term MF radar wind measurements of the upper mesosphere and lower thermosphere (MLT) at Adelaide (35°S, 138°E), Christmas Island (2°N, 157°W), and Kauai (22°S, 160°W) by Vincent et al. [1988, 1998] indicated a March/April tidal amplitude maximum and a QBO variation in the diurnal tide. The phase is such that the March tidal amplitude is larger when the equatorial zonal wind at 30 hPa is eastward. Analysis of satellite observations from the High Resolution Doppler Imager (HRDI) on the Upper Atmospheric Research Satellite (UARS) [Burrage et al., 1995; Lieberman, 1997] and from the Wind Imaging Interferometer on the same satellite [McLandress et al., 1996a, 1996b] also document the strong seasonal and interannual variations in wind tides. More recently, Wu et al.  found a strong semiannual variation and obvious interannual variation in the amplitude of the diurnal tide in horizontal wind data from the TIDI (the TIMED Doppler Interferometer) instruments on the TIMED (Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics) satellite. Because of the limited altitude range of both the ground-based and satellite techniques, the tides in wind and their seasonal oscillations are well known only in the upper mesosphere and lower thermosphere. The large-scale structure and long-term variability of tides in the horizontal wind in the lower mesosphere and stratosphere has not been previously reported.
 The global structure of the SAO and QBO in tidal temperature is less well characterized owing to the shortage of observations. Observations by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) and TIDI instruments on the TIMED satellite provide a good opportunity to investigate the global structure of temperature from the lower stratosphere to the lower thermosphere and wind in mesopause region.
 Although there have been many tidal observations in the past, there have been very few quantitative estimates of the long-term variability of the diurnal tide. Long-term variations of the mesospheric diurnal tide are often strongly affected by changes in the stratosphere. Hence, a better understanding of these long-term changes can shed some light on the stratosphere-mesosphere coupling.
 Satellites are necessary to determine the global structure but each satellite project has only limited observations of atmospheric parameters. One technique to extract additional information using theory together with wind observations was described by Svoboda et al.  and also used by Oberheide and Forbes . They use Hough mode extensions (HMEs), a technique developed by [Forbes and Hagan, 1982], to create complete global tidal fields of zonal and meridional winds, vertical wind, temperature and density in the mesopause region from the limited amount of horizontal wind data from UARS. The results show that this method performs well in the upper mesosphere and lower thermosphere, which is above the source region for propagating tides. The technique is not well suited for in situ generated (i.e., trapped or evanescent) tides.
 Another approach was used by Khattatov et al. . They used linearized tidal equations to solve for the diurnal tides of zonal and vertical winds and temperature starting from analysis of the diurnal tide in the meridional wind observed by HRDI.
 The TIMED satellite has the advantage of multiple independent measurements. TIDI retrievals give global horizontal winds in the MLT and SABER retrievals give global temperature profiles from about 20 km to above 110 km. We can use theory along with the SABER measurements to determine the mean flow and tides in horizontal wind in a manner analogous to that of Khattatov et al. . This provides knowledge of the global distribution and seasonal variations of tidal winds. A good similarity between the wind calculated using temperature data and that observed is necessary to verify the validity of the method. The TIMED satellite observations provide the opportunity to do this comparison.
 The major goal of this paper is to present a detailed description of the variability of the diurnal tide in temperature in the range 20–100 km and in winds near the mesopause using observations from SABER and TIDI. Tidal variations with semiannual (SAO), annual (AO) and quasi-biennial (QBO) periodicities are presented. The comparison between the wind calculated from SABER temperature data and TIDI wind data is another purpose of this paper. Wind observations from ground-based radar are also used in the comparison. This comparison provides independent validation of the methods of calculating balance zonal mean zonal wind and the tidal winds from temperature data.
 The paper is organized as follows. Section 2 describes the SABER and TIDI data and analysis methods, including the balance wind calculation and the method of extracting the tidal winds. The characteristics of the SAO, AO and QBO in the diurnal tide and the comparison between the different observation techniques are discussed in section 3. A summary and discussion are given in section 4.
2. Data Sets and Processing Techniques
 The TIMED satellite was launched in December 2001. SABER and TIDI began making observations of the global temperature, pressure and wind profiles in late January 2002. SABER retrievals give profiles of the global temperature and pressure in the stratosphere, mesosphere and lower thermosphere. TIDI retrievals give neutral horizontal winds in the upper mesosphere and lower thermosphere. In this paper, we use temperature and pressure profiles from SABER version 1.07 from February 2002 to December 2007 and wind data from TIDI (NCAR produced version 0307) from February 2002 to June 2007. Wind observations from the meteor radar at Maui (20.75°N, 156.43°W) [Franke et al., 2005] from May 2002 to May 2007 and the medium frequency radar at Adelaide (34.56°S, 138.48°E) [Vincent et al., 1998] from 2003 to 2005 are also used.
 We extract the tides in temperature and pressure from TIMED/SABER data throughout the middle atmosphere and the tides in wind from TIMED/TIDI and the meteor radar at Maui in the mesopause region where data are available. We also calculate the zonal mean zonal wind and the tidal information for the winds from SABER data using the assumption of balance wind and the linear tide equations. The methods are discussed in detail in sections 2.1 and 2.2.
2.1. Processing Method for Analyzing Tides
 The data analysis is done in two steps. First, the zonal mean temperature, pressure and wind and their migrating tides are separated using least square fitting. The TIMED orbit precesses slowly and it takes more than 60 days to complete a full 24-h coverage of local time. In order to analyze migrating tides effectively, we use 70-day windows of data in the calculation in this step. Seventy days was chosen for the length of the window because it resulted in the minimum error in the fit. Equation (6) of Xu et al.  is used to calculate the migrating tides and zonal means of temperature, pressure and wind. By moving the 70-day window in increments of 1 day, the temporal variations of the zonal mean and migrating tides of temperature, pressure and wind over the 6-year period are obtained. In the second step, the long-term variations of the zonal means and migrating tides of temperature, pressure and wind are calculated. The analysis solves for amplitudes and phases of the SAO and AO; amplitude, phase and optimal period of the QBO; and a possible solar-cycle influence. Since the period of the QBO in the lower stratospheric winds is variable [Baldwin et al., 2001], the analysis solves for the period rather than specifying it; the "optimal" period is that for which the error of the fitting reaches minimum. The QBO analysis looks for the strongest variation within the range 18–34 months.
 We have tested this method by taking SABER temperature as an example. The uncertainties in SABER temperature retrieval [Mertens et al., 2001; Remsberg et al., 2008; García-Comas et al., 2008] are about 4–5 K in the upper mesosphere. We have performed statistical tests of the multiple regression method in order to estimate the reliability of the analysis method for each step and found that the tidal variations found by the technique are statistically significant to the 95% confidence level. However, we cannot avoid the fundamental limitation of satellite measurements that the time taken to sample a full range of local time is fairly long (∼60 days in the case of TIMED). This can cause errors in the tide when the background temperature is also changing [e.g., Forbes et al., 1997]. The tides themselves have large day-to-day variations [e.g., She et al., 2004] that can also affect the analysis. Unfortunately, there is at present no measurement system that obtains short-term variations in global mean temperature and tides. Another problem is that the QBO in the lower stratosphere has a highly variable period [Baldwin et al., 2001]. Six years are not enough to obtain characteristics of this oscillation that are stable. We believe that these complications represent larger sources of uncertainty in the results than either errors in the SABER temperatures or the analysis method itself. Unfortunately, we cannot quantify these errors with the data currently available.
 A detailed discussion of the method used to separate the migrating tides and zonal mean temperature and to quantify their long-term variability is given by Xu et al. . Additional information about uncertainties in the analysis is included in the auxiliary material that accompanies this paper. The structures of the zonal mean temperature and tides calculated by our method are consistent with the results of Huang et al.  and Zhang et al.  although the methods of extracting zonal mean and tides are different. Also note that we use version 1.07 of the SABER data while both the Huang et al.  and Zhang et al.  studies used the previous version, 1.06. More details about the migrating diurnal tides in TIDI winds are given by Wu et al. [2006, 2008].
 In this paper, we focus on the features of the SAO, AO and QBO of the migrating diurnal tide in temperature and wind. Following equation (7) of Xu et al. , for the latitude ϕ and the altitude z, the amplitude Aj (t, ϕ, z) and phase Φj (t, ϕ, z) (in hours) of the temperature, pressure or wind jth tide can be expressed by
where j = 1, 2, 3, 4 correspond to the diurnal, semidiurnal, terdiurnal and 6-h tide, respectively. In equations (1) and (2), and are the average amplitude and phase of the tides; μjA and μjΦ are the trends in the amplitude and phase of the tides from 2002 to 2007; tc is the center day of the TIMED 6-year observations; Aj,SAO, Aj,AO, and Aj,QBO are the amplitudes of the SAO, AO and QBO in the amplitude of the tides over the 6 years; tj,SAOA, tj,AOA, and tj,QBOA are the phases of the three oscillations; Φj,SAO, Φj,AO, and Φj,QBO are the amplitudes of the SAO, AO and QBO in the phases of the tides over the 6 years; and tj,SAOΦ, tj,AOΦ, and tj,QBOΦ are the oscillation phases of the tides phase. The periods of the QBO in tidal amplitudes (Pj,QBOA) and phases (Pj,QBOΦ) are also variable. In this analysis, we solve for the period of the QBO within the range 18–34 months to get the best match to the QBO during the 6 years. The SAO, AO and QBO in the tides are determined simultaneously using a nonlinear least square fitting method.
 The SAO, AO and QBO in the temperature tide are obtained on a grid with 1 km spacing extending from 20 km to 135 km and with 5° spacing from 55°S to 55°N. In this paper, we present the oscillations of the migrating diurnal tide.
2.2. Calculation of Zonal Mean and Tidal Winds From Temperature
 TIMED/SABER provides data of temperature and atmospheric pressure and density that we can use to calculate the balance wind and the tides in horizontal winds.
 The background zonal mean zonal wind using the balance wind [Randel, 1987] satisfies
where f = 2Ωsin ϕ is the Coriolis parameter, is the zonal mean zonal wind, ϕ is the latitude, Ω = 2π/(24 × 60 × 60), ρ0 is the atmospheric density, is the zonal mean pressure, and a is the radius of the earth. Equation (3) can be used to estimate the zonal mean zonal wind in the extratropics. For the wind at the equator, the thermal wind balance with the vertical shear of the zonal winds is used [Andrews et al., 1987, equation 8.2.2],
where g is the acceleration of gravity and z is altitude. The lower boundary condition of zonal mean zonal wind is taken from the 50 hPa monthly mean wind at the equator from NCEP/NCAR reanalysis (from http://dss.ucar.edu/datasets/ds090.2/).
Figure 1 shows a comparison of the time mean zonal wind observed by meteor radar at Maui (20.75°N, 156.43°W) and the zonal mean zonal wind at 20°N calculated from SABER data. The comparison shows that the overall magnitude of the local wind and the vertical structure measured by the radar are similar to the zonal mean wind calculated from SABER data. We also compared the SABER zonal mean balance wind and the ground-based MF radar observations at Adelaide (34.56°S, 138.48°E) (2003–2005 data) and Yamagawa (31.20°N, 130.62°E) (2002–2003 data) and found similar agreement. We take 2003 as an example to calculate the seasonal mean winds, which are averaged between February and April, May and July, August and October and November and January. Figure 2 gives the vertical profiles of the seasonal mean zonal winds from meteor radar observations at Maui (20.75°N, 156.43°W) and MF radar at Adelaide (34.56°S, 138.48°E) and the balance winds at 20°N and 35°S calculated from SABER data. Figure 2 shows that the zonal mean zonal wind calculated from SABER data has a similar speed and seasonal variation to the zonal wind from the ground-based meteor and MF radar observations. We expect some differences because stationary planetary waves and other longitudinally fixed features will affect the radar winds. The differences are smallest during summer (May–July in the NH; November–January in the SH) when planetary waves are at their annual minimum. Additional differences in the mean zonal wind could result from differences in the observational techniques used. Past comparison between the meteor radar, MF radar and the satellite wind observations have shown no large wind magnitude discrepancies between the meteor radar and satellite observation but have found that the wind above 90 km observed by MF radar is smaller than that from meteor radar and satellite observation [Cervera and Reid, 1995; Burrage et al., 1996]. A recent further study also shows that MF radar observations at heights above about 90 km appear to underestimate wind speeds and tidal amplitudes [Manson et al., 2004]. This could contribute to the finding that the MF radar winds are smaller than those measured by satellite above 90 km, especially for May–July, August–October, and November–January cases (see Figure 2, bottom).
 The tides in the wind can also be calculated from SABER data. With the assumptions that ≈ 0 and ≈ 0, the linearized momentum equations [Holton, 2004, equations 2.19 and 2.20] in the zonal and meridional directions and the equation of continuity [Holton, 2004, equation 2.30] for the large-scale waves become
where λ is longitude and X′ and Y′ represent dissipation process. In the current study, we used the standard assumption [Forbes and Hagan, 1988] that the dissipation that has the largest impact on the diurnal tide is associated with vertical diffusion process. The diurnal tide has a short vertical wavelength in the MLT region and therefore is particularly sensitive to vertical diffusion. The vertical diffusion process includes molecular diffusion, the turbulent viscosity due to wave breaking and the gravity wave drag due to gravity wave breaking and other unresolved forcing. The molecular diffusion, Kmol, is well known and it is dominant above 110 km. We use the term Keff (for effective diffusion coefficient) to encompass all of these variable diffusion processes. These have been particularly difficult to determine on a global scale. The total diffusion coefficient Ktotal is the sum of the molecular diffusion coefficient and the effective diffusion coefficient. Similar to work by Forbes and Hagan , the dissipation terms in the above equations are
where kz = 2π/lz is the vertical wave number and lz is the vertical wavelength of the diurnal tide. On the basis of the analysis of the mean tide presented below, we use lz = 20 km in calculating the diffusion.
 For the migrating tides, any parameter y′, where y′ can be u′, v′, or w′, takes the form
where t is the universal time, and i = . j = 1, 2, 3, 4 corresponds to diurnal, semidiurnal, terdiurnal and 6-h tides, respectively. Y′j (ϕ, z) is a complex amplitude; |Y′j (ϕ, z)| is the amplitude of the tide and Φ = tg−1[Im(Y′j(ϕ, z))/Re(Y′j(ϕ, z))] is the phase. The basis frequency of the migrating tides is
where R′j and P′j are the complex amplitudes of the jth tide in atmospheric density and pressure, respectively. R′j and P′j are determined from SABER observations.
 The final input needed in order to calculate the wind tides from equation (9) is the total vertical diffusion coefficient, which is the sum of molecular diffusion and the effective diffusion induced by turbulence and gravity wave drag. The molecular diffusion coefficient can be calculated [Ortland and Alexander, 2006] by
Analysis of rocket observations by Lübken  and analysis of VHF radar by Balsley et al.  show that the turbulence can be quite large in a relatively small height range in the high-latitude mesopause. We assume that the effects of the gravity wave drag and gravity wave-tide interaction are also confined to a relatively small height range in the mesopause region. We choose a functional form for representing the effective vertical diffusion coefficient that captures this behavior:
In the diurnal tidal wind calculations, we take Kmax = 200 m2/s, zp = 100 km, and μ = 15 km for all latitudes and seasons. So, the total diffusion coefficient is
Singular latitudes for the diurnal tide calculation are 30°S and 30°N, where ∣f∣ = ∣2Ωsin ϕ∣ϕ=±30° = ω. If tides in the vertical wind are neglected, equation (9) reduces to two dimensions. For the diurnal tide, the solution is
Equation (11) verifies that, if the zonal wind and friction are zero, ±30° are singular latitudes. Therefore, the diurnal tide near the latitudes of 30°S and 30°N cannot be obtained from this method. Khattatov et al.  and Zhu et al. [1999, 2008] used a spectral model of Hough functions to solve this problem. In the current calculations, the diurnal tides of wind at 30°S and 30°N are calculated by interpolation with a cubic spline.
 Comparisons between the wind tides calculated using SABER temperature and pressure data and those measured by TIDI and ground-based meteor radar at 20°N are presented below and indicate that the analysis method performs well.
3. SAO, AO, and QBO in the Migrating Diurnal Tide
 In this section we present and discuss detailed information about the periodic oscillations of the diurnal tidal signals in temperature and wind. A quantitative description of the long-term oscillations in the tides will be useful in efforts to shed some light on the mechanisms that drive them and also on the stratosphere-mesosphere coupling process. Additionally, we compare the diurnal tides in wind obtained from different techniques: TIMED/TIDI observations, meteor radar observations, and the calculation using TIMED/SABER temperature data.
Figure 3 gives the averaged TIMED/SABER amplitude of the temperature migrating diurnal tide during 2002–2007 and the SAO, AO and QBO in the amplitude of the temperature migrating diurnal tide. Figure 3 indicates that the tide itself and the oscillations in its amplitude are strong in the tropical region. The 6-year averaged amplitude of diurnal tide reaches 15 K at about 98 km. The SAO in the diurnal tide amplitude has two peaks of about 4 K around 85 km and 100 km in the tropics and has weaker maxima near 30°. The SAO signal in the temperature diurnal tide amplitude nearly disappears at 20°S and 20°N. The QBO of the diurnal tidal amplitude is strong in the tropical MLT region and has a magnitude of about 3 K. The structure of the QBO in the temperature diurnal tide amplitude is similar to that of the SAO but its magnitude is slightly weaker. The AO of the diurnal tide amplitude is mainly apparent in the tropical MLT region and is slightly weaker than both the SAO and QBO.
Figure 4 gives the TIMED/TIDI observed averaged amplitude of the meridional wind diurnal tide during 2002–2007 and the SAO, AO and QBO in the amplitude of the meridional wind diurnal tide. All of the fields are strong around 20°N and 20°S and very weak near the equator. The analysis indicates that there is a slight hemispheric asymmetry in the meridional wind diurnal tide. Near the altitude of 95 km, the average amplitude of diurnal tide at 20°N reaches 32.6 m/s, which is a little stronger than at 20°S, where the amplitude is 31.7 m/s. However, this difference is less than the estimated root mean square deviations (RMS error) of the data process method, which is about 1.5 m/s, as shown in the auxiliary material that accompanies this paper. At other altitudes, the average amplitude of the diurnal tide at 20°S is slightly stronger than at 20°N. The SAO in the diurnal tide amplitude has a peak of about 13 m/s around 95 km at 20°N and a peak of around 10 m/s near 100 km at 20°S. The amplitude of the AO in diurnal tide is slightly weaker than the amplitudes of the SAO and is about 7 m/s in both hemispheres. The QBO of the meridional wind diurnal tidal amplitudes also has an obvious asymmetry. Its peak magnitude is about 7 m/s in the north and about 9 m/s in the south. These results are consistent with those of Wu et al. .
 In sections 3.1 and 3.2, we will concentrate on the features of QBO, SAO and AO in the migrating diurnal tide where the tide and its oscillations are strongest: at the equator for temperature and at 20°N and 20°S for the meridional wind. In addition, we will include comparisons with ground-based meteor radar observations of wind from Maui (20.75°N, 156.43°W).
3.1. Oscillations in the Temperature Diurnal Tide
Figure 5 gives vertical profiles of the 6-year averaged amplitude, the optimal period of the QBO, the amplitudes of the SAO, AO and QBO, and the phases of the SAO, AO and QBO (in days from 1 January 2003) of the temperature diurnal tide amplitude at the equator.
 First, we discuss the features of the QBO in the tide. Figure 5 shows two prominent characteristics of the QBO in the amplitude of temperature diurnal tide. The first is that the optimal period of the QBO of the diurnal tide amplitude above 75 km (Figure 5b), where the QBO signal is strong, is almost constant at around 24–25 months. The second is that above 50 km the phase of the temperature tide QBO is approximately constant, at around 450–500 days (peaks in March 2002, March 2004, and March 2006; see Figure 5d). However, in the stratosphere, there are large variations in the period of the tide amplitude QBO.
Figure 5c shows that the SAO is the dominant oscillation in the diurnal tide near the equator and its amplitude can reach about 4 K. The AO in the diurnal tide at the equator is weaker than either the SAO or the QBO. The phases of the SAO and AO of the temperature diurnal tide at the equator are about 80 days (Figure 5d) above 70 km, where the SAO and AO are strong; that is, the diurnal tide reaches maximum near the March equinox.
 We also calculate the seasonal and interannual variations of the phase of the temperature diurnal tide with equation (2). Figure 6 gives the vertical profiles of the mean phase of the temperature diurnal tide and the QBO, SAO and AO in the phase of the temperature diurnal tide at the equator. The mean phase of the temperature diurnal tide in Figure 6a indicates that the vertical wavelength of the temperature diurnal tide is about 20 km near the equator above 70 km. Figure 6b shows that there are very large variations in the optimal period of the QBO of the diurnal tide phase. Figure 6c indicates that the QBO in the phase of the diurnal tide is very weak in the tropical mesopause region. In the mesopause region, the QBO of the diurnal tide phase is less than 0.3 h except around 80 km where the QBO in diurnal tide phase is about 0.7 h. Figure 6c also shows that the QBO in the diurnal tide phase is weaker than the SAO and AO.
 The relationship between the QBO in the temperature diurnal tide and the oscillation of the lower stratospheric zonal wind is illustrated in the third and fourth panels in Figure 7. The monthly means of NCEP/NCAR reanalysis equatorial zonal wind in the lower stratosphere are from http://dss.ucar.edu/datasets/ds090.2/. In 2002, 2004 and 2006, the stratospheric zonal winds at 20 hPa are eastward and the phase of QBO (time of maximum) is at about 500 days. In the mesopause region, the amplitudes of the diurnal tide at the March/April equinox are stronger in these 3 years. The QBO in the amplitude of the diurnal tidal temperature in the mesosphere has a phase of around 450–500 days (Figure 5d); in other words, the maxima of the QBO in tidal amplitude coincide with those of the QBO in stratospheric winds at 20 hPa. Figure 7 also shows the time variations of the vertical wavelength and phase of diurnal tide in the mesopause region. The vertical wavelength varies in the range of 18–22 km. There are no obvious SAO, AO or QBO signatures in it. From Figure 7, we can also see that the tidal phase has SAO and AO variations but that it has no obvious QBO signature, consistent with Figure 6c.
 For the 6 years so far of the TIMED mission, the period of the QBO in the mesospheric tides is indistinguishable from a purely biennial oscillation. The amplitude maxima occur near the vernal equinoxes of years when the stratospheric QBO is eastward, which have been 2002, 2004, and 2006. With additional time, the stratospheric QBO phase will shift enough that a QBO tidal signal that appears only during March–April will diverge from a biennial signal. As an important reference point, we note that the large tides observed in HRDI winds occurred during odd-numbered years (1993, 1995) and, like the cases we present for 2002–2007, large amplitudes were found while the QBO in lower stratospheric wind was eastward [Burrage et al., 1995]. This is strong support for our interpretation that the oscillation follows the QBO even though it is seen primarily during the vernal equinox.
 One process that has been discussed as a possible mechanism for generating a QBO variation in the diurnal tide amplitude is variation in tidal damping due to variable transmission of gravity waves. In their numerical model, Mayr and Mengel  found that this mechanism was responsible for the interannual tidal variations they simulated. By this mechanism, the gravity wave flux into the upper mesosphere is altered by critical layer interactions in the stratosphere or lower mesosphere that filter out part of the spectrum. Figure 8 shows the monthly average zonal mean zonal wind calculated from SABER temperature using equation (4) for April of each year. Gravity waves that can propagate through to the upper mesosphere are restricted to those whose phase speeds are outside of the shaded region. Two things are evident from Figure 8. First, comparison of the results for 2002 and 2003 shows that the wind profiles for years at opposite phases of the QBO, and with very different tidal amplitudes, can have very similar effective filtering. Second, during 2004–2007, the apparent filtering does vary between even and odd years. Even years (2004 and 2006) have the smallest range of winds and the least apparent filtering while the range of winds in the odd years (2005 and 2007) is high. Since there is not a repeatable relationship between the apparent filtering of gravity waves in the stratosphere and the QBO in diurnal tide when all 6 years are considered, we cannot yet draw a conclusion about the role of gravity wave filtering in driving the QBO in the diurnal tide.
 Now, we discuss the SAO and AO in the temperature tide. The vertical profiles of amplitudes of the SAO and AO in the amplitude of the temperature diurnal tide at the equator in Figure 5c indicate that the SAO is the strongest oscillation of the diurnal tide in the mesosphere. The phases of the SAO and AO at the equator above 65 km are at equinoxes and at the March equinox, respectively. This means that the temperature diurnal tidal amplitude is somewhat larger at the March/April equinox than in September/October, which is consistent with Figure 7.
 For the oscillations in the phase of the temperature diurnal tide, the profiles of the SAO and AO in the phase of the temperature diurnal tide at the equator are given in Figures 6c and 6d. In the MLT region, the amplitudes of the SAO and AO in the phase of the temperature diurnal tide reach about 1 h. The phase of the SAO is near zero on day182.5 above 70 km, which means that there are increases of the tide phase at December/January and June/July solstices. The phase of the AO is near the June/July solstice, which means that there are increases of the tide phase at June/July solstice. Therefore, the increase of the tide phase near the June/July solstice can reach more than 2 h. Above 90 km, the SAO in the tide phase is stronger than the AO; therefore, the SAO variation of tide phase is dominant there.
3.2. Oscillations in the Meridional Wind Diurnal Tide
Figures 9 and 10 give the vertical profiles of the meridional wind diurnal tide at 20°N and 20°S, respectively. Profiles include the 6-year averaged amplitude and mean phase of meridional wind diurnal tide and the amplitudes and phases of the SAO, AO and QBO in the tide amplitude. Results of the meridional wind diurnal tide from TIDI observation and calculated by SABER data are included; Figure 9 also includes observations by the ground-based meteor radar at Maui. The SABER curves represent wind derived with the assumption that the diffusivity of Kmax = 200 (see equation (10b)).
Figures 9 and 10 indicate that the 6-year mean amplitudes of the meridional wind diurnal tide from TIDI observations at 20°N and 20°S are about 32 m/s. These can be compared with the amplitude computed by the linear Global Scale Wave Model (GSWM), which indicates that the tide reaches peak values of 30–40 m/s near 100 km around the latitude of ±20° [Hagan et al., 1995, 1999a].
 We note several differences between the tides determined from the different data sets. At 20°N, the peak amplitudes of the TIDI and meteor radar tides are similar. The mean amplitudes computed from SABER data reaches 31 m/s at 20°S but only 29 m/s at 20°N. Figures 9a and 10a show that the mean amplitude of tidal meridional wind computed from SABER data is slightly smaller than the TIDI observations at 20°N and 20°S in the mesopause region. The damping coefficient used in the SABER wind calculations might contribute to this discrepancy.
Figures 9b and 10b show that the mean phases of meridional wind diurnal tide from the meteor radar, TIDI and calculated from SABER data are very consistent with each other. Ground-based meteor radar observations by Batista et al. [2004, Figure 2] at 22.7°S and 45°W show meridional wind phases that vary from month to month. For most months, the tidal phases between 83 and 100 km are fairly close to the mean phases calculated from SABER and TIDI data at 20°S shown in Figure 10b.
 The amplitude of the SAO in the meridional wind diurnal tide at 20°N (Figure 9c) reaches about 13 m/s in the mesopause region and the phase is near the March equinox (Figure 9d). The amplitude of the AO (Figure 9e) is about 8 m/s and the phase varies from late summer (day 200) to winter over the altitude range from 80 to 100 km. The impact of this is that the peak wind diurnal tidal amplitude at 90–100 km is somewhat larger at the March/April equinox than at the September/October equinox, consistent with previous observations from the Upper Atmosphere Research Satellite (UARS) [e.g., Burrage et al., 1995; McLandress et al., 1996a] and ground-based radar observations [Vincent et al., 1988, 1998; Fritts and Isler, 1994]. Figures 9c–9f show that the amplitudes of the meridional wind tidal oscillations computed from SABER data exhibit similar features to those of TIDI except for relatively large differences in the phase of the annual oscillation. Figure 10c shows that the amplitude of the SAO in the TIDI diurnal tide wind amplitude at 20°S is about 9 m/s, which is smaller than that at 20°N (Figure 9c), but the amplitude from SABER data reaches about 14 m/s near 95 km. The discrepancy between the TIDI observation and SABER calculation for the SAO in diurnal tide at 20°S is larger than that at 20°N. For the AO in the diurnal tide, Figure 10e shows that the SABER calculation is larger than TIDI observation at 20°S.
 Now, we discuss the features of QBO of the meridional wind diurnal tide at 20°N and 20°S. Figures 9g and 10g show that the QBO in the amplitude of the meridional wind diurnal tide from TIDI observations at 20°N and 20°S are about 7 m/s and 9 m/s, respectively. Figures 9h and 10h show that, with the exception of the TIDI observations at 20°N, the phases of the meridional wind tide QBO from TIDI and meteor radar observations and those calculations from SABER in the mesopause region are all approximately constant, at around 400–500 days (peaks in March 2002, March 2004, and March 2006), which is similar to the phase of the temperature diurnal tide QBO. This characteristic is also very similar to ground-based [Vincent et al., 1998] and UARS [Burrage et al., 1995; Hagan et al., 1999a; Lieberman, 1997] observations. Figures 9h shows that, above 90 km, the phase of the QBO in meridional wind diurnal tide of TIDI observation at 20°N is between days 300 and 500. Below 90 km, the phase of QBO moves to 180 days but the QBO is weak there (see Figure 9g). The results from those studies indicated that, at the eastward phase of the stratospheric QBO, the meridional component of the diurnal tide is stronger than the average value, especially during the March/April equinox season. Figures 9g, 9h, 10g and 10h show that the difference between the SABER calculation and TIDI observation at 20°N is larger than at 20°S.
 The comparisons between the calculations using SABER, TIDI, and ground-based observations indicate that the calculated tidal wind using SABER data has some differences with the TIDI and meteor radar observations. These differences may be due to errors in any of three observations. The ground-based data could also differ from the satellite data because of local effects. There can also be a substantial difference in the derived winds due to the assumed diffusion/dissipation rate, so it is possible that the damping coefficient used in the SABER wind calculations is a major source of error. This term includes the effects of breaking or dissipating gravity waves, which are known to be a major momentum source in the mesosphere. In a companion paper (J. Xu et al., Estimation of the equivalent Rayleigh friction in MLT region from the migrating diurnal tides observed by TIMED, submitted to Journal of Geophysical Research, 2009), we explore using the discrepancy between the TIDI and SABER-derived tidal winds to determine a quantitative estimate of the tidal dissipation.
4. Discussion and Summary
 In this paper, we use 6 years of TIMED/SABER temperature data and TIMED/TIDI data of wind and meteor radar observation at Maui (20.75°N, 156.43°W) to analyze the characteristics of the SAO, AO and QBO in the diurnal tides of temperature and wind. We also take the TIMED/SABER data of temperature and atmospheric pressure and density to calculate the background wind and its tides. The comparison between our calculations and the observations of TIMED/TIDI and meteor radar indicates qualitative agreement, but there are some differences as well.
 The main characteristics of the diurnal tide during the 6 years are as follows.
 1. There are strong SAO, AO and QBO signatures in the amplitude of the diurnal tidal temperature in the tropical mesosphere and in the amplitude of diurnal tidal meridional wind around the latitudes of ±20°. The SAO and QBO are the largest oscillations of the temperature diurnal tide in the equatorial mesopause region and have comparable amplitudes (Figures 3 and 5). For the meridional wind diurnal tide near±20°, the SAO is the strongest oscillation; it reaches about 13 m/s at the latitude of 20°N and 9 m/s at 20°S around 95 km. The QBO and AO have similar intensities in the diurnal wind tide; they have amplitudes of 8–10 m/s at 20°N and 20°S (Figures 4, 9 and 10).
 2. The period of the QBO in the temperature diurnal tide in the mesosphere is around 24–25 months during these 6 years.
 3. The phases of the QBO of the temperature diurnal tide at the equator and of the meridional wind at 20°S are constant with altitude over the whole mesosphere. The tidal amplitudes reach maxima when the QBO in the zonal wind in the tropical lower stratosphere (30 hPa) is eastward (Figures 5d, 7, 9h, and 10h).
 4. The amplitudes of the diurnal tide of meridional wind are asymmetric between the two hemispheres. Both the mean tidal amplitude and the magnitudes of the oscillations in the diurnal tidal amplitude have differences between the Southern and Northern Hemispheres.
 The seasonal and interannual variations of atmospheric tides have received considerable attention in recent years, but have not been successfully explained, especially for the QBO in the diurnal tide. Two mechanisms have been proposed to explain the observations. The first mechanism is modulation of the tide by the QBO in the background wind in the stratosphere. Modeling studies [Hagan et al., 1999b; McLandress, 2002] have found that the amplitude and phase of the diurnal tide are sensitive to variations in the zonal wind. Hagan et al. [1999b] used the global-scale wave model (GSWM) to study the effects of variation of zonal wind on the diurnal tide. Their study included background wind variations in the lower stratosphere and also in the mesosphere. The GSWM model showed that variations in the zonal wind have an appreciable effect on the diurnal tide but the sign relative to the stratospheric QBO was opposite to that observed. Their study did not differentiate between the effects of the background wind in the stratosphere and that in the mesosphere. McLandress  used the Canadian Middle Atmosphere Model (CMAM) to simulate the effects of zonal wind on the variation of the diurnal tide. He found that the diurnal tide in the MLT region is sensitive to the QBO-like oscillation in the horizontal structure of the zonal mean zonal winds.
 Another mechanism that could force a QBO variation in the diurnal tide is momentum deposition from small-scale gravity waves. Mayr and Mengel  used a model to study the effect of the variation of small-scale gravity waves on the tide. They found that the QBO modulation of the tide in the upper mesosphere is caused to a large extent by variations in gravity wave momentum deposition resulting from filtering by the background winds in the middle atmosphere. In their model the QBO phase of diurnal tide of the zonal wind displays little variation in the vertical direction in the mesosphere. A look at effective gravity wave filtering by the April mean winds in the stratosphere and mesosphere calculated from SABER data (see Figure 8) does not indicate a consistent relationship with the QBO that would explain the observed tidal variations.
 In order to determine which of these mechanisms is responsible for the observed QBO in the temperature tide at the equator, a careful comparison should be made of the details of the mesospheric response in mean and tidal temperatures and winds between the observations and the models. The results presented in this study can contribute to the data needed for such an evaluation.
 TIMED, like other satellites in high inclination precessing orbits, takes a number of weeks to observe all local times. To obtain variability of global tides on short (days) time scales, multiple platforms in different orbits would be needed. Otherwise, it is not possible to fully separate tides from variations in the diurnal-mean background state.
 We are greatly grateful to R. A. Vincent, I. Reid, and Y. Murayama for providing the wind data of Adelaide and Yamagawa. This research was supported by the National Science Foundation of China (40890165, 40621003, and 40828003) and the National Important Basic Research Project (2006CB806306). The project is also supported by the Specialized Research Fund for State Key Laboratories. The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. The TIDI work at National Center for Atmospheric Research is supported by NASA grant NAG5– 5334.