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 An observational study of nonlinear interaction between the quasi 2 day wave (QTDW) and the diurnal and semidiurnal tides from meteor radar measurements at Maui is reported. The diurnal and semidiurnal tides show a short-term variation with the QTDW activity. The variation of amplitude of the semidiurnal tide is opposite to that of the QTDW. The minimum amplitudes of the diurnal tide appear several days later than the maximum amplitudes of the QTDW, and the diurnal tide obviously strengthens when the QTDW drops to small amplitudes. The bispectrum analysis shows significant nonlinear interactions among the QDTW and the tidal components. The two quasi 16 h modes with periods of 16.2 h and 15.8 h generated in the interactions of the QTDW with the diurnal and semidiurnal tides can clearly be distinguished because of the slight deviation of the QTDW period from 48 h. The bicoherence spectrum demonstrates that the QTDW and the semidiurnal tide have quite strong levels of coherence, indicating that the nonlinear interaction is a mechanism responsible for the variability of the semidiurnal tide. Although there is also some interaction between the QTDW and the diurnal tide, their coherence level is low. When the QTDW drops to very weak amplitudes, the background wind decreases and reverses. During this time, the diurnal tide holds large amplitudes. These results support the notion that the variability of the diurnal tide is mainly attributable to the strong QTDW-induced changes in the background atmosphere, which was shown in the modeling study by Chang et al. (2011). Hence, both the nonlinear interaction and the background flow changes are responsible for the observed variation of the diurnal tide.
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 The quasi 2 day wave (QTDW) is a global westward propagating planetary wave with a dominant zonal wave number s = −3 [Salby, 1981]. The structure and climatology of the QTDW have been extensively revealed by radar and satellite measurements [Muller, 1972; Harris and Vincent, 1993; Wu et al., 1993; Thayaparan et al., 1997; Zhou et al., 2000; Jacobi et al., 1998; Gurubaran et al., 2001; Pancheva et al., 2004; Limpasuvan et al., 2005; Offermann et al., 2011]. It can be observed in wind and temperature oscillations during most of the year and grows in amplitude routinely in January/February and June/July in both hemispheres. The amplitudes of the QTDW can exceed 50 m s−1 in the meridional wind and 12 K in the temperature perturbations in the mesosphere and lower thermosphere (MLT) region, with periods around 48 h, typically ranging from 44 to 53 h [Harris and Vincent, 1993; Thayaparan et al., 1997; Palo et al., 2007]. In the austral summer solstice, the large amplitude QTDW was often observed to be in a phase-locked relationship with local time [Hecht et al., 2010]. The weak eastward wind and equatorward temperature gradient in the summer mesosphere can contribute to its amplitude growth [Salby, 1981; Hagan et al., 1993; Liu et al., 2004b]. Salby  attributed the excitation source of the QTDW to the instability of the tropospheric flow and tropospheric stochastic forcing. An alternative interpretation proposed by Plumb  suggested that the QTDW is forced and amplified by the baroclinic instability of the summer jet.
 Atmospheric tides are global-scale perturbations with periods that are harmonics of a solar day. The main excitation sources are absorption of solar radiation and latent heat release in the troposphere and stratosphere. When the tides propagate to the MLT region, they usually have large amplitudes due to the exponential decrease in the atmospheric density. The migrating tides are a subset of tides propagating westward synchronously with the Sun, of which the migrating diurnal (s = −1) and semidiurnal (s = −2) tides are the most prominent tidal components in the MLT region [Liu et al., 2004a; Li et al., 2009; Xu et al., 2009; Lu et al., 2011]. These tidal components are strongly affected by the solar heating and the background wind fields [McLandress, 2002], showing a significant seasonal variability. Because of their large amplitudes, the tides and the QTDW are prominent features in the MLT region and often dominate the local dynamics.
 Observations show that the tides have significant variability on the time scales of a few days to several weeks. Local interaction between gravity waves and tides may contribute to the observed variability [Walterscheid, 1981; Fritts and Vincent, 1987; Nakamura et al., 1997; Liu and Hagan, 1998; Ortland and Alexander, 2006]. The variations of the relative amplitudes and phases of migrating and nonmigrating tidal modes can also lead to significant short-term tidal variability. Nonmigrating tides may be generated by the tropospheric latent heat release [Hagan and Forbes, 2002, 2003; Oberheide et al., 2002], and nonlinear interactions between tides and quasi-stationary planetary waves [Angelats i Coll and Forbes, 2002; Liu and Roble, 2002; Oberheide et al., 2002; Mayr et al., 2003; Lieberman et al., 2004]. The analyses based on the ground and spatial observations show the modulation of tidal amplitudes at periods of propagating planetary waves, and nonlinear interaction between the propagating planetary waves and the tides is regarded as a mechanism responsible for this modulated variability of tides [Kamalabadi et al., 1997; Jacobi et al., 1998, 2001; Beard et al., 1999; Pancheva, 2000, 2006; Pancheva et al., 2000, 2002; Zhou et al., 2000; Pancheva and Mitchell, 2004; Liu et al., 2007; Kumar et al., 2008]. In a nonlinear process, the interacting primary waves can generate two secondary waves whose frequencies and wave numbers are the sum and difference of those of the primary waves [Teitelbaum and Vial, 1991], which leads to the reduction in the amplitude of the primary wave with high frequency due to energy transfer to the generated waves [Huang et al., 2009, 2012].
 Since both the tides and the QTDW are intense perturbations in the MLT region, they should frequently interact with each other, yielding significant short-term tidal variability. According to the observations from meteor and MF radars, the amplitude of the diurnal tide decreases during the amplification of the QTDW [Harris and Vincent, 1993; Gurubaran et al., 2001; Pancheva et al., 2004; Lima et al., 2004; Hecht et al., 2010], implying the nonlinear coupling of the QTDW and the diurnal tide. Similarly, an obvious anticorrelation between the amplitudes of the QTDW and the semidiurnal tide is observed [Thayaparan et al., 1997], which is an indication of the interaction between the semidiurnal tide and the QTDW. The secondary waves with sum and difference frequencies of the QTDW and the tidal components corresponding to periods around 9.6 h, 16 h, and 48 h have been found in the MLT region, and bispectral analyses have further confirmed the nonlinear interactions between the QTDW and the tidal components [Beard et al., 1999; Jacobi et al., 2001; Pancheva, 2006; Babu et al., 2011]. Using Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED/SABER) measurements, Palo et al.  reported an eastward propagating s = 2 QTDW with frequency f = 0.53 cpd, which resulted from the nonlinear interaction between the observed QTDW (f = 0.47, s = −3) and the migrating diurnal tide. Walterscheid and Vincent  proposed a self-excitation of the QTDW by the interaction with nonmigrating diurnal s = −6 tide to account for its rapid amplification and phase locking, and evidence for this coupling in observational and assimilated data was found [Pancheva, 2006; McCormack et al., 2010].
 The QTDW and tidal interactions have also been verified in numerical experiments with general circulation models (GCMs) [Palo et al., 1998, 1999; Norton and Thuburn, 1999; Liu et al., 2007; Chang et al., 2011; Yue et al., 2012]. In the thermosphere-ionosphere-mesosphere electrodynamics–GCM results, the reduction in the amplitudes of tides is attributed to the generation of waves through the nonlinear interaction between the QTDW and the tides and the drag and diffusion of gravity waves that have been selectively filtered by the QTDW, and the nonmigrating diurnal s = −6 tide proposed by Walterscheid and Vincent  is also clearly identified [Palo et al., 1998, 1999]. By explicitly computing the linear and nonlinear advection tendencies to characterize the interaction of the QTDW and the tide, Chang et al.  revealed that the change of the mean flow induced by the QTDW could also drive the significant tidal variability.
 In previous observational studies, although the interactions among the planetary waves and the tides were identified, it is not clear how strong their interactions were and what the energy exchange rates among different wave components were. Since the interactions of the QTDW with the diurnal and semidiurnal tides often take place at the same time, quantitative analysis of their coupling strengths will provide insight into the differences in the interactions among the QTDW and the tides. In this study, we attempt to quantify the level of coherence among the different wave components by analyzing a nonlinear interaction event between the QTDW and the tides from meteor radar observations at Maui. By calculating their coherence levels, the dominant mechanisms responsible for the variations of the tidal amplitudes with the QTDW activity are explored.
 A brief description of the observed data is given in section 2. Concurrent nonlinear interactions among the QTDW and the diurnal and semidiurnal tides are verified in section 3. In section 4, the coherence levels of the QTDW and the tides are quantitatively analyzed, and the possible mechanisms responsible for the variability of the diurnal and semidiurnal tides with the QTDW activity are discussed. A summary is presented in section 5.
2 Meteor Radar Observation
 The Maui meteor radar is located in Kihei on Maui, Hawaii, at 20.8°N, 156.4°W. The system used an all-sky interferometric meteor radar [Hocking et al., 2001] operating at 40.92 MHz. The meteor trails were illuminated by a three-element Yagi antenna directed toward the zenith with an average transmitted power of approximately 170 W, which resulted from a 13.3 µs pulse length, 6 kW peak envelope power, and a 466 µs interpulse period. The meteor trail reflections were detected by five three-element Yagi antennas oriented along two orthogonal baselines. A center antenna was at the cross of the two orthogonal baselines, and four outer antennas were separated from the center antenna by 1.5 and 2.0 wavelengths. The receiving antennas were sampled every 13.3 µs, resulting in a 2 km range resolution. By assuming that vertical speed was negligible, the horizontal wind velocities were determined from the trail positions and Doppler shifts within a height interval of 4 km and a time bin of 1 h; and then, the hourly vertical profiles were oversampled at a 1 km height interval in the range from 80 to 100 km. A detailed description of the meteor radar system and the horizontal wind calculation can be found in previous works [Franke et al., 2005; Lu et al., 2011].
 The detection rate of meteors showed a strong dependence on altitude and season. The highest detection rate appeared at the solstices while the lowest at the equinoxes, and most echoes were detected around 90 km. Figure 1 shows the zonal (positive eastward) and meridional (positive northward) wind at the height of 90 km for the 50 days from 1 January to 19 February 2003. During this period, both the directions of the zonal and meridional winds vary alternately with time, indicating the intense wave activity, and the maximum velocities can attain 85.5 and 147.4 m s−1 in the zonal and meridional winds, respectively. These meridional wind data are used to investigate the coupling of the QTDW and tides in this study.
3 Interactions Among QTDW and Tides
 We first present the moving spectra to reveal the temporal evolution of the meridional wind at 90 km using a 4 day sliding window with a step of 1 day. A Lomb-Scargle periodogram analysis [Scargle, 1982], with a 4 times oversampling (an effective frequency resolution of 1/16 cpd), is performed on the 4 day series.
 In order to clearly exhibit the developing process of the QTDW, the moving spectrum is also calculated for the last 10 days of December 2002. Figure 2 shows the moving frequency spectrum during the 60 days from 22 December 2002 to 19 February 2003. It can be seen that the QTDW, diurnal, and semidiurnal tides are dominant components. The spectral amplitude of the QTDW increases gradually in the first 15 days (days −10 to 4) and remains strong from days 5 to 37, which is consistent with previous observations [Hecht et al., 2010]. During the times when the spectral amplitudes of the QTDW reach the maxima, such as in days 11–14, 20–23, and 31–33, the semidiurnal tide is weak and vice versa. After the QTDW spectrum decreases rapidly on day 37, the diurnal tide dramatically increases. According to the matching relation of frequencies of the interacting waves, the periods of the secondary waves generated by the sum and difference interactions between the QTDW and the diurnal tide are calculated to be 16 h and 48 h, and the secondary sum and difference waves excited through the interactions of the QTDW with the semidiurnal tide have the period of 9.6 h and 16 h. As shown in Figure 2, the 16 h and 9.6 h period waves are reinforced when the strong QTDW is present. This implies that there may be the nonlinear coupling between the QTDW and these tidal components.
 A least squares fitting is applied to estimate the evolution of these wave amplitudes with time. The meridional wind velocities v(t) are represented as a function of time by
where v0 is the mean wind velocity, and ai, Ti, and ϕi denote the amplitudes, periods, and initial phases for the 48 h, 24 h, 16 h, 12 h, and 9.6 h wave components, respectively. Because the fitted waves include periods as short as 9.6 h, we adopt a 3 day window with a 3 h increment, which can give a reasonable sensitivity for the temporal variation of these wave amplitudes. It is possible that the amplitudes derived by a 3 day series are slightly large for the 48 h wave but slightly small for the 9.6 h component. However, the variability of the amplitudes should be independent of a moderate window length. Figure 3 shows the evolution of the amplitudes of these wave components from days 1 to 50. The QTDW, diurnal, and semidiurnal tides obtained by band-pass filtering are also shown in Figure 3. The band-pass filters pass frequencies corresponding to periods between 40 h and 60 h for the QTDW, 20.7 h and 28.6 h for the diurnal tide, and 11.0 h and 13.2 h for the semidiurnal tide. The fitted maximum amplitude of the QTDW is 68.3 m s−1 on day 22, which is slightly larger than the peak of 65.9 m s−1 derived from the filtering. The diurnal and semidiurnal tides have the fitted maximum amplitudes of 58.0 and 32.8 m s−1 close to the filtering values of 59.6 and 34.5 m s−1, respectively. Hence, the fitting amplitudes are consistent with the filtered results, indicating these oscillations are robust features. Additionally, spectral leakage may occur in the fitting and filtering processes, in particular, the 3 day sliding window utilized is not an integer multiple of 48 h, potentially leading to a modulation of the QTDW amplitudes at tidal periods. Similarly, the fitted amplitudes of the tide may show an apparent vacillation at QTDW period due to the spectral leakage of the QTDW onto the tide, which is distinct from the tidal amplitude modulation derived from the beat between the tide and the secondary waves. The almost same amplitudes derived from the fitting and the filtering also show that spectral leakage is not severe in our analyses. Figure 3 shows that in the 28 days from days 8 to 36, the amplitudes of the QTDW and the semidiurnal tide clearly exhibit opposite variation, and their linear correlation coefficient is calculated to attain −0.80. Moreover, during this time, the 16 h and 9.6 h wave components are also robust with amplitude peaks of 30.8 and 16.1 m s−1, respectively. From days 36 to 38, the amplitude of the QTDW rapidly drops to less than 10 m s−1 from about 50 m s−1. In contrast, the amplitude of the diurnal tide increases to near 60 m s−1. After this time, the diurnal tide holds large amplitudes, while the QTDW remains at a low level. At the same time, the activity of the 16 h and 9.6 h waves is weak. This relationship between the QTDW and the diurnal tide has been found in observational and modeling studies [Hecht et al., 2010; Chang et al., 2011]. One can note an interesting phenomenon that the variation of the diurnal tide with the QTDW is considerably different from that of the semidiurnal tide. Similar results (not presented here) can be observed around 90 km. And the wave coupling is also seen in the zonal wind but is weaker than in the meridional wind because these waves have much smaller zonal wind amplitudes.
 When the QTDW interacts with the diurnal and semidiurnal tides, the frequencies of the corresponding secondary waves are equal to the sum and difference of their frequencies [Teitelbaum and Vial, 1991]. The frequency spectrum of the 50 day meridional wind is obtained with the discrete Fourier transform and is shown in Figure 4. The spectral peak of the QTDW is located at 0.48 cpd, or a period of 50 h, slightly larger than 48 h. The peaks of the diurnal, semidiurnal, and terdiurnal tides, respectively, are at 1.0, 2.0, and 3.0 cpd corresponding to the periods of 24 h, 12 h, and 8 h due to the solar heating with a 24 h cycle. The zonal wave numbers cannot be explicitly resolved from the ground-based observations and are therefore based on values expected from an assumed s = −3 QTDW, which is observed to occur during the northern winter (and southern summer) conditions of this study. When the QTDW (f = 0.48, s = −3) interacts with the diurnal tide (f = 1, s = −1), the two secondary waves should be at (f = 1.48, s = −4) and (f = 0.52, s = 2). The secondary waves generated in the interaction between the QTDW (f = 0.48, s = −3) and the semidiurnal tide (f = 2, s = −2) should appear at (f = 2.48, s = −5) and (f = 1.52, s = 1). It is interesting because of the slight deviation of the QTDW period from 48 h, we can distinguish the two quasi 16 h modes of (f = 1.48, s = −4) and (f = 1.52, s = 1) with periods of 16.2 and 15.8 h, as shown in Figure 4. The spectral peak of (f = 2.48, s = −5) with period of 9.68 h is also very clear in Figure 4, while (f = 0.52, s = 2) is mixed up in the strong QTDW spectrum. Based on SABER temperature observations in January 2005, Palo et al.  found the eastward propagating QTDW (f = 0.53, s = 2) that was created through the interaction between the QTDW (f = 0.47, s = −3) and the diurnal tide (f = 1, s = −1), but the corresponding quasi 16 h wave (f = 1.47, s = −4) could not be resolved due to the Nyquist sampling limit. In a GCM study under late January conditions [Chang et al., 2011], the QTDW was at (f = 0.46, s = −3), and both quasi 16 h waves (f = 1.46, s = −4) and (f = 1.54, s = 1) generated through the interactions among the QTDW and the tidal components were identified. Therefore, although the zonal wave number cannot be deduced from the observations at a single station, the power spectrum may support the interpretation that nonlinear interactions of the QTDW with the tidal components did occur.
4 Coherence Level Among QTDW and Tides
 The bispectrum analysis can be used to detect the three-wave nonlinear interaction since it reveals the phase information of the spectra [Kim and Powers, 1979]. A strong bispectral amplitude indicates the quadratic phase coupling arising from wave-wave interaction. Considering that the bispectrum estimates have a strong dependence on the amplitudes of the involved spectral components, a bicoherence spectrum analysis was introduced to measure the level of coherence among interacting three waves by properly normalizing the bispectrum [Kim and Powers, 1979]. The bispectrum and bicoherence spectrum estimators have been described in detail [Kim and Powers, 1979; Beard et al., 1999]. Here we take an 8 day sliding window with a 6 h shifting step to obtain a total of 169 segments from the 50 day meridional wind data. The bispectrum of each segment is calculated, and then these bispectrum estimates are averaged across all segments. The 169 segments are enough to cancel out the contributions of spontaneously excited modes to the calculated bispectrum. However, because of the limited spectral resolution for the 8 day series, the 50 h QTDW appears as a 48 h spectral component; both the 16.2 h and 15.8 h waves appear as a 16 h component, which is referred to as a quasi 16 h wave; and the 9.68 h wave appears as the 9.6 h component, which is referred to as a quasi 9.6 h wave. Figure 5 exhibits the bispectrum (in units of 103 m3 s−3) and bicoherence spectrum results. For the bicoherence spectrum, only values larger than 0.5 are shown, which represents a high confidence of strong wave-wave interaction. We use the periods (Ti, Tj, and Ti+j) of the interacting wave triad to denote the bispectral peak, where Ti and Tj are the spectral periods marked in the horizontal and vertical axes in Figure 5, and 1/Ti + 1/Tj = 1/Ti + j, whereas, Ti+j is not actually a coordinate on the plots. Notice that the wave with period Ti+j represents a primary wave in the difference interaction. The bispectral peak of the difference and sum interactions between the QTDW and the diurnal tide should appear at (48 h, 48 h, and 24 h) and (48 h, 24 h, and 16 h), respectively. As we expected, a strong peak at (48 h, 48 h, and 24 h) and a weak peak at (48 h, 24 h, and 16 h) can be seen in the bispectrum shown in Figure 5. However, there is no corresponding peak in the bicoherence spectrum. Hence, there was some interaction between the QTDW and the diurnal tide, but their coherence level was weak. The bispectrum also shows two strong peaks at (48 h, 16 h, and 12 h) and (48 h, 12 h, and 9.6 h), indicating the difference and sum interactions between the QTDW and the semidiurnal tide, respectively. Moreover, these two strong peaks also appear in the bicoherence spectrum. The bicoherence estimate values are 0.86 at (48 h, 12 h, and 9.6 h) and 0.67 at (48 h, 16 h, and 12 h), and these two bicoherence peaks reach up to 0.92 and 0.73 for the meridional wind from days 1 to 36. The peak value is smaller at (48 h, 16 h, and 12 h) than at (48 h, 12 h, and 9.6 h), which is mainly because the 16.2 h component of the quasi 16 h wave is quadratic phase coherent with the QTDW and diurnal tide, and only the 15.8 h component is generated through the interaction of the QTDW with the semidiurnal tide. Therefore, this is an intense interaction event between the QTDW and the semidiurnal tide, and their coherence level is much larger than that of the QTDW and diurnal tide interaction. In the wave-wave interaction, the energy exchange between a primary and a secondary wave is sensitive to the strength of the other primary wave [Huang et al., 2011, 2013]. The strong QTDW activity enhances the energy transfer from the semidiurnal tide to the secondary waves. Therefore, there is an apparent anticorrelation between the amplitudes of the QTDW and the semidiurnal tide, as shown in Figure 3.
 Figure 5 shows the peaks at (24 h, 24 h, and 12 h), (24 h, 12 h, and 8 h), and (12 h, 12 h, and 6 h) in the bispectrum or bicoherence spectrum. Besides possible nonlinear interactions, these peaks may also be attributable to a certain degree of phase consistency due to their common forcing. The interaction of the QTDW with the nonmigrating tide (f = 1, s = −6) created through the interaction between (f = 2.46, s = −5) and (f = 1.54, s = 1), or (f = 1.48, s = −4) and (f = 0.52, s = 2), is likely to give some contributions to the large bispectrum value at (48 h, 48 h, and 24 h). Through this process, the energy of the semidiurnal or diurnal tide may be pumped into the QTDW, which leads to the dramatic increase in the amplitude of the QTDW and the decrease in the amplitude of the semidiurnal or diurnal tide. This interaction was suggested by Walterscheid and Vincent  and observed in modeling studies [Palo et al., 1999; McCormack et al., 2010; Chang et al., 2011]. Although this nonmigrating tide cannot be separated from the diurnal tide based on the observations at a single site, we may infer that in this coupling event, this interaction was weak because the whole QTDW and tide coherence level is relatively weak, as shown in the bicoherence spectrum in Figure 5. In addition, a possible self-interaction of the QTDW with large amplitude should also be rather weak since there is no spectral peak of its second-order harmonic with frequency of 0.96 cpd in Figure 4.
 The high bicoherence between the QTDW and the semidiurnal tide indicates their strong coupling through wave-wave interaction. The low bicoherence between the QTDW and the diurnal tide shows that besides the nonlinear interaction, there may be other mechanisms responsible for the variation of the diurnal tide. From Figure 3, it can be noted that the variational tendency of the diurnal tide with the QTDW differs from that of the semidiurnal tide. The minimum amplitudes of the diurnal tide appear several days after the maximum QTDW amplitudes, which are consistent with the GCM results that the minimum tidal amplitudes occur roughly 4–6 days later than the maximum QTDW amplitudes [Chang et al., 2011]. When the QTDW drops to a small amplitude, the diurnal tide tends to increase and then remains at a strong level, such as from days 38 to 50. Hence, diurnal tide seems to be suppressed to a certain extent in the presence of the strong QTDW. In GCM studies, significant change in the mean background wind field of the MLT region was observed when the QTDW was present [Palo et al., 1999], and during the strong QTDW event, the amplitude of the diurnal tide decreased by 40% [Chang et al., 2011; Yue et al., 2012]. Chang et al.  calculated the influence of the linear and nonlinear advections on the tidal decay and found that the linear advection was more significant in producing the tidal variability caused by the QTDW than the nonlinear advection. Hence, the suppression of the diurnal tide in the presence of the QTDW was predominately due to the QTDW-induced change in the mean flow, rather than the wave-wave interaction. Our observational study indicates that indeed, there is rather small level of coherence between the QTDW and the diurnal tide, which is in agreement with this numerical result. By averaging 4 day wind velocities, we calculate the moving averaged zonal and meridional wind velocities using a 4 day sliding window with a 1 h increment, which is presented in Figures 1 and 3. This moving averaged wind may roughly be regarded as the background wind field because a 4 day smoothing can reduce the means of the QTDW, diurnal, and semidiurnal tides to near zero. The time-averaged wind may also contain any stationary planetary wave components that are possibly present at the radar location. During the northern winter, most stationary planetary wave activity tends to be in the northern middle to high latitudes, and it is therefore reasonable to assume that their influence on the time average at this low latitude location should be small. It can be seen that the averaged meridional wind is large in the presence of the strong QTDW in the meridional wind, and during the period when the QTDW is weak but the diurnal tide is intense, the averaged meridional wind is almost reversed. When the averaged zonal wind reverses between days 20 and 25, the averaged meridional wind shows a slight northward shift. This is consistent with the theoretical prediction that a westward forcing on the mean zonal winds would result in a northward mean meridional wind [Holton, 2004]. On the whole, the averaged meridional wind shows a linearly decreasing tendency. Considering that the data cross a period as long as 50 day, the evolution of the mean meridional wind may also include the normal seasonal variation from solstice to equinox. The study of Chang et al.  considered primarily the effect of zonal mean zonal wind, which was subject to westward acceleration by the QTDW. Based on the linear advective tendencies (8) and (9) presented in the study of Chang et al. , the effect of the increasing southward meridional wind on the tides is similar to that of the increasing westward zonal wind. A weaker influence of the mean flow change on the semidiurnal tide is likely due to its smaller amplitude, as shown in Figure 3. In fact, the recent model study of Jin et al.  also found the seasonal transition for the stratospheric sudden warming was capable of driving tidal variability via the background wind modification. Additionally, the diurnal tide is likely to increase after day 37 with the normal seasonal transition from solstice to equinox, whereas it is difficult to explain the evolution relation between the QTDW and the diurnal tide. Therefore, similar to the modeling studies [Chang et al., 2011], this observational study indicates that there are two mechanisms responsible for the variability of the tidal components with the QTDW activity, one through the direct nonlinear interaction and the other through the change in the mean flow. The evolutions of the different tidal components may be driven by the different mechanisms during the same event.
 By using the meteor radar observations at Maui during the period of 1 January to 19 February 2003, the nonlinear interactions of the QTDW with the diurnal and semidiurnal tides are studied. Considering that most radar echoes were detected around 90 km, meaning the observed winds around 90 km have less error, we present the analyzed results at 90 km. A 50 day wind is chosen to analyze the interaction event for improving the spectral resolution. During this observational period, the QTDW and the tides are robust, and the amplitudes of the diurnal and semidiurnal tides show a short-term variation with the QTDW activity; in particular, a clear opposite variation between the QTDW and the semidiurnal tide lasts for about 30 days. The bispectrum analysis shows that significant nonlinear interactions between the QDTW and the tidal components took place. Because the period of the QTDW slightly deviates from 48 h, the spectra of the two quasi 16 h modes with the periods of 16.2 h and 15.8 h generated in the interactions of the QTDW with the diurnal and semidiurnal tides can clearly be distinguished. The quasi 16 h and 9.6 h secondary waves generated through the interactions can attain large amplitudes of 30.8 and 16.1 m s−1, respectively.
 The bicoherence spectrum demonstrates that the QTDW and the semidiurnal tide have quite strong coherence levels, as large as 0.92 and 0.73. Hence, an intense nonlinear interaction between the QTDW and the semidiurnal tide occurred, which was responsible for the observed variation of the semidiurnal tide. However, even though there is some interaction between the QTDW and the diurnal tide, relative to their strong amplitudes, the coherence level is very low. The minimum amplitudes of the diurnal tide appear several days later than the maximum amplitudes of the QTDW, and the diurnal tide obviously strengthens when the QTDW drops to small amplitudes. The diurnal tide is suppressed to some extent in the presence of the strong QTDW. This observational phenomenon is consistent with the GCM results [Chang et al., 2011]. Modeling study by Chang et al.  has revealed that the background atmosphere changes induced by the strong QTDW could indeed drive the tidal variability at levels greater than the wave-wave nonlinear interaction. Hence, in this wave event, the variability of the diurnal tide is attributable to two mechanisms of the nonlinear interaction and the background flow change.
 We thank the Editor and anonymous reviewers for their valuable comments on this paper. This work was jointly supported by the National Natural Science Foundation of China through grants 41074110, 41174133, and 41221003; the National Basic Research Program of China (grant 2012CB825605); the Ocean Public Welfare Scientific Research Project, State Oceanic Administration People's Republic of China (201005017); and the U.S. National Science Foundation grants ATM-1049451 and ATM-1144343.