Sources, Sinks, and Propagation Characteristics of the Quasi 6-Day Wave and Its Impact on the Residual Mean CirculationQuan Gan1 , Jens Oberheide1 , and Nicholas M. Pedatella2

1Department of Physics and Astronomy, Clemson University, Clemson, SC, USA, 2High Altitude Observatory, NationalCenter for Atmospheric Research, Boulder, CO, USA

Abstract This study employs a troposphere to lower thermosphere assimilation model data set generatedby the Whole Atmosphere Community Climate Model with data assimilation provided by the DataAssimilation Research Test Bed (WACCM + DART) to explore the sources, sinks, and propagationcharacteristics of the quasi 6-day wave (Q6DW) in the year 2007. WACCM + DART reproduces the burst-likeQ6DW and compares well with Sounding of the Atmosphere using Broadband Emission Radiometry andThermosphere, Ionosphere, Mesosphere Energetics and Dynamics Doppler Interferometer observations. Themost prominent Q6DW took place in later February and mid-October, while the Q6DW was absent duringsolstice conditions in 2007. The occurrence of a large Q6DW in the equinoctial mesosphere and lowerthermosphere is highly dependent on wave amplification and overreflection processes associated withbarotropic/baroclinic instabilities and wave critical layers defined by the zonal mean zonal winds. Duringsolstices, the winter hemisphere waveguide is negative and prevents the vertical wave propagation from thesource region into the mesosphere and lower thermosphere. Meanwhile, the critical layer for the Q6DWencloses the unstable region in the summer hemisphere and thus blocks the energy conversion from themean flow to the wave. The resulting circulation pattern due to the Q6DWmomentum deposition is upwardand poleward in both hemispheres and thus weakens the residual mean circulation in the summerhemisphere but strengthens it in the winter hemisphere. Also, the Q6DW impact on the residual meancirculation points to broader implications for the mean state of the upper atmosphere, for example, thethermospheric O/N2 ratio due to upward constituent transport and related changes in theionospheric plasma.

1. Introduction

Planetary waves (PWs) play an important role in the momentum and energy budget of the middle atmo-sphere, where these waves propagate and are subject to dissipation and breaking. The westward propagat-ing quasi 6-day wave (hereafter Q6DW), with a period of approximately 5–8 days and zonal wave number 1, isone of themost salient and recurrent traveling PWs in themesosphere and lower thermosphere (MLT) region.Early reports of the Q6DW date back to Madden and Julian (1972), who presented the wave pattern in thesea-level pressure data. Afterward, the Q6DW was observed in various stratosphere and mesosphere para-meters via both ground-based and satellite instruments (Forbes & Zhang, 2017; Gan et al., 2015; Garciaet al., 2005; Geisler & Dickinson, 1976; Hirota & Hirooka, 1984; Lieberman et al., 2003; Pancheva et al., 2008;Riggin et al., 2006; Sridharan et al., 2008; Talaat et al., 2001, 2002; Venne, 1985; Wu et al., 1994). The Q6DWis occasionally referred to as the 5-day wave in the literature. One possible reason is the similarity of thelatitudinal structure between the Q6DW and the Rossby normal mode with a 5-day period and zonal wavenumber 1. Nevertheless, we will refer to it as the Q6DW because the predominant wave period is ~6.5 daysin the MLT, which is the focus of this study.

Wu et al. (1994) were the first to present the global Q6DW in mesopause winds by using Upper AtmosphereResearch Satellite/HRDI (High Resolution Doppler Imager) data. They reported on the transient nature of theQ6DW occurrence, peaking during equinoxes, and low-latitude and midlatitude wave maxima in zonal andmeridional winds, respectively. The latter characteristics are in agreement with the first symmetric Rossbynormal (resonant) mode ([m, n] = [1, �2],m and n are the zonal wave number and meridional index, respec-tively) as predicted by the classical tidal and PW theory (Longueth-Higgins, 1968). However, the Q6DWobserved by HRDI displayed a downward phase progression with a vertical wavelength of approximately65 km in the middle atmosphere. This is in contrast to the theoretical prediction, which suggests that the

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RESEARCH ARTICLE10.1029/2018JD028553

Key Points:• WACCM + DART reproduces the

Q6DW as observed by SABER andTIDI on TIMED satellite

• Wind instabilities and intersectingcritical layers in the high-latitudelower mesosphere favor a largeQ6DW during equinoxes

• The dissipative/breaking Q6DWweakens the residual meancirculation in the summerhemisphere but strengthens it in thewinter hemisphere

Correspondence to:Q. Gan,qgan@clemson.edu

Citation:Gan, Q., Oberheide, J., & Pedatella, N. M.(2018). Sources, sinks, and propagationcharacteristics of the quasi 6-day waveand its impact on the residual meancirculation. Journal of GeophysicalResearch: Atmospheres, 123, 9152–9170.https://doi.org/10.1029/2018JD028553

Received 19 FEB 2018Accepted 15 AUG 2018Accepted article online 27 AUG 2018Published online 6 SEP 2018

Author Contributions:

Conceptualization: Quan GanData curation: Quan Gan, Nicholas M.PedatellaFormal analysis: Quan GanInvestigation: Quan Gan, JensOberheideMethodology: Quan GanResources: Quan GanSupervision: Quan Gan, JensOberheideValidation: Quan GanVisualization: Quan GanWriting - original draft: Quan GanWriting – review & editing: Quan Gan,Jens Oberheide, Nicholas M. Pedatella

©2018. American Geophysical Union.All Rights Reserved.

Rossby normal mode has an infinite vertical wavelength and is incapable of transporting heat, momentum,and energy (note that the classical theory solves the Laplace’s tidal equation in an isothermal, windless,and dissipationless atmosphere). Also, the dominant wave period is ~6.5 rather than ~5 days. The departuresfrom the normal mode indicate that the Q6DW is not an external Lamb wave (Lieberman et al., 2003; Liu et al.,2004; Riggin et al., 2006; Talaat et al., 2001, 2002). Conversely, the Q6DW is more like an unstable wave modeas suggested by Lieberman et al. (2003) and Pancheva et al. (2008).

Enabled by the ever-increasing amount of satellite data, great efforts have been made over the past decadeto further reveal the global nature and effects of the Q6DW in the MLT. Garcia et al. (2005) presented SABER(Sounding of the Atmosphere using Broadband Emission Radiometry) observed Q6DW in a ~30-day time seg-ment around postvernal equinox in 2002. Sridharan et al. (2008) found that the Q6DW dominates the PWs ofzonal wave number 1 in the equatorial zonal winds acquired by TIDI (Thermosphere, Ionosphere, MesosphereEnergetics and Dynamics [TIMED] Doppler Interferometer). Pancheva et al. (2008) analyzed 5 years (2002–2007) of SABER temperature data to compile a Q6DW climatology and found a vertically double-peakedstructure of the Q6DW (peak heights are ~80–95 and ~105–110 km at midlatitudes). More recently, an ana-logous climatology was also reported by Gan et al. (2015) and Forbes and Zhang (2017) based on longer timeseries extended to the years 2013 and 2015, respectively. Gan et al. (2015) also showed the climatologicalQ6DW in TIDI zonal winds. These recent global diagnostics not only demonstrated a consistent behavior ofthe Q6DW but also provided new insights in the lower thermosphere (~110 km), for example, in terms ofQ6DW-tidal interaction and Q6DW dissipation. Several studies addressed the interannual variability of theQ6DW (Huang et al., 2017; Merkel et al., 2003; Merzlyakov et al., 2013; Riggin et al., 2006) by analyzing satellitedata sets, but a convincing mechanism has not been reached yet. The reason is at least partly due to that thesatellite observation, for example, made by SABER, cannot well capture the Q6DW peak amplitude occurringat midlatitudes because of the yaw cycle.

Furthermore, the Q6DW is an important ingredient to explain short-term tidal variability and in turn isexpected to significantly impact the thermosphere/ionosphere (T-I) system (Oberheide et al., 2009). UsingThermosphere-Ionosphere-Mesosphere Electrodynamics General Circulation Model simulations, Pedatellaet al. (2012) showed the Q6DW interaction with the DE3 and DE2 nonmigrating tides, while Gan et al.(2016) studied the interaction with the DW1 and SW2 migrating tides. Using SABER data, Forbes andZhang (2017) provided observational evidence of the interaction, even though the quasi-sun-synchronoussatellite orbit makes an explicit separation of secondary waves impossible. Gan et al. (2017) demonstratedthat the produced secondary waves would result in a subdiurnal variability in the ionospheric plasma verticaldrifts and the F region electron densities. In addition to its significant role in neutral dynamics and iono-spheric variability, the Q6DW-associated phenomena were also explored in chemical species like ozone,water vapor, and nitrous oxide (Belova et al., 2008; Egito et al., 2017; Nielsen et al., 2010; Pendlebury et al.,2008; Sonnemann et al., 2008).

Despite the aforementioned investigations, important characteristics of the Q6DW are still not fully under-stood, including its excitation and propagation. For instance, Wu et al. (1994) suggested the Q6DW can bethought of as the Doppler-shifted 5-day normal mode. Meyer and Forbes (1997) proposed that the Q6DWis more likely an unstable mode drawing energy from unstable regions in the midlatitude and high-latitudemesosphere. This argument was supported by Lieberman et al. (2003), who diagnosed the Q6DW in globalwinds from HRDI measurements and the U.K. Meteorological Office stratospheric analysis data. By analyzingthe same data sets, Talaat et al. (2002) concluded that the Q6DW is an internally forced wave because of thecoherent phase structure from the troposphere to the mesopause region. Liu et al. (2004) further illustratedthe significant role of the zonal mean winds in wave amplification based on a 1-year Thermosphere-Ionosphere-Mesosphere Electrodynamics General Circulation Model run (the lower boundary at ~30 kmwas forced by the National Centers for Environmental Prediction reanalysis data). Additional proposed wavesources could be, for example, tropical convective heating, the land-sea contrast, the nonlinear interactionbetween the quasi-stationary wave and the westward propagating 4-day wave with zonal wave number 2.(Miyoshi & Hirooka, 1999; Pogorel’tsev, 2007). In brief, the excitation of the Q6DW is complicated andmultiplesources may have important simultaneous contributions.

In the present study, we employ the Whole Atmosphere Community Climate Model with data assimilationprovided by the Data Assimilation Research Test Bed (WACCM + DART) assimilation model to investigate

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the Q6DW from the surface up to the lower thermosphere (~145 km) during 2007. Being an assimilativemodel, WACCM + DART is closer to reality than any of the aforementioned model studies and at the sametime provides physically self-consistent dynamical fields in all parameters needed to quantify Q6DW sources,sinks, and propagation characteristics. It also allows us to derive the residual circulation induced by the west-ward forcing of the background winds due to Q6DWmomentum deposition, an important parameter for theupward transport of constituents and consequently an overall change of the mean state in the T-I system.

The manuscript is organized as follows. Section 2 provides an overview of WACCM + DART and the SABERtemperature and TIDI wind data sets used in this work and compares the Q6DW in WACCM + DART withSABER and TIDI. Section 3 presents an analysis of wave sources, sinks, and propagation characteristics.Section 4 discusses the potential T-I effects to the strong Q6DW activity and resulting residual circulationchanges. Section 5 contains the conclusions.

2. Data and Methodology2.1. Whole Atmosphere Community Climate Model With Data Assimilation Provided by the DataAssimilation Research Testbed

WACCM extends from the surface to 5.1 × 106 hPa (~140 km) and is the high-top atmospheric component ofthe Community Earth SystemModel (Hurrell et al., 2013). WACCM incorporates the necessary chemical, dyna-mical, and physical processes to model the troposphere, stratosphere, mesosphere, and lower thermosphere.The reader is referred to Garcia et al. (2007) and Marsh et al. (2013) for a detailed description of WACCM. Forthe present study, the horizontal resolution is 1.9° in latitude and 2.5° in longitude, with a vertical resolution of1.1–1.75 km in the troposphere and stratosphere and 3.5 km in the mesosphere.

The WACCM meteorology is constrained by data assimilation using the DART ensemble adjustment Kalmanfilter (Anderson, 2001; Anderson et al., 2008). This enables WACCM to reproduce historical time periods. Weuse a 40-member ensemble with a 6-hr data assimilation cycle. In the troposphere and stratosphere, aircraftand radiosonde temperatures and winds, satellite drift winds, and Constellation Observing System forMeteorology, Ionosphere, and Climate refractivity observations are assimilated. Temperatures from theAura Microwave Limb Sounder (MLS) and TIMED/SABER are assimilated in the upper stratosphere, meso-sphere, and lower thermosphere. As demonstrated by Pedatella et al. (2014), the assimilation of MLS andSABER temperatures are critical for accurately representing the mesospheric dynamics. TheWACCM + DART fields employed in the present study were generated by Pedatella et al. (2016) to studythe short-term tidal variability during 2007. The temporal cadence is 1 hr for the WACCM + DART output.

2.2. TIMED Data Sets

SABER and TIDI onboard the TIMED satellite measure temperature and horizontal winds routinely since early2002. SABER is a 10-channel broadband radiometer covering the spectral range from 1.27 to 17 μm. Itprovides temperature profiles retrieved from two 15-μm and one 4.3-μmCO2 radiometer channels in the tan-gent heights of approximately 20–110 km. Remsberg et al. (2008) assessed the quality of version 1.07 tem-perature data. The reported precision is no more than 1 K below 70 km, 1.8 K at 80 km, and 6.7 K at100 km. The SABER version 2.0 data we employ in this study has the same precision, since the change fromversion 1.07 to 2.0 did not impact precision. Note that the temperature noise will not impact the derivedQ6DW amplitudes and phases in an appreciable manner because we combine several days of data for thediagnostics, as overviewed in section 2.3 below. The effective vertical resolution of the temperature profilesis about 2 km.

TIDI is a Fabry-Perot interferometer measuring horizontal vector winds in the MLT region with a vertical reso-lution of approximately 2 km and accuracy of ~3 m/s (Killeen et al., 2006). TIDI data are quite noisy, but thisdoes not impact the derivation of wave amplitudes and phases because of the combination of several days ofdata as for SABER. By limb viewing, TIDI observes emissions from OI 557.7 nm and rotation lines in the O2

(0–0) at 762 nm to determine the Doppler wind. The actual altitude range covered by TIDI measurementsis from 70–120 km during daytime and from 80 to 103 km in the nighttime. TIDI provides successive horizon-tal wind measurements during day and night from pole to pole. We employ TIDI version 0307 for the presentstudy. As the TIMED satellite is in a quasi-sun-synchronous orbit (the local time precession is approximately

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12 min/day), the limb scanning can lead to the asymmetric coverage between two hemispheres, which forSABER is from 53° in one hemisphere to 82° in the other.

2.3. Q6DW Diagnostics

For the Q6DW diagnostics in WACCM + DART, two-dimensional fast Fourier transform algorithm is performedto extract the amplitudes and phases of the Q6DW at each latitude and altitude grid. Prior to computing waveamplitude and phase, the fast Fourier transform filtering technique is undertaken on the original time seriesof the temperature and horizontal winds to separate the westward propagating perturbations with zonalwave number 1. Q6DW amplitudes and phases are derived on the 13-day (two wave cycles) basis with a1-day increment. The phase is defined as the longitude corresponding to the maximum perturbation at mid-night (00:00 UT). For SABER and TIDI, as the measurements are not synoptic and missing data are inevitable,we employ least squares fitting to extract wave amplitudes and phases instead. To compare withWACCM + DART, the observational data are analyzed by using the same running window (13 days with a1-day step). More details regarding Q6DW diagnostics in observations are referred to Gan et al. (2015).

2.4. Comparison of the Q6DW in WACCM + DART With SABER and TIDI

To test if WACCM + DART provides realistic Q6DW signals in 2007, we first perform a wavelet analysis(Torrence & Compo, 1998) of the time series of westward propagating perturbations with zonal wave number1 at each latitude and altitude. Figure 1 shows the normalized wavelet spectra of WACCM + DART equatorialzonal winds at five different heights, extending from the troposphere up to the mesopause region. The equa-tor is representative because of the aforementioned prior studies demonstrating a low-latitude Q6DW zonalwind peak. At 90 km (Figure 1a), two most remarkable Q6DW events took place in late February and mid-October. For these two events, the dominant wave period is centered at ~7.5–8 days and tends to increasetoward lower altitudes. The variable period with respect to height is to some extent due to the Doppler-shifteffect associated with background winds (Meyer & Forbes, 1997; Salby, 1981). Moreover, in late February, forexample, the spectral peaks with periods of 6–8 days are not statistically significant at 10 and 50 km, whichare probably due to the smaller magnitude relative to other wave components (e.g., ~10-day wave).Nevertheless, in view of the coherent timing of these peaks with the increasing height, the mesosphericQ6DW has a likely source in the lower atmosphere. A similar scenario was found for the mid-October eventexcept for the height of 30 and 10 km (Figure 1d). This means that the tropospheric wave source cannot com-pletely account for the mesospheric Q6DW. In other words, additional wave sources at higher altitudes mayplay a role as well. Also, a few less significant Q6DW activities were detected in late March, early May,August/September, and November at 90 km. Note that PWs with larger periods (like ~10 days) are presentduring solstice at all the heights shown in Figure 1, but they are beyond the scope of the current work.Similar Q6DW spectra have been reported before, for example, Gan et al. (2015), who analyzed multiyearSABER temperature and TIDI horizontal winds data sets.

We now turn to a direct comparison of the Q6DW in WACCM + DART with the TIMED observations. Figure 2illustrates the Q6DW amplitudes as a function of latitude and time in the year 2007. The Q6DWmaximizes at105 km (temperature) and 90 km (zonal wind), as discussed later in section 3 and Figure 4, and we thuschoose these altitudes for the comparisons. In addition to the strong zonal wind Q6DW (Figure 2a) nearthe equator in late February and mid-October as already revealed by the wavelet analysis (Figure 1), substan-tial Q6DW events occur in March/April and May, August/September, and November (Figure 1). The peakamplitudes are at low latitudes in zonal wind and at middle to high latitudes in temperature. For example,the late-February zonal wind amplitude can attain 18–21 m/s over the equator in WACCM + DART and com-pares well with that observed by TIDI (Figure 2b). Note that TIDI data are not assimilated into WACCM + DARTand thus represent a validation of the Q6DW in WACCM + DART by independent observations. The corre-sponding temperature amplitude (Figure 2c) is as large as 5–6 K at ~60° in the Southern Hemisphere (SH)and 3–4 K at ~30° in the Northern Hemisphere (NH). The interhemispheric difference of ~2 K in temperatureis likely the result of the background wind difference associated with the waveguide andbarotropic/baroclinic instabilities (the related details are formulated in section 3.2.1). It is not surprising tofind a similar latitudinal structure to the first symmetric Rossby normal mode as predicted by the classicaltidal and planetary theory, because the Q6DW has a very close period and the same zonal wave numberas the 5-day Rossby wave. As anticipated, the comparison with the SABER observations (Figure 2d) is goodbecause SABER data are assimilated into WACCM + DART. The 1-sigma uncertainties of the Q6DW

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magnitudes in the temperature are less than ~0.6 K in WACCM + DART and ~1.2 K in SABER (not shown),which are much smaller than the wave magnitudes by a factor of 2–3 and thus strengthen the consistencybetween WACCM + DART and SABER. For example, the timing of the peaks is in good agreementthroughout the year. The largest peak on the order of 7–8 K occurs at middle latitudes inAugust/September compares well between WACCM + DART and SABER. Note that the zonal wind peakoccasionally shifts toward higher latitudes, for example, the peak amplitude was actually located at ~20°Nin August/September in WACCM + DART and TIDI. A tentative explanation is the coupling between thefirst symmetric and antisymmetric modes.

We note that minor discrepancies do exist particularly between WACCM + DART and TIDI. For example, theQ6DW activity was not evident in March/April in TIDI observations. The TIDI-observed wave amplitude wasmuch larger (~20 vs. ~12 m/s) in late September, while it was weaker in mid-October (~12 vs. ~18 m/s), com-pared with WACCM + DART. Since the substantial Q6DW differences in the zonal wind exist betweenWACCM + DART and TIDI, we present the 1-sigma uncertainties of the wave magnitudes in Figure 3.WACCM + DART uncertainty is less than 2.5 m/s throughout the year and is indicative of the robustness ofthe Q6DW in WACCM + DART. Nevertheless, a much more substantial uncertainty is found in TIDI zonal windand the maximum is as large as ~8.4 m/s at low latitudes. This probably accounts for the weaker Q6DW in

Figure 1. Whole Atmosphere Community Climate Model with data assimilation provided by the Data AssimilationResearch Test Bed normalized wavelet spectrum (equator) of the westward propagating zonal wind perturbations withzonal wave number 1 at (a) 90, (b) 70, (c) 50, (d) 30, and (e) 10 km. The contour interval is 0.1. Dashed white lines mark theperiods of 5 and 8 days, respectively. Colored regions represent a significance level greater than 95%. White regionsindicate the cone of influence due to edge effects.

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March/April and the Q6DW absence in early and late November observed by TIDI. Another possible reason isthat although theWACCM+DART temperatures are directly constrained by the SABER andMLS observations,the WACCM + DART winds are adjusted based on the covariance information that is obtained from theensemble. That is, the temperature adjustment due to assimilating SABER observations produces acorresponding adjustment to the horizontal winds with a direction and magnitude that is based on thecovariance information. Given the relatively small ensemble size, and highly dynamic nature of the MLT,the temperature-wind covariance may not be entirely accurate. The sparsity of observations assimilated inthe MLT also only provides a relatively loose constraint at these altitudes. As such, there is no surprise tosee the differences between WACCM + DART assimilation model and observations. Nonetheless, ingeneral, WACCM + DART reproduces the observed Q6DW structure and magnitude within theuncertainties and thus allows us to explore the Q6DW sources, sinks, and propagation and dissipationcharacteristics. Although Figure 2 only compares the Q6DW at the peak altitudes, a similar level ofagreement is found throughout the whole middle atmosphere (not shown).

3. Results3.1. Altitude Versus Latitude Structure

Having ensured the quality of theWACCM + DART Q6DW, we will now focus on the altitude-latitude structureof the Q6DW during the prominent wave events in this section. Figure 4 exemplifies the vertical wave

Figure 2. Amplitudes of the quasi 6-day wave as a function of latitude and time in zonal winds at 90 km and temperaturesat 105 km simulated by the WACCM + DART (a, c) and observed by TIDI and SABER (b, d). White regions denote missingdata. SABER = Sounding of the Atmosphere using Broadband Emission Radiometry; TIDI = Thermosphere, Ionosphere,Mesosphere Energetics and Dynamics Doppler Interferometer; WACCM + DART = Whole Atmosphere Community ClimateModel with data assimilation provided by the Data Assimilation Research Test Bed.

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structure in three different fields (geopotential height, temperature, and zonal wind) on day 50,corresponding to the first Q6DW burst in 2007. The Q6DW shows a substantial vertical growth due to theexponential decline of air density. In geopotential heights, the peak amplitude (Figure 4a) reaches350–400 m and is located at around 110 km and ~60°S/N. At lower altitudes, a secondary peak of250–300 m is found at ~40 km and 75°N, while a localized maximum of 100–150 m is visible at ~60 kmand 50°S. The phases (Figure 4b) show an apparent downward progression at low latitudes in the MLTregion. At middle and high latitudes, the phases are characterized by both downward and polewardprogression, indicating that the wave energy flux is upward and equatorward. The temperature waveamplitude (Figure 4c) is as large as 6–8 K at ~120 km with a secondary peak of 4–6 K at ~85 km in bothhemispheres. Smaller peaks of 2–3 K occur at 50°S and 70°N in the stratosphere. The vertical two-peakstructure in geopotential height is self-consistent with the three-peak structure in temperature, since thegeopotential height is proportional to the vertical integral of temperature according to the hydrostaticequation in log-pressure coordinates. The zonal wind amplitudes (Figure 4e) maximize at a lower height of~90 km over the equator. The corresponding peak amplitude is on the order of ~20 m/s. The temperatureand zonal wind phases (Figures 4d and 4f) are consistent with geopotential height phases, that is,downward/poleward progression. Also, the estimated vertical wavelength of ~65–70 km in the MLT regionagrees well in all fields. It is worthwhile to point out that the apparent Q6DW equatorward propagation(shown in the phase) in the troposphere and stratosphere at the NH high latitudes is indicative of a high-latitude wave source region.

Figure 5 illustrates the altitude versus latitude distribution of wave amplitudes and phases during otherperiods of Q6DW activity, that is, days 85, 125, 245, and 285 (see Figure 1a). Here only the geopoten-tial height Q6DW is presented due to its self-consistency with temperature and zonal wind in themodel as discussed above. The general Q6DW structure during these periods is similar to the oneon day 50 with local maxima occurring in the NH and SH, respectively. Except for day 85 when thewave amplitude (Figures 5a and 5b) is more symmetric about the equator (close to the boreal vernalequinox), the summer hemisphere tends to have a larger amplitude. Specifically, the NH peak is largerthan the SH peak by a factor of 4 on day 245 (Figures 5e and 5f), while day 285 (Figures 5g and 5h)features a larger peak in the SH. Meanwhile, the wave propagation is upward and equatorward as thephase progression (right panels) is largely downward and poleward. Also, the stratospheric Q6DWtends to show a single peak in the polar region of one hemisphere (e.g., 30 km and 75°N on day85) rather than a paired-peaks symmetrical about the equator in the MLT region. Apart from this loca-lized peak in the magnitude, the corresponding phase shows the negative gradients with respect to

Figure 3. The 1-sigma uncertainty of the fitted Q6DW magnitude in zonal winds of (a) WACCM + DART and (b) TIDI.TIDI = Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics Doppler Interferometer;WACCM + DART = Whole Atmosphere Community Climate Model with data assimilation provided by the Data AssimilationResearch Test Bed.

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the increasing height and decreasing latitude. This indicates that the Q6DW may be excited in the NHpolar region and propagates equatorward and upward, growing to be a global mode at higheraltitudes. This is more closely discussed in the following section 3.2, which addresses waveexcitation, amplification, and attenuation.

Figure 6 displays two composites of the Q6DW amplitudes in temperature and zonal wind. The composite#1 is computed by averaging seven prominent wave events in 2007, while the composite #2 is the aver-age of four wave events occurring around days of 50, 285, 300, and 320, when the global zonal meanzonal winds (not shown) have a similar pattern. The composite #1 (left two columns) shows an almostsymmetric structure about the equator in the MLT temperature and zonal wind from bothWACCM + DART simulations and SABER and TIDI observations. This is not surprising because the antisym-metric component, which is likely caused by the wind instability associated with the zonal mean zonalwind pattern, has been reduced due to the averaging throughout the year. The composite #1 peak ampli-tude attains 5–6 K in the midlatitude temperature and 12–15 m/s in the low-latitude zonal wind. Thecomposite #2 (right two columns) is computed when the mesospheric/stratospheric zonal mean zonalwind is characterized by the westerlies in the NH and easterlies in the SH. In the lower thermosphere,the Q6DW (the third column) demonstrates a larger austral amplitude in the SH than in the NH by a fac-tor of 2, which indicates that the in situ wave source may play a role in magnifying the Q6DW as it isdiscussed in the section 3.2.

Figure 4. Whole Atmosphere Community Climate Model with data assimilation provided by the Data AssimilationResearch Test Bed amplitudes (left panels) and phases (right panels) of the quasi 6-day wave in geopotential heights(panels a and b), temperatures (panels c and d), and zonal winds (panels e and f) as a function of altitude and latitude onday 50. For amplitudes, the contour interval is 50m in geopotential heights, 1 K in temperatures, and 2.5 m/s in zonal winds.The contour interval is 30° for phases.

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3.2. Seasonal Dependence of Q6DW Excitation, Amplification, and Attenuation

Considering the burst-like occurrence of the Q6DW, we focus in the following on case studies centeredaround days of 50, 285, and 172. The first two cases correspond to the greatest Q6DW events at around equi-noxes in 2007, while the last case (boreal summer solstice) will demonstrate how the Q6DW is highly sup-pressed in the MLT region during solstices.3.2.1. Prevernal Equinoctial CaseWe first compute the Eliassen-Palm (E-P) flux, which describes the wave energy flow in the meridionalcross section (e.g., Andrews et al., 1987). In the spherical pressure coordinates, it takes the form ofequation (1).

Figure 5. Whole Atmosphere Community Climate Model with data assimilation provided by the Data AssimilationResearch Test Bed amplitudes (left panels) and phases (right panels) of the quasi 6-day wave in geopotential heights ondays 85 (Figures 5a and 5b), 125 (Figures 5c and 5d), 245 (Figures 5e and 5f), and 285 (Figures 5g and 5h). The contourinterval is 50 m for amplitudes and 30° for phases.

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F⃑ ¼Fϕ ¼ ρ0a cosϕ

v0θ0

¯θzuz � v0u0

!

Fz ¼ ρ0a cosϕ f � 1a cosϕ

u cosϕð Þϕ� �

v0θ0

θz� w0u0

� � ;

8>>>><>>>>:

(1)

where F⃑ is the E-P flux vector; Fϕ and Fz correspond to the meridional and vertical components, respectively;ρ0, a, f, ϕ, and Z are respectively the air density, mean Earth radius, Coriolis parameter, latitude, and log-pressure height; u

0, v

0, w

0, and θ

0represent the wave perturbations in zonal winds, meridional winds, vertical

winds, and potential temperatures, respectively. Overbar and subscript denote zonal average and derivative.Note that the E-P flux vector is scaled in the form of Ps

P

� �0:85 Fϕ

aπ ;Fz

3�105

n o, as proposed by Edmon et al. (1980).

This scaling method ensures that the wave E-P flux has a comparable magnitude in thetroposphere/stratosphere and in the mesosphere. Ps is the pressure at the surface, and P is the model stan-dard pressure levels. Also, the divergence of E-P flux (hereafter referred to as EPFD), as in equation (2), is usedto quantify the wave driving of the zonal mean circulation (Andrews et al., 1987). In this study, the EPFD isnormalized to ρ0a cos ϕ and thus has the unit of meters per second per day. A region of positive (negative)EPFD indicates a wave energy source (sink).

∇·F⃑ ¼ 1a cosϕ

Fϕ cosϕ�

ϕ þ Fz (2)

Figure 7a shows the E-P fluxes as a function of altitude and latitude on day 50. Above ~60 km, the E-P fluxvectors are characterized by two branches that are largely symmetric about the equator: The E-P flux isupward and equatorward as already indicated by the phase gradients in Figure 4. In the troposphere and stra-tosphere, however, the E-P fluxes display a coherent southward pattern from NH high latitudes to SH midla-titudes but with a dramatic weakening around the equator (the tropospheric southward E-P flux is clear evenif it is much weaker than that in the stratosphere. Figure 7c presents the plot of the individual EPY (meridionalcomponent of the E-P flux) which is definitely southward in the blue-shaded region. This means that theQ6DW could originate in the NH polar region and penetrate into the SH, growing to be a global mode. For

Figure 6. (left two columns) Altitude versus latitude cross section of composite 6-day wave amplitudes based on all sevenevents in 2007. (right two columns) Same as the left two columns but based on four events occurring around days of 50,285, 300, and 320. The upper (lower) panels are the simulated (observed) wave amplitudes in temperatures and zonalwinds fromWACCM+ DART (SABER and TIDI). Contour intervals are 1 K and 2.5 m/s, respectively, for temperature and zonalwind. SABER = Sounding of the Atmosphere using Broadband Emission Radiometry; TIDI = Thermosphere, Ionosphere,Mesosphere Energetics and Dynamics Doppler Interferometer; WACCM + DART = Whole Atmosphere Community ClimateModel with data assimilation provided by the Data Assimilation Research Test Bed.

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a more quantitative understanding, the meridional (EPY) and vertical (EPZ) components of the E-P fluxes areplotted individually in Figures 7c and 7d. Solid (dashed) line denotes northward (southward) EPY and upward(downward) EPZ. Blue shading indicates regions of southward EPY and upward EPZ. First, the southward EPYis the dominant feature below ~60 km between 40° and 60°N. There is a narrow but visible tube, located at40–60 km within 30°S/N, through which the boreal Q6DW is ducted into the SH. Afterward, the EPY isenlarged at 30°–50°S but close to be 0 in the polar regions at 60–80 km due to wave overreflection, whichcauses the cancellation of inflow (southward) and outflow (northward) wave energy. However, northwardE-P flux is enhanced above 80 km in the SH, indicating that the Q6DW is likely amplified along with theoverreflection. A similar scenario (Figure 7d) of the wave overreflection and amplification occurs in the NHpolar region at 60–80 km. It manifests more clearly in EPZ (Figure 7d), which is almost 0 at the heights of50–70 km (poleward of 60°N) due to the cancellation of inflow and outflow but becomes positive (upward)at the heights below and above. Accordingly, a positive EPFD (Figure 7b) appears at 60–80 km and 60°–80°of both hemispheres (stronger in the NH) and produces the eastward wave forcing, in correspondence tothe wave in situ sources. Moreover, the SH shows divergent E-P fluxes in the midlatitude lowermesosphere, which is centered at 60 km and 30°S and coincides with the enhanced E-P fluxes (Figure 7c).Conversely, the mesopause region is characterized by significant wave sinks, and the maximum E-P fluxconvergence attains 3–4 m/s/day at ~50°S and 30°N.

Figure 7. The E-P flux (a) and its divergence (b, in meters per second per day) of the quasi 6-day wave. The results areplotted as a function of altitude and latitude and correspond to day 50. The contour interval is 1 m/s/day for the EPFD.(c, d) The EPY and EPZ, respectively. Solid (dotted) line denotes northward (southward) EPY and upward (downward) EPZ.The contour interval is 0.2, and the blue-shaded region highlights the southward EPY and upward EPZ. (e) The negative ¯qϕ(red shaded) and wave critical layers (green line) superimposed by the zonal mean zonal winds. Black solid (dashed) linedenotes eastward (westward) winds. (f) The square of the refractive index. Yellow-shaded regions denote positive values. E-P = Eliassen-Palm; EPFD = divergence of E-P flux; EPY = meridional component of EP flux; EPZ = vertical component of EPflux.

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Wave overreflection and amplification processes are the key factors to understand the prominent Q6DW inthe MLT region. We thus further compute the meridional gradient of quasi-geostrophic potential vorticity( qϕ ) and the square of refractive index (m2), which are defined as in equations (3) and (4) below

(Andrews et al., 1987; Matsuno, 1970):

qϕ ¼ 2Ω cosϕ � u cosϕð Þϕa cosϕ

� �ϕ� aρ0

ρ0f2

N2 uz

�z

; (3)

m2 ¼ qϕa u� cð Þ �

ka cosϕ

�2

� f2NH

�2

; (4)

where c, k, N, H, and Ω are the wave zonal phase speed, zonal wave number, Brunt-Väisälä frequency, pres-sure scale height, and angular speed of the Earth’s rotation, respectively. Other quantities are as defined inequations (1) and (2). In principle, large positive m2 and qϕ are in favor of wave propagation, while concur-rently small m2 and qϕ would lead to wave breaking (Matsuno, 1970). The negative qϕ is a necessary butnot sufficient condition of barotropic/baroclinic instability, indicating energy conversion from the mean flowto the wave (Kuo, 1949; Matsuno, 1970; Meyer & Forbes, 1997).

Figure 7e displays the negative qϕ superimposed over the zonal mean zonal winds and critical layers of the

Q6DW as a function of altitude and latitude. The critical layer is defined as the wave phase speed (zonal) equalto the zonal mean zonal wind. It is noticeable that a pair of unstable regions (qϕ < 0) take place at 60–80 km

and high latitudes of both hemispheres with the critical layers colocated. As such, the Q6DW could be mag-nified by extracting the energy from the mean flow when it penetrates into these unstable regions. Moreimportantly, the enhanced wave would be further reflected by the critical layers and ultimately lead to thesignificant Q6DW in the mesopause region. The overreflection along with the energy conversion due tothe instability is hence acting as an in situ wave source, which in turn agrees with the positive EPFD(Figure 7b). Besides, a couple of negative qϕ patches are found at low and middle latitudes and likely play

a role in wave enhancement as well. For instance, the one located at 20°–40°S and 50–70 km is attributedto the easterly jets during summertime and probably strengthens the Q6DW passing through. Figure 7fshows the m2, which is positive equatorward of 50°–60°in both hemispheres, in correspondence with theequatorward and upward wave propagation pointed out before.

3.2.2. Postautumn Equinoctial CaseFigure 8 is the result for day 285, which corresponds to the second strongest Q6DW event as suggested bythe wavelet spectrum (Figure 1). With regard to the E-P fluxes above 80 km (Figure 8a), the austral branchis much stronger than the boreal one. The greatest EPY and EPZ in the SH, shown in Figures 8c and 8d, are~3 times as large as those in the NH. This is in agreement with the larger wave forcing of ~� 5 m/s/day inthe austral lower thermosphere (Figure 8b). Except for the asymmetry in E-P flux and its divergence, the gen-eral feature is similar to that in the prevernal equinoctial case (Figure 7). For example, the wave propagation isdominated by the equatorward and upward pattern, in support of the positivem2 at low andmiddle latitudes(Figure 8f). Significant wave sources are situated at high latitudes as indicated by the positive EPFD(Figure 8b). The large austral branch of E-P flux comes from the inner part of the unstable region (qϕ < 0,

Figure 8e) that is overlapped by the critical layer at 70–90 km. This situation demonstrates that the incomingQ6DW is amplified due to instabilities and overreflected by the critical layer, propagating away from thesource region. Though the instability due to the background wind curvature occurs at NH high latitudes aswell, the boreal branch is not significantly magnified yet. The likely reason is the absence of a wave criticallayer due to the eastward zonal mean zonal wind (Q6DW is westward propagating). This is also responsiblefor the weaker Q6DW activity on day 285 (when the critical layers disappear in both hemispheres) and thelarger wave amplitude in the NH on days 125 and 245 (the critical layer occurs only in the summer hemi-sphere). Note that the figures for days 125 and 245 are not shown, as the mechanism is the same.

3.2.3. Solstice CaseTo compare with the equinoctial cases and elucidate the reasons of the Q6DW absence in the MLT duringsolstices, Figure 9 summarizes the relevant quantities for boreal summer solstice conditions (day 172).Figure 9a shows the wave E-P flux vectors and the negativeqϕ as well as the critical layers and the zonal mean

zonal winds. The Q6DW has an obvious origin around the center of the westerly jets at 40°S and 50 km. Away

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from the source region, the Q6DW propagates upward and toward both the austral polar and equatorialsides. We note that the geopotential height wave amplitude (not shown) near the source region is on theorder of 150–200 m, which is even larger than those on days 50 and 285. However, the E-P flux decaysrapidly with increasing height in the SH. By superposing E-P flux vectors on the square of refractive index(m2), shown in Figure 9b, it can be seen that (i) the region of positive m2 shrinks toward the equator at 50–100 km in the SH and (ii) the Q6DW cannot propagate into the mesosphere and interact with the unstableregion there. Additionally, the E-P flux pointing to the equator away from the source region is strongly

Figure 8. Same as Figure 7 but for day 285. E-P = Eliassen-Palm; EPFD = divergence of E-P flux.

Figure 9. (a) The negative ¯qϕ (red shaded) and critical layers (green line) superimposed over the zonal mean zonal winds(black solid [dashed] line denotes eastward [westward] winds) and the Eliassen-Palm flux vectors (blue). (b) The squareof refractive index. Yellow-shaded regions indicate positive values. The results are plotted as a function of altitude andlatitude and correspond to day 172.

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attenuated. Although the zonal mean zonal wind in the NH shows instabilities at 50–70 km, the Q6DW cannotpenetrate into this unstable region to extract the energies from the mean flow. This is because the criticallayer is acting to enclose the unstable region in the NH. Consequently, the Q6DW is strongly absorbed bythe critical layer rather than being amplified.

The E-P flux divergence and negative ¯qϕ for the two composites are shown in Figure 10. The upper panels are

the results computed on the basis of seven Q6DW events in 2007 (composite #1). Above 90 km, the EPFD dis-plays a quasi-symmetric structure with respect to the equator. The most negative EPFD (upper-left panel)occurs at 20°–30°S/N and 100–110 km with a magnitude of 1–1.5 m/s/day, indicating significant wavemomentum deposition. A distinctive wave source corresponding to the positive EPFD shows up in the boreal

polar region, which is consistent with the negative ¯qϕ(upper-right panel) due to the wind instability. Also, the

composite #2 EPFD and ¯qϕ (lower panels) are computed by averaging four Q6DW events with the similar

zonal mean zonal wind pattern as aforementioned. The two composite EPFD distributions are very similar,although magnitudes are somewhat larger in the SH lower thermosphere of composite #2 (lower-left panel).We note that there is an instability region located at the SH high latitudes, which can lead to the waveenhancement as well.

Figure 10. The composite Eliassen-Palm flux divergence (a) and the negative ¯qϕ (b) based on seven quasi 6-day waveevents in 2007. (c, d) Same as those in the upper panels but based on four events occurring on days of 50, 285, 300,and 320. EPFD = divergence of Eliassen-Palm flux.

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3.2.4. Seasonal VariationThe case studies discussed above indicate that the key factors associated with a robust Q6DW in the MLT arethe zonal mean zonal wind instability (qϕ < 0), wave critical layer (u� c ¼ 0) and waveguide (m2 > 0). To

firmly establish this line of reasoning, Figure 11 demonstrates the time series of the meridional E-P flux com-ponent (blue and orange vectors denote southward and northward EPY, respectively.), negative qϕ (green

shaded) and wave critical layers (red lines) at five different altitudes covering from the wave source to peakwave amplitude height regions. The EPY has been normalized to themaximum value in the whole spatiotem-poral domain to make a direct comparison feasible. Also, the magnitude of EPY in Figure 11 represents thetotal magnitude of E-P flux vector with the EPZ magnitude taken into account (because the EPY and EPZare simultaneously amplified and overreflected). See in Figures 8a and 8b, the Q6DW is evident at middleand high latitudes in the winter hemisphere at 30 km and grows vertically, as seen in the larger EPY at50 km. Critical layers start to occur in the SH during boreal wintertime. The EPY in the NH can cross the equa-tor but is absorbed by the critical layers (for example, in December and January). At 70 km (Figure 11c), highlatitudes become more unstable and the critical layers occur in both hemispheres. We note that the criticallayers tend to expand equatorward during solstices but retreat and gradually disappear with approaching

Figure 11. Time series of critical layers (red line), negative ¯qϕ (green shaded) and meridional component of Eliassen-Palmflux (vectors). Blue and orange vectors denote southward and northward fluxes, respectively. From top to bottom, theresults are shown at the heights of (a) 30, (b) 50, (c) 70, and (d) 90 km.

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equinoxes. E-P fluxes approaching the critical layers during solstices (June and July in the NH and Decemberand January in the SH) decay rapidly, while E-P fluxes are magnified and overreflected duringpreequinox/postequinox (February in the SH and October in the NH). In late February, the southward EPYat 50 km and 20°S (Figure 11b) continues to propagate southward and eventually reaches the unstableregion at SH high latitudes, as seen at 70 km (Figure 11c). The E-P flux is then reflected by the critical layercolocated with the unstable region, resulting in the concurrent southward and norward E-P fluxes at20°–50°S. Due to the amplification and overreflection, the surviving Q6DW grows and becomes large inthe mesopause region, as seen at 90 km (Figure 11d). In late March, an obvious Q6DW is found at 90 kmas well, even if the critical layers were absent in both hemispheres. However, the energy conversion fromthe mean flow to the wave most likely still took place due to the presence of high-latitude instabilities.Overall, the evolution of the critical layer and qϕ explains the temporal evolution of the mesospheric

Q6DW very well. It is worthwhile to point out that the waveguide (m2) also plays a role in the wavetemporal variability (like preventing the Q6DW from reaching the mesosphere in the winter hemisphere).The related effect has already been closely elucidated in the solstice case (Figure 9).

Figure 12. (top panel) Meridional (v*, in meters per second) and (middle panel) vertical (w*, in centimeters per second)components of the residual circulation due to the dissipative 6-day wave on day 50. The bottom panel combines themeridional and vertical components as a vector plot. The contour interval is 0.1 m/s and 0.02 cm/s, respectively, for v* andw*. Solid (dotted) line denotes northward (southward) v* and upward (downward) w*.

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4. Discussions

In addition to its important role in the energy and momentum budget inthe middle atmosphere, the Q6DW also contributes appreciably to thevariability of the T-I system. Recently, a few efforts have been made onexploring the connection between the Q6DW and the T-I system (forexample, Pedatella et al., 2012; Gan et al., 2016, and reference therein).The strong Q6DW in the equatorial zonal wind has been found tomodulate the E region dynamo, plasma uplifting, and a Q6DW-like oscil-lation in F region electron density. Gan et al. (2017) also discusseddynamo wind modulation by secondary waves due to the Q6DW andtidal interaction. While WACCM + DART cannot simulate the electrody-namics in the ionosphere, the significant Q6DW in the low-latitude zonalwinds (shown in Figure 4) point to potential interaction with the Eregion dynamo.

Moreover, an alternative pathway by which the Q6DW can affect the T-I isassociated with constituent transport via wave-induced residual circula-tion. The westward momentum deposition in the MLT region (Figures 7b

and 8b) results in the generation of a poleward circulation that is described by equation (5) (Andrews et al.,1987):

v �6dw ¼ � 1

ρ0ρ0

v0θ0

θz

!z

;w�6dw ¼ 1

a cosϕcosϕ

v 0θ0

θz

!ϕ

;

8<: (5)

which is in the spherical pressure coordinates, and v�6dw and w�6dw correspond to the meridional and vertical

components of the residual circulation. Other quantities are as defined in equations (1)–(4) above.

Figure 12 exemplifies the residual circulation produced by the dissipative Q6DW on day 50. The meridionalcomponent (Figure 12a) is dominated by the poleward pattern with a maximum value of 0.3–0.4 m/s in bothhemispheres. The maximum vertical component (Figure 12b) at low latitudes is directed upward with valuesof 0.06–0.08 cm/s and downward at middle and high latitudes with values of 0.18–0.2 cm/s, which is approxi-mately 2 orders smaller than the meridional one. Figure 12c combines the meridional and vertical compo-nents into wind vectors. The circulation pattern is symmetric about the equator and composed ofupwelling at 10°–30° and downwelling at higher latitudes. Note that in contrast to this, the mesospheric resi-dual mean circulation driven by the gravity wave drag consists of upwelling in the NH polar region (winter)and downwelling in the SH polar region (summer) as well as the NH-to-SH circulation. Hence, the residual cir-culation induced by the Q6DWweakens the mean circulation in the NH but strengthens the mean circulationin the SH. Also, the Q6DW-induced circulation may transport molecular oxygen and nitrogen upward, result-ing in an overall depletion of the O/N2 density ratio and total electron density (These two parameters arepositively correlated at around the peak electron density height.) in the T-I system as proposed by Ganet al. (2015).

Figure 13 demonstrates the composite residual circulation based on seven Q6DW events in 2007. The generalpattern is characterized by the upward and poleward circulations in the MLT of both hemispheres, which is inline with the single circulation pattern of any particular event. This means that such circulation pattern is arobust nature of the dissipative Q6DW in the MLT.

5. Conclusions

In the current work, theWACCM+DART assimilationmodel was used to diagnose the Q6DW from the surfaceup to the lower thermosphere in 2007. The main findings are summarized as follows:

1. Two prominent Q6DW events occur in later February and mid-October. The wave period of ~7 days issomewhat larger than 6.5 days, likely due to Doppler shift. Somewhat weaker Q6DW events occurred inMarch and May, and in August/September and November. Overall, equinoctial conditions are favorablefor a robust Q6DW in the MLT, while the Q6DW is absent during solstices.

Figure 13. The composite quasi 6-day wave-induced residual circulation byaveraging the residual circulations of seven quasi 6-day wave events.

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2. The WACCM + DART Q6DW compares well with the Q6DW observed by SABER (temperature) and TIDI(zonal wind). The agreement with SABER is expected because these data are assimilated intoWACCM + DART. More importantly, the zonal wind (not assimilated) Q6DW shows also a reasonableagreement with the observations, in terms of both temporal variability and latitudinal distribution.Minor discrepancies are likely attributed to missing data and/or asynoptic sampling of TIDI measurements(tidal aliasing effect). This gives confidence into the WACCM + DART Q6DW, including fields that have notbeen assimilated.

3. Equinox case studies indicate that the salient Q6DW in the MLT is tied to wave amplification along withoverreflection. Wave amplification is attributed to the barotropic/baroclinic instability that largely occursin the high-latitude lower mesosphere for the Q6DW case. Overreflection takes place when the Q6DWencounters a critical layer. The interaction of a critical layer with an unstable region is thus the most favor-able condition for a large Q6DW in the MLT.

4. The Q6DW absence in the MLT during solstice conditions is explained as follows. In the winter hemi-sphere, the negative waveguide blocks the vertical wave propagation from the source region (close tothe center of the westerly jets). In the summer hemisphere, the critical layer envelops the unstable regionand leads to a rapid decay of the Q6DW.

5. The westward forcing on the background winds due to the wave momentum deposition by the Q6DWgenerates residual circulation that is upward and poleward in both hemispheres. The overall effect is thatthe residual circulation induced by the Q6DW weakens the gravity wave drag driven mean circulation inthe summer hemisphere but strengthens it in the winter hemisphere. In addition, the Q6DW-induced cir-culation is expected to transport constituents (molecular oxygen and nitrogen) upward and to furthercauses an overall change of the mean state of T-I system.

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AcknowledgmentsQ. G. and J. O. acknowledge support bythe National Science Foundation (NSF),through awards AGS-1139048, AGS-1112704, and AGS-1552176. TheNational Center for AtmosphericResearch is sponsored by the NationalScience Foundation. WACCM and DARTare open source, and the source code ispublicly available through the NCARwebsite. The WACMM + DART outputsare archived on the NCAR highperformance storage system, and thedata used to generate the figures areavailable through the link of https://1drv.ms/f/s!An2zQdOzk5phhLp_m9LUW7TTse4rYA. SABER and TIDI datasets are open access and can bedownloaded via the links of http://saber.gats-inc.com and http://timed.hao.ucar.edu/tidi/.

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