Waves propagating in the stably stratified atmosphere with buoyancy as a restoring force are traditionally called gravity waves. Gravity waves transport momentum upward from the troposphere to the middle atmosphere and are recognized as a major driving force for large-scale meridional circulation in the middle atmosphere (e.g., Fritts and Alexander, 2003). Because the horizontal wavelengths of significant parts of gravity waves are shorter than several hundreds of kilometers, many climate models use parameterization methods to calculate momentum deposition via unresolved gravity waves (e.g., McFarlane, 1987; Scinocca, 2003; Richter et al., 2010). Currently, many gravity wave parameterizations are based on very simple assumptions related to essential wave dynamics, such as source spectra and propagation properties. Even though physically based gravity wave parameterizations have recently been developed (e.g., Beres et al., 2004; Song and Chun, 2005; Cámara et al., 2014; Charron and Manzini, 2002; Richter et al., 2010), tuning parameters, which are ill-defined in general circulation models, such as the moving speeds of sub-grid convective cells related to the phase speeds of launched gravity waves (Beres et al., 2004; Choi and Chun, 2011) or the occurrence rate for wave launching for the frontogenesis function (Richter et al., 2010), still exist.

Geller et al. (2013) showed that parameterized gravity waves in climate models are not realistic in several aspects, particularly at high latitude, compared to high-resolution observations and high-resolution general circulation models. Such improper specifications of gravity wave momentum deposition by parameterizations are thought to lead to several serious problems, such as the so-called cold-pole bias problem (SPARC, 2010; McLandress et al., 2012; Garcia et al., 2017). However, many previous studies have suggested that the Antarctic region has multiple types of gravity wave sources, such as the mountains of the southern Andes and the Antarctic Peninsula (e.g., Eckermann and Preusse, 1999; Alexander and Teitelbaum, 2007; Sato et al., 2012), the small islands around the Southern Ocean (Wu et al., 2006; Alexander et al., 2010; Hoffmann et al., 2013), the leeward propagation of gravity waves from lower and high latitudes (Sato et al., 2009, 2012; Hindley et al., 2015), the upper tropospheric jet stream (Shibuya et al., 2015; Jewtoukoff et al., 2015), and the strong polar night jet (Yoshiki and Sato, 2000; Sato and Yoshiki, 2008; Sato et al., 2012). Therefore, these processes may frequently overlap in time and space, suggesting that process-based analyses based on observational data are unavoidable. In response to such recognitions of the importance of gravity waves in the Antarctic, several observational campaigns in the lower stratosphere have been conducted (e.g., VORCORE, Hertzog et al., 2008; CONCORDIASI, Rabier et al., 2010; DEEPWAVE, Fritts et al., 2016).

Due to the harsh environment in the Antarctic, it is still challenging to perform observation of the mesosphere. Previous studies have used several observational instruments at limited ground-based observation sites, such as medium-frequency (MF) radar (e.g., Dowdy et al., 2007), meteor radar (Tsutsumi et al., 1994; Forbes et al., 1995), metal fluorescence lidar (e.g., Gardner et al., 1993; Arnold and She, 2003; Chen et al., 2016), and airglow imagers (e.g., Garcia et al., 2000; Matsuda et al., 2014). Using these instruments, these studies have primarily focused on the temporal–spatial structures of migrating and non-migrating tides using observational data at one or a couple Antarctic stations (e.g., Murphy et al., 2006, 2009; Hibbins et al., 2010) and the generation and propagation mechanisms of tides using numerical models (e.g., Aso, 2007; Talaat and Mayr, 2011). However, the dominant vertical wavenumbers of gravity waves have rarely been examined due to the coarse vertical resolution of the MF radars. Moreover, due to the limited number of Antarctic stations, it is still very difficult to examine the spatial structures of gravity waves observed in the mesosphere. Therefore, discussions concerning the dynamics of gravity waves in previous studies have been based on results from frequency spectrum analyses of the horizontal winds (e.g., Kovalam and Vincent, 2003) or from variance analyses of gravity wave wind fluctuations and their seasonal (e.g., Hibbins et al., 2007) and interannual (e.g., Yasui et al., 2016) variations. Even though a few studies using ground-based observations attempted to estimate the sources of the observed mesospheric gravity waves using heuristic ray tracing methods (e.g., Nicolls et al., 2010; Chen et al., 2013), a statistical analysis is required to understand the dynamical characteristics of mesospheric gravity waves.

Observational instruments on board satellites have also been used to detect the spatial distributions of temperature (radiance) data in the mesosphere (MLS: Wu and Waters, 1996; Jiang et al., 2005; CRISTA: Preusse et al., 2006; SABER: Preusse et al., 2009; Yamashita et al., 2013). In addition, the momentum flux of mesospheric gravity waves is estimated using the SABER temperature data (Ern et al., 2018). However, the variances and momentum fluxes estimated from satellite data contain contributions from a limited portion of the gravity wave spectrum due to the observational filtering effects of each satellite instrument (e.g., Alexander et al., 2010).

To examine the dynamical characteristics of gravity waves, high-resolution general circulation models that directly resolve a relatively wide range of the gravity wave spectrum are powerful tools. At present, however, only four models have been used to directly resolve mesospheric gravity waves with minimal resolved horizontal wavelengths (λmin) of less than 400 km and with fine vertical resolutions (dz) of less than 600 m in the middle atmosphere. Becker (2009) used the Kühlungsborn Mechanistic General Circulation Model (KMCM) to examine the sensitivity of the state of the upper mesosphere to the strength of the Lorenz energy cycle in the troposphere. Zülicke and Becker (2013) used KMCM to examine the dynamical responses of the mesosphere to a stratospheric sudden warming (SSW) event. In addition, by combining KMCM simulations and MF radar observations in the Northern Hemisphere, Hoffman et al. (2010) explored the relationship between the activities of mesospheric gravity waves and critical level filtering via background wind. Liu et al. (2014) used the mesosphere-resolving version of the Whole Atmosphere Community Climate Model to create a horizontal map of mesospheric perturbations such as concentric gravity waves, which are likely excited by deep convection in the low to middle latitudes. The KANTO model (Watanabe et al., 2008) is based on the atmospheric component of version 3.2 of the Model for Interdisciplinary Research on Climate (MIROC; K-1 Model Developers, 2004; Nozawa et al., 2007). Sato et al. (2009) used KANTO to discuss the dominant sources of mesospheric gravity waves using characteristics of the 3-D momentum flux distribution. Tomikawa et al. (2012) examined the dynamical mechanism of an elevated stratopause event associated with an SSW event that spontaneously occurred in the KANTO model. Last, the JAGUAR model is the KANTO model with the model top extended to ztop≅150 km including nonlocal thermodynamic equilibrium (non-LTE) for infrared radiation processes. Using JAGUAR, Watanabe and Miyahara (2009) examined the dynamical relationship between migrating tides and gravity wave forcing at low latitudes. Note that all the current models permitting mesospheric gravity waves described above are hydrostatic general circulation models.

As mentioned above, a few studies have focused on the dynamical characteristics of gravity waves, such as their propagation and/or generation processes in the Antarctic mesosphere. However, no study has attempted to simulate mesospheric gravity waves whose reality is confirmed via high-resolution observations for a long time period. This is partially because there are few observational instruments with a sufficiently high resolution to validate mesospheric gravity waves simulated in models. Therefore, the dynamical characteristics of gravity waves observed in the Antarctic mesosphere have not been fully examined using both observations and numerical simulations.

This study uses two novel methods. One is the first Mesosphere–Stratosphere–Troposphere/Incoherent Scattering (MST/IS) radar in the Antarctic, which was recently installed at Syowa Station (39.6∘ E, 69.0∘ S) by the “Program of the Antarctic Syowa MST/IS radar” project (the PANSY radar; Sato et al., 2014). The PANSY radar is capable of capturing the fine vertical structures of horizontal and vertical mesospheric wind disturbances when the mesosphere is ionized, primarily by solar radiation during the daytime. Such a high resolution is unique in the Antarctic. This means that the observational data from the PANSY radar can be used to validate the results of models permitting mesospheric gravity waves at fine vertical resolution. Furthermore, this study uses the high-top version (Shibuya et al., 2017) of the Non-hydrostatic Icosahedral Atmospheric Model (NICAM; Satoh et al., 2014). This is a global cloud-resolving model with a non-hydrostatic dynamical core with icosahedral grids. Such a non-hydrostatic model is likely preferable for simulations of the high-intrinsic-frequency gravity waves contributing to a large portion of the momentum flux convergence in the upper-middle atmosphere (e.g., Reid and Vincent, 1987; Fritts and Vincent, 1987; Fritts, 2000; Sato et al., 2017). Moreover, gravity waves generated by deep convection are expected to be correctly resolved in non-hydrostatic models.

Recently, using continuous PANSY radar observations of polar mesosphere summer echoes (PMWEs) at heights from 81 to 93 km, Sato et al. (2017) showed that relatively low-frequency disturbances from 1 day-1 to 1 h-1 primarily contribute to the zonal and meridional momentum fluxes. This study examines the dynamical characteristics of gravity waves with relatively low frequency in the Antarctic mesosphere, such as the wave parameters, propagation, and generation mechanisms, via a long-term simulation using the high-top high-resolution non-hydrostatic general circulation model for 5 months from April to August in 2016. The simulated wind fields are closely compared to the PANSY radar observations at small scales and the MERRA reanalysis data at large scales. In addition, the statistical characteristics of the mesospheric disturbances simulated by NICAM, such as the frequency (ω) spectra of each variable, the kinetic and potential energies, and the momentum and energy fluxes of the gravity waves, are examined.

This paper is organized as follows. The methodology is described in Sect. 2. The numerical results are compared to the observational results in Sect. 3. The gravity wave characteristics are examined based on a spectrum analysis in Sect. 4. A discussion is presented in Sect. 5, and Sect. 6 summarizes the results and provides concluding remarks.

Recently, Sato et al. (2017) estimated the power spectra of horizontal and vertical wind fluctuations and momentum flux spectra over a wide frequency range from 2π/8 min to 2π/20 days using continuous PMSE observation data from the PANSY radar over three summer seasons. It was shown that the spectral slope of Pw(ω) at frequencies from 2π/2 h to 2π/5 days is nearly flat in the height range of 84–88 km, which is particularly clear in the spectra of observations by the full PANSY system in the 2015–2016 austral summer season. Even though the altitude range and season examined by Sato et al. (2017) are different from those studied in this study, Pw(ω) simulated by NICAM, as shown in Fig. 8c, is consistent with the PANSY radar observations. Moreover, Sato et al. (2017) demonstrated that the power spectrum of the vertical flux of the zonal momentum (Re[U(ω)W∗(ω)]) has a positive isolated peak near the inertial frequency in the eastward background zonal wind in the summer season. The shape of Re[U(ω)W∗(ω)] shown in NICAM is consistent with the results of Sato et al. (2017), even though the sign shown in this study is negative under the westward background zonal wind in winter. Conversely, using the Fe Boltzmann lidar at McMurdo Station (166.7∘ E, 77.8∘ S), Chen et al. (2016) showed that Pt(ω) has a broad spectrum peak at frequencies from 2π/3 to 2π/10 h centered at approximately 2π/8 h at a height of 85 km in June for the 5 years of 2011–2015, which is also consistent with the Pt(ω) result in Fig. 8d. The latitude–height section of Re[ρ0V(ω)W∗(ω)̃] in Fig. 12b indicates that the spectral peak from 2π/3 to 2π/10 h is composed of gravity waves originating over the Antarctic continent. These results indicate that the spectra of the mesospheric disturbances simulated in NICAM are very realistic at high latitudes in the Southern Hemisphere.

The spectral peaks of Pv(ω) without the migrating tides in the mesosphere are simulated near the inertial frequencies at latitudes from 30 to 75∘ S. Therefore, the quasi-12 h inertia–gravity waves at Syowa Station examined by Shibuya et al. (2017) can be interpreted as quasi-inertial period gravity waves. Moreover, it is shown that Re[U(ω)W∗(ω)] also has negative isolated peaks near the inertial frequency. One explanation for the existence of these isolated peaks can be derived from the propagation characteristic of the gravity waves following Sato et al. (1999). The horizontal group velocity Cgh and the vertical group velocity Cgz of the gravity waves are expressed as Cgh=2m2ω^2-f2kk2+m2kk+U and Cgz=-2mω^2-f2k2+m2. It is easily confirmed from Eqs. (9) and (10) that Cgh and Cgz become zero when the intrinsic frequency ω^ is equal to the inertial frequency f at a latitude called the critical latitude. When gravity waves propagate poleward and then reach the critical latitude, the energies of the gravity waves may be accumulated with small Cgh and Cgz and be seen as isolated peaks near the inertial frequency. Therefore, it is likely that the existence of the clear isolated peaks near the inertial frequencies in the mesosphere is explained by the poleward propagation of gravity waves with quasi-inertial frequencies and negative Re[U(ω)W∗(ω)].

The feature at which the horizontal scales of the gravity waves become larger near the inertial frequency in Fig. 14 is also explained by the accumulation of gravity waves. Assuming that the explicit dependence of the absolute frequency function Ω on x and t is contained entirely in the background wind U(xt) and that the background vertical wind velocity is negligible (Bühler and McIntyre, 2005), the time evolution of the horizontal wavenumber vector is described by dgdtkl=-UxVxUyVykl, where U denotes the background wind velocity, Ω is defined as Ω=ω^+k⋅U, and dg/dt denotes the time derivative along the ray defined as ∂/∂t+Cg⋅∇.

Here, the time evolution of the wavenumber is simplified by only considering the meridional shear of the zonal background wind Uy: dgdtl=-Uyl. Because the signs of Re[V(ω)W∗(ω)] for gravity waves with ω^∼f are primarily negative, the signs of l are also negative assuming upward propagation. In the high-latitude region where Uy>0 (Fig. 12), the absolute value of negative l becomes small, indicating an increase in the horizontal wavelengths. Such a deformation is effective for gravity waves with ω^∼f due to their small Cgh and Cgz. This is likely the reason why large-scale gravity waves contribute to the spectral peaks of Re[U(ω)W∗(ω)] near the inertial frequencies primarily in the mesosphere. In addition, the deformation may also contribute to small Re[V(ω)W∗(ω)̃] around f in the mesosphere (Fig. 11) owing to small negative l.

Note again that the analysis in this study is based on the ground-based frequency and not on the intrinsic frequency; the effects of the Doppler shift are inevitably included. Here, the qualitative comprehension of the Doppler shift has been posed in the austral winter mesosphere. In Fig. 12, it was shown that Re[U(ω)W∗(ω)] has negative spectral values at heights from 25 to 70 km in the high-latitude Southern Hemisphere. This indicates that gravity waves have negative zonal wavenumbers in the westerly jet. As a result, the intrinsic frequency should be larger than the observed frequency (Eq. 3). In addition, gravity waves with relatively low frequencies propagate poleward since the signs of Re[V(ω)W∗(ω)] at frequencies slightly longer than the inertial frequency are negative (Figs. 11 and 12). In the case with gravity waves propagating poleward with frequencies lower than 2π/12 h in the Southern Hemisphere, poleward propagation of gravity waves stalls at a latitude where ω^∼f. This latitude is poleward of a latitude where “ω” ∼f since ω^ is larger in the high-latitude region. Thus, assuming that the observed frequency of gravity waves is nearly conserved during the propagation, the energy peak likely appears at frequencies slightly smaller than the inertial frequency. In addition, according to the dispersion relation of gravity waves, k/m becomes small at latitudes where ω^∼f. As a result, the ratio of the kinetic and potential energies shifts toward the kinetic energies, and then a parcel motion on the gravity waves becomes horizontal. Thus, it is suggested that the isolated peak at frequencies slightly smaller than the inertial frequency is more evident in the spectra of the meridional wind than that of the temperature, which is consistent with the result in Fig. 9.

However, further studies are required to understand the existence of the isolated peaks in the mesosphere. At a height of 25 km, gravity waves with large negative Re[U(ω)W∗(ω)] tend to prefer frequencies from 2π/12 to 2π/24 h, which is related to the existence of the isolated peaks in the mesosphere. The physical reasons why these observed frequencies are preferred are still unclear. Moreover, the signs of Re[V(ω)W(ω)] at the isolated peaks from 2π/8 to 2π/10 h from 77 to 90∘ S are positive throughout the middle atmosphere, suggesting that these peaks are due to gravity waves originating from a region over the Antarctic continent and/or the coastal region and not from low-latitude regions. These points should be examined relative to the generation mechanisms of gravity waves, which are related to the observed frequencies of the gravity waves.

It appears that the quasi-12 h gravity waves have horizontal scales larger than at least 1000 km. Such gravity waves are not fully resolved by the MERRA reanalysis data (Fig. 5), likely because the vertical resolution of MERRA (Δz∼3.2 km) is insufficient to simulate gravity waves with such vertical wavelengths. The momentum deposition caused by the quasi-inertial-period gravity waves may not be calculated by parameterizations because current parameterization schemes focus only on gravity waves with short horizontal wavelengths. The momentum deposition missed from such quasi-inertia–gravity waves may be one of the key components needed to solve the cold-bias problem in the winter–spring polar middle atmosphere.

On the contrary, as mentioned in Sect. 3.2, the high-top NICAM overestimates the wave amplitude in the mesosphere. Lane and Knievel (2005) showed that gravity waves that were vertically propagating in simulations with coarse resolutions become vertically trapped in those with fine resolutions. A similar discussion was also given by Watanabe et al. (2015), although they focused on a vertical resolution in a numerical model. Thus, it is inferred that some simulated gravity waves that propagated to the mesosphere are trapped or breaking in lower altitudes in the actual atmosphere, leading to the overestimation of the wave energy in NICAM compared with the observation.

The first long-term simulation using the high-top non-hydrostatic general circulation model was performed to analyze mesospheric gravity waves in the period from April to August 2016. Successive runs lasting 7 days were run using initial conditions from the MERRA reanalysis data with a 2-day overlap between consecutive runs. The data for the analyses were compiled using the final 5 days of each simulation. The analysis was carefully performed to avoid the influence of artificial gaps between the different runs. Our main results are summarized as follows.

The mesospheric wind fields simulated by NICAM are realistic according to a comparison with the PANSY radar observations, even though the amplitudes of the wind disturbances appear to be larger than those of the observations. In addition, the large-scale structure of the zonally averaged zonal winds in the latitude–height section is also comparable to the features in the MERRA reanalysis data.

This study offers a quantitative discussion based on high-resolution observations and numerical models. Statistical analyses of inertia–gravity waves in the mesosphere in different seasons are required to understand the momentum budget in the mesosphere combining the PANSY observations and numerical simulations using NICAM.