Large-Amplitude Inertia Gravity Waves Over Syowa Station: Comparison of PANSY Radar and ERA5 Reanalysis Data

Abstract

We examined large-amplitude inertia gravity waves (GWs) over Syowa Station, Antarctica using the PANSY (Program of the Antarctic Syowa MST/IS) radar data and the latest reanalysis (ECMWF reanalysis v5; ERA5) from October 2015 to September 2016. Focusing on large-amplitude events with large absolute momentum flux (AMF), hodograph analysis was applied to both data to estimate the wave parameters. It showed that the inertia GWs with a downward phase velocity becomes dominant in the stratosphere. Although their vertical wavelengths got shorter with altitude, their intrinsic periods and horizontal wavelengths got longer with altitude. In addition, their southward propagation was predominant in the stratosphere. Although height dependence of the estimated wave parameters is consistent with previous studies investigating inertia GWs over Syowa Station, some features specific to large-amplitude inertia GWs were also observed. The GW features obtained from PANSY were mostly consistent with those from ERA5 except for their amplitudes. Comparison of AMF between PANSY and ERA5 indicated that ERA5 significantly underestimated the AMF by a factor of 5 between 5 and 12.5 km altitudes and more above 12.5 km. Difference of horizontal and vertical wind power spectra between PANSY and ERA5 is quantitatively consistent with the difference of AMF and its height dependence. It was found that underestimation of vertical wind spectra primarily contributed to the underestimation of AMF in ERA5. The greater underestimation of AMF in the stratosphere might be due to larger vertical grid spacing in ERA5 and the shorter vertical wavelengths of the dominant GWs in the stratosphere.

Key Points

• We investigate the large-amplitude gravity wave events over Syowa Station, Antarctica using PANSY radar and ERA5 reanalysis

• The absolute momentum flux from ERA5 is smaller than the observed one by a factor of 5 at 5–12.5 km altitudes and even smaller above that

• Underestimation of absolute momentum flux in ERA5 can be explained by the underestimation of the power spectra of horizontal and vertical winds

Plain Language Summary

Gravity waves (GWs) are important waves that transport momentum and energy in the atmosphere but it is known that atmospheric reanalysis data cannot adequately represent them. In this study, we compared the PANSY (Program of the Antarctic Syowa MST/IS) radar, which can capture gravity waves over almost the entire frequency range above Syowa Station over Antarctica with the latest atmospheric reanalysis ERA5 (ECMWF Reanalysis v5), which has high spatiotemporal resolution to determine the extent to which ERA5 can represent gravity waves. The results showed that ERA5 reproduced the properties of gravity waves (i.e., wavelength and direction of propagation) fairly well but underestimated the momentum flux of gravity waves by a factor of about five in the troposphere and more than that in the stratosphere. Furthermore, a comparison of their spectra quantitatively revealed that the underestimation of momentum flux in ERA5 is mainly due to the underestimation of the vertical wind disturbances and high-frequency components by ERA5. These results indicate that state-of-the-art atmospheric reanalysis is a useful tool for understanding the nature of gravity waves and that further improvement of the resolution of the models used in atmospheric reanalysis is necessary for a quantitative understanding of gravity waves.

1 Introduction

Atmospheric gravity waves (GWs) carry momentum to distant regions and contribute to driving the residual meridional circulation in the middle atmosphere (stratosphere, mesosphere, and lower thermosphere) (Holton, 1983; Lindzen, 1981). The residual meridional circulation in the mesosphere forms a characteristic temperature structure with low temperatures at the summer pole and high temperatures at the winter pole owing to adiabatic compression and expansion, respectively (Andrews et al., 1987). The (intrinsic) periods of GWs range from the Brunt-Väisälä period (∼10 min in the troposphere and ∼5 min in the stratosphere), which is the period of buoyant oscillations, to the inertial period, which varies with latitude (∼13 hr at 69°S where Syowa Station, the focus of this study, is located). The horizontal scales range from a few kilometers to >1,000 km (e.g., Alexander et al., 2010; Preusse et al., 2008).

GWs can be classified as orographic or nonorographic GWs. Orographic GWs are excited by topography such as mountains (e.g., Eckermann & Preusse, 1999; Kruse et al., 2022; Lott & Miller, 1997; McFarlane, 1987); nonorographic GWs are excited by strong convection (e.g., Ern et al., 2022a, 2022b; Fovell et al., 1992; Pfister et al., 1993; Piani et al., 2000; Song & Chun, 2005; Stephan et al., 2019a, 2019b), jet-front systems (e.g., Charron & Manzini, 2002; Geldenhuys et al., 2021; Kim et al., 2016; Plougonven & Zhang, 2014; Wei et al., 2016; Zhang, 2004; Zülicke & Peters, 2006), and instabilities and auroral heating at high altitudes (Fritts & Alexander, 2003; Oyama & Watkins, 2012). In addition, the generation of upward- and downward-propagating GWs from the momentum deposition that follows GW breaking is an important source of GWs in the stratosphere (Becker & Vadas, 2020; Kogure et al., 2022; Vadas et al., 2018, 2023).

An important element that characterizes GW is its spectrum. It is known that the horizontal and vertical wind spectra of GWs have a characteristic shape following the power law. It is theoretically expected that the slopes of the horizontal and vertical wind frequency spectra are −5/3 and 1/3, respectively (VanZandt, 1982, 1985). Moreover, several factors, including Doppler effects due to background winds and vertical wind shears, can significantly change the frequency spectra (Hocking et al., 2021; Okui et al., 2023; VanZandt et al., 1990). Minamihara et al. (2016) analyzed PANSY radar data at Syowa Station, Antarctica and found that the spectral slopes of the lower tropospheric horizontal and vertical winds were −1.89 and −1.04, respectively.

Improved computing power has enabled weather and climate models to achieve higher resolutions and explicitly reproduce some GWs. Nevertheless, it is not possible to reproduce directly the GWs with horizontal and/or vertical scales smaller than the grid spacing of the model. Parameterization is used to compensate for the shortage of the forcing due to unresolved GWs, with assumptions such as steady wave sources and instantaneous vertical propagation of GWs (Alexander & Dunkerton, 1999; Lindzen & Holton, 1968). However, actual wave sources are unsteady and GWs propagate horizontally especially inertia GWs (e.g., Preusse et al., 2009). Additionally, these parameterizations do not account for the generation of upward- and downward-propagating secondary GWs that result from the rapid deposition of momentum that occurs during wave breaking (Vadas et al., 2003, 2023). Thus, the current parameterization does not represent the meridional propagation, transience, or secondary generation of GWs. For example, the convergence of GW momentum flux into the polar night jet (Sato et al., 2009) is not well represented in most current climate models because of the absence of meridional propagation in the GW parameterization. This leads to weaker GW drag in the model than in the real atmosphere and causes a cold bias in the winter lower stratosphere and a delay in polar vortex breakup (McLandress et al., 2012).

The representation of GWs in models and objective analyses (i.e., operational analysis and reanalysis) has been examined by comparison with observations from balloons, radar, and satellites (e.g., Ern et al., 2022a, 2022b; Jewtoukoff et al., 2015). These studies mostly focused on the statistical features of GWs, such as the horizontal and vertical distributions of GW kinetic and potential energy and (absolute) momentum flux. Jewtoukoff et al. (2015) compared data from super pressure balloon observations made over Antarctica with those of operational analysis with a horizontal resolution of ∼80 km and showed that the mean momentum flux of the operational analysis underestimated the balloon observations by approximately a factor of 5. In addition, the occurrence rate of GW events with large momentum fluxes was lower in the operational analysis. On the other hand, Hertzog et al. (2012) examined the intermittency of gravity waves (i.e., probability distribution functions of momentum flux) using balloon and satellite observations and mesoscale simulations. They showed that rare large-amplitude GW events primarily contributed to the total momentum flux in the Antarctic stratosphere especially during winter.

The Program of the Antarctic Syowa MST/IS radar (PANSY) is the only large-aperture MST/IS radar over Antarctica that can capture GWs over the entire frequency range (i.e., from Brunt-Väisälä to inertial frequencies) in the troposphere and lower stratosphere (Sato et al., 2014). Minamihara et al. (2018) examined the characteristics of inertia GWs over Syowa Station using the PANSY radar and showed that inertia GWs observed over Syowa Station are generated by several types of sources, including topography, tropospheric jets, and polar-night jets. In addition, Minamihara et al. (2020) examined the intermittency of GWs over Syowa Station using PANSY radar and indicated that the probability distribution of the GW momentum flux over Syowa Station was different from past super pressure balloon observations (Hertzog et al., 2012). They inferred that this was because the primary wave source of orographic GWs at Syowa Station is a steady katabatic wind from the northeast direction, whereas on the Antarctic Peninsula, the main source is strong winds caused by synoptic-scale disturbances.

In this study, we examine the characteristics of GWs over Syowa Station using PANSY radar data and ERA5 reanalysis data. The present study focuses on large-amplitude inertia GWs because they are likely responsible for much of the total momentum flux. In addition, although the GW amplitudes are known to be the atmospheric reanalysis tends to underestimate, large-amplitude GWs maybe expected to be represented to some extent in the reanalysis data. In the following, we primarily focus on the absolute momentum flux (AMF) and discuss difference in AMF between PANSY and ERA5. The remainder of this paper is organized as follows. Descriptions of the PANSY radar and ERA5 data used in this study are provided in Section 2. The methods used for the hodograph analysis and extraction of GW events are described in Section 3. The results of the statistical analysis are presented in Section 4 and discussed in Section 5. Finally, a summary and concluding remarks are presented in Section 6.

2 Data

2.1 PANSY Radar Observations

The PANSY radar is a mesosphere-stratosphere-troposphere (MST) radar installed at Syowa Station (69.0°S, 39.6°E) in 2011. It can observe three-dimensional wind vectors in the troposphere and lower stratosphere with high temporal and vertical resolutions (Sato et al., 2014).

Five beams are used in PANSY radar observations, which are pointing to the vertical and to the north, east, south, and west at the same zenith angle of 10°. Vertical wind velocities are estimated directly from the vertical beam, and the east-west (north-south) component is obtained from the line of sight velocity of the east-west (north-south) beam. The accuracy of wind velocity is approximately 0.1 ms⁻¹ for vertical wind and approximately 0.5 ms⁻¹ for east-west and north-south wind. The spatial resolution along the beam direction is approximately 150 m. Beam width is approximately 1.0°, corresponding to a horizontal width of approximately 350 m at an altitude of 20 km. The time resolution of tropospheric and stratospheric observations is approximately 200 s. In this study, we used 3-dimensional wind velocities estimated from echo spectra incoherently integrated over 30 min since the 30-min integrated data can extend the upper limit of the observation altitude range by 3–5 km. For comparison with ERA5, the 30-min integrated data were interpolated to hourly intervals.

The data used in this study correspond to the period of continuous observations performed from 1 October 2015 to 30 September 2016. Such long-term continuous observations are unprecedented at other latitudes and reveal seasonal changes in the intermittency and vertical distribution of GWs over Syowa Station (Minamihara et al., 2018, 2020).

2.2 ERA5 Reanalysis

ERA5 is the latest atmospheric reanalysis data set provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach et al., 2020). The data are provided on 137 model levels vertically from the surface up to the pressure level of 0.01 hPa (∼80 km altitude). The altitude interval in the troposphere and lower stratosphere (∼1.5–20 km), which was the focus of this study, ranges from 150 to 400 m. The latitude and longitude intervals were 0.25° × 0.25°, and the time interval was 1 hr. Data from the grid point closest to Syowa Station (69.0°S, 39.5°E) were used for analysis. We confirmed that the analysis results using the data of the other three grid points surrounding Syowa Station (69.0°S, 39.75°E; 69.25°S, 39.5°E; and 69.25°S, 39.75°E) did not significantly change.

Figure 1 shows the time-altitude cross sections of zonal and vertical winds with time interval of 1 hr and vertical spacing of 150 m from PANSY and ERA5 for January 2016. The ERA5 zonal wind is in good agreement with the PANSY zonal wind both in magnitude and phase structure (Figures 1a and 1b). Although the vertical wind in ERA5 shows large-amplitude disturbances at nearly the same time as that in PANSY (e.g., ∼1.5–10 km around January 9, 13, 20, and 30), their ground-based periods look significantly shorter in PANSY than in ERA5. In addition, their amplitudes in ERA5 are much smaller than those in PANSY (Figures 1c and 1d).

Figure 1

Time-altitude cross sections of zonal (a), (b) and vertical (c), (d) winds from PANSY (a), (c) and ERA5 (b), (d) for January 2016. PANSY data are interpolated to hourly intervals. ERA5 data are interpolated to 150 m vertical intervals. See the text for details.

3 Method

3.1 Extraction of GWs

The intrinsic period of GWs ranges from the Brunt-Väisälä period (i.e., ∼5 min in the stratosphere and ∼10 min in the troposphere) to the inertial period (i.e., ∼13 hr at Syowa Station). Since hourly 3-dimensional wind data were analyzed, we focused on inertia GWs. To extract inertia GWs, a band-pass filter with cutoff periods of 4 and 24 hr was applied to the data as in Minamihara et al. (2020). In addition, since the vertical wavelengths of inertia GWs over Syowa Station are mostly 1–5 km (Minamihara et al., 2018), a band-pass filter with cutoff vertical wavelengths of 0.8 and 8 km was also applied. Time-altitude cross-sections of filtered wind data often show superposition of wave-like structures with upward and downward phase propagation (e.g., Figure 6 of Minamihara et al., 2018). This feature makes it difficult to estimate GW parameters using hodograph analysis, because it assumes that the wind disturbance is due to a monochromatic GW. To obtain wave components as monochromatically as possible, a two-dimensional (i.e., temporal and vertical) Fourier series expansion was applied to the wind data. Then, wind disturbances with upward and downward ground-based phase velocities ($${C}_{z} > 0$$ and $${C}_{z}< 0$$, respectively) were obtained separately (Yoshiki et al., 2004). The hodograph analysis was applied to both of them.

Figure 2 shows the time-altitude cross sections of zonal and vertical wind disturbances with $${C}_{z}< 0$$ from PANSY and ERA5 in January 2016. Comparing the zonal wind disturbances between PANSY and ERA5, the phase and amplitude of wave-like events were generally consistent in the troposphere. However, some events, such as those between January 17 and 22 around an altitude of 18 km, showed a similar phase structure, but their amplitudes were significantly different (Figures 2a and 2b). A comparison of the vertical wind disturbances shows that ERA5 failed to reproduce the wave-like events observed in the PANSY observations between January 17 and 22 at an altitude of 18 km (Figures 2c and 2d). The meridional wind disturbances with $${C}_{z}< 0$$ components showed features similar to the zonal wind disturbances with $${C}_{z}< 0$$ components (not shown).

Figure 2

Same as Figure 1 except for wind disturbances with downward phase velocities ($${C}_{z}< 0$$).

Hodographs depict the altitude variation of horizontal wind disturbance vectors in velocity space. They are elliptical for inertia GW (Hirota & Niki, 1986). The direction of the major axis indicates the direction of the horizontal wavenumber vector with an ambiguity of 180°. The direction of rotation of the hodograph with altitude indicates the direction of the vertical propagation of energy (i.e., vertical group velocity). When the rotation is counterclockwise (clockwise) with the altitude in the Southern Hemisphere, the energy propagation is upward (downward). The radii of the major and minor axes of the ellipse represent the amplitudes of horizontal wind disturbances parallel and perpendicular to the horizontal wavenumber vector ($$\tilde{u}$$, $$\tilde{v}$$), respectively. The altitude width of one rotation of the hodograph represents the vertical wavelength (Tateno & Sato, 2008). The polarization relation for inertia GWs gives the intrinsic angular frequency ($$\widehat{\omega }$$ s⁻¹) as follows (Fritts & Alexander, 2003):

$$$\begin{array}{c}\vert \widehat{\omega }\vert =\vert \frac{\tilde{u}}{\tilde{v}}{f}_{i}\vert ,\end{array}$$$ (1)

where $${f}_{i}$$ is the inertial frequency (i.e., $$1.36\times {10}^{-4}$$ s⁻¹ corresponding to the inertial period of 12.8 hr at Syowa Station).

The dispersion relation for inertia GWs under the hydrostatic approximation is

$$$\begin{array}{c}{\widehat{\omega }}^{2}={{f}_{i}}^{2}+\frac{{N}^{2}{K}^{2}}{{m}^{2}},\end{array}$$$ (2)

where $$N$$ is the Brunt-Väisälä frequency, $$m$$ is the vertical wavenumber, and $$K$$ is the horizontal wavenumber. Note that $$K$$ can be estimated using Equation 2. The ground-based angular frequency ω is obtained from the equation of Doppler shift given by $$\omega =\widehat{\omega }+UK$$, where $$U$$ is the horizontal wind amplitude along the GW propagation direction. The direction of the horizontal wavenumber vector (θ) is uniquely determined by

$$$\begin{array}{c}\text{sgn}(K)=-\text{sgn}\left({{u}_{\mathit{{\Vert} }}}^{\mathit{\prime }}{w}^{\mathit{\prime }}\right)\mathit{\cdot }\text{sgn}(m),\end{array}$$$ (3)

where $${{u}_{\mathit{{\Vert} }}}^{\mathit{\prime }}$$ is the horizontal wind disturbance parallel to the horizontal wavenumber vector, $${w}^{\mathit{\prime }}$$ is the vertical wind disturbance, and $${u}_{\mathit{{\Vert} }}\mathit{{\rhook}}w\mathit{{\rhook}}$$ is the covariance.

Although a hodograph can be drawn from a vertical profile at one time, in our analysis, a single hodograph was drawn using vertical profiles at multiple times to improve the fitting accuracy. Figure 3 shows example hodographs for PANSY and ERA5. The x-axis and y-axis show the zonal and meridional wind components, respectively. Each filled circle represents a data point, color represents time in UT on 22 September 2016, and the black line represents a fitted ellipse.

Figure 3

Results of the hodograph analysis applied to (a) PANSY and (b) ERA5 data in the height range of 2.55–4.95 km at 0400–1400 UT on 22 September 2016 (dots—data, star—bottom data, black line—fitted ellipse, red x—center of fitted ellipse). Black arrows represent propagation direction of GWs.

3.2 AMF Estimation

Absolute momentum flux (AMF) was used to compare the PANSY radar and ERA5 data. AMF was estimated using three types of methods.

1. AMF was estimated from GW parameters obtained by the hodograph analysis as follows:

$$$\begin{array}{c}\text{AMF}=\vert \frac{\overline{\rho }\tilde{u}\tilde{w}}{2}\vert \end{array}$$$ (4)

Where $$\tilde{w}=-\frac{m}{K}\frac{{\widehat{\omega }}^{2}-{{f}_{i}}^{2}}{{N}^{2}-{\widehat{\omega }}^{2}}\tilde{u}$$ (Fritts & Alexander, 2003), and $$\overline{\rho }$$ is density obtained from ERA5.

This method was applied to both of PANSY radar and ERA5 data.

2. AMF was estimated directly from the horizontal and vertical wind disturbances of ERA5 (Minamihara et al., 2018) as follows:

$$$\begin{array}{c}\text{AMF}=\overline{\rho }\sqrt{{\left(\overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}\right)}^{2}+{\left(\overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}\right)}^{2}}\end{array}$$$ (5)

This method was not applied to the PANSY radar data, because the different beams used to measure the horizontal and vertical winds captured different air masses.

3. AMF was estimated from line of sight velocity along the radar beam direction (Vincent & Reid, 1983) as follows:

$$$\begin{array}{c}\text{AMF}=\overline{\rho }\sqrt{{\left(\frac{\overline{{{u}_{1}^{\mathit{\prime }}}^{2}}-\overline{{{u}_{2}^{\mathit{\prime }}}^{2}}}{2\,\sin \,2\theta }\right)}^{2}+{\left(\frac{\overline{{{v}_{1}^{\mathit{\prime }}}^{2}}-\overline{{{v}_{2}^{\mathit{\prime }}}^{2}}}{2\,\sin \,2\theta }\right)}^{2}},\end{array}$$$ (6)

where $${u}_{1}^{\mathit{\prime }}$$, $${u}_{2}^{\mathit{\prime }}$$, $${v}_{1}^{\mathit{\prime }}$$, and $${v}_{2}^{\mathit{\prime }}$$ are line of sight velocity perturbations toward the east, west, north, and south, respectively, and $$\theta $$ is the angle of the oblique beam from zenith, which is $$10\mathit{{}^{\circ}}$$ for the PANSY radar. This method enabled us to estimate AMF with greater accuracy than the aforementioned methods (i.e., Equation 5).

Figure 4 shows time-altitude cross sections of AMF with $${C}_{z}< 0$$ in January 2016 calculated by Equations 6 and 5 (Figures 4a and 4b, respectively). Large AMF events observed by the PANSY radar were roughly captured in the ERA5 data. However, in most cases, the magnitudes were several times larger for PANSY than they were for ERA5.

Figure 4

Time-altitude cross sections of AMF with $${C}_{z}< 0$$ in January 2016. AMF was calculated using Equation 6 from PANSY (a) and Equation 5 from ERA5 (b). Black rectangles show the identified large-amplitude GW events.

3.3 Event Identification Criteria

In this study, we focused on large-amplitude inertia GW events identified from PANSY and ERA5 data using the following procedures.

1. Calculation of the AMF using data with a time interval of 10 hr and an altitude range of 2.4 km was repeated by shifting the time and altitude by one step (i.e., 1 hr and 150 m, respectively) for both of $${C}_{z} > 0$$ and $${C}_{z}< 0$$.

2. Hodograph analysis was applied only to the top 10% of cases having the largest AMF (calculated using Equation 6) at each altitude.

3. When the explained variance was greater than twice the mean square of the residuals, the case was considered quasi-monochromatic. The following procedure (i.e., 4 and 5) was applied to only the quasi-monochromatic cases.

4. When the aspect ratio of the hodograph was >0.1 and <0.9 and the horizontal wind amplitude perpendicular to the horizontal wavenumber vector (i.e., short radius of the hodograph) was >0.5 ms⁻¹, estimates of the parameters of inertia GWs were regarded successful (e.g., Minamihara et al., 2018).

5. Cases adjacent to each other in the time and altitude directions were considered one GW event.

Consequently, 231 and 362 GW events with $${C}_{z} > 0$$ and $${C}_{z}< 0$$, respectively, which satisfied the above conditions, were identified using PANSY radar data. Of these, 59 and 191 events with $${C}_{z} > 0$$ and $${C}_{z}< 0$$, respectively, were identified from the ERA5 data too. Comparison of the hodograph analysis results between PANSY and ERA5 was performed on 250 cases extracted as GW events in both.

Figure 5 shows the seasonal variation in the number of GW events identified in the troposphere (below 8 km altitude), tropopause (8–12 km altitude), and stratosphere (above 12 km altitude) from the PANSY radar data. Separation of the height region was determined based on a previous study of tropopause height above Syowa Station (Tomikawa et al., 2009). The upward- and downward-propagating components (i.e., $${C}_{z} > 0$$ and $${C}_{z}< 0$$) were also separated. In the troposphere, the number of identified GW events was similar for $${C}_{z} > 0$$ and $${C}_{z}< 0$$, and the significant seasonal variation is not observed. In the stratosphere, the number of $${C}_{z}< 0$$ events is maximized in austral fall (i.e., MAM) and is greater than $${C}_{z} > 0$$ events throughout the year. The number of $${C}_{z} > 0$$ events in the stratosphere is maximized in austral winter (i.e., JJA) and minimized in austral summer (i.e., DJF). The tropopause region has a larger number of GW events for $${C}_{z}< 0$$ and the significant seasonal variation is not observed as in the troposphere.

Figure 5

Seasonal variation in the number of identified large-amplitude inertia GW events (n) in the troposphere (olive; below 8 km), tropopause (red; 8∼12 km), and stratosphere (blue; above 12 km) from the PANSY radar data. Solid and dashed lines denote $${C}_{z} > 0$$ and $${C}_{z}< 0$$ events, respectively.

The division based on the vertical phase velocity in this analysis does not necessarily coincide with that based on the vertical group velocity. The vertical phase and group velocities ($${C}_{z}$$ and $${C}_{gz}$$ , respectively) are given by

$$$\begin{array}{c}{C}_{z}=\frac{\omega }{m}=\frac{\widehat{\omega }+KU}{m},\end{array}$$$ (7)

$$$\begin{array}{c}{C}_{gz}=-\frac{m\left({\widehat{\omega }}^{2}-{{f}_{i}}^{2}\right)}{\widehat{\omega }\left({K}^{2}+{m}^{2}\right)}.\end{array}$$$ (8)

These equations indicate that if the background wind is weak, the vertical phase and group velocities will be in opposite directions. However, if the background wind is sufficiently strong in the opposite direction of the horizontal wavenumber vector, the vertical phase and group velocities will be in the same direction. In our analysis, almost all GW events with $${C}_{z}< 0$$ had $${C}_{gz} > 0$$, whereas approximately half of the GW events with $${C}_{z} > 0$$ had $${C}_{gz} > 0$$.

4 Results

4.1 Momentum Flux

Figure 6 shows the vertical profiles of the annual mean AMF for PANSY and ERA5 (i.e., AMF_PANSY and AMF_ERA5, respectively) and its ratio between PANSY and ERA5 (i.e., AMF_ERA5/AMF_PANSY as AMF ratio (ERA5/PANSY)). AMF_PANSY and AMF_ERA5 were calculated using Equations 6 and 5, respectively, for $${C}_{z} > 0$$, $${C}_{z}< 0$$, and their sum. Although the magnitude of AMF for both PANSY and ERA5 decreased with altitude up to 15 km, it decreased with altitude above 15 km only for ERA5. Magnitudes of AMF are larger for PANSY than for ERA5 at all heights. These features are common to $${C}_{z} > 0$$, $${C}_{z}< 0$$, and their sum. The AMF ratio is larger around 5–12.5 km and decreases with altitude above 12.5 km for $${C}_{z} > 0$$, $${C}_{z}< 0$$, and their sum. The AMF ratio for the sum of $${C}_{z} > 0$$ and $${C}_{z}< 0$$ is approximately 0.2 from 5 to 12.5 km but reaches ∼0.05 at around 20 km. The AMF ratio for $${C}_{z}< 0$$ is greater than that for $${C}_{z} > 0$$ at all heights. These features are common across all seasons (not shown).

Figure 6

Vertical profiles of (a) the annual mean AMF magnitudes for PANSY (solid) and ERA5 (dashed) and (b) the annual mean AMF ratio (ERA5/PANSY) for C_z > 0 (red), C_z < 0 (olive), and their sum (blue). Thick and thin lines indicate the means and standard deviations, respectively, at each height.

Although the AMF is useful for comparison with satellite observations, information on the propagation direction of GWs is lost. Therefore, the probability density distribution of zonal and meridional momentum flux (i.e., $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ and $$\rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$) is shown in Figure 7. Black lines represent 90th percentile values of absolute zonal and meridional momentum fluxes, whose outside corresponds to the large amplitude GWs. The 90th percentile values of $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ and $$\rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ in PANSY get larger above 15 km altitude, while it continues to get smaller with altitude in ERA5, which is the same as in Figure 6a. The probability density distribution shows that the region of higher probability density in ERA5 extends beyond the black line than in PANSY, suggesting a larger intermittency. Comparing $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ and $$\rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$, both PANSY and ERA5 have a similar shape. On the other hand, although little significant asymmetry is observed between positive and negative values of $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ and $$\rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ in the troposphere, the large probability density of $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ tends to extend more toward the negative side.

Figure 7

Probability density distributions of (a), (b) $$\rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ and (c), (d) $$\rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}$$ for (a), (c) PANSY and (b), (d) ERA5. Black lines represent 90th percentile values of zonal and meridional momentum fluxes (i.e., $$\vert \rho \overline{{u}^{\mathit{\prime }}{w}^{\mathit{\prime }}}\vert $$ and $$\vert \rho \overline{{v}^{\mathit{\prime }}{w}^{\mathit{\prime }}}\vert $$, respectively). Probability density in this paper is calculated by dividing the number of events contained in each 5 mPa bin by the total number of events per altitude and 5 mPa.

4.2 Spectra

Figure 8 shows the frequency spectra of the zonal and vertical winds from PANSY and ERA5 in the troposphere (Figures 8d–8f) and stratosphere (Figures 8a–8c). From left to right, sum of $${C}_{z} > 0$$ and $${C}_{z}< 0$$, $${C}_{z} > 0$$, and $${C}_{z}< 0$$ components are plotted. Their spectral slopes were calculated using the spectra from ω = 2π/4 hr to $$\omega ={f}_{i}$$ by linear least squares fitting. As these spectra were drawn in an energy-content form (i.e., frequency times power spectrum), their exponents were spectral slope obtained from the power spectrum plus one. The meridional winds show features similar to those for the zonal winds (not shown). The frequency spectra were calculated using the Blackman-Tukey and Welch's Overlapping methods (Blackman & Tukey, 1958; Welch, 1967) because the PANSY radar data have a few missing values. Each frequency spectrum was calculated for a 30-day window, which was shifted by 15 days and averaged. In the Blackman-Tuckey method, the maximum lag in the covariance calculation was about 10% of the data length, in other words, ±3 days lag in order to reduce the standard deviation of the frequency spectra. The maximum period for the frequency spectra was therefore 6 days.

Figure 8

Frequency spectra (energy-content form) of zonal and vertical winds from PANSY and ERA5 in the troposphere (d, e, f) and stratosphere (a, b, c). From left to right, sum of $${C}_{z} > 0$$ and $${C}_{z}< 0$$ (a), (d), $${C}_{z} > 0$$ (b), (e), and $${C}_{z}< 0$$ (c), (f) components are plotted. Black dashed lines indicate periods of 2 hr, 12 hr, and 24 hr. Green dashed-dotted lines indicate $$2\pi /{f}_{i}$$ (i.e., inertial period). Their spectral slopes were calculated using the spectra from ω = 2π/4 hr to $$\omega ={f}_{i}$$ by linear least squares fitting and shown in the figures. Error bars are given by red, which are the same at all frequencies because the error is estimated based on the χ-squared distribution.

Power spectra of zonal winds show a good agreement between PANSY and ERA5 for the period longer than the inertial period (i.e., $$\omega < {f}_{i}$$) both in the troposphere and stratosphere for all of the sum, $${C}_{z} > 0$$, and $${C}_{z}< 0$$. On the other hand, the spectral slope is steeper for ERA5 in the period shorter than the inertial period (i.e., $$\omega > {f}_{i}$$), which suggests that the amplitude of GWs in ERA5 is more underestimated for the shorter wave periods. Another interesting feature is that a clear spectral peak is seen near the inertial period only in the stratosphere for the sum and $${C}_{z}< 0$$. ERA5 shows a weak spectral peak near the inertial period even for $${C}_{z} > 0$$ unlike PANSY.

The power spectra of vertical winds show features that are clearly different from those of zonal wind. The spectral power of PANSY is one order of magnitude greater than that of ERA5 at all frequencies. In addition, the spectrum from PANSY has a positive slope at all frequencies, while that from ERA5 shows a negative slope on the high frequency side (i.e., $$\omega > {f}_{i}$$). These features are common both in the troposphere and stratosphere for all of the sum, $${C}_{z} > 0$$, and $${C}_{z}< 0$$.

4.3 Hodograph Analysis

The statistical properties of the identified GW events were investigated based on the hodograph analysis results. Although 593 GW events were identified from the PANSY radar data, we apply the hodograph analysis to only 250 GW events, which were identified as GW events satisfying the criteria in Section 3.3 both in PANSY and ERA5.

First, the AMF obtained from each of the methods (see Section 3.2) were compared (Tables 1 and 2). P1 and E1 represent AMF obtained using Equation 4 for PANSY and ERA5, respectively. P2 and E2 represent AMF obtained using Equation 6 for PANSY and Equation 5 for ERA5, respectively. As P1 and E1 were calculated using wave parameters estimated from horizontal wind data, their comparison suggests how consistent the horizontal winds of identified GW events are between PANSY and ERA5. On the other hand, P2 and E2 were calculated using both the horizontal and vertical winds (i.e., exactly speaking, P2 uses line of sight velocity, which includes both the horizontal and vertical winds), their comparison suggests how consistent both the horizontal and vertical winds are between PANSY and ERA5. If E1 (E2) was more than half of P1 (P2) and less than twice as large as P1 (P2), the two were considered sufficiently close [that is, P1(P2) ≈ E1 (E2)].

Table 1. Number of Events of P1 > E1, P1 ≈ E1, and P1 < E1 for C_z > 0 and C_z < 0

	$$\mathrm{P}1\approx \mathrm{E}1$$	$$\mathrm{P}1 > \mathrm{E}1$$	$$\mathrm{P}1< \mathrm{E}1$$	Total
$${C}_{z} > 0$$	13	33	13	59
$${C}_{z}< 0$$	47	127	17	191
Total	60	160	30	250

Table 2. Same as Table 1 but Comparison of P2 and E2 Amplitudes

	$$\mathrm{P}2\approx \mathrm{E}2$$	$$\mathrm{P}2 > \mathrm{E}2$$	$$\mathrm{P}2< \mathrm{E}2$$	Total
$${C}_{z} > 0$$	8	51	0	59
$${C}_{z}< 0$$	10	181	0	191
Total	18	232	0	250

As shown in Table 1, P1 > E1, P1 ≈ E1, and P1 < E1 are 50%–65%, 20%–25%, and 5%–25%, respectively, for both $${C}_{z} > 0$$ and $${C}_{z}< 0$$. This indicates that ERA5 tends to slightly underestimate the horizontal wind amplitudes of identified GW events compared with PANSY. However, as shown in Table 2, E2 is almost always significantly smaller than P2 for both $${C}_{z} > 0$$ and $${C}_{z}< 0$$. This suggests that ERA5 tends to significantly underestimate the vertical wind amplitudes of identified GW events.

Figure 9 shows the scatter plots of aspect ratio (i.e., $$\left\vert {f}_{i}/\hat{\omega }\right\vert $$), vertical wavelengths ($${\lambda }_{z}$$), and horizontal wavelengths ($${\lambda }_{h}$$) obtained from hodograph analysis as a function of altitude. Thick and thin solid lines represent means and standard deviations of the wave parameters, respectively. Only sum of $${C}_{z} > 0$$ and $${C}_{z}< 0$$ are shown here, because the number of $${C}_{z} > 0$$ events are too few to show height dependence of the wave parameters. The aspect ratio approaches unity with increasing altitude, which suggests that the intrinsic wave period approaches the inertial period. This feature is common to PANSY and ERA5. The vertical wavelength decreases with increasing altitude for both PANSY and ERA5. However, the vertical wavelength of ERA5 is 100∼400 m longer than that of PANSY at every altitude.

Figure 9

Scatter plots of (a) aspect ratio (i.e., $$\left\vert {f}_{i}/\hat{\omega }\right\vert $$), (b) vertical wavelengths ($${\lambda }_{z}$$), and (c) horizontal wavelengths ($${\lambda }_{h}$$) obtained from hodograph analysis as a function of altitude. Blue and orange dots denote PANSY and ERA5 data, respectively. Thick and thin solid lines show their means and standard deviations, respectively, that are taken every 1.5 km.

Horizontal wavelength increases with increasing altitude for both PANSY and ERA5. In addition, it is longer for ERA5 than for PANSY at all altitudes. The difference is due to the longer intrinsic wave period and longer vertical wavelength in ERA5 because the horizontal wavelength is obtained from the dispersion relation by the following equation:

$$${\lambda }_{h}=2\pi {\left\{\left({\widehat{\omega }}^{2}-{{f}_{i}}^{2}\right)\ast \frac{{m}^{2}}{{N}^{2}}\right\}}^{-\tfrac{1}{2}}$$$

$$${=}\vert \frac{N}{f}{\lambda }_{z}\vert {\left\{{\left(\frac{\tilde{u}}{\tilde{v}}\right)}^{2}-1\right\}}^{-1/2}$$$ (9)

Figure 10 shows the number of events for each propagation direction of GWs (east, west, north, and south) from (a) all altitudes for PANSY and ERA5, (b) each altitude (stratosphere, tropopause, and troposphere) for PANSY, and (c) each altitude for ERA5. Southward propagation is the most frequent in all altitude regions for PANSY and in the stratosphere for ERA5. In addition, eastward propagation is also dominant in the stratosphere for both PANSY and ERA5. Directional preference in the troposphere is small for PANSY, but westward propagation is relatively large in the troposphere for ERA5.

Figure 10

The number of identified GW events in each direction (i.e., east, west, north, and southward). (a) All altitudes for PANSY (blue) and ERA5 (orange). The troposphere (olive), tropopause (red), and stratosphere (blue) for (b) PANSY and (c) ERA5.

5 Discussion

5.1 Characteristics of Large-Amplitude Inertia GWs Above Syowa Station

Minamihara et al. (2018) applied hodograph analysis to PANSY radar data from October 2015 to September 2016 in both the troposphere and stratosphere to investigate the characteristics of inertia GWs over Syowa Station. This study applied the same hodograph analysis to the PANSY radar and ERA5 data for the same period. Although Minamihara et al. (2018) applied hodograph analysis to individual vertical profiles to extract all inertia GWs, this study extracted large-amplitude GW events corresponding to the top 10% of AMFs and focused on inertia GWs captured in both of PANSY and ERA5. We compared the results obtained from our hodograph analysis with those of Minamihara et al. (2018) and considered the characteristics of large-amplitude inertia GWs over Syowa Station.

Large-amplitude inertia GWs over Syowa Station are dominated by those with $${C}_{z}< 0$$ as the altitude increases (see Section 3.3). In addition, the seasonal variation is larger at higher altitudes (i.e., the stratosphere), where inertia GWs with $${C}_{z}< 0$$ are most frequent in austral autumn and those with $${C}_{z} > 0$$ are most frequent in austral winter. These characteristics are consistent with those of Minamihara et al. (2018). They suggested that topography, tropospheric jets, and polar night jet are the main sources of inertia GW excitation, which also applies to large-amplitude inertia GWs.

The intrinsic period of inertia GWs tends to be longer, the vertical wavelength is shorter, and the horizontal wavelength is longer as altitude increases (see Section 3.3). These features are consistent with Minamihara et al. (2018). On the other hand, the vertical wavelength is approximately 4 km in the troposphere and 3 km in the stratosphere, and the horizontal wavelength is approximately 250 km in the troposphere and 500–700 km in the stratosphere. These values are greater than those reported by Minamihara et al. (2018). This difference suggests that inertia GWs with large amplitudes tend to have longer horizontal and vertical wavelengths.

The propagation direction of inertia GWs is generally dominated by a southward component, which is particularly pronounced in the stratosphere. In addition, the propagation direction tends to be more eastward in the stratosphere for PANSY. On the other hand, propagation direction in the troposphere is relatively isotropic compared to the stratosphere. This small directional preference in the troposphere is consistent with the findings of Minamihara et al. (2018). However, the predominance of southward propagation in the stratosphere has not been reported and could be an inherent feature of large-amplitude inertia GWs. In view of the fact that the power spectrum of horizontal winds with $${C}_{z}< 0$$ has a peak near the inertial period in the stratosphere (see Figure 8), our results may reflect southward propagation of GWs generated in the tropical troposphere as described by Sato et al. (1999).

5.2 AMF Difference Between PANSY and ERA5

The AMF of ERA5 is ∼0.2 times that of PANSY in the troposphere and decreases with altitude in the stratosphere to ∼0.05 at 20 km altitude (see Section 4.1). Although horizontal winds have similar power near the inertial period between PANSY and ERA5, the spectral slope of ERA5 is steeper than that of PANSY (see Figure 8). The power spectra of the vertical winds are approximately one order of magnitude larger in PANSY even near the inertial period, and the difference increases at higher frequencies. We compared the results of the hodograph analysis of large-amplitude inertia GWs and showed that ERA5 underestimates the vertical wind amplitude (see Section 4.3). To clarify why ERA5 underestimates the AMF compared to PANSY, we examined whether the difference in the power spectra between PANSY and ERA5 can quantitatively explain the difference in AMF.

Jewtoukoff et al. (2015) compared the horizontal distribution of AMF obtained from super pressure balloon observations with operational analysis data from ECMWF and reported that AMF calculated from ECMWF data was approximately 1/3 to 1/5 of that from super pressure balloon observations. They demonstrated that the difference in the AMF between the two can be largely explained by the difference in their resolvable horizontal wavenumber ranges. Since PANSY radar observations, unlike super pressure balloon observations, provide time-height cross sections of AMF at Syowa Station, we attempted to explain the difference not in terms of horizontal wavenumber but in terms of the frequency range in which GWs can be resolved.

Jewtoukoff et al. (2015) assumed that the operational analysis data of ECMWF can reproduce GWs with horizontal wavenumbers smaller than a certain cutoff wavenumber, and that their amplitudes are zero for larger wavenumbers. However, as shown in Figure 8, the frequency spectra of horizontal and vertical winds in ERA5 do not become zero at any cutoff frequency but show spectra with a different slope from PANSY in the entire frequency range of GWs. Figure 11 shows hypothetical regions in the horizontal and vertical wavenumber spaces, where the original PANSY and ERA5 data can resolve by oblique lines and shading, respectively. The solid lines represent the isopleths of the intrinsic wave period obtained from the dispersion relation of inertia GWs (Equation 2). PANSY can capture almost any period over a wide range of horizontal and vertical wavenumber regions, whereas ERA5 can resolve narrower horizontal and vertical wavenumber regions as the intrinsic period decreases. In other words, it can be considered that the shorter the intrinsic period (i.e., higher frequency), the narrower the resolvable region becomes, which is reflected in the difference in the slope of the frequency spectrum in Figure 8.

Figure 11

Hypothetical regions in horizontal and vertical wavenumber space where PANSY and ERA5 can resolve are shown by oblique lines and shading, respectively. Solid lines represent isopleths of intrinsic wave period obtained from the dispersion relationship of inertia GWs (i.e., Equation 2).

Suppose the frequency power spectra of the horizontal and vertical winds in an energy content form follow the power law:

$$$\begin{array}{c}\hspace*{.5em}fP\left(f\right)=b{f}^{a},\end{array}$$$ (10)

where $$f$$ is the frequency normalized by the inertial frequency $${f}_{i}$$, $$a$$ is the exponent of the spectral slope, and $$b$$ is the power at $${f}_{i}$$. By integrating it over the frequency range of inertia GWs between $$f=1$$ and $$f={f}_{h}=2\pi /4\hspace*{.5em}\mathrm{hr}/{f}_{i}$$, the AMF ratio between PANSY and ERA5 can be obtained as follows (see Liu (2019)):

$$$\begin{array}{c}\text{AMFratio}\left(\frac{\mathrm{ERA}5}{\text{PANSY}}\right)=\frac{{b}_{u\mathrm{ERA}5}{b}_{w\mathrm{ERA}5}}{{b}_{u\text{PANSY}}{b}_{w\text{PANSY}}}\frac{\frac{1-{\left({f}_{h}\right)}^{\tfrac{{a}_{u\mathrm{ERA}5}+{a}_{w\mathrm{ERA}5}}{2}}}{{a}_{u\mathrm{ERA}5}+{a}_{w\mathrm{ERA}5}}}{\frac{1-{\left({f}_{h}\right)}^{\tfrac{{a}_{u\text{PANSY}}+{a}_{w\text{PANSY}}}{2}}}{{a}_{u\text{PANSY}}+{a}_{w\text{PANSY}}}},\end{array}$$$ (11)

where subscripts $$u$$ and $$w$$ represent horizontal and vertical wind components, respectively.

The vertical profile of the AMF ratio between PANSY and ERA5 obtained from the power spectra of horizontal and vertical winds using Equation 11 is shown in Figure 12a. Parameters $$a$$ and $$b$$ were estimated from Figure 8. The AMF ratio is approximately 0.15 at altitudes of 5–12 km, which is slightly smaller than the ratio in Figure 6. However, the altitude variation is in good agreement. Thus, the difference in AMF between PANSY and ERA5 can be roughly explained by the magnitude and slope of their wind power spectra; in other words, the difference in AMF between PANSY and ERA5 depends on the range of GWs resolved in the model used for ERA5.

Figure 12

Vertical profiles of power spectral ratio of $$u$$ (cyan), $$w$$ (olive), and the AMF (blue) between PANSY and ERA5 obtained using Equation 11. Power spectra in (a), (b), and (c) are computed using estimated parameters $$a$$ (i.e., spectral slope) and $$b$$ (i.e., power at $${f}_{i}$$), only $$a$$ (i.e., parameter $$b$$ is assumed to be the same between PANSY and ERA5), and only $$b$$ (i.e., parameter $$a$$ is assumed to be the same between PANSY and ERA5), respectively. Thick and thin lines represent estimated ratios and their standard deviations.

Next, we confirmed which of the horizontal and vertical winds contribute to the underestimation of AMF in ERA5. The ratios of the power spectra of the zonal and vertical winds are shown in Figure 12a. The powers of the zonal and vertical winds in ERA5 are a factor of 2 and 50 smaller than in PANSY, respectively. Since horizontal and vertical winds contribute to the momentum flux by the square root of their power, contributions of horizontal and vertical winds to the underestimation of AMF in ERA5 are estimated at the factors of √2 and 7, respectively.

The relative contributions of parameters $$a$$ and $$b$$ were also examined. Figure 12b shows the vertical profile of the AMF ratio when the power at $${f}_{i}$$ (i.e., parameter $$b$$) was assumed to be the same for PANSY and ERA5. ERA5 underestimates AMF by approximately a factor of two owing to the difference in parameter $$a$$ (i.e., spectral slope). The contribution of parameter $$a$$ for the vertical wind to the underestimation of AMF in ERA5 is slightly larger than that for the zonal wind. The contribution of parameter $$b$$, assuming that parameter $$a$$ is the same for PANSY and ERA5, is shown in Figure 12c. It is found that ERA5 underestimates AMF by approximately a factor of four owing to the difference in parameter $$b$$ (i.e., power at $${f}_{i}$$). Although this is mostly due to the underestimation of parameter $$b$$ for vertical winds, the contribution of parameter $$b$$ for zonal winds increases with altitude above 12.5 km.

The above analysis shows that the underestimation of AMF in ERA5 can be largely explained by the underestimation of the vertical wind spectrum both in the troposphere and stratosphere and also that of the horizontal wind spectrum in the stratosphere. As shown in Figure 11, it is likely that the underestimation of the spectra is mainly due to the limited resolution of the model used in the ERA5. However, it is not clear why the underestimation of AMF in ERA5 increases with altitude above 12.5 km. Figure 12c shows that above 12.5 km altitude, the power at $${f}_{i}$$ in ERA5 is smaller than that in PANSY not only for the vertical wind but also for the zonal wind. Although the vertical grid spacing in the ERA5 model is approximately 300 m in the middle and upper troposphere, it increases with altitude above approximately 12 km (Hersbach et al., 2020). This suggests that the vertical wavenumber range of GWs resolved by the ERA5 model may decrease with altitude. In addition, the vertical wavelengths of the dominant inertia GWs become shorter with increasing altitude (see Section 4.3). Wicker et al. (2023) also demonstrated that GW potential energy in the ECMWF IFS model, which was the same as that used for ERA5, was smaller in the model version with 91 vertical levels than in that with 198 vertical levels in the polar stratosphere during a sudden stratospheric warming event, suggesting importance of vertical resolution for the representation of GWs. Therefore, both the coarsening of the vertical resolution with altitude and the shortening of the dominant vertical wavelength of GWs may contribute to the larger underestimation of AMF with altitude in ERA5.

6 Conclusion

The characteristics of large-amplitude inertia GWs over Syowa Station, Antarctica were examined and compared between PANSY radar observations and ERA5 reanalysis data from October 2015 to September 2016. Focusing on large-amplitude events with a large AMF, hodograph analysis was applied to estimate the wave parameters. The percentage of large-amplitude GWs with a downward phase velocity increased with altitude. Their vertical wavelengths and intrinsic periods became shorter and longer with increasing altitude, respectively, resulting in longer horizontal wavelengths. In addition, the southward propagation of the GWs was predominant, especially in the stratosphere. Compared with the results of Minamihara et al. (2018), who applied a similar hodograph analysis to the PANSY radar data for the same period and examined inertia GWs including small-amplitude GWs, the altitude variation of the wave parameters was the same, whereas the dominant horizontal and vertical wavelengths were longer than those in Minamihara et al. (2018). In addition, Minamihara et al. (2018) did not report the dominance of southward propagation in the stratosphere. Thus, this feature is considered to be characteristic of large-amplitude inertia GWs over Syowa Station.

Next, we compared the AMF obtained by PANSY and ERA5 to verify how well ERA5 represented momentum transport due to GWs. The results show that ERA5 underestimates AMF by approximately a factor of 5 at altitudes between 5 and 12.5 km. The degree of underestimation increases with altitudes above 12.5 km. To clarify the reason for the underestimation of AMF in ERA5, AMF was estimated from the power spectra of the horizontal and vertical winds and compared with the above results. It was found that the underestimation of AMF in ERA5 can be explained by the underestimation of the power spectra of horizontal and vertical winds, especially vertical winds. The larger degree of underestimation with altitude in the stratosphere may be due to the larger vertical grid spacing of the ERA5 model in the stratosphere and the shorter dominant vertical wavelength of GWs with altitude.

In this study, we examined how well large-amplitude inertia GWs over Antarctica are quantitatively represented in ERA5. However, the relationship between the degree of GW representation in ERA5 and wave sources is unclear and should be investigated in future studies. Although GWs over Syowa Station are considered to be mostly caused by topography, tropospheric jets, and polar night jets, observations at different locations where GWs from different wave sources may predominate (i.e., McMurdo Station (Chen & Chu, 2017; Chen et al., 2013; Zhao et al., 2017)) or horizontal distribution observations using super pressure balloons (Tomikawa et al., 2023) may be effective.

Acknowledgments

The PANSY radar was operated by Japanese Antarctic Research Expedition (JARE). This work was supported by the JST SPRING (Grant JPMJSP2104).

Open Research

Data Availability Statement

The ERA5 on model levels are available from the Copernicus Climate Data Store (Hersbach et al., 2017). The processed data from the PANSY radar observations are available from Yoshida et al. (2023).