Gravity wave observations were taken at the Southern Space Observatory (SSO), located in São Martinho da Serra (SMS) (29.44° S; 53.85° W), Rio Grande do Sul, Brazil, using a single-filter (SF) imager that began operation from April 2017 to date. The observatory that hosted the imager belongs to the National Institute for Space Research (INPE) under the Southern Space Coordination (COESU/INPE). The imager comprises a fisheye lens, a telecentric lens system, and an objective lens. The instrument uses a single 2.5 in. (715–930 nm, with a notch at 865.5 nm) filter for the OH observation. The airglow layer has ∼ 7 to 10 km thick layer located at ∼ 87 km altitude.

This imager is equipped with a charge-coupled device (CCD) camera (SBIG, STL-1001E model), which has a resolution of 1024 × 1024 pixels, with each pixel measuring 24.6 × 24.6 µm, and 50 % of the quantum efficiency in the near-infrared spectrum. The image was not binned but cropped to 512 × 512 pixels, producing a final image size of 12 × 12 mm on the CCD chip with a spatial resolution of 512 × 512 km. Each image has an integration time of 20 s and a readout time of 10 s. Since the imager does not have a filter wheel, the temporal resolution is 38 s . Airglow observations were taken when the Sun and Moon elevations were lower than −12 and 10°, respectively. This mode allows 28 nights of observation per month, centered on the new Moon.

The Geostationary Operational Environmental Satellite (GOES)-R series is used to observe and study tropospheric convection. The infrared channels of the Advanced Baseline Imager (ABI) are used in this work. This channel has a spatial resolution ranging from 0.5 to 2 km and a temporal resolution of 10 min that allows the observation of critical weather and climate products for full disk and mesoscale. The cloud-top brightness temperature (CTBT) product is derived from the 11, 12, and 13.3 µm infrared observations. These channels are used in the observation of cloud-top and cold-front activities.

A ray-tracing model was used to investigate the propagation conditions of QMGWs and their source locations. In this work, the ray-tracing model follows the approach of , , and , with the underlying formalism from . However, in this version of the ray-tracing model, kinematic viscosity and thermal diffusivity are incorporated in the group velocities, and the dispersion relations are similar to the work of . The longitude, latitude, and altitude (at 87 km) of the first visible crest/trough and the observation time of the wave are assumed as the initial positions and times of the wave, and the wave characteristics are then used as the input parameters for the model.

The next step, thus, in longitude, latitude, altitude, and time of the iteration, which formed six ordinary differential equations, was solved using the fourth-order Runge–Kutta method . An initial altitude step size of 0.2 km was set, and the subsequent step sizes were determined from z=cgzt, with the boundary conditions of imposed. The next step of iteration is conducted if the following criteria are satisfied: 1.

The group velocity of the GWs must be less than or equal to 0.9 times the speed of sound (cg≤0.9Cs).

Items (3) and (4) from in the list above are important for studying GW propagating into the thermosphere. If there is a violation of the above-defined criteria, the iteration will be interrupted, and then all the calculations end and are saved automatically. The stopping conditions are discussed in and .

Atmospheric background wind and temperature used in the ray tracing were obtained from the Modern-Era Retrospective and analysis for Research and Application, Version 2 (MERRA-2), data , the Horizontal Wind Model 2014 (HWM14) version , and the United States Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere (NRLMSISE-00) empirical atmospheric model . Due to the limited altitude range of MERRA-2 wind and temperature data, which is up to 75 km, we concatenated the MERRA-2 wind data with HWM14 at an interpolated step at each 1 km. Similarly, the temperature data of MERRA-2 and NRLMSISE-00 are also concatenated. This procedure is done to attain an altitude range from near the surface of the ground up to 100 km. Since two different datasets with different resolutions are being concatenated, there may exist discontinuities at the concatenation altitude. The discontinuities are minimized using the approach of . As a result of the temporal resolution of MERRA-2, which is 3 h, an interpolation was performed for each time step of the ray-tracing iteration. The propagation of the wave through the atmosphere leading to the determination of the source location of the wave is investigated using ray tracing in a backward mode.

Observations of QMGWs began in April 2017 and ended in April 2022 in São Martinho da Serra. A total of 1512 nights of clear-sky images were analyzed. From 64 nights, 209 QMGW events were obtained. The monthly distribution of observed QMGWs is presented in Fig. . Each bar shows the accumulated QMGW cases observed each month, with the individual colors in gray showing the number of events observed each year. The color bar defines the year of observation. It can be seen from Fig.  that the highest number of QMGW events was observed in August, followed by July. The following section will discuss details on the distribution of the QMGW events in Fig. .

The 5 years of observed OH airglow images were subjected to spectral analysis to estimate the QMGW characteristics. Specific criteria were imposed to select the QMGW events used in this work. After the spectral analysis, the confidence level (CL) of the estimated wave spectrum is estimated. The spectrum having peak power spectral density with CL ≥ 95 % is accepted . Before selecting the QMGWs, the waves must first and foremost be visible in the OH images of the entire night for not less than 2 h. Next, the wave parameters were determined every 10 min. This is done to track the variations in the wave parameters (precisely the horizontal wavelength) to ensure it is the same wave. If the criteria of CL ≥ 95 %, visibility of wave, and the determined wave being similar are satisfied, then the wave is then subjected to the following conditions: i.

the λH must be greater than or equal to 10 km (λH ≥ 10 km);

Note that the cH > 150 m s-1 was considered the upper limit to avoid interference with the acoustic wave spectrum. mentioned that GWs with cH ∼ 250 m s-1 cannot propagate below 100 km. However, we chose this value, since it will take a wave with 150 m s-1 approximately ∼ 12 min to travel 100 km. If all of these conditions are satisfied, then the wave is selected. On the contrary, the wave will be removed even if CL ≥ 95 % and one of the other conditions are not met. In Fig. , the characteristics of the selected QMGWs obtained from the spectral analysis are presented. Panel (a) shows the QMGW horizontal wavelength distribution over the 5 years of observation. Panel (b) is the distribution of the propagation period, whereas panel (c) is the histogram of the phase speed distribution. Panel (d) shows the distribution of the propagation direction of the QMGWs.

For the λH distribution in Fig. a, an average wavelength of 22.50 km was observed with a peak value of ∼ 15 km, with a broad and dominant distribution ranging between 10 and 35 km. However, the normal distributions of the τ (Fig. b) and cH (Fig. c) are narrow, with a dominant peak period and phase speed skewed toward ∼ 10 min and ∼ 9 m s-1, respectively. The propagation direction of the QMGWs is presented in Fig. d. The direction of wave propagation is significantly anisotropic, mainly between northwest to northeast during the summer and in the southeasterly direction during the winter.

Ray-tracing model is used to study the propagation of the QMGWs and to determine their possible source locations. Two wind models were considered when running the ray-tracing model: zero wind and model wind modes. The model wind mode consists of concatenated MERRA-2 and HWM14 wind. However, in this work, only the model wind result of the ray tracing is presented. The ray-tracing results for the 209 QMGW events are presented in Fig. . The ray paths of the QMGWs in a model wind atmosphere are shown in blue lines, and their respective stopping positions are in red squares. The open triangle shows the observation site location.

The propagation time of the waves from their source to the observation altitude in the mesosphere is presented in Fig. a, while the duration of propagation (thus the time span of visibility of the propagating waves in the OH images during the night) of the waves in the OH images is presented in Fig. b. It can be seen that majority of the waves propagated less than 1 h from the source position in the lower atmosphere to the OH emission layer. Similarly, the observed wave packet from which the individual QMGWs were selected in the OH airglow images were visible over the field of view of the all-sky imager and propagated for 2–3 h.

Most mesospheric GWs have their primary sources in the lower atmosphere. Various generation mechanisms, such as the mechanical oscillator effect, obstacle effect, and latent heat of deep convection and orographic, are known to be prominent source mechanisms . From the ray-tracing result presented in Fig. , it was observed that 12.4 % of the ray path stopped above 60 km. This implies that these waves were generated in situ but not in the troposphere. However, the source mechanisms of these waves will not be discussed in this current work. On the other hand, the ray path of the remaining 87.6 % stopped in the troposphere. It indicates that this percentage of the wave is most probably generated in the troposphere. Figure  presents the distribution of the minimum cloud-top brightness temperature near the stopping positions of the ray paths in the troposphere.

Panels (a), (b), (c), and (d) show the seasonal distributions of CTBT for summer, autumn, winter, and spring, respectively. The selection time of the CTBT ranges from 18:00 to 06:00 UT on the following day. The selection of this time range was due to the observation time of the QMGWs and possible excitation time determined by the ray tracing. The overall distribution of the CTBT for each season agrees with the propagation directions presented in Fig. d.

On 20 July 2017, at around 22:00 UT, GW structures with λH ∼ 10–60 km were observed in the OH airglow propagation towards the northwestern direction. The waves with similar wavelengths gradually propagated toward the west and southwest as time progressed. In Fig. , the sub-panels labeled (i) show the λH at each 1 h, whereas the sub-panels labeled (ii) show the variation in ϕ at each hour. The sub-panels labeled (iii) show the variation of ϕ in a polar plot representation. Panels (a), (b), and (c) with the sub-panels labeled (i) depict the variation of λH between 30–40, 40–50, and 50–60 km of the GWs with time. The corresponding sub-panels labeled (ii) and (iii) of each panel represent the azimuth versus time and azimuth in a polar plot. The color representing λH in the sub-panels labeled (i) at each hour corresponds to the same color in the sub-panels labeled (ii) and the arrow in the sub-panels labeled (iii).

We observed that the maximum variations in the three groupings of the wavelengths are within ±5 km. These variations fall within the average error range of each group. In relation to the variation in the azimuth with time, the change in the propagation direction is evident that all the groups of the wave propagated from the northwest at the beginning of the observation to the southwest at the end. The variations in the propagation direction in the sub-panels labeled (ii) were affirmed in the polar plots in the sub-panels labeled (iii).

Similar to the 20–21 July 2017 event, GW structures with λH ∼ 30–50 km were observed in the OH airglow images propagating toward the northwesterly direction. Contrarily, these waves propagated mainly toward the northwest throughout the entire night. The variation in the λH and ϕ values at each 1 h and the ϕ in a polar plot are presented in Fig. . The sub-panels labeled (i), (ii), and (iii) have the same meaning as defined in Fig. . Panels (a) and (b) depict the sub-panels labeled (i), (ii), and (iii) for λH between 30–40 and 40–50 km for the 15–16 August event, respectively, whereas panels (c) and (d) show that of the 20–21 August event.

In the sub-panel labeled (i) in panel (a), no significant variations were observed in the λH. The propagation direction (ϕ) showed some variation with time but generally (the fit is the solid black line) varies from north to northwest. Even though the 40–50 km GWs lasted for just 3 h, it is clear that this GW was propagating mainly in the northwestern direction (see the sub-panels labeled ii and iii for panel b). The characteristics of these GWs clearly show that their source may be the same.

The GW structures observed on 20–21 August 2017 have a similar range of λH to that of 15–16 August 2017. The two wavelength group (30–40 and 40–50 km) variations in the λH and the respective ϕ (in time and polar plot) are presented in panels (c) and (d) of Fig. . Like the propagation direction of the waves in Fig. a and b, the wave (30–40 km) in Fig. c propagates in a similar direction. However, the 40–50 km wave propagated from the northwesterly to the northerly direction. The different propagation directions of the wave in this spectrum suggest that this wave might be excited by a different source. The propagation of these GWs is studied, and their possible source location is investigated using the ray-tracing result presented in Fig. .

Lightning activity is used to indicate the severity of deep convection. used lightning distribution in space to show the direct relationship to CTBT. and references therein used the lightning rate as an indicator of overshooting of the tropopause, while investigating the sources of three concentric gravity events. Strong correlations were observed between the lightning rate and overshooting tops in space and time. In this study, the lightning activity in space (Fig. ) and time (not shown) were used to show whether the convective system present during the three case studies was active.

To determine the lightning density, we binned the lightning flashes by 0.15° × 0.15° in longitude and latitude from 18:00 to 06:00 UT. The density distribution was then overplotted on the map, as shown in Fig. . Interestingly, the density distribution of the lightning during these case studies is low, especially for the cases of 20–21 July and 20–21 August. The maximum density distribution occurred during the 15–16 August event (Fig. b). However, the distribution of this event is far from the ray-traced source locations. In general, the density distributions of the three events are low. This is another indication that these convective systems were not active. Even though the lightning distribution of the 15–16 August QMGW event (Fig. b) was relatively high, the lightning rate (not shown) did not present characteristics of overshooting. Using lightning activity, it has been further proven that the observed waves are not excited through the overshooting mechanism.

A cold front is the leading edge of a cooler air mass at ground level that replaces a warmer air mass and lies within a pronounced surface trough of low pressure. A cold front generates a cumulous cloud with precipitation, emitting GWs. Since the systems for case studies 1, 2, and 3 are not overshooting, further analysis of the characteristics of the system is conducted using GOES images to study the cold-front characteristics. According to , among the GOES-16 products, channel 10 captures the activities of the lower/midlevel water vapor (fronts) between 500 and 750 hPa (2.5–5.5 km) in the infrared wavelength at 7.3 µm.

Figure presents a 3 h resolution time series of GOES-16 infrared images of a cold front between 18:00 UT and 06:00 UT. Figure a–d presents the spatiotemporal evolution of the cold front during the 20–21 July 2017 case study, whereas panels (e)–(h) and (i)–(l) of Fig.  present that of the 15–16 and 20–21 August case studies, respectively. The time of each image is written in the upper-left corner. The color bar in the upper left shows the temperature scale of the cold front. Cold fronts are used, among others, to monitor severe weather potential. For this reason, complementary data such as reanalysis and spaceborne observation were used to investigate the possibility of severe weather.

First, convective available potential energy (CAPE), an essential parameter in predicting severe weather, is used. From CAPE, the maximum updraft velocity (w=2⋅CAPE) is mainly used to determine possible overshooting of the tropopause that can lead to gravity wave excitation. As discussed earlier, no overshooting was observed before the observation of these case studies. However, to confirm that no overshooting was observed, CAPE maps within the same time and spatial range, as shown in Fig. , were plotted and presented in Fig. . The color bar in the upper-left corner shows the values of CAPE.

In Figs.  and , the contour lines of omega (dp/dz) at 850 hPa were overplotted on the cold front and CAPE maps. In Fig. , the contour lines and their magnitude are represented in red, whereas in Fig. , they are in gray lines. The omega data were obtained from the National Centers for Environmental Prediction (NCEP). More details on the omega data can be seen elsewhere in . The following section will discuss the omega contours, the cold front, and CAPE. The omega is plotted over the cold front and CAPE maps to show the regions with cold brightness temperature and high CAPE values to show strong upward vertical air motion. The omega (upward vertical motion of air mass) in gray contour lines is overplotted on the spatiotemporal evolution of the CAPE maps. Even though, in Figs.  and , omega at 850 hPa was overplotted on the cold front and CAPE maps, the following question still remains: what are the characteristics of omega with altitude?

Figures and present the results of coincident observations and reanalysis data used to investigate the state of the tropospheric activity. Figure  clearly shows the passage of the cold fronts during the three selected case studies. For the case of 20–21 July, the cold front was moving eastward, whereas the 15–16 and 20–21 August events were moving southwestward. A close observation of the omega over the cold front showed that the region with colder temperature has negative omega at 850 hPa, which indicates a consistent ascending motion of the atmosphere . In the cases of 20–21 July and 15–16 August, regions with negative omega are over Uruguay and part of Argentina between 18:00 and 06:00 UT. These regions are to the south and southwest of the observation site. For the case of 20–21 August, the region of the passage of the cold front was over latitudes higher than -25° and the majority over the Atlantic Ocean. The omega with a negative sign coincides with these regions. The characteristics of the cold fronts are further affirmed using the CAPE maps (Fig. ).

CAPE is used as an indicator of atmospheric instability, which measures the integrated work that the upward buoyancy force would perform on a given mass of air to rise vertically through the entire atmosphere . In this work, we used CAPE further to show the state of instability of the atmosphere. Several works by researchers (e.g., ) used CAPE (updraft) to infer the possibility of severe weather that can lead to overshooting and consequently GWs excitation. According to the Storm Prediction Center (SPC) of the National Oceanic and Atmospheric Administration (NOAA) , CAPE is classified as marginally unstable when 0 ≤ CAPE ≤ 1000, moderately unstable when 1000 ≤ CAPE ≤ 2500, very unstable when 2500 ≤ CAPE ≤ 4000, and extremely unstable when CAPE ≤ 4000.

The higher the value of CAPE, the greater the possibility of the formation of severe weather and also the higher the maximum updraft velocity that may lead to overshooting of the tropopause and thereby exciting GWs. In the case studies considered in this work, the values of the CAPE were very low, especially in the regions indicated by the ray tracing to be the possible source location of the QMGWs, as shown in Fig. . This, therefore, strengthens the result in Figs.  and that the source mechanism of the GWs observed in these case studies is not through the mechanical oscillator (overshooting) effect.

The observed CTBT map did not show overshooting, implying that the clouds did not extend too high to the upper troposphere. To further confirm this, the vertical column of the cloud (see Fig.  in Appendix ) was analyzed. For the case study of 20–21 July, there was no observation of CloudSat. On the other hand, there were observations during the case studies of 15–16 and 20–21 August, where CloudSat passed right through the region of negative omega (see Figs.  and ). Clearly, Fig.  showed the presence of only low-level clouds. Another piece of evidence to show that the three case studies in this work were not excited through the mechanical oscillator (overshooting) mechanism is the vertical profile of omega at fixed longitude and varying latitude, as shown in Fig. . The vertical profiles of the cloud and omega are specifically presented to further affirm the result of the cold front (Fig. ) and CAPE (Fig. ) maps, which indicate that no overshooting took place, despite being clearly depicted in Figs.  and . For details on the vertical profiles of the clouds and omega, see Appendix .

All this evidence clearly shows that the QMGW events selected for the three case studies are not excited through the mechanical oscillator effect mechanism of convection. However, other mechanisms associated with a cold front can excite these waves. We now investigate this possible mechanism.

Cold fronts are known to be characterized by temperature field but also by pressure, wind speed, and the direction that precede and succeed its passage. Pressure zones, wind speed, and direction can also identify cold fronts. The characteristics of the wind are such that a sudden change in wind direction commonly occurs with the passage of a cold front. According to , before the arrival of the front, winds ahead of the front (in the warmer air mass) are typically from the south-southwest. Still, the winds usually shift to the west-northwest (in the colder air mass) after the front passage. These case studies, however, occurred during the winter season when strong wind shear and jet streams are prominent.

Strong wind shear in the upper troposphere–lower stratosphere are responsible for generating tropopause shear layers, which generate local turbulence and consequently can lead to mixing air between these two different layers . This mixing air contributes to the emergence of dynamic instabilities that conduct waves to overturn, followed by the turbulent flow breakdown in this transition region. This approach has been discussed in the context of clear-air turbulence (CAT) since 1970 (e.g., ). Recently, a midlatitude cyclone was simulated using the high-resolution numerical model in which much turbulence were reported. This information highlights the importance of the tropospheric jet streak, wind speed, and shear enhancement within upper-tropospheric outflow with the occurrence of CAT and the generation of gravity waves on different scales . A jet streak is a section of the overall jet stream in which winds are greater along the jet core flow than in other parts of the jet stream.

Following this approach, the horizontal winds at 200 hPa are analyzed for each event in these selected case studies (Fig. ). The horizontal wind speed (contour plot) and direction (overplotted vector in red arrows) at 200 hPa of the case studies of 20–21 July, 15–16 August, and 20–21 August are presented in panels (a), (b), and (c) of Fig. , respectively. These winds are obtained from the National Centers for Environmental Prediction (NCEP) . The sub-panels labeled (i) and (ii) represent the wind speeds and directions at 18:00 UT on the previous day and 06:00 UT on the next day of each case study, with their respective speed in the color bar.

It is important to note that these events occurred during the winter when the polar jet stream (wind ∼ 60 m s-1) is generally displaced southward, as observed in these three events. showed many possible source mechanisms of gravity waves observed in the mesosphere that appear to be closely related to tropospheric jet streams, principally on the polar side of jets. showed that the gravity waves generated by tropospheric jet streams may have the ability to propagate vertically to the upper atmosphere, such as the ionosphere . Using two synchronized automated digital cameras at Krasnogorsk and Obninsk, located near Moscow, Russia, demonstrated that a particular transient isolated gravity wave in the summer mesopause is associated with the passage of an occluded front or the point of occlusion or possibly both. The source mechanism of the wave generation, according to , was likely due to strong horizontal wind shear at about 5 km altitude. Similarly, illustrated that gravity waves, observed in the summer mesopause, were associated with the upper-tropospheric jet stream at altitudes 8–10 km.

Figure a shows a strong and clear bifurcation of the strong wind flow close to longitude -60°, coinciding with the source location of the gravity waves. This bifurcation was persistent with strong wind flow throughout the 12 h, suggesting a constant emission of the gravity waves in this region. It can be observed that the wind was toward the northeasterly direction at 18:00 UT on 20 July and 06:00 UT on 21 July. The propagation direction of the wave during this case study was northeastward at the beginning of the observation on 20 July 2017.

Now we investigate the source of the QMGWs of the 15–16 August case study. Similar to the case study of 20–21 July, Fig. b shows a confluence of the strong wind flow from the north and southwest towards the southeasterly direction over the region. This unidirectional wind flow may suggest a persistent and unidirectional emission of gravity waves throughout the 12 h. Close to the observation site, the omega was upward where the clouds were formed (see Fig. e–h). In Fig. b, omega extends almost throughout the altitude ranges considered in the sub-panels labeled (i) and (ii).

Finally, similar to Fig. b, a confluence of the strong wind flows from the northwest and south to the southeast direction close to the region of study is observed in Fig. c. The wind considered to be associated with the source mechanism of the case study of the 20–21 August QMGWs presented a different characteristic. Figure c–d shows that the two wavelength groups of these QMGWs have different propagation directions. The 30–40 and 40–50 km wavelengths had no well-defined propagation direction. The ray tracing, on the other hand, showed that only three of the waves were generated in the troposphere. The remaining waves reflected above ∼ 60 km. The ray path of the wave that reached the troposphere revealed that these waves were generated in the southwestern part of the observation site. In the troposphere, Fig. i–l showed that the cold front extends from the northeastern, eastern, and southwestern parts of the observation site. This system is quite distant from the observation site. Considering the propagation direction of the waves, there is no way these waves can be excited by this system. According to , wind shear can excite GWs, so considering the propagation of this wave, wind shear is most likely the source of this wave.

The vertical profiles of the omega (Fig. ), zonal wind (Fig. ), and wind shear (Fig. ) at fixed longitudes are analyzed to identify the main characteristics of the vertical position of the jet streams close to the observation site. The fixed longitudes (Figs.  and ) in case study 1 are 60 and 65° W (panels a), in case study 2 are 50 and 60° W (panels b), and in case study 3 are 50 and 40° W (panels c), respectively. The fixed longitudes for Fig.  are 62.5° W (case study 1; panel a), 55° W (case study 2; panel b), and 45° W (case study 3; panel c), respectively.

The vertical positions of the jet streams are close to 400 hPa for these three case studies, due to their occurrences during the winter season. The bifurcation (indicated by the dashed–dotted rectangle) of the wind flow is easily identified in panel (a) for the first case study, while the confluences (indicated by the dashed–dotted rectangle) of the wind flows are observed in case studies 2 (panels b) and 3 (panels c). The latitude with strong jet stream signatures corresponds to the latitude of the observation site.

The vertical profiles of the omega (Fig. ) show the ascendant motions slightly below the jet stream and descendant motions in the jet stream core, suggesting that the presence of the wind shear is close to the source region of all the events in this study. This behavior of the vertical motions may trigger the physical processes responsible for generating the turbulence close to the tropopause, which can lead to gravity wave generation. The excited waves can propagate vertically to the upper atmosphere (see , and ). Also, the vertical profile of the wind shear presented in Fig. , estimated using horizontal wind obtained from the NCEP Global Forecast System (GFS) data, is studied.

The vertical profiles of the wind shear in Fig.  show values greater than 15×10-3 s-1 close to the center of the jet streams (dashed–dotted dark gray rectangles), where the vertical displacement of the wind shear (dark gray rows) is observed in these three events. This indicates the occurrence of turbulence close to the jet stream region with the vertical upward extension. These values are in accordance with the literature, which indicates the occurrence of CAT in the troposphere . The vertical extension of wind shear can generate gravity waves capable of propagating vertically.

Several possible source mechanisms for generating the selected case studies have been presented in the previous section. However, some of these mechanisms cannot be responsible for the excitation of these events because they did not meet the necessary requisite conditions. For instance, the overshooting mechanism is not possible based on the inability of the convective system to overshoot. This is not obvious, since the selected cases were observed in winter, where deep convection is less prominent. On the other hand, jet streams associated with the cold front have been strong before, during, and after these events.

Jet streams are relatively narrow bands of strong wind blowing from west to east in the upper troposphere–lower stratosphere (UTLS). As the jet stream changes in intensity and location, the strength and motion of air masses are affected, and when the air masses converge, they form fronts. When colder air mass replaces warmer air mass, colder fronts are formed. This is the exact condition in the lower atmosphere during these events. As a result, further analysis was conducted on the jet stream to establish a relationship between the jet streams, namely the GW excitation mechanism and the observed GWs.

GWs observed in the upper mesosphere can be excited by jet streams in the lower atmosphere (, and references therein). From the above analyses, it is clear that the activities of jet streams may be the mechanism that led to the emission of the observed QMGWs in the selected case studies.