The Variations of Gravity Wave Activities During the Formation of the Large Horizontal Wind Shears in the Static State Lower Thermosphere

Abstract

Large horizontal winds and shears across the mesopause region have been observed by sounding rockets and satellites but with limited simultaneous temperature profiles to date. This feature is critical to the diagnosis of the insitu dynamic conditions. Theories suggest this feature may be related to variations of the atmosphere static stability, Brunt-Väisälä frequency square (N²), and the wave activity in the mesosphere and lower thermosphere (MLT) that cannot be resolved by the models. Since 2020, the Na Doppler lidar at Utah State University has attained several hundred hours of wind and temperature profiles in the MLT up to ∼110 km altitude. This paper focuses on the variations of these large winds and shears (>40 m/s/km), along with their potential relation to the activities of the various scales of gravity waves in the static state upper mesosphere, measured coordinately by the Advanced Mesospheric Temperature Mapper operating alongside the lidar. The investigation reveals that larger shears tend to occur in the meridional direction than the zonal direction and are observed more frequently in winter. The shears are comparable in both directions in summer and more large shears were observed in zonal direction. In addition, small shears occur when the medium-scale waves are completely or partially blocked by the mean wind, though no convincing evidence relates small-scale wave activities with these large winds and shears. Furthermore, small and decreasing N² in the upper mesopause region are associated with insignificant magnitude of the shears.

Introduction

The lower thermosphere is an important transition region, where the dominant atmospheric processes change from eddy diffusion to molecular diffusion. This is also the region that defines the lower boundary of the ionosphere, where prominent ion-neutral coupling processes are driven by the strong neutral winds. Occasional rocket measurements have indicated massive winds and shears occur in this region (Larsen, 2002; Lehmacher et al., 2022; Mesquita et al., 2020). The latest observations from the Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) instrument on board the Ionospheric Connection Explore (ICON) have documented extensive new information on this dynamic feature in different scales (England et al., 2022). In those observations, the zonal and meridional wind shears were found to increase quickly in the lower thermosphere, peaking around 105 km and, then, decrease going into the middle thermosphere. Note that these large horizontal winds and the associated shear are in the same altitude range of ionosphere sporadic E layer (Es) and the metal ion layers observed between ∼100 and 115 km and, thus, may play a critical role in the formation and propagation of Es (Mathews, 1998; Carter & Forbes, 1999; Bernhardt, P. A., 2002). Furthermore, the neutral winds in the lower thermosphere are highly important in driving the E region dynamo (Forbes et al., 2008). Such dynamic horizontal wind features also form critical layers filtering upward propagating gravity waves (GWs), resulting in wave dissipation, energy deposition, and secondary wave generation in this highly dynamic region, further controlling the GW spectrum penetrating the ionosphere and the associated ionosphere anomalies. It is also believed that these fundamental dynamic wind features are critical to the formation of the lidar-observed thermospheric Sodium (Na) layers at middle latitudes around the globe, which is investigated comprehensively in both lidar observations (Yuan et al., 2013, 2014) and the numerical simulation studies (Cai et al., 2017, 2019).

Ever since the discovery of strong winds and associated large shears in the lower thermosphere by sounding rocket observations (Larsen, 2002), various modeling and theoretical investigations have been conducted to study the underlying mechanisms of this exceptional dynamic feature in this region (Liu, 2007, 2017; Liu et al., 2014). Liu (2007) used Richardson number, $$Ri={N}^{2}/{\left(\sfrac{d{U}_{h}}{dz}\right)}^{2},$$ criteria for dynamics stability (Ri < 1/4 is a necessary but not sufficient condition for the instability) to estimate the maximum horizontal wind shear allowed in the mesopause region (∼80–105 km). Note that the static stability (Brunt-Väisälä frequency square, $${N}^{2}=g/T\left(dT/dz+\frac{g}{{c}_{p}}\right) > 0$$) enhances considerably due to the large vertical temperature gradient in the lower thermosphere above the mesopause. The simulation shows the wind shear profiles closely follow the background N² profile in the MLT, suggesting this feature occurs in static states where the GW amplitude can grow significantly before generating dynamic instabilities that hinder the growth of the horizontal wind perturbations. This hypothesis is supported by the lidar observations up to ∼105 km (∼100 km altitude in summer) (Yue et al., 2010), although the region above 105 km was not accessible to the Na lidar in summer at that time due to low Na number density. In that experimental study, Yue et al. (2010) found positive correlation between N² and the observed large wind shears that is consistent with the simulation by Liu (2007). Lund and Fritts (2012) suggested these large shears could also be induced by nonlinear interactions between the breaking GWs and the mean wind. Liu et al. (2014) summarized this nonlinear interaction as: First, the breaking and dissipating GWs and their momentum deposition induce dramatic mean wind acceleration. Second, the accelerated mean wind reduces the vertical wavelengths of GWs due to the decrease of intrinsic GW frequency. Third, both the accelerated mean winds and the reduced vertical wavelengths of GWs contribute to the enhancement of wind shears. This, in turn, creates a condition that favors the occurrence of GW breaking and momentum deposition, as well as mean wind acceleration. Enhanced mean wind further reduces the vertical wavelength and induces larger wind shears. The whole process is positive feedback among GWs momentum deposition, mean wind acceleration, decreasing vertical wavelength, wind shear enhancement, and instability. In addition, Liu et al. (2014) argued that the large wind and shears in this region could also be due to the interactions between inertia GWs and tides (tidal modulations of GW breaking in the lower thermosphere), and the wind and shears are found to be sensitive to the relative phase between the two types of waves in their numerical simulations. Kelvin-Helmholtz instability, which moves with the mean flow horizontally and carries large winds and shears, are frequently observed in the lower thermosphere becoming another candidate for the formation of large winds and shears. It also contributes considerably to the observed quasi-periodic echo structures in sporadic E layer (Bernhardt, 2002). Utilizing high-resolution NCAR Whole Atmosphere Community Climate Model (WACCM), Liu (2017) conducted a comprehensive numerical study focusing on this unique atmospheric feature. This numerical investigation suggested that in addition to the criteria for dynamics stability, the large wind shear may be related to the vertically highly compressed GW modulations due to increasing N² in the same altitude range, where their vertical wavelength decreases.

By following the Fritts and Alexander (2003) Equation 24, which corresponds to the Boussinesq approximation, the vertical wavenumber of a gravity wave can be written as [Image Omitted. See PDF]

This formula (Equation 1) indicates that the decrease of vertical wavelength (an increase of the vertical wavenumber, m) of an atmospheric gravity wave is closely dependent upon the difference between the background Brunt-Väisälä frequency square, N², and the intrinsic frequency square, $${\widehat{\omega }}^{2}$$. Here, f represents the Coriolis frequency; k_h is the horizontal number of the wave and H is the scale height with typical values around ∼8 km in the mesopause region. Because the GW modulation-induced shear is inversely proportional to its vertical wavelength, the increase of its vertical wavenumber due to the increasing N² above the mesopause could potentially enhance the shear magnitude. The same numerical investigation also indicated that those unresolvable small-scale gravity waves in the model may contribute significantly to this horizontal wind feature in the lower thermosphere, while tide may be the secondary contributor. The argument is that the observed large winds and shears around the globe do not seem to show a clear location and seasonal dependence and have been observed at low, middle and high latitudes, while tides may follow relatively robust latitudinal distributions and seasonal dependence (Forbes, 1995). Additionally, this theory suggests that, in the lower thermosphere, growing wind shears are due to the GW's increasing amplitude before the dynamic instabilities are generated. It is possible the unique dynamic conditions in this region could further enhance the shear by compressing the GW packet vertically and shortening the vertical wavelength of the wave.

Thus, to understand the underlying mechanism of this dramatic and dynamic atmospheric feature, in addition to the temperature and wind profiles, it is important to look at the simultaneous gravity wave activities with different scales in the upper mesosphere during the occurrence of these large shears in the mesopause region near and above ∼105 km. However, such coordinated observations are limited, leaving these theories and numerical simulations unchecked. This is mainly due to challenges associated with measurements of high quality temperature and horizontal winds in the atmosphere region above 100 km, making it one of the least known atmospheric regions. Rocket sounding observations can only provide a few wind profiles during each campaign, while the satellite observations cannot diagnosis critical information of GWs, such as the short term temporal variations of small-scale and medium-scale GWs. In this study, in addition to a comprehensive quantification of the large wind shears in the lower thermosphere by a Na Doppler lidar, the coordinated observations by an Advanced Mesospheric Temperature Mapper (AMTM) at Utah State University (USU) are utilized to study the potential relationship between the lidar-observed large wind shears in the mesopause region and the gravity wave activities in the upper mesosphere. The Na Doppler lidar at USU was upgraded in 2019 to enhance sensitivity and extend winds and temperature observation altitude above 115 km consistently during nighttime (Yuan et al., 2021). The results of the Na lidar observations during these campaigns are reported in Section 2. The co-located AMTM observations and results are presented in Section 3, and the potential connection between the GWs in the upper mesosphere and wind shears in the mesopause region is discussed in Section 4. Conclusions of this investigation are summarized in Section 5.

The Na Lidar Observed Horizontal Winds and Shears

The USU Na Doppler lidar observes mesopause region temperatures and winds by measuring the thermal broadening and Doppler shift of the laser induces fluorescence spectrum of the mesospheric Sodium (Na) atoms (Krueger et al., 2015). In this study, the lidar measurements cover nocturnal observations at USU campus (42°N, 112°W) from December 2020 to December 2022, including 179 hr of summer (June and July) data and 237 hr of winter (December and January) data. The co-located AMTM observations, measuring horizontal temperature variations of the hydroxyl (OH) layer centered at ∼87 km (Pautet et al., 2014), were obtained in summer 2022. To reflect the static state dynamic in the mesosphere and lower thermosphere (MLT), the lidar results for the wind shear quantification studies are processed with 1-hr temporal resolution and 4-km vertical resolution, respectively, in Figures 1–4. Temperature measurements with statistic uncertainty larger than 5 K, along with wind measurements with uncertainty larger than 10 m/s, are treated as bad data. This data processing approach also smooths out all the small-scale modulations. However, their secondary effects, such as wave breaking induced wind acceleration or secondary wave generations, which have larger spatial and temporal scales, can still contribute to the lidar results.

Figure 1. The USU Na lidar observed absolute values of the zonal wind shear (top left), the meridional wind shear (top right), the horizontal wind shear (bottom left) and temperature gradient (bottom right) in the winter mesosphere and lower thermosphere.

Figure 1 illustrates the lidar-observed absolute values for shears of zonal, meridional, total vector (horizontal) winds and profiles of N² in winter. Both the zonal and meridional wind shears demonstrate similar vertical variations: The shears are more or less constant up to ∼90 km with their magnitude less than ∼20 m/s/km; starting from ∼95 km altitude, they increase dramatically, reaching more than 40 m/s/km for the zonal wind and larger than 50 m/s/km for the meridional wind. The shears of both wind components peak around 105 km, decrease quickly above that. The vertical variations of these lidar-observed horizontal wind shear profiles are quite similar to the rocket chemical release observations reported by Larsen (2002), except that the magnitude is less that the rocket measurements. This is mostly due to the different resolutions in the experiments' sampling (rocket observations are instantaneous measurements). The shear of the horizontal vector wind increases with altitude in the MLT, and appears to peak slightly above 105 km. Notice that the horizontal wind shear is non-zero throughout the MLT, while those of zonal and meridional winds have many occasions with zero wind shear. The profiles of N² show all positive values except one (−1.3 × 10⁻⁴) above 107 km, illustrating this region is mostly static-stable when the temporal and spatial scales are 1-hr and 4-km, respectively.

The temporal variations of the zonal and meridional wind shears at 105 km in winter are demonstrated in Figure 2, along with the probability distribution function of the maximum absolute shear values between 95 and 110 km. Each data point in this figure represents 1 hour of lidar data. While the variabilities of the shears are significant for both wind components, the mean shears are clearly modulated by some large-scale wave activity, likely atmospheric tide. The histogram of the maximum absolute shear between 95 and 110 km altitude (Figure 2c) illustrates that the most likely maximum absolute shear value in this region is between ∼12 and ∼23 m/s/km. Furthermore, within this altitude range, the probability of meridional wind shear reaching absolute value larger than 40 m/s/km in this data set (237 hr) is more than 9.1%, while that of the zonal wind is only about 4.2%. To estimate the potential bias due to more winter observations than summer, we reduce the number of winter hours to match that of the summer. The probability of the magnitude of shear larger than 40 m/s/km for the meridional wind stays almost the same, while that of the zonal wind drops to 2.2%. Figures 2a and 2b show that the variability of these shears in this region is quite large, ∼146 m/s/km (from −84 to 62 m/s/km) for the meridional wind and ∼102 m/s/km (from −49 to 53 m/s/km) for the zonal wind. Overall, in winter, the meridional wind is more likely to experience much larger shear than the zonal wind, and the magnitude of the absolute shear of the former is larger than that of the later. The variability of the shear of meridional wind is considerably larger than that of zonal wind.

Figure 2. The USU Na lidar observed temporal variations of the winter time zonal wind shear (top) and meridional wind shear (middle) at 105 km altitude, along with the probability distribution function of the maximum absolute values of winter time zonal wind (plus signs) and meridional wind (triangles) within the altitude range of 95–110 km altitude. Each data point represents one hourly averaged lidar measurement. The solid lines in the top and middle plots represent the corresponding mean shear values.

The shear and N² profiles in summer are shown in Figure 3. For zonal and meridional wind shears, they demonstrate similar characteristics to those in winter: the magnitude of the shear is more or less constant below 95 km but increases dramatically above. However, the shear peaking altitudes, where the largest shears occur, appear to be lower than those in winter, spreading between ∼100 and 105 km. The magnitude of the absolute shears of zonal and meridional winds are also similar to those in winter, reaching as much as ∼50 m/s/km. And again, the shear of the horizontal vector wind is almost non-zero. The shear profiles of the vector wind in summer are not much different from those in winter as shown in Figure 1. The N² profiles are all positive except one. Note that these very small and/or negative N² near the edges of the Na layer could be due to relatively large measurement uncertainties. On the other hand, above 100 km, there are many N² values that are considerably less than those in winter. Note that N², with which the shear is correlated, is highly dependent upon the vertical temperature gradient. The temperature gradient in summer starts to increase slightly below 95 km compared to ∼100 km in winter, due to lower mesopause altitude in summer. This may explain the spreading of shear peaking altitudes to a lower altitude in the summer MLT. The temporal variations of the wind shears at 105 km, as well as the probability distribution function of the maximum absolute shear values between 95 and 110 km, are illustrated in Figure 4. Because of the short summer night, the wave modulation of the shears is not as clearly demonstrated as those in the winter plots, while the large variabilities of the shears are still quite visible. Nonetheless, the modulation of the shear by tides in summer is expected, since the tidal amplitudes of both diurnal and semidiurnal tides in this region across 105 km altitude above USU are found to be quite large (Yuan et al., 2021). The range of the zonal wind maximum shear variability in this region (95–110 km) is more than 88 m/s/km (from −56 to 32 m/s/km), similar to that of winter. The variability of the meridional wind shear is close to 119 m/s/km (from −56 to 63 m/s/km), which is about the same magnitude as its winter counterpart. The probability distribution function in Figure 3c shows similar feature to those in winter. In this altitude range the probability of the occurrence of absolute shear values larger than 40 m/s/km is 6.2% for meridional wind and right 7.3% for zonal wind. Therefore, in summer, large shear occurs slightly more frequently in the zonal wind than in the meridional wind field (opposite to the winter scenario), the magnitude of the absolute maximum shear values is similar for these two wind components, and the variability of the maximum shear of meridional wind in the upper mesopause region is similar to that of winter.

Figure 3. Same as Figure 1, except for summer.

Figure 4. Same as Figure 1, except for summer.

The USU AMTM GWs Observations in Summer 2022

The AMTM observations provide a 2-D map of the temperature variations of the hydroxyl layer within the mesopause region, centering at ∼87 km. It achieves one temperature measurement across its field of view every ∼30 s integrating vertically throughout the hydroxyl layer, giving temperature measurements (±1–2 K) over a field of view of about 120° with an horizontal resolution of 0.5 km, ideal for small-scale wave (period of less than 1 hr and horizontal wavelength less than 100 km) observations in the upper mesosphere. On the other hand, because of their large horizontal scale (larger than the AMTM field of view), to derive the parameters of the medium-scale gravity waves (period larger than 1 hr and horizontal wavelength of several hundreds of km), the east-west and north-south sliced keograms of the temperature data are filtered and the fast Fourier transform (FFT) is applied (Fritts et al., 2014). Note that both types of GWs are very challenging to resolve by the current general circulation models.

Figure 5 shows the distribution of the power spectrum density of the small-scale waves during 9 summer nights measured by the co-located AMTM on USU campus during a coordinated campaign in July 2022. These results are calculated based upon the 3D FFT algorithm introduced by Matsuda et al. (2014). Based on Figure 5, the magnitude of the phase spectrum power of the small-scale waves during these nights varies considerably night-to-night. It also illustrates larger wave energy in the meridional direction by the small-scale wave activities on three nights (Matsuda et al., 2017). For example, on the nights of July 05–06 (DOY187), July 11–12 (DOY 193), and July 20–21 (DOY202), the power of these waves was more or less concentrated in the northward direction, implicating the GWs are mostly propagating in this direction, with more energy and momentum than the zonal direction. As we mentioned earlier, while these small-scale modulations are smoothed in the 1-hr and 4-km lidar resolutions, their overall secondary effects, such as those due to wave breaking induced wind accelerations and secondary wave generations that have much larger scales, can still contribute to the lidar results.

Figure 5. The phase power spectrum distribution function of small-scale wave (period less than 1 hr and horizontal scale less than 100 km) for each night measured by the USU AMTM in the nine-night collaborative campaign with the Na lidar. The three highlighted nights by the red squares are when very large zonal or meridional wind shear (>50 m/s/km) were observed.

The medium-scale waves with large amplitudes and periods between 1-hr and 4-hr have been found to be the dominant GW components in the midlatitude MLT and have been consistently observed by ground-based instruments (Cai et al., 2017; Yuan et al., 2016). Their large amplitudes, when overlapping in phase with tidal waves, can generate transient instabilities that trigger dramatic wave breaking processes (Cai et al., 2014). Here, the AMTM observed horizontal parameters for the dominant medium-scale wave for each of these nights are listed in Table 1, along with their intrinsic phase velocities, vertical wavenumber and momentum flux at 95 km calculated based on the horizontal wind observations by the Na lidar. The periods of these waves vary from 75-min to 195-min, while the horizontal wavelength covers from 250 to 1,200 km. The amplitudes of these waves are all relatively small, <5 K within the OH layer. Assuming the wave's observed horizontal phase speed, propagating direction and horizontal wavelength do not change much between the hydroxyl layer and 95 km, we estimate the horizontal intrinsic phase speed, $${\widehat{C}}_{ph},$$ of these waves with respect the horizontal wind at this altitude right before the shears start their considerable growth above. This assumption is based upon previous work by Cai et al. (2014), which reported the centroid height of the OH layer can vary from ∼83 to ∼93 km. Coupled with 4-km vertical resolution of the lidar data processing, this assumption is legitimate in this investigation. This is further supported by Yuan et al. (2016), in which the Mesospheric Temperature Mapper demonstrated the medium-scale wave activities in the OH and O₂ layers (centroid height is ∼94 km) are similar with the uncertainties within ∼10%, which is normal for this type of GW detection. The second and third column show the lidar observed maximum magnitude of the zonal and meridional wind shears between 95 and 110 km for each night. The average values are 35 and 36 m/s/km, respectively for zonal and meridional winds. The nightly averaged N² values are listed in the fourth column, which shows all positive values. This is expected, since the MLT should stay in static state on a nightly average basis. The AMTM observed wave periods and horizontal wavelength are shown in the fifth and sixth column. Utilizing the lidar temperature and wind profiles, the calculated intrinsic phase speed, vertical wavenumber and momentum flux at 95 km altitude are listed in the seventh, eighth and ninth column. The wave during the night of July 4–5 (DOY186) shows a negative horizontal intrinsic phase speed in the table, because its observed phase speed is less than the horizontal wind throughout the night, thus, the wave is completely blocked due to critical level filtering. The magnitudes of the maximum shear in both zonal and meridional directions are relatively small compared to the average value, less than 30 m/s/km between 95 and 110 km. In addition to this night, there are two more nights when the magnitude of the maximum zonal and/or meridional wind shears are less than 30 m/s/km in this region: July 20–21 (DOY203) and July 25–26 (DOY207). The averaged N² around 95 km of both nights (4.6 × 10⁻⁴ for DOY203 and 4.7 × 10⁻⁴ for DOY207) are noticeably less than the 9-night averaged N² (5.5 × 10⁻⁴) and the momentum flux it carried during DOY203 (3.97 m²/s²) was the second least among the nine nights. Note that the wave during night DOY192 carries the least amount of momentum flux (2.83 m²/s²) and propagates with the slowest intrinsic horizontal phase speed, $${\widehat{C}}_{ph}=47\,\mathrm{m}/\mathrm{s}$$. The shears observed by the lidar, 23 m/s/km for zonal wind and 33 m/s/km for meridional wind, were below average values. The largest shears were observed on the night of July 5–6 (DOY187), when shears larger than 50 m/s/km occurred in both zonal and meridional winds. On the night of July 11–12 (DOY193), a zonal wind shear of 52 m/s/km was also detected. Such large shears are most likely associated with instability. We further discuss these results in Section 4.

Table 1 Maximum Absolute Shears (95–110 km) and the Associated Medium-Scale GWs Parameters Observed by the USU Na Lidar and AMTM During Nine Nights in July 2022

Date (DOY)	$${\vert \frac{dU}{dz}\vert }_{\mathit{max}}$$ (m/s/km)	$${\vert \frac{dV}{dz}\vert }_{\mathit{max}}$$ (m/s/km)	N2@95 km × E04	GW_τ (min.)	GW_λh (km)	$${\text{GW}\_\widehat{C}}_{ph}$$ @95 km (m/s)	GW_|m| @95 km ($$\frac{2\pi }{m}$$) × E-04	GW_MF@95 km (m2/s2)
07/04–05 (186)	25	28	5.0	160	250	−19 (blocked)	NA	20.8
07/05–06 (187)	50	58	5.7	105	720	143	1.67	5.79
07/06–07 (188)	44	37	5.8	90	330	76	3.16	6.27
07/07–08 (189)	46	29	5.6	105	380	99	2.39	29.7
07/10–11 (192)	23	33	7.0	195	710	47	5.64	2.83
07/11–12 (193)	52	37	6.0	100	1,200	172	1.42	13.3
07/20–21 (202)	37	44	5.0	100	800	196	1.15	15.3
07/21–22 (203)	16	23	4.6	100	1,100	188	1.14	3.97
07/25–26 (207)	26	29	4.7	75	270	96	2.25	8.15

Note. DOY represents Day of Year; MF stands for momentum flux that the GW carries; τ is period, λ_h is the horizontal wavelength of the wave. The wave parameters at 95 km is calculated based on the assumption that the observed horizontal phase speed and horizontal wavelength varies little as the wave propagates from the OH layer to 95 km. For the momentum flux calculation, the amplitude of the GW modulation measured by the AMTM is multiplied by a factor of e to approximate its magnitude near 95 km.

For medium-scale waves, the intrinsic frequency is $$N\gg \widehat{\omega }\gg f$$. Thus, Equation 1 can be simplified as $$\vert m\vert =\frac{N}{{\widehat{C}}_{ph}}$$, along with a simplified expression for its intrinsic frequency, $$\widehat{\omega }=N\vert \frac{{k}_{h}}{m}\vert $$, and vertical group velocity, $${C}_{gz}=-\frac{\widehat{\omega }}{m}$$, (Equation 32, 33, and 34 in Fritts & Alexander, 2003). Based on these equations, the vertical wavelength of each wave at 95 km can be calculated as well (see Table 1), assuming the observed horizontal phase speed and horizontal wavelength do not change between the OH layer and 95 km. The calculations show that waves with large horizontal intrinsic phase speeds have considerably small vertical wavenumbers (longer vertical wavelength). When such waves were observed, the lidar detected shears larger than 40 m/s/km in the horizontal wind. One exception is the night of July 21–22 (DOY203), when the intrinsic horizontal phase speed is 188 m/s but the N² is the least among these nights. As discussed earlier, the small N² limits the magnitude of the shear based on Liu (2007), making the overall shear on the night of DOY203 noticeably less than the other three nights. Furthermore, since k_h ≪ m for these waves, their vertical group velocities, C_gz, are also very slow, implying the wave packet can exist within the upper mesopause region for a considerable amount of time. These results suggest that some of the largest maximum shears are associated with medium-scale waves with small vertical wavenumbers (long vertical wavelength, λ_z), long horizontal wavelengths, λ_h, and very fast horizontal intrinsic phase speeds, but slow vertical group velocity. To better understand the behaviors of the medium-scale GWs during these nights, Figure 6 shows the AMTM observed horizontal phase speed and direction of the medium-scale waves (black solid arrows) for each night during this campaign. In addition, the lidar observed changing horizontal winds at 95 km throughout each night (red solid lines) are also illustrated. As mentioned earlier, the wave on the night of DOY186 had a horizontal phase speed less than the horizontal wind and, thus, was completely blocked by the horizontal wind below 95 km. The waves during the night of DOY187, DOY189 and DOY202 were propagating against the wind and, thus, moved freely upward across 95 km into the lower thermosphere. The scenarios on the nights of DOY188 and DOY192 are very similar. The horizontal wind varied mostly southwest to northwest and the wave was propagating almost northward (∼340° to the north and ∼350° to the north) with phase speed (∼60 m/s and 65 m/s) faster than the horizontal wind, meaning the wave experienced little blocking. The relative direction between the wave and the horizontal wind on the night of DOY207 is similar to those of DOY188 and DOY192, but the wave's horizontal phase speed was less than the magnitude of the horizontal wind for some portion of the night. On the night of DOY193, the wave was propagating in the southeast direction (∼−40° with respect to the east) with observed phase speed of ∼200 m/s, while the horizontal wind was mostly in the southwest direction (varying from ∼170° to ∼330° to the east) with wind speed of ∼40 m/s. Note that the observed horizontal phase speed for the wave on the night of DOY189, ∼60 m/s, is considerably less than those during the nights of DOY187 (∼120 m/s), DOY193 (∼200 m/s), DOY202 (∼150 m/s), and DOY203 (∼190 m/s). This small velocity could increase the possibility of wave blocking at higher altitudes on this night, where the horizontal wind changes its magnitude and direction.

Figure 6. The AMTM observed horizontal phase velocity of the medium-scale gravity wave with respect to the changing horizontal wind at 95 km for each night of the 9-night collaborative campaign with the Na lidar.

To investigate these medium-scale waves' behaviors in the upper mesopause region of 95–110 km altitude range, where the maximum shears are observed, N², |m|, and the intrinsic phase speeds of the waves were calculated and are shown in Table 2. As expected, the ratios of Brunt-Väisälä frequency square (second column) increases in this region except on the night of DOY192 when it dropped 6%. This decreasing N² implicates the dynamic condition did not favor shear enhancement. Indeed, the maximum shears for that night were all below the averaged values (35 m/s/km for zonal wind and 36 m/s/km for meridional wind) and insignificant compared to those of the other nights. The increase of N² on DOY187 is a 24% to 7.06 × 10⁻⁴, when very large shears with magnitudes over 50 m/s/km were observed in both zonal and meridional winds. The largest enhancement is on DOY207 (36%). The N² for DOY203 is still the smallest among the nine nights in this region (5.8 × 10⁻⁴) and the maximum shears are all significantly less than the average values. It is worth noting that maximum shears >50 m/s/km were observed only on DOY187 and DOY193 when N² in this region were >7.0 × 10⁻⁴. With the exception of DOY188 (56% increase), based on the ratio of the absolute values of the vertical wavenumber (the fifth column), |m| either decreases (DOY187, DOY189, DOY192, and DOY202) or exhibits little change (DOY193, DOY203, and DOY207) above 95 km in the upper mesopause region, indicating increasing or no changes in vertical wavelength, instead of compressing the wave packet counter to what Liu (2017) suggested. The magnitude of the reducing |m| in this altitude range varies from 1%–2% to 57% with the largest reduction happened on the night of DOY192. The night of DOY188 is an exception and is the only night when both vertical group velocity, C_gz, and intrinsic horizontal phase speed, $${\widehat{C}}_{ph,}$$ of the wave clearly decreased with an increasing vertical wavenumber, resembling the wave propagating “downshear.” The waves' $${\widehat{C}}_{ph}$$ and C_gz during the other nights were all increasing with decreasing |m| as the wave propagated into higher altitudes. Such changes reflect the typical features of a medium-scale gravity wave propagating “upshear,” when its group velocity, vertical wavelength and intrinsic frequency all increase (Fritts & Alexander, 2003). However, the observed maximum shear magnitudes of 44 m/s/km in zonal wind and 37 m/s/km in meridional wind on DOY188 are all larger than the average values, implicating the magnitude of the shear is somewhat independent of the vertical wave direction relative to the shear.

Table 2 The Medium-Scale Waves Parameters and N² in the Altitude Range of 95–110 km of the Same Nine Nights and Their Ratios to Those at 95 km

Date (DOY)	N2 × E04 (95–110 km)	$$\sfrac{{N}_{95-110}^{2}}{{N}_{95}^{2}}$$	$${GW\_\widehat{C}}_{ph}$$ (m/s)	GW_|m| (95–110 km) ($$\frac{2\pi }{m}$$) × E-04	$$\frac{{\overline{\vert m\vert }}_{95-110}}{{\overline{\vert m\vert }}_{95}}$$	$$\frac{{\vert \overline{{C}_{gz}}\vert }_{95-110}}{{\vert \overline{{C}_{gz}}\vert }_{95}}$$
07/04–05 (186)	6.34	1.26	NA	NA	NA	NA
07/05–06 (187)	7.06	1.24	198	1.32	0.80	1.72
07/06–07 (188)	6.31	1.09	51	4.93	1.56	0.43
07/07–08 (189)	5.95	1.06	121	2.07	0.84	1.45
07/10–11 (192)	6.61	0.94	107	2.48	0.43	5.35
07/11–12 (193)	7.43	1.24	193	1.42	0.99	1.13
07/20–21 (202)	5.86	1.16	228	1.05	0.92	1.26
07/21–22 (203)	5.80	1.26	215	1.11	0.99	1.17
07/25–26 (207)	6.33	1.36	108	2.26	1.04	1.09

Note. NA represents Not Applicable, because the wave was found to be blocked below 95 km.

Discussion

Based on the dynamic stability theory proposed by Liu (2007), the Brunt-Väisälä frequency square, N², sets up the condition for the maximum absolute shear allowed in the static lower thermosphere. This is consistent with this experimental study, in which the nights with small N² in the upper mesopause region such as DOY203 in 2022, did not have significant shear. Another example is the case of DOY192 during the same campaign when N² decreased in the upper mesopause region and relatively small shears were observed. The other insignificant shear occurrence on the night of DOY186 is most likely due to wave blocking, as was discussed in the previous section. The medium-scale-wave on DOY207 could experience both small N² and critical level filtering (see Figure 6), resulting on relatively small shear magnitude. Such positive correlation between N² and shear has been investigated in detail in Yue et al. (2010). Liu (2017) further pointed out that the potential underlying mechanism of the large shear is the shortening of the vertical wavelength of the ubiquitous GWs in the lower thermosphere, where the vertical gradient of temperature increases dramatically, thus, enhancing the value of N (see Equation 1). For high-frequency, small-scale GWs, satisfying the Boussinesq approximation, their intrinsic frequencies, $$\widehat{\omega }< N$$, are in a similar order of magnitude as N, while $$\widehat{\omega }\gg f$$ in the denominator. Therefore, the increasing N² in the lower thermosphere does not have significant impact on the vertical wavenumber of these high frequency, small-scale GWs. This is consistent with the AMTM measurements of the small-scale waves presented in Figure 5, providing no evidence to demonstrate a clear relation between these waves and the Na lidar-observed day-to-day variability of the maximum shears in the upper mesopause region.

To further investigate the activities of gravity waves at different altitudes above the OH layer, Figure 7 shows the power spectrum of temperature perturbations at 95 km, 100 and 105 km for each of the six nights (DOY179, DOY186, DOY192, DOY193, DOY198, and DOY202) in July 2022, attained by the USU Na lidar temperature measurements by the north pointing beam with 3-min temporal resolution. As demonstrated by the figure, the perturbations at these altitudes are dominated by the low frequency components with periods longer than 4 hr, while the relative activities of the small-scale high frequency GW components (period less than 1 hr) were fairly consistent during these nights. In fact, for each night, the high frequency waves' activities at 95 km are quite similar to those at 105 km, where the large shears were mostly observed. Note that these low frequency components include tide and medium-scale gravity waves and, probably, some potential random inertia gravity waves. The power spectrum analysis of the high-resolution lidar temperature data in Figure 7 shows minimal day-to-day variabilities of these high frequency modulations relative to the other components and, thus, may not contribute considerably to the observed large shear. Furthermore, the small-scale, high frequency GWs have small amplitude in the MLT and they only become significant dynamic sources in the middle and upper thermosphere. Because of their relatively slow horizontal phase speeds, they could be completely or partially blocked before reaching the upper mesopause region. On the other hand, the vertical wavenumber of the medium-scale GWs can be simplified because of $$N\gg \widehat{\omega }\gg f$$, and can be written as $$\vert m\vert =\frac{N}{{\widehat{C}}_{ph}}$$. Therefore, if the intrinsic phase velocity, $${\widehat{C}}_{ph}$$, of the wave does not vary much when the wave propagates into the mesopause region, the quick enhancement of N in the lower thermosphere due to the increasing temperature vertical gradient could directly increase the vertical wavenumber of the medium-scale GW in this region, shortening the wave's vertical wavelength and, thus, increasing the wind shear according to Liu (2017).

Figure 7. The power spectrum density of temperature perturbations of the six summer nights in 2022 enabled by the lidar high resolution (3-min) temperature measurements at 95 km (dotted lines), 100 km (solid lines) and 105 km (dot-dash line), along with the 95% confident levels for each altitude.

The 2022 summer observations do not reveal considerable enhancement of the nightly averaged vertical wavenumber in the upper mesopause region between 95 and 110 km. In fact, during the aforementioned nine-night summer campaign in 2022, the average medium-scale GWs' vertical wavenumber in this region was found to be either decreasing or changing little in eight nights, indicating increasing or constant vertical wavelengths. In the meantime, the background N² increases mostly with increasing altitude, except on the night of DOY192 when N² dropped ∼6% in this altitude range compared to its value at 95 km. However, it needs to be pointed out that this conclusion is based upon the nightly averaged values and it is quite possible that, although the overall nightly average vertical wavenumber decreases, during some portion of the night within certain altitude range, the wave's vertical wavelength can be shortened by some atmospheric dynamic conditions (see the discussion in the next paragraph). In addition, slow intrinsic phase speed and small momentum flux can also contribute to the observed insignificant shears, as is the case on the night DOY192, when both are the least around 95 km among these nights. Fast phase speed is necessary to ensure the wave does not meet any critical level as it propagates upward throughout the upper mesopause region. This study shows that the decreasing |m| of these waves is due to the fact that increasing intrinsic phase velocity outpaces the increasing N above 95 km when the waves propagate “upshear.” However, such fast horizontal intrinsic phase speed means the vertical wavenumber of the wave becomes small (large vertical wavelength and increasing vertical phase speed) based on Equation 34 in Fritts and Alexander (2003). Furthermore, based on the polarization relation of the medium-scale GWs, $$\widetilde{w}=-\frac{{k}_{h}}{m}\widetilde{u}$$ (Equation 36 in Fritts & Alexander, 2003), the long horizontal wavelength of the medium-scale wave, k_h ≪ m, determines that the ratio between the vertical wind component, $$\widetilde{w}$$, and the horizontal wind component, $$\widetilde{u}$$, of the wave is quite small, implicating the relatively large horizontal wind modulation for this type of waves. Note that the same description applies to even larger scale inertia GWs as well. These experimental results contradict Liu (2017) on the GW contributions to the large shear through shortening vertical wavelength of GWs in the lower thermosphere, resulting in compressing the GW packet vertically and increasing the shear. Of course, Liu (2017) also stated that the vertical gradient of the mean wind and tidal modulations also contribute to these large shears in static state thermosphere, but play a secondary role. Note that OH nightglow observations of long vertical wavelength waves could suffer from cancellation effects.

In addition, Liu et al. (2014) pointed out another mechanism for “shortening” the GW vertical wavelength in the upper mesopause region when studying the inertia GW-tidal wave interactions. Based on linear GW theory, the vertical wavenumber can change with respect to the vertical gradient of horizontal wind through, $$\frac{dm}{dt}=-{k}_{h}\frac{\partial \overrightarrow{{U}_{h}}}{\partial z}$$, where $$\overrightarrow{{U}_{h}}$$ represents horizontal wind (Jones, 1969). Thus, when a large positive vertical gradient of horizontal wind occurs, $$\sfrac{dm}{dt}< 0$$. For upward propagating GWs, m < 0, indicating the vertical wavenumber becomes even more negative with larger absolute value, decreasing the vertical wavelength. Furthermore, by combining Equations 33 and 34 in Fritts and Alexander (2003), the vertical group velocity can be written as, $${C}_{gz}=\frac{N{k}_{h}}{{m}^{2}}$$. This formula indicates that, if very large vertical gradient of horizontal wind occurs in the region, the sharply increasing absolute value of vertical wavenumber, m, can outgrow the increasing N in the lower thermosphere. This can lead to slowing of vertical propagation of the GW packet, extending the duration of the GW packet and the associated large shear in the lower thermosphere. As a single point measurement, the lidar technique is ideal to investigate this hypothesis of GW vertical wavelength changing over time. In the winter 2022 campaign, we uncovered several prominent cases for this scenario, implicating this may be a potential mechanism of the large horizontal wind shear. As an example, Figure 8 shows the lidar observed variations of the temperature perturbations, along with the associated N² and absolute values of the meridional wind gradients during four nights around the middle of November 2022. The large scale background is calculated through a seventh order polynomial fit, and the temperature perturbations are the residuals in this process. As Figure 8 shows, the most noticeable case occurred on the night of day 22,321 (DOY321 in 2022), when the slope of the temperature modulation was seen decreasing overtime, especially during the second half of the night and early morning hours in the upper mesopause region, implicating the vertical wavelength of the GW was decreasing during the second half of the night. Such changes of vertical wavelength were also observed in the early morning of day 22,320 (DOY320 in 2022) around and above 95 km altitude, but were not as evident as the case in day 22,321. Note that the magnitude of the shear in the early morning hours of DOY22321 is not as large as that of DOY22320, mainly because of the smaller values of N². The variations of the meridional wind of these two nights demonstrate the occurrence of large shear throughout the upper mesopause region, further supporting the mechanism described above, when the negative vertical shear occurred on day 22,319 and on 22,323, with no shortening of the vertical wavelength. Another possibility is simply the natural evolution of a wave spectrum from a source. Notably, the faster, longer vertical wavelength portion of the spectrum arrives at a given altitude first, followed by the slower, shorter wavelength components later, leading to the apparent shortening of the vertical wavelength of a wave packet/wave train over time. Such events were indeed reported in Yuan et al. (2016). Unfortunately, there were no AMTM observations during the winter campaigns at USU, and those previous calculations of medium-scale GW parameters, along with the associated wave feature investigations critical for the shear formation, cannot be conducted for the winter campaigns. Note that observations of the evolution of such relatively long period medium-scale GW's vertical wavelength is very challenging in summer due to relatively short nights (8 hr or less in summer compared to more than 14 hr in winter) at the USU location.

Figure 8. The Na lidar observed variations of Brunt-Vaisala frequency square (top row), the absolute magnitude value of meridional wind shear (middle row) and temperature perturbation (bottom row) for four nights in November 2022.

Conclusions

As one of the most prominent dynamic feature in the MLT, the large horizontal winds and the associated shears formed near the mesopause have been investigated for more than two decades since they were first reported by Larsen (2002) using rocket wind observations around the globe. While there have been various theories and numerical simulations on its potential underlying mechanisms and the suspicion that GWs contribute significantly to the formation of this feature, limited experimental observations by other instruments have been reported. In this experimental study, simultaneous temperature and winds observations in the upper mesopause region, up to ∼110 km, between 2020 and 2022 by the upgraded USU Na Doppler lidar have been utilized to study and quantify this dynamic feature, such as summer-winter differences and local time variations. In addition, the co-located AMTM was operating in summer 2022 alongside the Na lidar and provided critical information on the role of GW activities and their variabilities during the formation of these large winds and shears.

In this investigation, the lidar observations reveal that the peak altitudes of the horizontal wind shears in the static state lower thermosphere concentrate near 105 km in winter, but occur at lower altitudes and spread between 100 km and below 105 km in summer. It is also found that these shears are modulated by tides. In addition, at the USU location, the magnitude of the meridional shears is larger and occur more frequently than zonal shears in winter. In summer, magnitude of the shears in these two directions are similar and more likely to be observed in the zonal wind field than the meridional wind field. More specifically, the possibility of the meridional wind shear exceeding 40 m/s/km in the winter (summer) upper mesopause region (95–110 km) is more than 9.1% (∼6.2%), while that of the zonal wind is only around 4.2% (∼7.3%). Because the semidiurnal tide dominates the middle latitude upper mesopause region and the tide-GW interaction may be one of the mechanisms of this large shear formation (Liu et al., 2014), this feature may be related more to the overall larger semidiurnal tidal amplitude meridional wind than the zonal wind (Forbes, 1995; Yuan et al., 2008) in winter. Based upon the dynamic stability theory by Liu (2007), which suggests the temperature gradient dependent Brunt-Väisälä frequency limits the maximum allowed shear without inducing dynamic instability, this phenomenon (larger shear more frequently occurs in winter than summer) may be related to the distinct temperature profiles between seasons. The temperature gradient in summer is mostly positive from the upper mesosphere to thermosphere, but in winter, it has negative gradient approaching the mesopause altitude, ∼100 km, then turns sharply positive. The lidar observations in the upper mesopause region confirm that, when the Brunt-Väisälä frequency is small, the magnitude of the observed shears in this region becomes relatively less than those observed during the nights with average values of the Brunt-Väisälä frequency. In addition, the variability of the meridional wind shear is also found to be larger than that of the zonal wind shear.

Liu (2017) suggests that ubiquitous GWs in the MLT are the primary contributor to the large shears, where the vertical wavelength of the wave can be shortened due to the increasing Brunt-Väisälä frequency above the mesopause. The coordinated campaign between the USU's Na lidar and AMTM in summer 2022 revealed that there is no clear evidence to relate the shear variabilities with the small-scale waves (temporal and spatial scales less than 1-hr and 100 km, respectively). However, in addition to the medium-scale waves blocking, some of the small shears observed between 95 and 110 km were associated with small or decreasing N². Slow intrinsic phase speed and small momentum flux carried by the medium-scale waves are also related to the observed insignificant shear. The calculations of the vertical wavenumber in the upper mesopause region indicate the nightly average vertical wavelength of the medium-scale waves are mainly increasing or change little in the altitude range where the large shears occur, contradicting the aforementioned theory. This is mainly due to the increasing intrinsic phase speed of the wave in the lower thermosphere that outpaces the increasing Brunt-Väisälä frequency. Nonetheless, the lidar observations do reveal some cases of compressed GW packet in the upper mesopause region during some portion of the night, when the wave's vertical wavelength decreases. Based on the linear GW theory (Jones, 1969), this shortening of GW vertical wavelength may be due to the occurrence of a large positive vertical gradient of the horizontal wind, as the wave propagates upward. This is consistent with the lidar observations of the horizontal winds in winter 2022, when the shortening vertical wavelength mostly occurred during the same time a large positive vertical gradient of the horizontal wind was observed in the MLT. Therefore, in the upper mesopause region, although the nightly averaged vertical wavelength increases compared to that at lower altitudes, during some portion of the day, the vertical wavelength can decrease due to the considerable increasing positive vertical gradient of the horizontal wind in this altitude range. Such a large vertical gradient can occur due to large amplitude tide, especially the semidiurnal tide, whose amplitude increases significantly in the upper mesopause region at midlatitude (Yuan et al., 2008) and has been found to have large day-to-day variability (She et al., 2004).

Overall, this experimental investigation, conducted by the USU Na Doppler lidar and AMTM has revealed the seasonal variations of the large horizontal wind shears peaking near the mesopause and its relationship with the medium-scale gravity waves activities in the MLT. These experimental results further reveal the complexity of the mechanism of this unique dynamic feature. However, coordinated AMTM observations during the winter campaigns are also needed during future Na lidar campaigns to extend this study. Furthermore, the regional high resolution gravity waves numerical simulations that can adapt these experimental observations will help us fully understand the geophysical processes involved in the formation of this significant dynamic feature in the upper atmosphere.

Acknowledgments

The work by the USU Na lidar was supported by National Science Foundation AGS 1954308: Exploratory measurements of large winds and shears in the lower thermosphere and their variability using an enhanced Na lidar. The USU AMTM was designed under the Air Force DURIP Grant F49620-02-1-0258, and operated under the NASA contract number 80GSFC18C0007. We would also like to thank Dr. Hanli Liu at National Center for Atmospheric Research for the discussion we had on this topic.

Data Availability Statement

The USU Na lidar data of this investigation are available at https://doi.org/10.26078/27d9-185c, which is managed by the USU library DigitalCommons (Yuan, 2023). The AMTM data used in this study is available through the Harvard Dataverse repository (https://doi.org/10.7910/DVN/DIJGNW) (Pautet, 2023).