In this study, we use observations obtained with six meteor radars operating in the SH between 53 and 79∘ S in latitude. Four of the meteor radars can be grouped into a cluster around the Drake Passage consisting of the Southern Argentina Agile Meteor Radar (SAAMER) at Rio Grande, Tierra del Fuego, Argentina (hereafter referred to as TDF), King Sejong Station on King George Island (KSS), Rothera (ROT) on the Antarctic Peninsula, and King Edward Point (KEP) on South Georgia island. The other two radars are located almost opposite the Drake Passage at McMurdo (McM) and Davis Antarctic stations (DAV). Figure  shows two panels with stereographic projections of the SH, where the radar locations are represented by red dots (left panel and Table ). The right panel in this figure shows a color contour map of the mean elevations around each radar system to identify potential orographic wave forcing sources underneath the observation volumes.

A technical summary of the radars is provided in Table . Most of the systems have been in operation for more than a decade and have provided reliable and continuous observations. Although most of these systems have been operated without major parameter changes, both ROT and TDF meteor radars have been upgraded during the observing period of our study. Until February 2019, the ROT system used a high pulse repetition frequency (PRF) meteor mode, with a PRF of 2144 Hz, a 2 km range sampling, and four coherent integrations. After this time, the system was upgraded and resumed operation transmitting a 7 bit Barker code with 1.5 km range sampling and a PRF of 625 Hz. We also noted a significant noise or interference at ROT before the upgrade in January/February that did not allow trustworthy momentum fluxes to be derived. Further, we also restricted our analysis of mean winds and tides to the altitude range between 80–100 km. In addition, in September 2019, the TDF transmitting scheme also changed. The original design of the TDF transmitter (TX) configuration used eight three-element crossed Yagi antennae arranged in a circle of diameter 27.6 m, each transmitting in opposite phasing of every other Yagi . In 2019, the system transmission strategy was upgraded with the deployment of a single new TX antenna, with the goal of improving the detection rate of meteors at larger zenith angles for astronomical purposes . By concentrating the full power of TDF in one TX antenna, a more uniform detection pattern is achieved that satisfies this original requirement but also increases the number of events detected at larger zenith angles. Finally, the McM radar is the most recent installation, which, although it is not the most powerful radar, provides a very good altitude coverage. This is partly explained by the sporadic meteor sources and the southern location of the McM meteor radar. The helion, antihelion, and the south apex meteor source are above the local horizon all the time, contributing to the observed sporadic meteor fluxes at McM and yielding a much weaker seasonality in the altitude variation of the meteor layer . In addition, meteors arriving from these sources enter the atmosphere at fairly low entry angles (<20∘; see for a Northern Hemisphere radar), leading to a much smoother ablation profile of the meteoroids, and, hence, the released meteoric material is spread over a larger segment of the meteor flight path, increasing the detectability. On the other side, the orbit geometry alone does not yet provide a sufficient explanation for the better altitude coverage at McMurdo; however, a more detailed investigation is beyond the scope of the paper.

Several of the meteor radars used in this study employ the standard meteor radar configuration of an array of five Yagi antennas for reception, with a spacing of 2 and 2.5λ . McM was set up in a different configuration with 1.5 and 2λ spacing due to topographic constraints. Similar to other meteor radars, most of them use a single Yagi antenna for transmission. Only TDF employed a beam forming transmission scheme, resulting in eight main beams, as described earlier, but changed to the use of the single crossed Yagi antenna late during the period studied here . A more detailed description of the King Sejong Station meteor radar can be found in and for the DAV meteor radar in .

Meteor radars have been used to measure winds in the mesosphere–lower thermosphere (MLT) for several decades. Typically winds are obtained by least-squares fits, solving for the horizontal wind velocities after binning the data into altitude and time intervals . In this study we retrieve winds using the algorithm presented in , which includes the treatment of the geometry of the full Earth, based on the WGS84 rotation ellipsoid to provide more precise altitude estimates and geodetic coordinates for each meteor, a spatiotemporal Laplace filter, and a nonlinear error propagation, which is described in more detail in . The wind retrievals are cross-validated against NAVGEM-HA . The results presented in this paper are based on winds with a temporal resolution of 1 h and a vertical resolution of 2 km. The minimum number of meteors per time and altitude bin for a successful fit is four.

For the case of momentum fluxes, proposed a method using typical meteor radars, which was later echoed and reformulated as correlations by . In this work, we present a brief derivation of the Reynolds stress tensor and show how the different tensor elements are estimated from the meteor radar observations. The starting point is the well-known radial wind equation. Each meteor will form a trail that will be detected by the radar and will drift with the background wind. The radar will then detect that radial velocity, via Doppler shift in the received signal, and the three components of the background wind can be calculated for each detected meteor using the mathematical convention (reference to east and counterclockwise rotation): 1vrad=u⋅cos⁡(ϕ)sin⁡(θ)+v⋅sin⁡(ϕ)sin⁡(θ)+w⋅cos⁡(θ), where u, v, and w are the three wind components (zonal, meridional, and vertical, respectively), ϕ is the azimuth angle, θ is the off-zenith angle, and vrad is the observed radial wind velocity. Further, it is straightforward to use the standard Reynolds decomposition of the wind, separating the wind components into a mean flow (u‾,v‾,w‾) and wind fluctuations (u′, v′, w′): 2u=u‾+u′v=v‾+v′w=w‾+w′. As we are mainly interested in the momentum flux associated with GWs, the mean flow terms containing the background wind and the diurnal and semidiurnal tide have to be subtracted/removed from the observed radial velocities for each meteor. Thus, we model the mean flow radial velocity by 3vradm‾=u‾⋅cos⁡(ϕ)sin⁡(θ)+v‾⋅sin⁡(ϕ)sin⁡(θ)+w‾⋅cos⁡(θ). The radial velocity fluctuations (vrad′), which now only contain GW contributions, are obtained by subtracting the mean flow radial velocity (vradm‾) from the observed radial velocity (vrad) measurements: 4vrad′=vrad-vradm‾. Furthermore, the GW fluctuations can be modeled by 5vradm′=u′⋅cos⁡(ϕ)sin⁡(θ)+v′⋅sin⁡(ϕ)sin⁡(θ)+w′⋅cos⁡(θ). Considering that these radial velocity fluctuations are mostly driven by GW, the Reynolds stresses can be computed by minimizing the following quantity : 6Λ=∑(vrad′2-vradm′2)2. Inserting Eq. (5) into Eq. (6) leads to the well-know momentum flux terms: 7Λ=∑(vrad′2-(u′2⋅cos⁡(ϕ)2sin⁡(θ)2+v′2⋅sin⁡(ϕ)2sin⁡(θ)2+w′2⋅cos⁡(θ)2+2u′v′⋅cos⁡(ϕ)sin⁡(ϕ)sin⁡(θ)2+2u′w′⋅cos⁡(ϕ)sin⁡(θ)cos⁡(θ)+2v′w′⋅sin⁡(ϕ)sin⁡(θ)cos⁡(θ)))2. Solving Eq. (7) for the unknown Reynolds stress components is straightforward. Typically, the terms u′w′, v′w′, and u′v′ are also called momentum fluxes, and the symmetric Reynolds stress tensor is given by 8τij′=ρuiuj‾=ρ⋅u′2u′v′u′w′u′v′v′2v′w′u′w′v′w′w′2, where ρ is the atmospheric density at the altitude of the measurement, and the other terms in the tensor denote the Reynolds stress components (wind variances and momentum fluxes), which have units of squared velocity fluctuations. The Reynolds stress components are derived from the RANS (Reynolds-averaged Navier–Stokes) equations, assuming an incompressible Newtonian fluid and that the Reynolds average of the fluctuations vanishes (u′‾=0), which requires the averaging to be long enough to cover the inertia GW periods of several hours or longer. The spatial scales can theoretically be estimated by selecting different volumes inside the domain area; however, practically the meteor statistics is often not sufficient to get reliable results.

However, there are some caveats of the theory outlined above, when it comes to implementing the algorithm and actually applying it to meteor radar observations. One difficulty is the Reynolds decomposition into the mean flow and the GW fluctuations. Previous studies often limited the analysis to a narrower angular region using only off-zenith angles between 10–50∘, reducing significantly the number of meteors for the analysis per time and altitude bin, which in turn required longer averaging or was achieved by an active beam forming antenna. Such an antenna directed more energy towards an angular region as for TDF or the meteor radar at Trondheim . The process by which this much stricter angular selection of meteors improved the momentum flux estimates was the reduction of projection errors due to the Earth's ellipsoid shape, which caused apparent and arbitrary contributions to the fluctuation terms. proposed to minimize this type of uncertainty by computing each meteor's geodetic position relative to the WGS84 reference ellipsoid, which improves the altitude determination but also reduces projection errors for the azimuth and off-zenith angle. The benefit of this full Earth geometry correction is that there is no longer a need to reduce the angular region, and all meteors up to off-zenith angles of 65∘ can be used for the analysis. Typical specular meteor radars (single Yagi antenna on transmission) detect most meteors at off-zenith angles between 50 and 70∘. However, meteors at larger zenith angles are further away from the radar and, thus, are more prone to altitude errors. The typical angular precision of the employed receiver arrays is approximately 1.5–1.7∘ . A limit of 65∘ presents a more optimal choice to maximize the number of meteors entering the analysis while keeping a sufficient altitude precision.

Another important aspect related to the momentum flux estimation is the proper removal of the background flow, which was already outlined by , , and and later confirmed by . In particular, tides have large amplitudes in the MLT, causing large vertical and temporal shears within a time and altitude bin. Noting that and suggested the use of at least 30 meteors for a successful momentum flux fit, which is often achieved by temporal averaging, the importance of the temporal shear becomes evident.

In this study we use the adaptive spectral filter (ASF) to perform the Reynolds decomposition to characterize the background flow and the GW fluctuations. A first version of the ASF(1D) (temporal domain) was presented in . Here we make use of the ASF(2D), which employs a vertical regularization constraint for the mean wind and tides, assuming a smooth vertical phase progression for each wave without an explicit vertical wavelength threshold . The ASF accounts for the continuous variation of the mean flow as well as for the intermittent behavior of the tides. Thus, we obtain hourly resolved background wind fields for each altitude and time bin for the zonal, meridional, and vertical wind component, respectively. This background wind field contains the mean flow and the diurnal, semidiurnal, and terdiurnal tidal component. However, the terdiurnal tide usually has a much smaller amplitude compared to the diurnal and semidiurnal tides and, thus, is not discussed here further. Furthermore, we perform a linear interpolation of the background wind field to the actual occurrence time and altitude for each meteor to estimate the vradm term, minimizing any contribution from the background flow. This procedure is effective in mitigating possible contamination due to tides and permits the use of a much longer averaging window. In this study we use 64 h and a minimum of 100 meteors to determine the Reynolds stress components. However, for the seasonal climatology, only solutions with more than 1000 meteors enter the statistics.

The algorithm is implemented similar to that performed for wind retrievals in . The first guess is provided by a classical least-squares fit. Based on this initial iteration, we compute the spatiotemporal Laplace filter, which provides a predictor for each time and altitude bin. This predictor enters all further iterations as regularization (Tikhonov) and is updated each time. The spatiotemporal Laplace filter turns out to be beneficial for ill-conditioned problems due to the random occurrence of meteor detections and asymmetries in the spatial sampling; these can result in difficulties in determining all parameters with similar quality.

Furthermore, we perform a nonlinear error propagation similar to the one presented in . The statistical uncertainties are updated in each iteration step. We also tested barrier functions to penalize negative values of u′2,v′2, and w′2, respectively. Such negative values were reported in , but this appears to be a minor issue in our retrievals. Only a negligible number of fits resulted in negative values for just some of the radar systems utilized in this work.

In addition, we performed some test retrievals to account for the vertical velocity bias intrinsic to the meteor radar observations. Specular meteors have trail lengths of up to several kilometers where the radio waves are scattered, and, thus, meteors entering the Earth's atmosphere at steep entry angles can encounter strong vertical wind shears, which lead to a rotation of the trail, causing systematic errors. In particular, during the local summer months, this can lead to a systematic deviation of a few centimeters per second for midlatitude stations.

Very often wind fits are performed by assuming w=0 m s-1 . However, here we use the retrievals as presented in , who used the vertical wind velocity as quality control. Typically, we obtain daily mean values of the order of ±0.25 m s-1, which is more than an order of magnitude less than reported by . However, the remaining bias due the vertical winds, which potentially has the wrong sign, had no impact on the retrieved Reynolds stresses.

Finally, in order to get confidence in the retrievals, we performed several test cases similar to the ones presented in . Therefore, we extracted the observed meteor detections from TDF and synthesized wind fields including altitude-dependent mean winds and tides with a vertical wavelength of 80 km and various altitude-dependent GW fields to optimize the retrieval setting with respect to the regularization strength, the required statistics, and the applied averaging. Performing these tests, we find minor deviations from the synthetic wind and GW fields only at the upper and lower edges of the meteor layer. The tidal amplitudes were retrieved within ±2 m s-1 compared to the synthetic data. The momentum fluxes agreed for the 30 d median remarkably well. We also tested the possibility to retrieve the vertical wind fluctuation amplitudes and found mean deviations of ±0.01 m s-1 residual bias for the synthetic fields and about ±0.25 m s-1 bias in our observations.

To bring the local radar observations into the global context we calculate the geostrophic zonal wind as described in from geopotential height (GPH) data from the Microwave Limb Sounder (MLS) on board the Aura satellite . MLS has a global coverage from 82∘ S to 82∘ N on each orbit and a usable height range from approximately 11 to 97 km (261–0.001 hPa), with a vertical resolution of ∼4 km in the stratosphere and ∼14 km at the mesopause. The temporal resolution is 1 d at each location, and data are available from August 2004 until the present . Version 4 MLS data were used in this paper, along with the application of the most recent recommended quality screening procedures from . For our analyses the original orbital MLS data are accumulated in grid boxes with 10∘ grid spacing in longitude and 5∘ in latitude. Afterwards they are averaged at every grid box and for every day, generally resulting in a global grid with values at every grid point.

As pointed out in the previous section, we perform a Reynolds decomposition in order to separate a mean flow from the GW fluctuations. Thus, we analyze the data with the adaptive spectral filter (ASF) technique to obtain daily mean winds, as well as diurnal and semidiurnal tides.

We first compare the seasonal zonal and meridional winds of all six locations to identify any seasonal and local differences. Figure  shows the seasonal zonal and meridional wind pattern during 2019 obtained from the daily mean zonal and meridional winds after applying a 30 d running median shifted by 1 d. This reveals any seasonal variability by removing atmospheric waves with shorter periods. A similar analysis was applied in for meteor radars in the Northern Hemisphere in order to derive mean wind climatologies. Significant differences between the locations can be observed from this figure, in particular during the SH winter seasons (JJA). Both TDF and KEP observations, operated at almost the same latitude at 54∘ S, show a similar morphology for the zonal winds, and only the meridional winds deviate from each other during June and July. At the tip of South America, TDF shows that the meridional winds experience a sign reversal around June/July, which is not present over KEP. The meridional winds also seem to have a semiannual oscillation at both locations.

Further polewards at KSS and ROT (62 and 67∘ S, respectively), which are at a similar longitude as TDF, the zonal winds reflect a similar seasonal behavior compared to KEP and TDF but with a slightly weaker wind magnitude. However, the meridional winds are fairly consistent during the summer months compared to the midlatitude radars but deviate considerably during the winter season. There is even a noticeable difference between KSS and ROT, even though the systems are located rather close together. At ROT and KSS the meridional winds only show a typical winter behavior during April, May, and June and approximately northward winds for the other months above 80–85 km. Only during September and at altitudes above 90 km above KSS does a short southward wind patch occur.

Comparing the observed wind fields measured at ROT and DAV, which are only separated by 2∘ in latitude but by 170∘ in longitude, further emphasizes the existence of a significant asymmetry in the southern hemispheric wind systems. As expected, looking at the general morphology, the seasonal zonal wind pattern for 2019 is remarkably similar between both locations. There are only marginal differences in the zonal magnitudes considering the overall agreement of the zonal wind structures. This is also the case for the meridional winds during the summer months (DJF). However, during the winter season, the meridional wind structure is significantly different between both stations. The morphology at DAV appears to be less asymmetric, with a tendency to show increased southward wind magnitudes towards the end of the winter season, whereas at ROT the highest southward winds are recorded at the begin of the winter season 2019.

The southernmost location in our analysis is McM at 78∘ S. The seasonal zonal wind morphology compares well with that measured at DAV and ROT but shows much weaker wind magnitudes. Similar to observations in the Northern Hemisphere, the summer zonal wind reversal altitude also increases with increasing southern latitude. Compared to DAV, the meridional winds are intensified during the summer and winter seasons. Furthermore, the asymmetry during the winter months is also present at McM, which shows, similarly to DAV, the highest southward meridional winds towards the end of the winter season as a double structure. In fact, the southward meridional winds at McM during July and September 2019 are the strongest of all locations.

Atmospheric tides provide a time-variable background filter for the vertical propagation of GWs, which can, depending on the tidal phase and the propagation direction of the GW, lead to GW breaking and dissipation. These breaking events might trigger/foster the generation of secondary or non-primary waves . Thus, tides are essentially contributing to the Reynolds decomposition. In particular, the day-to-day variability is crucial for the momentum flux analysis. Typically, atmospheric tides are derived assuming phase stability over a certain period of time, which can be several days, weeks, or months . More recent studies favor much shorter windows of 24 to 48 h to account for the intermittent behavior of tides , in particular, phases of atmospheric tides that appear not to be constant with time . In this study, all tidal amplitudes and phases were determined with the ASF, which, similar to wavelet spectra, adapts the window length to the period of the fitted frequencies. The obtained daily tidal amplitudes are vector-averaged using 30 d medians centered at the respective day to derive the seasonal variation.

Figure  presents the seasonal variation of the diurnal tidal amplitudes measured at each station. Although the daily mean winds showed significant differences between TDF, KEP, KSS, and ROT, the seasonal behavior of the diurnal tide is rather consistent between all four locations. There is a pronounced summer maximum in the zonal and meridional amplitudes from January to February at altitudes from 78–106 km. The meridional tidal amplitudes tend to exceed the zonal amplitude by up to 10 m s-1. At altitudes above 100 km the diurnal tide remained of significant magnitude until May 2019. Evidently, for the other months the diurnal tidal amplitudes remained fairly weak (<10 m s-1) at altitudes between 80–100 km during 2019. KSS and ROT indicate a small diurnal tidal enhancement for July/August and in December below 80 km and above 100 km altitude. The December enhancements are also found at TDF but almost disappear at KEP. DAV measurements show basically the same seasonal diurnal tide behavior but with weaker amplitudes. The winter diurnal tidal enhancement in June/July appears to be more pronounced. However, the southernmost meteor radar at McM observes a significantly different seasonal diurnal tidal pattern. The summer maximum is much more pronounced compared to the other stations and shows amplitudes of 20 m s-1 from January to April at 90 km and above and again from October to December. There is also a noticeable difference between the zonal and the meridional diurnal tidal amplitude. The zonal component indicates a winter minimum, whereas the meridional component shows a tidal enhancement.

Diurnal tidal phases are shown in Fig. . The tidal phases are given in UTC; hence, longitudinal differences are present as phase shifts. As expected the diurnal phases are much more variable during time with low tidal amplitudes for TDF, KEP, KSS, and ROT. During the summer months of January and February 2019, the diurnal phases are more stable and indicate rather long vertical wavelengths but with significant differences between the zonal and the meridional components. However, the phase plots indicate a distinct seasonal pattern, showing phase drifts of several hours at the same altitude over the course of the year. The further south the location of a meteor radar is, the less characteristic the seasonal behavior is. Measurements at DAV and McM indicate a decreased variability of the diurnal tidal phases throughout the year. At DAV there are periods suggesting almost phase stability over several weeks, instead of the typical continuous variation reflected by the other stations.

At midlatitudes and high latitudes, semidiurnal tides are the dominating tidal wave during the course of the year . Figure  shows the vector-averaged semidiurnal tidal amplitudes measured by all six meteor radars using again a 30 d median shifted by 1 d in analogy to the mean winds and diurnal tides.

The seasonal structure of the semidiurnal tide reveals a rather interesting pattern for the SH. Semidiurnal tides measured at TDF, KEP, KSS, and ROT show some similarities for the zonal component, resulting in amplitudes with values below <10 m s-1 during the summer months January to mid-March. From April to June, all four stations show a strong semidiurnal tidal activity, with amplitudes up to 40 m s-1, another minimum of the tidal activity in July, and a secondary maximum from August to the end of the year. Furthermore, the tidal amplitudes show a decrease with increasing polar latitude, which is also observed at the Northern Hemisphere. However, the meridional semidiurnal tide shows a clear longitude dependence and asymmetry compared to the zonal tidal amplitudes, which was not reported previously . At the longitude of TDF and ROT the meridional tidal component is much weaker during April to June compared to the zonal. At KSS, which is further east, similar amplitudes for the zonal and meridional component are observed. This was also found at KSS in a previous study reporting the tidal amplitudes under solar maximum conditions, which resulted in larger amplitudes of the semidiurnal tide . KEP, which is 25∘ eastward, shows the opposite behavior, and the meridional component of the semidiurnal tide reaches the highest amplitudes in April to June. Such differences with longitude might be related to the superposition of migrating and non-migrating tides .

The semidiurnal tidal seasonal behavior observed at DAV looks quite different from the stations that are located further to the north. The amplitudes are much weaker and barely reach values of 25 m s-1, and there are four periods during which an increased activity is observed, which are during January–February, May, August–September, and December. The largest tidal amplitudes are observed during May 2019.

Further to the south, at McM station, the semidiurnal tide exhibits only a very faint seasonal structure. Most of the time the amplitudes are below 10 m s-1. Only during March, May, and November–December and below 90 km altitude are there periods where amplitudes exceed 10 m s-1. This is surprising when we compare these values with measurements performed at geographically conjugate Northern Hemisphere latitude. For instance, at Svalbard (78.17∘ N, 15.99∘ E), the semidiurnal tide still reflects a similar seasonal activity to other polar and midlatitude locations . This is obviously not the case in the SH and represents a remarkable interhemispheric difference.

Semidiurnal tidal phases are displayed in Fig. , where it can be seen that the semidiurnal tidal phases reflect similar features than those present in the amplitudes. TDF, KEP, KSS, and ROT show a very similar seasonal structure, indicating continuous changes of the tidal phases throughout 2019 at all altitudes. At DAV and McM, on the other hand, the observed phases indicate an even more pronounced seasonal structure and faster gradual phase drifts. In particular, at McM the phases appear to be more variable, which is likely due to the generally weaker amplitudes, pointing towards a much weaker and more intermittent excitation of the tides.

Comparing the seasonal phase behavior of the SH to that measured at conjugate latitudes in the Northern Hemisphere indicates that there are some differences. In the Northern Hemisphere, from midlatitudes to high latitudes, the semidiurnal tides show a seasonal asymmetry between the winter to summer transition and the fall transition . The fall transition is accompanied by a significant phase change from September to November, whereas in the SH this feature is very weak at TDF and ROT (March to May) and almost negligible for KEP and KSS.

Finally, we briefly discuss the presence of a potential lunar tide. estimated the lunar tide amplitude from two northern hemispheric meteor radars and Davis MF radar in the SH and found values of 1–2 m s-1, which is negligible compared to the typical GW amplitudes of about 20–30 m s-1 for the resolved waves. However, investigated a potential lunar tide amplification due to the Pekeris resonance. They found favorable conditions to shift the Pekeris peak towards the lunar tide periods M2 (12.42 h) and N2 (12.66 h), during the time of major sudden stratospheric warming in 2009 in the Northern Hemisphere, as only during the time of the wind reversal do the vertical temperature and wind structure satisfy the resonance conditions. Later, argued that the Pekeris resonance peak is rather broad, and, thus, more or less each sudden stratospheric warming can cause a lunar tide amplification.

These reports triggered several studies investigating the lunar tide and its relevance for mesosphere dynamics. However, most of the observational diagnostics (wavelet or harmonic fitting) separating the lunar tide from the semidiurnal tide applied long windows of 21 d or even longer periods up to several months, assuming phase stability of the semidiurnal tide . However, as shown in Fig. , the semidiurnal tidal phase shows considerable variability and seasonal changes, and, thus, the assumption of phase stability for the semidiurnal tide is not valid. Therefore, we performed a holographic analysis to test whether a temporally variable semidiurnal tidal phase could be misinterpreted as a lunar tide (see Appendix ) . In fact, the holograms often exhibit a shift towards the M2 frequency (12.42 h) uncorrelated with the lunar orbit. Given these results, and considering that there was only a minor stratospheric warming in September 2019 , we consider the lunar tide to be a minor wave with a negligible amplitude compared to GWs, and we did not make an attempt to remove this tidal component in our Reynolds decomposition.

For the sake of completeness, we also estimated the vertical wavelengths of the semidiurnal tide, which is presented in Fig. . The vertical wavelength provides a good overview to identify potential changes in the Hough modes of the tide, which are solutions of the Laplace tidal differential equation . The vertical wavelengths show a similar latitude and longitude dependence as already discussed for the semidiurnal tidal amplitudes and phases. The observations at TDF, KEP, KSS, and ROT indicate almost the same vertical wavelengths from March to October 2019 of about 70–100 km. This corresponds to the time with the largest semidiurnal tidal amplitudes. However, the seasonal summer months January–February and November–December show a longitudinal difference. KEP and KSS observe much longer vertical wavelengths of up to 1000 km during these months, compared to the stations located to the west. These very long vertical wavelengths are associated with times with a small semidiurnal tidal amplitude. The results obtained at DAV reflect a slightly different seasonal behavior. There, the longest vertical wavelengths are observed in March–April, followed by a stable hemispheric winter season until August, and a gradual decreasing of vertical wavelengths towards the end of the year. The results at McM show an even more complicated picture due to the almost vanishing semidiurnal tidal amplitudes. Only during the local summer months of January/February and November/December are meaningful vertical wavelengths derivable, with vertical wavelengths of about 70–100 km. It is also worth mentioning that the agreement between the zonal and meridional wavelengths is remarkable and provides further confidence in the applied ASF technique used for the Reynolds decomposition.

Gravity waves are an essential driver of the MLT dynamics and variability, carrying energy and momentum from their source region to the altitude of their deposition. The breaking of GWs can trigger the generation of non-primary GWs, which again can propagate upwards , causing a complex interaction chain for the GW activity and the resulting forcing at the MLT. The acceleration and deceleration of the mean flow due to momentum and energy transfer by breaking GW can be estimated from the vertical gradient of the gravity wave momentum flux .

From our Reynolds decomposition and the retrieval, we determine three momentum fluxes, which are often referred to as the vertical flux of zonal momentum <uw>, the vertical flux of meridional momentum <vw>, and the horizontal momentum flux <uv>, where the <> denotes temporal averaging.

Figure  shows all three momentum flux components as a 30 d median shifted by 1 d for the year 2019. There are three groups of panels presenting the vertical flux of zonal momentum (panel a), the vertical flux of meridional momentum (panel b), and the horizontal momentum flux (panel c). The stations are sorted according to their latitude within each panel to allow for an easier comparison between the sites. The results shown in this figure indicate that, for all six meteor radar observations, there is a characteristic seasonal pattern, with noticeable differences between the different locations.

The vertical flux of zonal momentum <uw> is rather variable with longitude and latitude. Observations at TDF and ROT show some similarities regarding the seasonal structure. During the local summer, both indicate positive zonal momentum fluxes at the altitude of the zonal wind reversal. At higher altitudes, above 95–100 km, the zonal momentum flux reverses to negative values. The winter season appears to be more variable, which might be related to the minor warming in September 2019 and the wave activity before. To the east, at KEP and KSS, positive zonal momentum fluxes at the higher altitudes (95–105 km) are observed throughout the year but a rather different behavior during the local winter season at the altitudes below. In particular, at KSS a variable zonal momentum flux is measured that seems to be in better agreement with TDF and ROT results. Further to the south, at DAV and McM, the seasonal behavior of the zonal momentum flux seems to reflect the features that are already found at KEP but with different magnitudes.

The vertical flux of meridional momentum presented in Fig.  exhibits some longitudinal dependence. Observations at TDF and KEP show approximately the opposite vertical structure of the meridional momentum flux, pointing out that the meridional drag (acceleration and deceleration) reverses between their longitudes. Furthermore, results from KEP, KSS, and ROT show a good agreement of the vertical structure and seasonality of the meridional momentum flux throughout the year. Measurements at DAV still show some features of the seasonal meridional momentum flux behavior but with decreasing magnitude, while at McM, the results show once again a seasonal dependency comparable to that obtained at KEP.

Only the horizontal momentum flux <uv> shows a similar seasonal behavior at TDF, KEP, KSS, ROT, and DAV, with negative values of -50 m2 s-2 during the seasonal summer and positive values in winter from April to October. The local winter shows more variability and a semiannual structure at some sites, similar to the mean zonal and meridional winds. At McM this seasonal variation is still visible but with a much weaker magnitude.

The seasonally dependent Reynolds stress components on the main diagonal of the tensor are also investigated. These terms are also often called zonal, meridional, and vertical wind variances. Figure  shows all three variances for each station. Note that the color scale for the vertical variances is 5 times smaller compared to the horizontal wind fluctuations. The zonal and meridional variances exhibit a seasonal structure and a rather obvious altitude dependence. The highest variances are observed at the highest altitudes, which is expected, considering that the Reynolds stresses are weighted by the atmospheric density, which decreases exponentially with altitude. It is also a common feature for all sites that the meridional velocity variances exceed the zonal fluctuations. The seasonal behavior of the zonal and meridional variances at all stations reflects a semi-annual variation, showing minimum variances during the equinoxes, when the mean winds are smallest at altitudes below 95–100 km. Above 100 km the seasonal characteristic appears to be less pronounced. The vertical wind variances are the most challenging values to retrieve. Their seasonal behavior is less obvious. However, the vertical wind variances also indicate increasing values with decreasing density. Results at McM are exceptional in this respect, and the vertical wind variances exceed the values that are derived at all other stations. At present we can only speculate on the source of these large values. A possibility is that McM lies underneath the auroral oval, and, thus, the altitudes above 90 km are strongly influenced by precipitating particles and associated effects like Joule heating that might trigger stronger vertical variations .

To gain confidence in our retrieved horizontal wind variances, we performed a test by estimating the GW wind variances of the resolved GWs directly. It is straightforward to derive a gravity wave residual from the hourly observed wind time series by subtracting mean winds and the diurnal and semidiurnal tide. Thus, we obtain a hourly time series of the GW residuals, which corresponds to the kinetic energy of the resolved GWs with periods longer than 2 h and horizontal wavelengths of more than 300 km, whereas the wind variances obtained using include the GW variances from all temporal and spatial scales. The GW variances from the residuals are shown in Fig.  in the Appendix.