Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

. We describe in this study the analysis of small and large horizontal scale gravity waves from datasets composed of images from multiple mesospheric airglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 campaign. These ground-based measurements are supported by temperature and neutral density proﬁles from TIMED/SABER satellite in orbits near Kühlungsborn, northern Germany (54.1 ◦ N, 11.8 ◦ E). The scientiﬁc goals here include the characterization of gravity waves and their interaction with the mean ﬂow in the meso-5 sphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We have obtained intrinsic parameters of small and large scale gravity waves and characterized their impact in the mesosphere via momentum ﬂux ( F M ) and momentum ﬂux divergence ( F D ) estimations. We have veriﬁed that a small percentage of the detected wave events are responsible for most of F M measured during the campaign from oscillations seen in the airglow brightness and MSMR winds taken over 45 hours during four nights of clear skies observations. From the analysis of small-scale gravity 10 waves ( λ h < 725 km) seen in airglow images, we have found F M ranging from 0.04–24.74 m 2 s − 2 (1.62 ± 2.70 m 2 s − 2 on average). However, small-scale


Introduction
variation associated with a large-scale wave in a region tilted from top to bottom during 1930 UTC to 2230 UTC, indicating a coherent oscillation traveling from north to south. The tilt in the brightness region is not pronounced in the zonal keogram in the same time span and indicates the wave horizontal vector has a small, negligible component in the west-east direction.
Perturbations of the same nature are also seen in the O 2 and OH emissions for the same nights. 90 The right side panels of Fig. 1 show zonal and meridional keograms of the same clear nights built using time-difference airglow images. Time-difference operation involves subtracting an image from the previous one (same emission) with the goal of filtering out long-term variations in the airglow brightness (e.g., Swenson and Espy, 1995;Tang et al., 2005;Vargas et al., 2016). The result is an image where the contrast of short-period, small-scale oscillations is enhanced. These small-scale waves show up in the keograms as tilted bright/dark bands. Because long periods are eliminated, time-difference keograms permit 95 rapid access to the activity of short period waves each night.

Multistatic specular meteor radar
During the SIMONe-2018 campaign, MSMR measurements were obtained during seven days continuously. Briefly, the campaign consisted of 14 multistatic links that were obtained by using two pulse transmitters located in Juliusruh (54.63 • N, 13.37 • E) and Collm (51.31 • N,13.00 • E), respectively, and one coded-continuous wave transmitter located in Kühlungsborn. 100 Eight receiving sites, receiving the scattered signal of at least one transmitter, were used. This campaign combines the multistatic approach called MMARIA (Multistatic Multifrequency Agile Radar Investigations of the Atmosphere) (Stober and Chau, 2015) with the SIMONe (Spread Spectrum Interferometric Multistatic meteor radar Observing Network) concept . In the latter case a combination of spread-spectrum, multiple-input multiple-output, and compressing sensing radar techniques is implemented (Vierinen et al., 2016;Urco et al., 2018Urco et al., , 2019. The winds used in this work have been obtained 105 with a gradient method, i.e., besides the mean horizontal and vertical winds, the gradients of the horizontal components have also been obtained (Chau et al., 2017). Data from one day of this campaign has been used to test a second-order statistics approach by Vierinen et al. (2019). More details of the SIMONe-2018 campaign as well as results of second-order statistics are given in the accompanying paper of this publication (see Asokan et al., 2020).
Here, we have used the MSMR winds in combination with the airglow data to give a full characterization of the gravity 110 wave dynamics observed during the campaign. The background wind is dominated by 12 hours of tidal oscillations presenting maximum amplitudes larger than 50 m/s, but spectral analysis reveals the presence of higher tidal harmonics of 8 and 6 hours (see Fig. 6 and Fig. 7). For instance, see the filtered meridional wind (Fig. 2d) on Nov. 3-4 that shows a coherent oscillation (red ellipse) throughout the night. This oscillation is also evident in the airglow brightness variation (meridional keogram in Fig. 1c) during the same night.
We have also collected observations of the SABER instrument on board the TIMED satellite within four degrees from the observation site (Fig. 3). SABER profiles used here are presented in Fig. 4a-c, while Fig. 4d shows the calculated volume emission rate of the mesosphere airglow emissions as explained below. The thick lines in Fig. 4 indicate the mean of corresponding individual profiles (dotted lines) for the various orbits of the satellite during the campaign. The corresponding orbits are specified in the legend of each chart.

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From Fig. 4a, we can verify that the atmosphere is stable once the atmosphere lapse rate is larger than the adiabatic lapse rate in the altitude range of 88-99 km. The lapse rate is even positive below and above that range. Even though the satellite orbits registered during SIMONe-2018 were not exactly over the observatory, they are within the field of view of the imager (Fig. 3).
Thus, there is a good chance the background atmosphere above the observation site is similar to that indicated by SABER ( Fig.   4), although the temperature might still be influenced by gravity waves once we have averaged only a few profiles. Because of 130 that, we are confident using SABER background profiles to make inferences about the propagation conditions for the waves seen over the observatory. These VER profiles were calculated using the mean temperature, atomic oxygen, molecular oxygen, and molecular nitrogen profiles in Fig. 4a-b along with the reaction rates of each emission from Vargas et al. (2007). The characteristics of each layer 135 (measured and calculated VERs) are obtained from a Gaussian model (thin lines in Fig. 4d) to fit each profile from which we obtain the layer peak, width, and FWMH. The mean characteristics of the airglow layers are presented in Table 2. The goodness of fitting scores R 2 >0.95 for all five VER curves. The layer centroids, obtained by estimating z VERdz VERdz , are in general a few kilometers above the estimated layer peaks because of departures of the actual VER vertical structure from the Gaussian fitting model.

Data Analysis and Results
A full characterization of the gravity wave field requires knowledge of the background wind over the observation site. The significant background wind acting in the vicinity of an airglow layer is a function of the vertical structure of the emission (the volume emission rate) that has finite thickness (see Fig. 4d). We take that into account in this study by calculating the weighted background wind (Fig. 6a-c) by using the individual volume emission rate of each layer as weighting functions. The weighted 145 wind expression for a given VER is , where u w and v w are the weighted zonal and meridional winds ( Fig. 6), respectively. Notice that the weighted winds are still a function of time.

Short-scale gravity wave analysis
The majority of waves observed during SIMONe-2018 are of short-scale, fast oscillations presenting periods of less than one hour. The keograms of Fig. 1  of the campaign. These short-scale gravity waves are analysed here using the auto-detection method (Tang et al., 2005;Vargas et al., 2009;Vargas, 2019).
The auto-detection method uses a set of three sequential frames of an emission to detect the gravity wave content around the acquisition time of the central frame. We repeat this procedure for all the images taken throughout the night grouped into several sets of three sequential frames. From each set, two time-difference (TD) images are obtained and the cross-spectra of 155 the set are calculated from these two TD images (see Fig. 1 in Vargas et al., 2009). We then obtain the wavenumber coordinates (k x , k y ) of dominant peaks in the cross-spectra periodogram as well as the phase δφ of these peaks from the phase periodogram at the same peak coordinates. The horizontal wavelength λ h and the wave orientation θ are calculated using the spectral position (k x , k y ). The phase velocity and period are retrieved using δφ and λ h of each peak along with δt =10 minutes, the filter wheel cycle period (see Fig. 2 in Vargas, 2019). We then obtain the vertical wavelength from the gravity wave dispersion relation for 160 high frequency waves. Northwest and Southwest (Fig. 5a), but the polar histogram in Fig. 5f shows a large number of waves traveling southeastward into the dominant wind orientation (Fig. 5k). The estimated intrinsic periods shown in Fig. 5e range within 20-40 min, with intrinsic phase speeds in the interval of 30-80 m/s in the campaign (Fig. 5b). The largest wave relative amplitude estimated from the images is 7% in Fig. 5d, but this does not necessarily translate into large momentum flux waves, which depends on 170 other wave parameters.
Because of the ASI long integration times (two minutes/image) and filter wheel cycle (10 minutes), we have detected only waves of periods longer than 20 minutes. However, as we fully characterize the intrinsic parameters of every wave captured by the auto-detection method, we were able to estimate the momentum flux of the observed events (e.g., Vargas et al., 2007).

Large-scale gravity wave analysis
During SIMONe-2018, we have also observed the presence of large-scale gravity waves modulating simultaneously the airglow 180 brightness keograms ( Fig. 1c and 1e) and the horizontal wind ( Fig. 2c and 2d). To study these large-scale oscillations in the wind at the altitude of the airglow, we have calculated the wind fluctuations weighted by the volume emission rate of each layer ( Fig. 6d-f). The dashed boxes represent the periods of simultaneous operation of the MSMR and ASI systems.
The weighted wind fluctuations are similar in each layer once the layers peak within ±2 km from each other (see Table 2) and are thicker than expected with mean FWHM of 15 km (e.g., Greer et al., 1986;Gobbi et al., 1992;Melo et al., 1996).

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Thus, the overlap of the VER profiles is non-negligible and the rms values of the filtered winds are expected to have similar magnitude. The calculated rms magnitudes are 6.9±1.0 m/s and 5.9±0.9 m/s in the zonal direction and meridional directions, respectively.
The spectral content of the weighted wind fluctuations is shown in Fig. 7. Several tidal harmonics are still present in the spectra due to energy leakage (vertical dotted red lines in Fig. 7) even after wind filtering carried out to remove periods larger 190 than 5 hours. However, there are a few persisting peaks that we attribute to gravity waves. For instance, the peaks in the vicinity of 0.21 cycles/hour (zonal direction) and 0.24 cycles/hour (meridional direction) are seen clearly in the wind fluctuation of Nov.
3-4. The spectra of the fluctuations show a salient peak near 0.11 cycles/hour (zonal and meridional directions), corresponding to a wave of 8.9±1.0 hours that can be seen in the keograms of Nov. 6-7, 2018, close to the peak of the 12 hour period associated with the semidiurnal atmospheric tide. A hodograph analysis of the filtered winds must be carried out in a separate 195 work to clarify the nature of the dominant peaks shown in Fig. 7.
We have analysed the wind fluctuations against obvious wave features present in the keograms of Nov. 3-4 and Nov. 6-7.
We carry out this analysis by overlapping the O( 1 S) weighted wind fluctuations on top of the corresponding keograms for these two observation nights (Fig. 8).
On Nov. 3-4, a strong, coherent feature presenting period of 4±1 hours is observed in the meridional wind indicated by the 200 dashed black lines. As the meridional wind peaks, the meridional keogram brightness dims (Fig. 8a); as the meridional wind decreases and reverses direction, the airglow brightens. Both zonal and meridional keograms present an enhanced brightness at 2100 UTC, but a second brightness peak in the airglow is only seen near the edges of the meridional keogram later on at 0100 UTC ( Fig. 8a bottom). The meridional keogram shows a tilt in the brightness structure between 1900 and 2100 UTC that indicates a wave is traveling southwards. In the same time span, the zonal keogram has no obvious tilt in the enhanced 205 brightness, suggesting no wave propagation in the east-west direction. The filtered zonal wind confirms this as it shows a quite distinct and incoherent wind variation compared to that in the meridional direction. We have also verified, by visual inspection of the images, that this wave horizontal structure does not fit within the airglow image field of view (512x512 km 2 ) and is only noticeable via keogram analysis.
Similarly, we have also observed enhancements in the airglow brightness on Nov. 6-7 (dashed black lines) associated with 210 a large-scale wave with period longer than ∼8±1 hour. The wave activity, evident in the weighted wind fluctuations (Fig. 8b), coincides well with the O( 1 S) airglow enhanced brightness in the zonal keogram of Nov. 6-7 around 0000 UTC. This brightness enhancement shows a slight tilt that indicates a wave propagating from west to east. The negligible tilt of the airglow brightness in the meridional keogram implies the wave has no evident north-south component.
A spectral analysis of the keograms of Nov. 3-4 and Nov. 6-7 in Fig. 9 enables finding the zonal (k x ) and meridional (k y ) 215 wavenumber, which are components of the horizontal wavenumber as k h = k 2 x + k 2 y , while the wave observed frequency is τo . We show the zonal and meridional keogram spectra for Nov. 3-4 in Fig. 9a and c, and for Nov. 6-7 in Fig. 9b and d.

Discussion
The propagation conditions for gravity waves during SIMONe-2018 are depicted in Fig. 4 showing the temperature and constituent densities over the observatory. While the vertical structures of the atomic oxygen density appear normal, the mean temperature indicates convectively favorable conditions for gravity waves vertical propagation, as the ambient lapse rate is 240 positive below ∼87 km and above ∼99 km. Within 86-98 km range, the ambient lapse rate is negative but still sub-adiabatic, and convective instabilities are unlikely to form under these conditions. Thus, gravity wave dissipation due to convective instabilities would not affect the vertical evolution of the gravity wave field during the campaign. Conversely, because the horizontal winds occasionally have relatively large amplitudes of >50 m/s ( Fig. 2a and Fig. 2b), the wind field could cause critical levels where waves are absorbed or reflected. Waves having specific sets of intrinsic parameters would hardly propagate 245 beyond these critical level altitudes.
We can verify the effect of background wind on the propagation direction of the waves by examining 2018, the total momentum is 586.96 m 2 /s 2 , where 50% of this total is due to waves carrying flux > 3 m 2 /s 2 (40 events). Thus, 11% of the waves are responsible for carrying 50% of the momentum flux estimated from our auto-detection method during the campaign.
In spite of the small mean value, momentum flux bursts between 10 and 30 m 2 /s 2 were mainly seen in the O 2 emission during the campaign. These highly energetic waves were traveling northwestward, presenting intrinsic periods of 30-40 min, which would lead to considerable mean flow deceleration and body forces capable of exciting secondary waves as point-like sources (Vadas and Becker, 2018). For example, by considering the primary wave source and wave breaking mechanism in a given altitude acting for four hours (about half of a typical nighttime observation period), we estimate a potential deceleration 300 in the mean flow of 3.7-6.8 m/s in the same time span (four hours) caused by the breaking of the primary wave.
We have estimated the observed horizontal wavelength and frequency parameters of the large-scale waves shown in the airglow (Fig. 8) using the spectrum of the zonal and meridional keograms in Fig. 9. We can combine the observed frequency with the observed unfiltered background wind to derive the intrinsic period of the waves using ω = ω o − k h · v (Doppler correction), where ω o is the frequency measured by an observer on the ground, k h = (k x , k y ) and v = (u, v) are the horizontal 305 wavenumber and wind vectors with components oriented in the zonal and meridional directions, respectively.
We then estimate the vertical wavelength of the events by applying the gravity wave dispersion relation, which constrains the horizontal and vertical wavenumbers, and the wave frequency as m 2 = (N 2 −ω 2 ) (ω 2 −f 2 ) k 2 h , where m = 2π/λ z is the vertical wavenumber, N is the Brunt-Väisälä frequency, and f the inertial frequency. In the calculations that follow, we have assumed a Brunt-Väisälä period of 5.5 min (N = 0.01904 rad/sec) and an inertial period of 14.8 hours (f = 0.11816 × 10 −3 rad/sec) 310 for Kühlungsborn latitude (54.1 • N).
The wave occurring on Nov. 3-4 has k x ∼ 0, k y = −0.7×10 −3 cycles/km (i.e., λ y ∼ 1365 km), and ω o = 0.215 cycles/hour estimated from the keogram spectra. The unfiltered, weighted background wind field over the observatory had components u = 28.5 m/s and v = −1.4 m/s at 2315 UTC, the instant when the wave was in the dimmer phase of its cycle in the airglow.
Applying then the Doppler correction, we estimate an intrinsic frequency ω = 0.211 cycles/hour for the wave. Finally, using 315 the dispersion relation, we derive a vertical wavelength of λ z = 25.1 ± 1.0 km for the Nov. 3-4 wave, which compares well with the value of λ z = 25.6 ± 1.0 km obtained in Section 3.2 by visual inspection of Fig. 10.
Likewise, the Nov. 6-7 wave has k x = 0.2441 × 10 −3 cycles/km (i.e., λ x ∼ 4096 km), k y ∼ 0, and ω o = 0.11 cycles/hour.  Recently, Vadas and Becker (2018) have modeled the evolution of mountain waves over the Antarctic Peninsula after observational results of large-scale, long-period waves seen in the mesosphere (Chen et al., 2013(Chen et al., , 2016 attributed to an unbalanced flow in the lower stratosphere. This imbalance excited upward (downward) propagating oscillations from the knee of fishbonelike structures at 40 km altitude, which are associated with the excitation of secondary waves from the breaking of extensive mountain wave structures. Although other modeling efforts also attribute the excitation of non-primary waves to localized 345 turbulence eddies from gravity wave breaking (e.g., Heale et al., 2020), we believe that the large-scale waves observed in this study are the product of the Vadas and Becker (2018) mechanism at play in the stratosphere. In fact, preliminary analysis of temperature profiles at 0-90 km altitude acquired by the IAP Rayleigh Lidar system on Nov. 6-7 revealed fishbone structures at 40-45 km, resembling the predictions of Vadas and Becker (2018). We will investigate this possible connection in detail in a separate paper; specifically, we will identify the primary wave sources in the vicinity of IAP during SIMONe-2018, and trace 350 the observed large-scale waves back to their excitation altitude (the fishbone knee region) at 40-45 km revealed in the filtered lidar temperatures.
In this paper, gravity waves of small and large horizontal scales were characterized by their intrinsic wave parameters, amplitudes, momentum fluxes, and momentum flux divergences. We have focused the analysis on data recorded simultaneously by 355 an airglow all-sky camera, multistatic specular meteor radar, and TIMED/SABER satellite to obtain a more extensive collection of complementary information about the state of the mesosphere region over the observatory during the campaign. To uncover small horizontal scale features, we have used an auto-detection method to process all-sky airglow images and background meteor radar winds. Large-scale waves were characterized by spectral analysis of airglow keograms and altitude vs. time cross section of filtered wind fluctuations.

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Our results indicate that 11% of all detected gravity wave events have large amplitudes and carry 50% of the total momentum flux estimated during the SIMONe-2018. These fewer wave events could impart mean flow decelerations of 21-43 m/s/day toward the wave propagation direction at breaking or dissipation levels. If these high-amplitude waves are of secondary wave generation origin due to their set intrinsic wave features, our results permit verification of the significance of secondary waves in the mesosphere and lower thermosphere dynamics via excitation of large momentum flux gravity waves.

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Given the relatively large vertical and horizontal wavelengths of the observed large-scale waves, there is a possibility that these events are the product of secondary wave excitation via the mechanism identified by Vadas and Becker (2018). This possibility is supported by stratosphere fishbone structures uncovered in filtered lidar temperatures collected over the IAP observatory. A complete analysis of these structures will be given in a separate paper, in which we also plan to show the origin of the primary waves in the troposphere from weather images as well as the presence of non-primary waves in other datasets 370 such as that of the AIRS on board the AQUA satellite.
Author contributions. FV devised the data processing methods, carried out data analysis, and wrote the manuscript. JLC conceived SIMONe and ran the campaign. HCA provided preprocessed, filtered meteor radar wind data. MG provided lidar data and revised the manuscript.  , 58, 1935-1942, 1996.    Table 3. Estimated features of the large-scale waves observed in the airglow and meteor radar wind data.      Figure 9. Composite (kx, ω) and (ky, ω) spectra of the keograms in Fig. 8 for the nights of Nov. 3-4 (panels a and c) and Nov. 6-7 (panels b and d).