Horizontal Wavenumber Spectra Across the Middle Atmosphere From Airborne Lidar Observations During the 2019 Southern Hemispheric SSW

Horizontal wavenumber spectra across the middle atmosphere are investigated based on density measurements with the Airborne Lidar for Middle Atmosphere research (ALIMA) in the vicinity of the Southern Andes, the Drake passage and the Antarctic peninsula in September 2019. The probed horizontal scales range from 2000 to 25 km. Spectral slopes are close to k−5/3 in the stratosphere and get shallower for horizontal wavelengths <200 km in the mesosphere. The spectral slopes are shown to be statistically robust with the presented number of flight legs despite the unknown orientation of true wave vectors relative to the flight track using synthetic data and a Monte Carlo approach. The largest spectral amplitudes are found over the ocean rather than over topography. The 2019 sudden stratospheric warming caused a critical level for MWs and a reduction of spectral amplitudes at horizontal wavelengths of about 200 km in the mesosphere.

found that MWs have a major impact on the energy spectrum: linear waves entirely constitute the divergent mode while breaking waves energize rotational and divergent modes.
The questions which dynamical mechanism underlies the mesoscale k −5/3 spectrum and whether there is a universal dynamical mechanism at all have still not been unequivocally answered, as studies suggest that the spectral energy is rather intermittent because of the intermittency of the dynamical processes, for example, convection or GWs (Menchaca & Durran, 2019;Selz et al., 2019). However, knowing and understanding the atmospheric spectra is of importance for NWP and atmospheric predictability (Charney, 1971), and for the development and application of GW parameterizations in all layers of the atmosphere (Harvey et al., 2022;Kim et al., 2003;Plougonven et al., 2020).
In this paper we close the gap in altitude coverage of previous measurements and present horizontal wavenumber spectra of lidar photon counts (proportional to density) across the middle atmosphere from 20 to 80 km altitude. The spectra were calculated from measurements by Airborne Lidar for Middle Atmosphere research (ALIMA) onboard the High Altitude and Long Range Research Aircraft (HALO) taken during the Southern Hemisphere Transport, Dynamics, and Chemistry -Gravity Waves (SouthTRAC-GW) campaign in 2019 (Rapp et al., 2021). The campaign covered the period of the 2019 Southern Hemisphere (SH) sudden stratospheric warming (SSW) (e.g., Lim et al., 2021;Shen et al., 2020). The aim of the study is to investigate the horizontal wavenumber spectra over the southern hemispheric hotspot for MWs in the middle atmosphere with ALIMA. Recent technological advances since the first airborne lidar observations in the 1990s have improved the data quality, resolution and altitude range of airborne lidar measurements . Based on these data, we will consider the following research questions: 1. What is the shape of horizontal wavenumber spectra throughout the middle atmosphere in the vicinity of the MW hotspot above the Southern Andes? 2. How are the horizontal wavenumber spectra in the middle atmosphere affected by GWs and the SSW?
The paper is structured as follows: in Section 2 the SouthTRAC-GW campaign, the ALIMA lidar and the spectral analysis are described. In Section 3, we present the middle atmospheric horizontal wavenumber spectra. The consequence of the unknown orientation of wave vectors, the role of GWs and the SSW for the horizontal wavenumber spectra, are discussed in Section 4, followed by our conclusions in Section 5.

SouthTRAC-GW
SouthTRAC-GW was conducted in the southern part of South America and above the Antarctic peninsula in September 2019 to gather a unique data set comprising temperature and trace gas observations from the troposphere up to the mesosphere (Rapp et al., 2021). The intention was to study MWs near their orographic sources, their vertical and horizontal propagation, and their breaking and dissipation. SouthTRAC-GW delivered measurements for the comparison and validation of other measurement techniques, high-resolutions simulations, and NWP models. The data set used in this study includes measurements from six dedicated MW research flights: ST08 on 11/12, ST09 on 13/14, ST10 on 16/17, ST11 on 18/19, ST12 on 20/21, and ST14 on 25/26 September 2019 (see Table 3 in Rapp et al. (2021)) of HALO. Typical traveled distances are around 7,000 km, within the region from 35°S to 65°S and from 82°W to 46°W, typical crusing altitudes between 10 and 14 km, and typical aircraft ground speeds between 200 ms −1 to 300 ms −1 .
The campaign period coincided with a rare SH SSW (e.g., Dörnbrack et al., 2020;Lim et al., 2021). The SSW started at the end of August, therefore, all flights were conducted during the SSW.
The tropospheric flow was dominated by blocking ridges upstream of the Southern Andes causing a synoptic flow rather parallel to the mountain ridge in the first week of September 2019 (see Figure 4 in Rapp et al. (2021)). From 8 September 2019 a mostly zonal flow or propagating troughs dominated the tropospheric flow. Because the flights were planned to be temporally aligned with a zonal upstream flow in the troposphere (Bauer et al., 2022), all flight days have in common that there were good excitation conditions of GWs at the Southern Andes and/or Antarctic Peninsula. Figure S1 in Supporting Information S1 summarizes the six individual flight tracks and the prevailing horizontal winds at 10 hPa. At 10 hPa, the polar night jet (PNJ) was shifted toward the tip of South America with mostly zonal flow during ST08 and ST09. A deformation of the stratospheric polar vortex (more elliptic) induced a strong curvature with strong meridional flow of the PNJ over the Southern Andes at 10 hPa during ST10, ST11, and ST12.
The weakening of the PNJ and the warming of the stratospheric polar vortex caused a critical level for MWs (Rapp et al., 2021). The critical level descended from about 60 km at the beginning of September 2019 to 40 km at the end September 2019 and decreased the MW activity in the upper stratosphere (Kogure et al., 2021;Rapp et al., 2021) and mesosphere (Kohma et al., 2021). The vertical propagation of observed MWs was affected by the SSW during the flights ST09, ST10, ST11, ST12 and ST14, whereas during flight ST08 observed MWs were able to propagate up to 60 km.

ALIMA
ALIMA is a compact Rayleigh lidar system developed for airborne operation. The instrument consists of an upward pointing frequency-doubled, diode-pumped and pulsed neodymium-doped yttrium aluminum garnet (Nd:YAG) laser with a wavelength of 532 nm, a pulse energy of 125 mJ, and a pulse repetition frequency of 100 Hz; a receiving telescope of 48 cm diameter; a mechanical chopper for gating of backscattered photons from the lowest altitudes to protect the detectors from saturation, and three height-cascaded elastic detector channels (low, mid and far) to cover the full dynamic range of the lidar return signal from the lower stratosphere to the upper mesosphere. The ALIMA photon counts are about two orders of magnitudes larger compared to the first airborne Rayleigh lidar observations by Hostetler and Gardner (1994) and Gao and Meriwether (1998) which highlights the advance of the lidar technology in the last 30 years and allows us to extend our altitude range of observations throughout the entire middle atmosphere.
The photon counts are aggregated in bins of 100 m vertical resolution, are integrated over a period of 10 s and corrected for the dead time of the detectors, the range, the photon background and the attenuation of the laser beam by Rayleigh extinction (a correction for ozone absorption is omitted due to the lack of sufficient ozone observations). The such processed photon counts are proportional to the atmospheric density.

Spectral Analysis
The horizontal wavenumber spectra presented in this study are based on the range corrected photon counts γ(t, z) from ALIMA with t and z denoting time and altitude, respectively. γ(t, z) is proportional to atmospheric density and thus horizontal wavenumber spectra are proportional to potential energy. We use the photon counts of the low channel below 30 km, the far channel above 50 km and the mid channel between 30 and 50 km. First, the measurements of each research flight are separated into individual flight legs, which are straight and of near constant pressure altitude. The observations are screened for instrumental effects, for example, temporary drops in the signal-to-noise ratio (SNR) due to misalignment of the laser beam or icing on the laser window. Overall, 43 flight legs with traveled distances between 150 and 2,400 km are considered in the spectral analysis. Detailed information of the individual flight legs can be found in Supporting Information S1. Lidar photon count profiles are temporally integrated to a 1 min resolution and smoothed in the vertical with a 900 m LOWESS (Locally Weighted Scatterplot Smoothing) filter. A filter width of 900 m is large enough to (a) satisfactorily reduce photon noise and (b) small enough to not attenuate vertical scales that are above the noise floor and not noticeably affect the horizontal scales. Second, γ(t, z) is normalized by a respective temporal average of each flight leg: The normalization eliminates the exponential decrease of photons counts with altitude due the decreasing air density. Remaining fluctuations of photon counts are either caused by geophysical processes, for example, GWs, or by photon noise.
The spectra are presented as the power spectral density (PSD): where ̂′ is the fast Fourier transform (FFT) of ′ . Δx, and are the horizontal bin size and the length of a flight leg, respectively. The horizontal wavenumber spectra are calculated between altitudes of 20-80 km for each vertical bin (every 100 m) and, for statistical certainty, averaged over an altitude range of 10 km. Above 80 km the signal is dominated by photon noise.
The horizontal wavenumber k and the horizontal wavelength λ k are given by: where = ∕Δ and Δ = ⋅ with as temporal spacing and as the leg mean ground speed of HALO. During the research flights varied due to changing horizontal winds. The actual spacing of the measurements in the horizontal is thus irregular (Cho et al., 1999). However, the absolute error in λ k due to the usage of a leg mean ground speed instead of the time varying ground speed is small (0.03%-0.9%). The smallest λ k is typically between 22 and 30 km, considering the sampling rate in space which depends on , the temporal integration of 60 s and the Nyquist-frequency.
As the flight legs have different lengths and , the calculated horizontal wavenumber spectra are interpolated to the same values of k and λ k before averaging over all flight legs and research flights to obtain flight-mean spectra and SouthTRAC-GW-mean spectra.
Additionally, photon noise spectra for each flight leg are calculated based on ( ) and the assumption that the photon noise follows a Poisson distribution. The calculation is repeated 1,000 times in a Monte-Carlo experiment. The obtained mean photon noise spectra reveal white noise and are constant over all scales (Figure 1b).  (Figures 1a and 1b).

Middle Atmospheric Horizontal Wavenumber Spectra
The distribution of integrated over the λ k = 50 km to λ k = 150 km spectral range of all 43 flight legs classified for their position above Land, Ocean or both (Land/Ocean) is shown in Figure 2. The values were scaled by the respective of photon noise. This is necessary in order to make flights and legs comparable in . The signal strength strongly varies for the different research flights and decreases with altitude. Hence, the relative impact of the photon noise increases. Therefore, normalized gets smaller with altitude. The largest values and the greatest variability of are found above the ocean. However, is on average  Values of normalized close to 1 indicate the signal approaching the noise floor while values of normalized larger than the 3σ-value (outside the gray-shaded area) indicate a large SNR and thus statistically significant data. Except for the highest altitude range and research flight ST10, the signal approaches the noise floor, if at all, at the smallest resolved scales. For the highest altitude range from 70 to 80 km the noise limit is reached at λ k ∼ 200-500 km (Figure 3f). The flight legs of research fight ST10 had a constant but much weaker signal compared to the other flights due to icing of the laser window, which resulted in a higher absolute noise floor.
Generally, the spectral slopes in Figure 3 are close to k −5/3 and partly flatten at higher wavenumbers to a shallower spectral slope depending on the altitude range, research flight and the horizontal wavenumber. In the upper stratosphere and mesosphere only the horizontal wavenumber spectra of research flight ST08 (at the beginning of the SSW) follow closely the k −5/3 slope while the other research flights (during the SSW) feature a reduction of approximately 25% in at λ k ∼ 200 km and a transition to a shallower slope at larger λ k (Figures 3c-3e).
For all research flights, increases with altitude. However, due to the normalization applied before averaging, this behavior is not visible anymore in Figure 3. We also want to point out that the signal strength of the lidar return signal affects the of photon spectra. This becomes apparent at altitudes where switches of detection channels with higher to lower sensitivity take place, for example, smaller and larger 3σ-values in the altitude ranges 30-40 km and 40-50 km (Figure 3). Finally, few long legs were flown and as a consequence, the averages include ≤7 of spectra with λ k > 1,000 km.

Orientation of Wave Vectors
The observed wavelengths are not true wavelengths. The observed wavelength is the distance between wave fronts sampled along the flight track with an unknown angle of intersection. If a wave is sampled at an angle of 60° relative to its wave vector, the true wavelength is half of the observed wavelength. If the angle approaches about 85°, the true wavelength will be about one order of magnitude smaller than the observed wavelength.
The unknown orientation of the observed GWs introduces a complication for the interpretation of the spectral analysis. While sampling multiple waves in one flight leg, we can not necessarily assume that all of them have  10.1029/2023GL104357 7 of 10 the same wave vector. This complication affects all past airborne spectral analyses (e.g., Bacmeister et al., 1996;Cho et al., 1999;Gao & Meriwether, 1998;Hostetler et al., 1991;Hostetler & Gardner, 1994;Kwon et al., 1990;Nastrom & Gage, 1985), and, to our knowledge, has not been discussed previously.
Each observed horizontal wavelength may be shifted to a smaller true horizontal wavelength, which influences the spectral shape. In order to investigate this influence, we performed Monte-Carlo experiments. Each wavenumber of a given horizontal wavenumber spectrum is N times randomly perturbed by a perturbation in wave orientation 0° ≤ α ≤ 90° drawn from a Gaussian (experiment A) with an expected value α = 0° and uniform (experiment B) distribution, for example, λ k * cos(α). Experiment A represents the case of flight legs which are rather aligned with the wave orientation and experiment B regards a random orientation of flight legs with respect to waves. For both experiments no significant difference (p-value >0.1) but still a large correlation (Pearson coefficient >0.94) were found between the given and the averaged randomly perturbed horizontal wavenumber spectra for N > 5 realizations. In general, a shift in horizontal wavenumber can be expected but the experiments reveal only a minor influence on the spectral shape if the number of averaged spectra is sufficiently large (N > 5). Therefore, we conclude that the presented flight-means of ST08, ST09, and ST12 and the SouthTRAC-GW-mean spectra are statistically robust in spectral shape for λ k < 1,100 km. For larger λ k , the statistics are not statistically robust. The number of legs N of ST10, ST11 and ST14 are <5 (see Table S1). Still, the spectral slopes of these flights are similar to the spectral slopes of ST09, ST14 and the SouthTRAC-GW-mean, suggesting that unknown wave orientations have a negligible impact even in the case of a small number of averaged spectra.
The differences in orientation between the wave vectors and the flight path do not affect the spectral amplitudes as long as at least one full wavelength is sampled. If this condition is not fulfilled, the spectral amplitudes are underestimated.

Physical Cause of Spectral Slope
The horizontal wavenumber spectra are close to k −5/3 in the stratosphere for all observed horizontal scales down to λ k ≈ 100 km. In the mesosphere, the spectral slope is close to k −5/3 for λ k > 300 km. For λ k < 100 km, the spectral slope tends to be shallower than k −5/3 , similar to results in the mesopause region found by Kwon et al. (1990). However, why the mesoscale range follows a k −5/3 power law dependence (Nastrom & Gage, 1985) or why it deviates from k −5/3 (Bacmeister et al., 1996;Hostetler et al., 1991;Kwon et al., 1990), is still an open question for the scientific community. Lindborg (2006) proposed that GW spectra in the middle atmosphere are affected by stratified turbulence arising from nonlinear dynamics and predicted that observed horizontal GW spectra would exhibit a spectral slope of k −5/3 . The vertical resolution of the ALIMA observations (100 m grid with 900 m smoothing) is coarser than the vertical resolution needed for the detection of layers of stratified turbulence (Brune & Becker, 2013;Lindborg, 2006). Therefore, and due to the vertical averaging over 10 km altitude ranges, our horizontal wavenumber spectra cannot be associated with stratified turbulence (Rodriguez Imazio et al., 2023) nor can we exclude the occurrence of stratified turbulence. Our findings support the prediction by Lindborg (2006).

Impact of the SSW
The reduction of at horizontal wavelengths of about 100-300 km for all research flights except ST08 above 40 km or 50 km altitude was potentially caused by the co-occurring SSW. The SSW induced a critical level for vertically propagating MWs due to the slowing of the PNJ and the displacement of the stratospheric polar vortex. During ST08, the observed MWs were able to propagate up to 65 km altitude while MWs were filtered by the critical level at about 40 km altitude during ST12 (see Figures 4a, 12b, and 12d in Rapp et al. (2021)) and other research flights. The decrease in GW activity in the mesosphere due to the SSW during flights ST09, ST10, ST11, ST12, and ST14 resulted in a decrease of by 25% in the range 300 km > λ k > 100 km. This result suggests that these are wavelengths of MWs excited by the Southern Andes. Furthermore, the spectra of flights ST09, ST10, ST11, ST12, and ST14 obey no distinct k −5/3 slope for 300 km > λ k > 100 km in the mesosphere. This spectral response to the SSW highlights the sensitivity of the horizontal wavenumber spectra to the temporal decline in MW activity and ultimately the absence of MWs. Turning the argument around, the observed decrease in spectral power due to the decreased MW activity during the SSW supports GWs as driver of the k −5/3 slope of the mesoscale range in the middle atmosphere. 10.1029/2023GL104357 8 of 10

Land Versus Ocean
On average, the study found only slightly smaller values of over ocean than over topography, while the largest individual values occurred over ocean. Previous studies detected an enhanced spectral power above orography compared to smooth terrain or ocean (Gao & Meriwether, 1998;Lilly & Petersen, 1983;Nastrom et al., 1987).
There are two potential causes for the observed enhancement of spectral energy over the ocean: (a) horizontal MW propagation and (b) non-orographic GWs. The large values of over the ocean were observed during unique stratospheric dynamical conditions associated with the SSW. Generally, the occurrence of a SSW diminishes the MW activity in middle atmosphere and the contribution of non-orographic GWs preponderates. Still, Geldenhuys et al. (2023) and Krasauskas et al. (2023) provided evidence for cases of horizontal MW propagation, for example, refraction, during flight ST08 and ST12.

Conclusions
High-resolution and high-quality observations by ALIMA enabled the determination of horizontal wavenumber spectra of density within the horizontal scale range of 2,000 km to about 22 km across the middle atmosphere from 20 to 80 km altitude during SouthTRAC-GW. The presented horizontal wavenumber spectra are the first based on airborne lidar observation between 40 and 80 km altitude and during a SSW.
Our main findings are: (a) the averaged horizontal wavenumber spectra are statistically robust, rather smooth and exhibit slopes close to k −5/3 in the stratosphere even though the number of research flights and flight legs was limited; (b) the derived horizontal wavenumber spectra in the middle atmosphere are influenced by horizontally and vertically propagating MWs and potentially non-orographic GWs; and (c) the SSW caused an attenuation of spectral power of the horizontal wavenumber spectra in the mesosphere. The impacts of horizontal MW propagation, non-orographic GWs and GW-SSW interactions on the horizontal wavenumber spectra support the importance to include such processes in future GW parameterizations (Plougonven et al., 2020). However, since SouthTRAC-GW coincided with the SSW, it is difficult to generalize our conclusions, for example, observed deviations from k −5/3 for λ k < 200 km in the mesosphere might be less distinct or not present during strong stratospheric polar vortex conditions and without a critical level for MWs.
Turning to the research questions we formulated in the beginning, we infer concerning the first question that the derived horizontal wavenumber spectra across the middle atmosphere are close to k −5/3 . Deviations from this canonical spectral slope mainly appear for λ k < 300 km in the mesosphere. Regarding the second question, we conclude MWs and the SSW have a relevant influence on the horizontal wavenumber spectra. Altogether, this study provides observational evidence that the k −5/3 spectral slope in the middle atmosphere can be explained by the occurrence of GWs.
Future applications of ALIMA can be used for the studying of horizontal wavenumber spectra of GWs in the middle atmosphere during strong stratospheric polar vortex conditions or the in-depth investigation of horizontal GW propagation. The planned extension of ALIMA by an iron resonance lidar channel (Kaifler et al., 2017) will extend the vertical measurement range into the lower thermosphere and allow for wind measurements. Wind measurements are required for future applications of an airborne lidar in order to estimate the character of the observed GWs.