2.1 All-sky airglow imager

An all-sky imager (ASI) assembled at Boston University was deployed in late 2016 at the Leibniz Institute of Atmospheric Physics (IAP) in Kühlungsborn, Germany. The imager is equipped with an Andor back-illuminated bare CCD camera and a 30 mm fish-eye lens which record several nightglow emissions over the entire 180^∘ of the night sky. Andor's iKon-M 934 camera is a 1024 × 1024 array and 13 µm pixel pitch with a 13.3 × 13.3 mm active image area. High sensitivity is achieved through a combination of > 90 % QE (quantum efficiency; back-illuminated sensor), low noise readout electronics, and deep TE (thermoelectric) cooling down to −60^∘C. The ASI system uses six interference filters enabling the observation of four mesosphere airglow emissions with a background filter for the hydroxyl emission. A filter for the thermospheric redline (at 630.0 nm) is also available, but images of this emission were not taken during SIMONe–2018 due to filter technical issues. The imaging system operates autonomously via a PC on a nightly basis during moonless periods. Images are obtained on a continuously repeating cycle every ∼ 2 min with each particular filter accessed every ∼ 10 min. The specifications of filter wavelengths and integration times are in Table 1. Emission altitudes are discussed in Sect. 2.3. Preprocessed, low-resolution images collected by the ASI are available for visualization at http://sirius.bu.edu/data/ (last access: 6 September 2021). Raw images used in this study are available at https://doi.org/10.13012/B2IDB-8585682_V1 (Vargas, 2021)​​​​​​​.

Table 1Configuration of the all-sky imager system used to collect airglow images during the SIMONe–2018 campaign. Airglow images of the campaign are available at http://sirius.bu.edu/data/. NaD represents a sodium atom at the D transition line.

Download Print Version | Download XLSX

Figure 1Composite keograms of O(¹S) airglow images taken on clear nights during the SIMONe–2018 campaign. The keograms in panels (a), (c), (e), and (g) were built using light frame images, while keograms in panels (b), (d), (f), and (h) were built using TD images. Time–difference keograms show short-period waves at higher contrast, while light frame keograms show mainly long-period oscillations. Note the enhanced airglow brightness (red ellipses) on 3–4 November (meridional keogram) and 6–7 November (zonal keogram) associated with large-scale gravity waves also seen in wind fluctuations of Fig. 2.

Download

The SIMONe–2018 campaign was carried out for more than a week, but clear skies were seen only during four nights, which limited the optical observations with the all-sky imager. The sky conditions for the four clear nights are summarized in Fig. 1 by zonal and meridional keograms of the O(¹S) emission. Appendix C discusses in detail how keograms are built from airglow images. The reader is also referred to Vargas et al. (2020) for more keogram analysis information. Although only keograms of the O(¹S) emission are shown here, we have also built keograms for the other three mesospheric emissions, which are available as Supplement files of this paper.

The left-hand side panels of Fig. 1 show keograms built directly from O(¹S) preprocessed images (Appendix A). The contrast of the images was optimized to show variable features in the brightness present throughout the night. Long-period oscillations seen in the airglow brightness on 3–4 and 6–7 November keograms indicated by the red ellipses are associated with large-scale, long λ_h gravity waves perturbing the green line layer. For instance, note in the meridional keogram of 3–4 November the orientation of the brightness variation associated with a large-scale wave in a region tilted from top to bottom during 19:30 to 22:30 UTC, indicating a coherent oscillation traveling from north to south. The tilt in the brightness region is not pronounced in the zonal keogram for the same time span, indicating a small, negligible wave component in the west–east direction. Perturbations of the same nature are also seen in the O₂ and OH emissions for the same nights.

The right-hand side panels of Fig. 1 show zonal and meridional keograms built using time–difference (TD) 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 Mende, 1994; Swenson and Espy, 1995; Tang et al., 2005; Vargas, 2019). The result is an image where the contrast of shorter-period, smaller-scale oscillations is enhanced. These small-scale waves show up in the keograms as tilted bright/dark bands. Because long-period waves are suppressed, time–difference keograms permit rapid access to the activity of short-period waves each night.

2.2 Multistatic specular meteor radar

During the SIMONe–2018 campaign, MSMR measurements were obtained continuously for 7 d. 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. Eight receiving sites were used to receive the scattered signal of at least one transmitter. 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 (Chau et al., 2019). 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., 2018, 2019). The winds used in this work have been obtained 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 1 d of this campaign have 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 can be found in Charuvil et al. (2020).

Figure 2(a) Zonal and (b) meridional wind measurements for the duration of the SIMONe–2018 campaign generated by the MSMR network. Note the dominance of the semidiurnal tide on the horizontal wind. (c) Zonal and (d) meridional wind fluctuations of τ_o ≤ 4 h. Note the presence of coherent gravity wave features (red ellipses) on 3–4 November in the meridional wind fluctuations and on 6–7 November in the zonal wind fluctuations coincident with enhanced keogram brightness for the same nights in Fig. 1. Dashed boxes indicate hours of simultaneous operation of the ASI and MSMR systems.

Download

Here, we have used the MSMR winds in combination with the airglow data to give a full characterization of the gravity wave dynamics observed during the campaign. Figure 2 shows the (a) zonal and (b) meridional background winds in the range of 75–105 km measured during SIMONe–2018. Dashed boxes indicate hours of simultaneous operation of the ASI and MSMR systems. The background wind field is calculated from the MSMR measurements using 30 min temporal and 1 km spatial windows. Observe the daily cycle for z < 80 km and z > 100 km in the plots that is associated with the variation in meteor detections throughout the day; the meteor density is larger in earlier morning hours and smaller in afternoon hours. Because wind calculation relies on the number of meteors to make quality wind estimations, when not enough meteors are detected, the wind cannot be estimated within a reasonable uncertainty level. The background wind is dominated by a 12 h tidal oscillation presenting amplitudes larger than 50 m s⁻¹, but spectral analysis reveals the presence of higher tidal harmonics of 8 and 6 h (see Figs. 6 and 7).

Figure 2c and d also present the zonal and meridional wind fluctuations associated with oscillations caused by gravity waves. To obtain the wind fluctuations, we first average the MSMR raw data over a 400 km² field of view using a square 4 h temporal, 4 km vertical window. Then, we subtract the result from the background wind field. Note that oscillations of τ_o > 4 h and λ_z < 4 km will be suppressed but not completely eliminated in the resulting wind fluctuations. The fluctuation winds show short-period gravity waves perturbing the wind that are also seen in the airglow. For instance, the oscillation evident in the airglow brightness variation (red ellipse) for 3–4 November (Fig. 1c, meridional keogram) is also evident as coherent oscillations in meridional wind fluctuations (red ellipse) on 3–4 November (Fig. 2d).

2.3 Satellite data (TIMED-SABER)

We have also collected observations of the SABER instrument on board the TIMED satellite (Russell et al., 1999; Mlynczak, 1997) within 4^∘ of the observation site (Fig. 3). The profiles cover the height range from approximately 10 km to more than 100 km. The vertical resolution is ∼ 2 km. The instrument covers ∼ 52^∘ latitude in one hemisphere to 83^∘ in the other in a given day. The viewing geometry alternates every 60 d due to 180^∘ yaw maneuvers of the TIMED satellite (Russell et al., 1999). Approximately 1200 temperature profiles are taken each day. SABER publications are available at http://saber.gats-inc.com/publications.php (last access: 6 September 2021).

Figure 3Individual TIMED/SABER satellite orbits near Kühlungsborn during the SIMONe–2018 campaign. The colored lines represent the location where vertical atmospheric profiles were measured, not the actual satellite locus. The day and time of each orbit is indicated in the legend. The field of view of 512 × 512 km² of the airglow camera projected at ∼ 95 km is indicated by the O(¹S), TD image mapped onto geographic coordinates, while the ellipse indicates the field of view of the MSMR system. The white crosses indicates the coordinates of the imager system in the Kühlungsborn observatory and the meteor radar system.

Download

Figure 4(a) Temperature, (b) atomic oxygen, molecular oxygen, molecular nitrogen number densities, and (c) OH20 (2.1 µm OH(A)) and OH16 (1.6 µm OH(B)) volume emission rates collected by TIMED/SABER satellite near Kühlungsborn during the SIMONe–2018 campaign within 4^∘ of latitude or longitude of the observatory. (d) Calculated volume emission rates for OH(8,3), O₂(0,1), and O(¹S) layers (thick black lines) using SABER mean profiles in panels (a) and (b). Colored dotted lines in (a), (b), and (c) indicate individual orbits of the satellite, while thick lines indicate the mean of the individual orbits. Gray dash–dot lines in (a) indicate the adiabatic lapse rate Γ_ad = −9.8 K km⁻¹. Thinner black lines in (d) are Gaussian fits of the calculated VER profiles. Individual VER airglow layer features for both measured and calculated VER are in Table 2. We have used SABER data version 2.07 to compose these plots.

Download

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.

From Fig. 4a, we can verify that the atmosphere is, on average, stable in the altitude range of 88–99 km since the atmosphere lapse rate ($\mathrm{d}T/\mathrm{d}z=-\mathrm{3.7}$ K km⁻¹) is larger than the adiabatic lapse rate ($\mathrm{\Gamma }=-\mathrm{9.8}$ K km⁻¹) and is positive ($\mathrm{d}T/\mathrm{d}z=\mathrm{1.6}$ K km⁻¹) below and above the 88–99 km range. Even though the satellite orbits registered during SIMONe–2018 were not exactly over the observatory, the instrument measurements are performed in the vertical limb plane that is near or within the field of view of the imager (Fig. 3). Note that the colored dots indicate where the measurements were made, not the satellite position. 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 that, we are confident using SABER background profiles to make inferences about the propagation conditions for the waves seen over the observatory.

Table 2Centroid, peak, and FWHM of the OH, O₂, and O(¹S) layers measured and calculated using TIMED/SABER data collected near Kühlungsborn during the SIMONe–2018 campaign.

Download Print Version | Download XLSX

Figure 4d corresponds to our estimation of volume emission rate (VER) profiles for the OH, O₂, and O(¹S) airglow emissions. 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 (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 the full width at half maximum (FWHM). The mean characteristics of the airglow layers are presented in Table 2. The goodness of fitting scores R² > 0.95 for all five VER curves. The layer centroids, estimated from

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. We have simulated the VER profile for the OH(8,3) using the SABER mean temperature and atomic oxygen profiles for the campaign. The difference between the simulated OH VER and SABER OH VER lies on the averages used as inputs in the VER simulation. However, SABER OH VER and simulated OH VER are much closer in structure if we use individual SABER temperature and oxygen profiles.

3.1 Short-scale gravity wave analysis

We have defined here as small-scale the waves presenting λ_h < 725 km, while large-scale waves present λ_h > 725 km. This 725 km threshold corresponds to the length of the diagonal across the field of view of an airglow image mapped onto a 512 × 512 km² grid. Thus, a 725 km horizontal-scale wave would present one crest and one trough fitting the image frame entirely. More details about raw airglow image preprocessing can be found in Appendix A.

The majority of waves observed during SIMONe–2018 are small-scale, fast oscillations of τ_i < 1 h. The keograms of Fig. 1 (right-hand side panels) show the most prominent waves of this category registered during the clear nights of the campaign. These short-scale gravity waves are analyzed here using the auto-detection method (Tang et al., 2005; Vargas et al., 2009; Vargas, 2019). The auto-detection method relies on three sequential airglow frames to obtain two time–difference images used in the cross-spectral analysis to obtain gravity wave parameters. The calculation of time–difference images leads to a change in the amplitude of the waves (in the TD images compared to the original ones). The amplitude influences the Fourier analysis and therefore also the result of the cross-correlation. However, this issue is properly taken care of by restoring the amplitude of the waves as seen in the original images. Further details about this correction and the auto-detection method are found in Appendix B.

Figure 5Short-period wave parameters obtained from OH, O₂, O(¹S), and Na airglow image analysis using the auto-detection method (Tang et al., 2005; Vargas et al., 2009; Vargas, 2019). The mean measurement error is indicated in the chart of each wave parameter. Plots of waves detected in each emission separately are in the Supplement of this paper.

Download

Figure 6(a) O(¹S), (b) O₂, and (c) OH volume emission rate weighted zonal and meridional background (unfiltered) winds. (d) O(¹S), (e) O₂, and (f) OH volume emission rate weighted zonal and meridional wind fluctuations. Wind fluctuations were obtained first by averaging the wind over 400 km² field of view using a 4 h temporal, 4 km vertical window to obtain winds representing large-scales variations and then subtracting these estimates from the background wind field. The vertical blue arrows indicate coherent wind fluctuations also seen in the airglow brightness. Dashed boxes indicate hours of simultaneous operation of the ASI and MSMR system.

Download

Figure 5 shows the results from the auto-detection method for all the emissions recorded during SIMONe–2018. Weighted background winds in Fig. 6a–c were used to carry out the Doppler shift correction on τ_o. Thus, the parameters shown correspond to intrinsic properties of the waves. We have calculated the error bars for the parameters of each wave event measured using the methodology in Vargas et al. (2019). The average error of each parameter is shown in their respective charts in Fig. 5. Since we rely on a set of three images at the time to compute the cross-spectrogram of a set, the time span of each set is about 20 min. It is possible that the observed wave events represent waves independent from one another because the observed waves have relatively long vertical wavelength and propagate vertically fast under weak horizontal winds. However, we recognize that this is not always the case, and, as the oscillations slow down as they propagate vertically, their residence time within a given airglow layer could be long. Therefore, some of the detected waves could have been counted twice while evaluating the average momentum flux and other wave statistics.

Because every image of a given airglow layer is taken at 10 min pace (the filter wheel cycle period), we are only able to resolve wave-apparent periods > 20 min. On the other hand, the exposure time used here is mostly 2 min; aliasing could be present due to this relatively long exposure time. However, we have assured the aliasing is minimal in this case because there is no smudging of the small-scale wave structures seen in the images.

The top-center box (Fig. 5c) contains a statistics summary of the measured wave parameters. Figure 5j shows λ_z ranging from 10 to 40 km, while λ_h in Fig. 5m clusters around 75–125 km. Waves transporting large F_M are mainly oriented towards the 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). Estimated τ_i shown in Fig. 5e ranges within 20–40 min, with intrinsic phase speeds in the interval of 30–100 m s⁻¹ during 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 F_M waves, which depends on other wave parameters.

Since the auto-detection method returns wave intrinsic parameters, we are able to estimate F_M of every measured event (e.g., Vargas et al., 2007). Figure 5l shows the daily F_M of waves detected during SIMONe–2018, with larger F_M waves appearing on 2–3 and 3–4 November. The momentum flux vs. intrinsic wave period chart (Fig. 5g) reveals a tendency of larger τ_i waves carrying larger F_M. Conversely, Fig. 5h (Fig. 5i) reveals that large λ_h (λ_z) waves associate with small F_M quantities.

3.2 Large-scale gravity wave analysis

During SIMONe–2018, we also observed the presence of large-scale gravity waves modulating simultaneously the airglow brightness (Fig. 1c and e) and the horizontal wind (Fig. 2c and d). 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 using

The result is seen in Fig. 6d–f, where the dashed boxes indicate hours of simultaneous operation of the ASI and MSMR systems.

The weighted wind fluctuations are similar in each layer as the layers peak within ±2 km from each other (see Table 2) and are thicker (mean FWHM ∼ 15 km) than expected (e.g., Greer et al., 1986; Gobbi et al., 1992; Melo et al., 1996; Wüst et al., 2017). The similarity of these fluctuations is related to larger-scale λ_z waves seen in Fig. 2c and d. Moreover, because the overlap of the VER profiles is non-negligible, the rms values of the weighted winds fluctuations are expected to have a similar magnitude. Calculated rms magnitudes are 6.9 ± 1.0 and 5.9 ± 0.9 m s⁻¹ in the zonal and meridional directions, respectively.

Figure 7Spectra of weighted zonal and meridional wind fluctuation of Fig. 6. The dashed red lines indicate tidal periods. The vertical blue arrows indicate wave frequencies of persisting wave structures also seen in the airglow brightness. Statistical 99 % significance level is indicated by dotted blue lines.

Download

The spectral content of the weighted wind fluctuations is shown in Fig. 7. Several tidal harmonics are still present in the spectra (vertical dotted red lines in Fig. 7). This is due to how the wind fluctuations are calculated, i.e., by first using a 4 h temporal, 4 km vertical window to obtain winds representing larger scales, then subtracting the result from the background wind. Thus, the obtained wind fluctuations will contain some of the energy of the tidal modes. However, there are persisting peaks attributed to gravity waves because of their presence in wind fluctuations and keograms. For instance, the peaks in Fig. 7 at the vicinity of 0.24 cycles h⁻¹ are seen in the wind fluctuation of 3–4 November (meridional direction). Likewise, Fig. 7 shows a peak near 0.11 cycles h⁻¹ corresponding to a wave of 8.9 ± 1.0 h also seen in the keograms of 6–7 November (zonal direction). A hodograph analysis of the winds must be carried out in a separate work to clarify the nature of the significant peaks in Fig. 7.

Figure 8Enhanced contrast keograms of O(¹S) airglow for (a) 3–4 November and (b) 6–7 November 2018. The keogram of 3–4 November shows a large-amplitude, large-scale gravity wave at 20:00–22:00 UTC heading south. A large-scale wave is also seen on 6–7 November propagating eastward at 00:00 UTC. The white continuous lines on the keograms indicate the wind fluctuations weighted by the O(¹S) volume emission rate.

Download

We have studied further the wind fluctuations against obvious wave features present in the keograms of 3–4 and 6–7 November. By visual inspection of the images, we have verified that these large-scale waves do not fit within the airglow image field of view (512 × 512 km²) and are only noticeable via keogram analysis. We carry out the analysis by overlapping the O(¹S) weighted wind fluctuations on top of the corresponding keograms for these nights (Fig. 8).

On 3–4 November (Fig. 8a), a strong and coherent oscillation is observed in the meridional wind fluctuation, while both zonal and meridional keograms present enhanced brightness structures around 21:00 UTC (dashed black lines). As the meridional wind fluctuation peaks, the meridional keogram brightness dims (Fig. 8a bottom); as the meridional wind fluctuation reverses direction, the airglow brightens. We have estimated τ_o ∼ 4.0 ± 1.0 h for this oscillation from the meridional wind fluctuations, where the assigned uncertainty in τ_o corresponds to the smallest division in the keogram temporal axis. The tilted brightness structure between 19:00 and 21:00 UTC in the meridional keogram indicates a wave is traveling southwards. The zonal keogram shows no obvious tilt in the enhanced brightness, suggesting no wave propagation in the east–west direction. That is confirmed from zonal wind (Fig. 8a top) that does not show any apparent oscillation in the same time span.

Similarly, we have observed enhancements in the airglow brightness on 6–7 November associated with a large-scale wave with τ_o ∼ 8.0 ± 1.0 h estimated from the wave activity in the zonal wind fluctuation seen in Fig. 8b top. The zonal wind fluctuation coincides well with the O(¹S) enhanced brightness structure in the zonal keogram around 00:00 UTC. This brightness enhancement shows a slight tilt that indicates a wave propagating from west to east. The negligible brightness tilt in the meridional keogram (Fig. 8b bottom) implies the wave has no evident north–south component.

Figure 9Composite (k_x,ω_o) and (k_y,ω_o) spectra of the keograms in Fig. 8 for the nights of 3–4 November (a, c) and 6–7 November (b, d).

Download

Spectral analysis of keograms for the two nights showing large-scale waves is shown in Fig. 9. The zonal and meridional keogram spectra for 3–4 November are in Fig. 9a and c, while zonal and meridional keogram spectra for 6–7 November are in Fig. 9b and d. Appendix C gives further details about the keogram spectral analysis carried out here.

For 3–4 November, the zonal keogram spectrum indicates a peak at k_x=0 and ${\mathit{\omega }}_{\mathrm{o}}=-\mathrm{0.17}$ cycles h⁻¹ (τ_o = 5.7 ± 1.0 h), where the negative sign is associated with a forward-evolving time. The meridional keogram spectrum shows a dominant peak at ${\mathit{\omega }}_{\mathrm{o}}=-\mathrm{0.21}$ cycles h⁻¹ (τ_o = 4.6 ± 1.0 h) and $k_y\sim -\mathrm{0.7}\times {\mathrm{10}}^{-\mathrm{3}}$ cycles km⁻¹ (λ_y ∼ 1365 ± 136 km), where the negative sign indicates a southward-propagating wave. The error in λ_y is based on Vargas (2019), who estimates 10 % error in measurements of large horizontal-scale waves (> 100 km) from spectral analysis. Note that because the horizontal scale of the wave in the meridional direction is twice as large as the mapped image field of view (FOV; 512 × 512 km²), the entire horizontal wave structure is hardly seen in a single airglow image but is doubtless recognized in the keogram.

The large-scale wave occurring on 6–7 November is represented in the zonal spectrum by the peak near ${\mathit{\omega }}_{\mathrm{o}}\sim -\mathrm{0.11}$ cycles h⁻¹ (τ_o = 9.1 ± 1.0 h) and $k_x\sim \mathrm{0.2}\times {\mathrm{10}}^{-\mathrm{3}}$ cycles km⁻¹ (λ_x ∼ 4096 ± 409 km), where the positive sign indicates an eastward-propagating wave. The meridional keogram spectrum indicates a peak at the same frequency but k_y∼0, indicating no wave propagation in the meridional direction.

Figure 10Time–altitude cross section of the zonal and meridional wind fluctuations for the nights of 3–4 and 6–7 November 2018. The continuous (dashed) white lines indicate crests (troughs) of the oscillations as well as the descending phase (ascending energy propagation) of the waves. Note the coherent τ_o ∼ 4.3 h gravity wave oscillation on 3–4 November with λ_z ∼ 25.6 km. The zonal wind oscillation on 6–7 November corresponds to a λ_z ∼ 21.3 km, τ_o ∼ 8.0 h gravity wave.

Download

Figure 10 shows the time–altitude cross section of the zonal and meridional wind fluctuations for the nights of 3–4 and 6–7 November, respectively. The descending phase progression in time–altitude cross section reveals that these large-scale waves are propagating upwards. We have drawn continuous (dotted) white lines on top of the crests (troughs) of the salient wave structures to estimate λ_z and τ_o of the oscillations. The lines were drawn where the wave structures are better defined on top of the meridional wind (3–4 November) and zonal wind (6–7 November) fluctuation cross sections. From these lines, we have estimated λ_z = 25.6 ± 1.0 km and τ_o = 4.3 ± 1.0 h for the wave seen on 3–4 November. Note that the assigned error of 1 km in λ_z corresponds to ∼ 2 times the vertical resolution of the vertical axis in Fig. 10, while the assigned error of 1 h in τ_o corresponds to the resolution of the temporal axis in Fig. 10.

For the wave seen on 6–7 November we have obtained τ_o = 8.0 ± 1.0 h and λ_z = 21.3 ± 1.0 km. This long-period wave is not related to the 8 h tide since the horizontal structure of the oscillation can be seen in the keogram of Fig. 8b entirely. The apparent periods derived here from the descending phase analysis are consistent with those from the keogram spectral analysis shown earlier.