A concerning aspect of this manuscript is that the data are “detrended” to remove the background, which is likely a large-scale wave or tide. This method lacks detailed description. However, it should be noted when a linear background is subtracted from a wave such as a tide, which is sinusoidal, the residual remains near the inflection of the tide creating a false perturbation.

Putting this aside, the methodology used to analyze the residuals (if we make the assumption these residuals are waves) is otherwise very concerning. I have provided reviews of this below in case the initial point is not enough.

Unfortunately, the improper use of multiple filters, FFTs, and detrending make it difficult to discern what is actually present in the dataset versus what is an introduced artifact or noise. The color plots are interpolated as well, which is problematic for the coarse resolution of data used.

Additionally, there is no propagation of error analysis included in the calculations. The errors associated with Ri and, N^2, and m^2 are expected to be quite large, possibly even so large that these calculated values are irrelevant.

While the equations used to calculate Ri, N^2, and wave parameters such as horizontal phase speed are correct, applying these equations to data is not a novel technique and has been published many times before. The methodology used to extract data in tables 1 and 2 is not provided or clearly justified.

Specific comments are included below:

Line 144 “The detrended temperature measurements in different directions are shown in Figure 2”

What sort of detrending method was used? Why are the original data not being shown here? Detrending in the presence of a sharp tidal structure can cause the appearance of a perturbation.

Line 145 “Abundant wave components of various periods are identified from measurements of all directions, and distinct downward phase progression is seen in the perturbations, which implies an upward wave propagation.”

Are these “abundant wave components” or noise?

Line 147 “A strong peak is found at around 90 km altitude from 09:00 UT onwards”

The “peak” at 90km is not in agreement with figure 4, which shows all sorts spectral power at a range of altitudes and not necessarily a peak at 90km.

Line 148-150 “The wave patterns of the perturbations in different directions are very similar, so they are likely the same wave packets spreading a larger area and captured by the laser beams in different directions. Closely inspecting the wave pattern (crests and troughs) in different directions, some shifts in time could be noticed, which are the results of the spatial separation of laser beams in different directions.”

What sort of scientific interpretation was used to come to this conclusion? How are you coming to the conclusion that the perturbations are “similar” and “likely the same wave packets spreading a larger area.” There appears to be a jump in temperature between 9-10UT, but it is unclear what the background temperatures are and whether this is an artifact or real.

Line 150-152 “The detrended perturbations of different wind components are shown in Figure 3, similar wave patterns with a downward phase progression can be identified in zonal and meridional winds, with an amplitude of up to 20 ms−1.”

This is not readily apparent. The data shown are quite noisy. Again, the readers are not shown the original data before detrending, so there may be an artifact here.

Line 153-54 “The wave pattern is still clear in the vertical wind perturbation, with an amplitude +/-2 ms−1. However, the downward phase progression is less evident. This is likely due to the magnitude of perturbation being equal to or less than the uncertainty of vertical winds.”

This statement is problematic for multiple reasons. First, there is a wave apparent in w’ provided by the authors, but with different periods than what is shown in the other plots. So, “the wave pattern is still clear” is not relevant. “The downward phase progression is less evident” implies there is a downward phase progression that can be observed, but then it is stated that it is likely the magnitude of the perturbation is equal to or less than the uncertainty of vertical winds. What is being claimed here?

Line 159 “Figure 4 shows the spectra of temperature perturbation in

five directions, which all show a similar pattern. The average spectrum of all five directions is shown in the upper right corner.”

This is extremely misleading. The dataset shown in figure 2 has a lot of noise structure on the order of 30 minutes to a few hours without any coherent structure. Of course applying a Fourier analysis is going to show spectral power associated with periods of one to a few hours, but this does not mean it is an actual wave. Furthermore, the dataset shown is only 4.5 hours, with an interpolation of 6 minutes. In reality, data in the off-zenith direction has an effective resolution of 10.2 minutes. So while waves with a 20 minute period could technically be detected, noise can also be observed on the order of 20 minute periods or greater.

What is most misleading about Fig 4 is the interpolation in the plots. Based on the dataset used (6:30-11UT) being 4.5 hours and an interpolation of 6 minutes (so sampling frequency of 10 points/hr), the highest frequency possible should be ~.222/hr or 4.5 hours (the length of the dataset). But the plot shows 6.4hr, 3.2hr, and 1.6hr points. Is the dataset used actually longer? Was zero padding used? Also, it is very important to point out here that there are a limited number of datapoints at these low frequencies. The plots shown in Fig 4 are heavily interpolated when in reality there are just a few data points at the lower frequencies for each altitude. Also noise can be easily interpreted as a wave. There is not necessarily coherence between the perturbations at each altitude, and the FFT could also be sensitive to noise or artifacts from detrending.

Line 161 “Overall, there exist two prominent peaks; one has a period of about 3.2-hr and the

other one about 1.6 hr.”

No, these are just two adjacent data points in an FFT and NOT two distinct peaks. Yes, the dataset has spectral power in this frequency range which does not necessarily imply a gravity wave with a specific period.

Line 165: “Overall, there exist two prominent peaks; one has a period of about 3.2-hr and the

other one about 1.6 hr.”

Given the short length of the dataset and the sampling resolution, it would be extremely difficult to distinguish these two periods from each other.

Line 169 “Two spectral peaks are quite close in the frequency domain, so we used Chebyshev type II filters with flat passband and steep transition to stopband.”

Yes, these are indeed quite close spectrally, and given the short length of the dataset and the coarse resolution, it would be difficult to distinguish the two peaks using a filter. One must consider the effective resolution of the dataset. Essentially, at the sampling resolution used of 6 minutes (its technically 10, but data were interpolated), and the length of the dataset being 4.5 hours, your frequency resolution is 0.222 hr^-1. The author is attempting to distinguish between 0.625hr^-1 and 0.3125 hr^-1. The frequency resolution does not permit the application of a filter that can separate these two waves.

Line 170: “To filter out the 1.6-hr wave component, the cut-off period of a high-pass filter is selected as 2.2-hr (0.46 hr−1). To separate the background state from two wave components, the cut-off period of a low-pass filter is selected to be 6-hr (0.17 hr−1).”

The sampling resolution and length of the dataset would not permit this. The dataset is not even 6 hours. Also, weren’t the data already detrended?

Additionally, applying a filter to a dataset, especially a sharp cutoff filter can create ringing and edge effects, which would make waves appear in the filtered data that aren’t real.

Line 172-173: “To fully understand the propagation condition of waves, the background atmosphere states were analyzed. Figures 5(a)–5(c) show the background temperature T0, zonal wind u0 and meridional wind v0 retrieved by low-pass filtering as defined above.”

What was described above was incorrect use of a filter to attempt to retrieve long period waves from a short dataset. Its not clear how the background is now obtained, especially since the waves in question were retrieved using a “detrending.”

Line 174-175: “The background atmosphere states show clear modulation of tides, as shown by a slow downward phase progression in both temperature and winds.”

Yes, the background atmosphere does have tides, and filtering effects or detrending can cause artifacts in these tidal regions that can be misinterpreted as waves. It is difficult to tell without seeing the original data, and these should be shown in addition to these “background” data.

Figure 5 and line 185: The calculation of N^2 and Ri requires the use of multiple data points and when accounting for propagation of error, these errors can be quite high. What is the error associated with the calculated Ri and N^2?

Looking at plot A1, the wind error at best is 5m/s for the off zenith beams (U, V measurements), 15m/s at 100km, and 30m/s at 105km. To calculate Ri, two points are used to calculate dU/dz and two points are used to calculate dV/dz. Even with averaging, this would result in quite a large error, especially at higher altitudes.

Furthermore, parameters such as Ri and N^2 are parameters associated with the atmosphere itself including all waves and features. Generally, a GW propagating through the atmosphere itself generates regions of low Ri and N^2, not necessarily the “background state.” These calculations are not only problematic due to the significant errors, but they are not relevant as they are based on a heavily filtered background that does not include all of the localized dynamics which determine Ri and N^2.

Figure 6 and 7: As previously discussed, there are issues with the filters applied to the data here.  

Line 176: “and there is a clam layer around 90km”

What does this mean?

Line 193: “However, the long-period (3.2-hr) wave effectively acts as the background for the shorter-period (1.6-hr) wave.”

Again, this dataset cannot resolve a separate 3.2 and 1.6 hr wave based on the number of samples and length of the dataset. Effectively, these two periods are two adjacent data points in the frequency domain, and one would expect a power spectral density with higher power for lower frequencies to exist in the mesosphere in general. Even zero padding will not change this, as it is merely an interpolation in the frequency domain.  If a sharp filter is applied essentially only allowing 1 or 2 points in a spectrum of noise, then what results is a wave. This does not mean a wave is present.  

Figure 6: The artifact that may have arisen due to filtering and tidal removal is being referred to as a 3.35 hour wave, although an entire period of the “3.35 hr wave” isn’t readily visible over the 4.5 hour dataset.

Line 202: “After applying the desired filters on the temperature and wind perturbations, the two dominant wave components are isolated.”

What filters? This analysis appears to isolate two different Fourier components associated with the background noise spectrum.

Line 203-204: “Using the improved spectral peak determination method, the exact periods of the two dominant components are determined to be 3.35 hr (0.2986 hr−1) and 1.63 hr (0.6148 hr−1).”

What is the “improved spectral peak determination method.” These aren’t peaks. They are two adjacent points in the frequency domain for the given dataset.

Lines 205-215: Aside from the concerning heavily filtered data, and the contour plot that has an interpolation associated with it, it is also important to note that outside one region between 9-11UT and 87-92km in a few of the plots in Fig 7, many of these perturbations are close to the noise of the temperature measurements. The perturbations are mostly just a few K, which is also the noise associated with T between 85-95km. Note that above 100km, the noise drastically increases from 5K to 15K at 105km. Likely the data above 100km in altitude are noise.

Interestingly, the plots of the filtered winds are hidden in the appendix A3 and A4 plots with a dotted line drawn on which does not appear to follow any mathematical or analytical methodology to placement other than an attempt to convince the reader that there is a phase progression that is not actually apparent in the data.   

Line 218: “The wave signatures of both components are evident in the horizontal winds with the visible downward phase progression”

No, the downward phase progression is not readily visible.

Line 218-219: “and the node structure is clear in the vertical direction with at least two maxima at different altitudes.”

The vertical winds are plotted on an axis range from -2.5 to 2.5 m/s, which is below the noise of the wind measurements even in the best cases.

Lines 220-225: While there is discussion of waves in the wind data, the waves are not apparent from the plots provided.

Line 235-240: Assuming that the parameters used for the waves are not noise or artifacts arising from detrending or improper filtering, there were clearly many assumptions that would go in to a calculation of phase speed. How were the propagation azimuth and phase speed determined?

Lines 240-245: “The horizontal wavelength wave #1 and wave #2 are estimated to be around 975 km and 438

km, both with a ∼20%uncertainty. The propagation azimuth angles are estimated to be 299◦ and 233◦ for two waves, both with a 15◦–20◦ uncertainties. These wavelengths and azimuths correspond to phase shifts of -32◦ and 18◦ between measurements of E-W and N-S for wave #1, and phase shifts of -65◦ and -49◦ for wave #2.”

Again, there are no details on how these calculations were made, what the assumptions were, and how the uncertainty was determined.

Tab1e 1: No information is given on how these parameters were calculated.

Line 260: “When the atmosphere is treatedas incompressible and background temperature varies slowly within the vertical wavelength of the wave, we have cs →∞and dHs/dz →0.”

This is not a valid assumption, the speed of sound does not go to infinity (although this was mentioned 20 years ago in the Fritts and Alexander 2003 paper).

Section 3.3 Wave Diagnosis:

The math here is not new, and has been used in observational analysis in many other publications. The calculations presented here use GW parameters that were determined in the previous section of the manuscript. As previously mentioned in this review, it is not clear that these are real waves. What is also problematic here is the calculation m^2. There is no noise calculation or propagation of error, which is presumably very high. The value of u is used multiple times in the chosen dispersion relation, each time with an associated error.

Furthermore, there is mention of “layered structures for both waves, potentially creating ducts for the gravity waves.” Based on Figure 9, these layers are very small, just a few km in altitude, so it seems strange that these would create a duct for GWs that, according to Tab1e 1 have vertical wavelengths >20km.

More derived parameters are provided in Table 2, and again, there is no discussion of how these parameters are obtained. Despite u’ and v’ not being readily apparent in the provided plots, these are somehow included in a calculation necessary for the parameters presented in Table 2.