Review for paper “Momentum Flux characteristics of vertical propagating Gravity Waves” by P. Nyassor et al.

General Comments

The paper shows results from a case study of 2 mesospheric gravity wave events above São João do Cariri. They are able to demonstrate that the momentum flux differences between two different altitudes agrees with what is expected from theory with regards to upward and downward propagating waves. They show this in their figures and explanations in the text. Some refinement of the figures and explanations in the text are required, in my opinion, before it can be accepted for publication.

Specific Comments

This paper examines 2 nights of data and compares them. One of these nights the meteor radar data is not available, so they are not able to do a complete analysis comparison of the energy. Are these the only 2 nights with a similar period GW in all four filters over the7 year dataset?  Are there no others where the meteor radar is working so you can do a full comparison of momentum flux and energy?

Abstract – please mention that you are only looking at 2 events at the start of the abstract to aid clarity. You also mention reflected non-primary waves in the abstract, but surely this technique can just show that the wave observed is up/downward propagating, you can’t say whether it is primary/non-primary or a reflected wave of any order?

Throughout – you use the term “energy” throughout the paper, but given the potential energy can only be examined for both events I would recommend altering this phrasing to relfect the results.

Section 2.1 – please include at least the altitudes of the different airglow layers at the start of this section to aid the reader or someone who is new to airglow studies. I know that you have pointed to the Nyassor et al paper, which does contain all the details, and mention them much later in the paper but the basics that are relevant to this study should be included early on.

Section 2.2 – please include the height range that the radar observes at, you’ve mentioned the vertical resolution, but the height range is needed for context.

Line 124 – it is not clear what is meant by “19-25” hours. If the spikes in Fig. 2a are between 21-23 hours then the remaining dataset left is between 23 and 27, as per Fig. 2b-d, not 19-25 hours.

Section 3.3 – you mention Lomb-Scargle periodogram in this section but only show results from the wavelet analysis, is the L-S method used in this paper? If so, how closely does it match the wavelet results?

Section 3.3 – the widths of some of the airglow layers overlap, does that influence your results at all?  Also, the altitudes given in this section (see my earlier comment about section 2.2) are the average altitudes for the layers, but there has been work that shows that these layers do tend to vary in their altitude over time, would this affect your interpretation of the results?

Figure 3c – this is not very clear, the dotted lines all look near vertical apart from the last one in the bottom two lines. Maybe this needs to be highlighted on the figure. Also it needs to be clear which of the two observed gw periods this is referring too or if they’re combined somehow. E.g. Fig 5 is much clearer.

Figure 3d – is this just for the airglow intensity (photometer data) or the temperature data?

Figure 4: - Figures e-h are duplicated in Fig. 7 – do they need to be?  

• 4 g and h need to have the same X-scale as the rest of the plots (same for Fig. 7) to help with interpretation.
• 4e and f – these are on a different temporal resolution than KE, could you show them on the same scale but with error bars on to represent the small-scale variability seen in the MF and PE plots.

Section 6.2, 300-301 – can the phrases “ a small fraction” and “a great amount” be replaced with something more precise please.

Technical comments:

Line 124 – I think you mean Figure 2a not 1a

Line 272 – the word wave is missing at the end of this sentence.

Line 273 – replace “using” with “calculated from”.

Overview:

This manuscript presents results of two gravity wave events at 36.31W, 07.40S using photometer, all-sky imager, and meteor radar data. The authors use this data to determine characteristics about the present waves and associated momentum and energy fluxes. The technique presented is interesting, and could provide beneficial scientific information. It is a useful idea from the authors to use multiple airglow layers to better understand gravity wave propagation in the MLT region. Nevertheless, there are several issues with the manuscript that are concerning. Importantly, the calculated values need to be better explained in the context of what assumptions were made, and what specific measurements were used. The “reconstructed” waves need more discussion and justification for how the wave parameters were chosen.

It is concerning that the kinetic energy calculation does not seem to be for the wave itself, rather it is based off of  >1hr wind perturbation measurements (1hr resolution) that do not have the resolution to capture the waves being studied in this manuscript. Additionally, there is lacking information on exactly how the momentum flux was calculated. A temperature perturbation value is used, but it is not clear how this was obtained. It should be the average perturbation value over the wave packet, or the actual temperature perturbation amplitude. Instead, it appears that the raw residual temperatures were applied directly to the MF calculation.

Given these aspects, and the other concerns listed below, I am suggesting the paper be rejected. If these analysis issues can be mitigated, and the techniques more properly explained, there is potential that the manuscript could be resubmitted.

Detailed concerns are listed below:

-Lines 67-68 “The temporal resolution of the observation is 2 minutes, thus GWs with periods greater than 2 minutes can be observed.” Lines 67-68

The airglow photometer that measures OI, O2, NaD, and OH is said to have a 2 minute resolution. That would mean that GWs with periods of greater than 4 minutes can be observed (at best). More importantly, the authors need to provide explanation as to how phase shifts can be determined with a 2-minute resolution. Also, a 3 point running mean has been applied to the data (discussed on lines 125-126), which would further reduce the resolution. Furthermore, the data itself will have associated noise. The fit (equation 2) would also have some errors associated with it. So, how does this affect the calculation of phase differences between the different airglow layers?

-In the processing section, “a Lomb-Scargle periodogram and Wavelet analysis were used to determine the dominant periods in the time series of each emission layer. At least a dominant peak is chosen and used to reconstruct new harmonics and over plotted on the residual.” Lines 135-136.

In this case, if there is any error in the harmonics chosen, how would this influence the result? The waves present appear to have a spectrum of associated periods. Is one chosen harmonic effectively characterizing the waves present?

-Lines 146-147: “After the residual time series was determined, the periodicities were calculated. For these residuals, the dominant period are 25.47 min and 33.47 min.”

What process was used to determine these were the periods? Was a peak finding routine used with the PSD shown in figure 3d? Was this the period at all times? Was a particular time period chosen for each emission line? Are they all the same?

Furthermore, looking at figure 3a, the “reconstructed” signal appears to fit well for some portions of the night, but not for others. Was there a particular time used to determine the phase differences between the emission layers? Just a slight offset between the fit and actual data could result in significant differences for the vertical wavelength calculation.

-Lines 152-153: “From the reconstructed time series, it is clear that all the emission layers are similar, indicating that the same GWs propagate through these layers.”

How was this determined? There are certainly similarities in all of the layers. This could also be expected for a ducted wave as well. It also appears that the wavelets in Figure 3d are not the same for all of the layers, so more explanation should be provided here. While it is mentioned that the wavelet shows the presence of waves from 30-90 minutes, there is still variability between the layers.

-Section 3.4 needs more discussion about how the parameters were calculated, this is detailed in the following comments:

-How was the Brunt Vaisala Frequency in Figure 4d calculated? What assumptions were made to calculate the potential temperature? How was dT_pot/dz, the change in potential temperature with altitude calculated, and were there any assumptions made? Figure 4c shows a variable potential temperature, but the Brunt Vaisala frequency is plotted as a constant at each altitude.

-What measured parameters are used for the energies? How is T’/T being calculated? Is the amplitude of the residual temperatures being used? How is the amplitude being calculated?

-Where are u’ and v’ being calculated from in equation 4 for kinetic energy? What assumptions were made for the calculations of Ek shown in figure 4g?

-For horizontal momentum flux, as you show in equation 6, this is typically assumed to be the average vertical flux of horizontal momentum over a wave packet. Over what time period is the wave packet defined? What is being used at the T’ calculation?

-For equations 6/7, on line 175 it says “where rho_o is the density at the emission layers” but it is not clear where or how this density was obtained to make the calculation shown in Figure 4e.

-For equation 6/7, how was kh, the horizontal wavenumber, calculated from the data? This was not discussed elsewhere.

-Similarly, how was the intrinsic frequency calculated or measured for the MF calculation?

-Line 187-188: “Since the meteor radar wind has a temporal resolution of one (1) hour, Ek at each hour was determined and presented in a contour plot”

The meteor radar is giving you the background wind. However, with a 1 hour resolution, the meteor radar is unable to give the perturbations u’ and v’ associated with the gravity wave that would be necessary to calculate Ek. The gravity wave periods present are all less than 1 hour. These Ek calculations are not correct.

-Lines 193-194: “The spectral analysis technique described in Wrasse et al 2024 was used to determine the horizontal wavelength, period, phase speed, and propagation direction”

More details need to be given here about what exactly was done. This is a very cursory explanation for a significant calculation within the manuscript.

In the referenced 2024 paper, it appears that Fig 1 is a flow chart and Figure 2 shows individual images and keograms. This case presented there is a little different because the waves were very clear both in the individual images and in the keograms. In the manuscript here, and the data presented in A2, the waves are not necessarily clear in the keogram. It is also a little strange that individual images are not shown. Looking at data in Tabe 1, the determined kh was between 20-35km, which should be within the field of view of the imager. Why were spatial images not included? The horizontal wavelengths can easily be obtained from the images themselves and not a keogram. There needs to be more discussion about how all of these parameters were obtained.

-Lines 200-207: For event 1 “the dominant periods used in the reconstruction of the waves of these events are 00.42 hr (25.47 min) for all emission layers, and 00.50 hr (30.29 mins) for IO 557.7, O2 (0-1) and NaD. However, the period of the OH (6 - 2) was 0.55 hr (33.47min).”

This is a bit contradictory to read. It sounds like there were three different periods used here. Why are there so many different periods? Shouldn’t they all be the same? These are also very close periods, close enough that a 2-minute measurement resolution would suggest a slight error in the fit could describe differences in presumed periods. Can it be demonstrated that this is not a fitting error and these periods are real? From Figure 5b, it looks like there is a lot of variability in periods over the dataset.

-Figure 5a makes it appear that there is little to no phase change between the different layers/altitudes. This is usually indicative of a ducted wave. Yet, the vertical wavelength listed in Table 1 is only 10km. Wouldn’t there would be more variation in phase over the layers if the vertical wavelength were only 10km?

-Lines 210-215: descriptions of the wavelet plots are given, but it really is not clear how the peaks/wave periods were determined. The plots show a broad spectrum. How was one particular peak chosen to represent a wave across the entire dataset?

-Table 1: Are there any errors associated with these measurements/calculations?

-Table 1: It is still not clear how the vertical wavelength was calculated from the measurements.

Lines 218-291: “Only the potential energy for Event #02 could be determined due to unavailability of observed winds. Hence, no estimated values for kinetic energy and subsequently total energy were presented in Table 1.”

It would appear based on what has been presented in this paper that Ek cannot be calculated for any of the events.

-Lines 220-225 and Figure 5c and d: The wavelet analysis shows periods that are all over the place. The final fitted waves based on “dominant periods” in the wavelt are shown in Figure 5c. However, the original data plotted with the fit are never shown like they were for event 1 in Figure 3. This needs to be included.

-Lines 237-238: “two events with similar periods were selected. For Event #01, two dominant periods were detected, however, the first period present no phase change, implying it is possibly a ducted wave.”

It is still not clear how the “dominant periods” were chosen. It would also appear that there is little to no phase change between the different layers.

-Line 229: “For Event #02, the two dominant periods are within the gravity wave spectrum.”

This is not at all clear from the wavelet.

-Line 233-235: “From the phases of the GWs of Event #01, OH leads NaD by 08.60 min, whereas NaD leads O2 by 01.21 min. O2 lags OI by 03.25 min. A consistent phase lead can be observed from OH through NaD to O2 except between O2 and OI, where a phase lag is observed.”

Where was this demonstrated in the data? Figure 5a shows nearly identical phases over each layer. Furthermore, the resolution of the measurements would not allow for these sorts of phase differences to be measured. 1.21 minutes is less than the resolution of the measurement.

-Line 235: “The phase lag observed between the emission layers of O2 and OI was induced by the background wind due to a shear.”

Where? How was this proven mathematically in any of the previous data/measurements/calculations presented?

-Line 236-238: “Despite this phase lag, the mean phase propagation of these GWs shows that OH leads OI by ∼06.58 min. Using this phase information and the period, Figure 6(a) is produced. Clearly, it is observed that the similar GW oscillation in the OH (red line) emission layer leads to the OI (green line) emission.”

None of these phase differences have clearly been shown. The calculations to obtain them have not been clearly demonstrated.

A sinusoid can be fit to anything. There needs to be a determination of how good the fit actually is. Figure 6 shows “reconstructed waves” but it is not clear where this is obtained from. Is this from the data shown in Figure 3? The original data should be plotted with the fits.

The discussion of “leading” and “lagging waves” needs to be tied back to the data more clearly, and this also needs to be put into context of the actual resolution of the measurements. Ultimately, instrument resolution is going limit the ability to determine phase differences.

-The section “Momentum Flux and Wave Energy” will likely need to be redone with more explanation regarding how the different parameters were calculated and what assumptions were made for the calculations. Most importantly, how was the average temperature perturbation determined for the wave packets present in the measurements?

Additionally, it does not seem that the kinetic energy calculations for a wave are not correct.

-The conclusions that there are upward and downward propagating gravity waves need to be better supported. It seems like arbitrary wave periods were chosen from the wavelet analysis, and sinusoids were plotted based off of this. There needs to be more quantitative analysis performed and a justification for the reconstructed waves provided.