This work introduces a promising tool for gravity wave analysis that could contribute to the understanding of multi-scale atmospheric dynamics. The manuscript is well written; however, it requires additional clarification and explanation of certain choices.

General comments:

• Why are the chosen windows different between methods? It needs some justification.
• It would be useful to see a comparison of the MRA to a conventional wind analysis.
• Section 3.1 Case Study: Several mentions are made of wind, tides, and GWs observed on the day, but the corresponding figures are not shown. Since the paper focuses on the method and the case study, including these figures would help the reader follow the discussion without having to rely solely on the authors’ statements.
• Throughout the article, the same method is called differently, e.g. ‘buttlerworth filter’ and ‘spectral filtering’. Select one way of calling it and use it everywhere.
• There is a misuse of GW and GWPE throughout the entire article. GWPE is defined but then used as GW potential energy. Please change it everywhere, and remove densities after GWPE.
• The summary, conclusions and perspectives need some emphasis on the method comparisons and their weaknesses.

Specific comments:

Figure 4: It could be useful to see a plot with the difference between the temperature and method next to the temperature one.

L007: In an abstract, you should try to avoid the use of acronyms to help readability. It’s okay to use them; however, don’t use an acronym for defining another acronym GW potential energy (GWPE). You are not space-limited, so avoid this practice.

L017-021: Paragraph small, only one citation.

L023: Here the ‘e.g.’ is used. If you are giving an example, only one or two citations are enough. It could be one old and a new one. Instead, 10 are given and not even one is a recent one (2020+). I suggest removing e.g. and adding a later one too.

L024: Duck et al. 2001, the link is broken.

L025: I agree that Lidar observations are capable of inferring long-term trends; however, some of the cited publications are campaigns or techniques, which aren’t studies in long-term trends.

L028-29: Same as before, there are newer studies of GW with Lidar observations.

L085: cal/val is only used twice and in the same sentence. If it is not used later, it is unnecessary to define it.

L150: verticalsinterval

L163/164: You defined MRA in the second sentence but use it in the first sentence, please switch.

L190: eq:3 is the equation of the gravity wave potential energy. Remove density and all the references to it. You have already defined GWPE, so now you can use it.

L200: The reference to the figure is there, but no in-text full explanation of the figure.

Fig2: caption double km.

L205: Again, defining an acronym with an acronym and it should be defined before. Particularly in this case, you don’t need it because it’s the GWPE.

L207: GWE?

Fig. 3: second line: “above” La Réunion, it sounds narrower than actually is. Change to centred over or similar. And the longitude is written with a “,”

Figure 8: red dots? Only one is shown at which I guess is the start.

Figures 7 and 8: Increase label size.