Review of “GLOFI - A methodology and toolbox for scale-separation of satellite

observations for analysis of gravity waves” by Mathew et al.

The manuscript describes an interesting methodology to derive GW perturbations by using a scale-separation Python-based toolbox. The methods and assumptions are mostly clearly outlined with some missing details. I recommend publication after addressing the following comments.

Specific comments:

1. In Section 4.2 (Figure 4) and Appendix: In describing the comparisons between the temperature background estimated by GLOFI and actual temperature perturbations – “almost identical”, virtually identical” and the model spectrum is “very well” reproduced, “stronger deviations” is not quantitative. Please provide for e.g. differences and/or standard deviation etc.

1. Section 2: (a) It might be useful to the reader to summarize the spatial technique in Strube et al (2020).

(b) The text and figures in Figure 2 are too small. Please make this more readable.

(c) Please clarify if ‘GW residuals’, ‘GW perturbations’, ‘residual GW perturbations’ (Sec 3) all mean the same thing

1. There are 3 Appendices that are not referenced anywhere in the main text (except for the mention of Figure C1)

1. Section 4.4/Figure 8. No discussion/summary of the differences is provided.

1. Line 25: ‘… hard to resolve in atmospheric models” – please clarify that GWs can indeed be resolved in high-resolution models (e.g. Becket et al., 2022)

Becker, E., Vadas, S. L., Bossert, K., Harvey, V. L., Zülicke, C., & Hoffmann, L. (2022). A High-resolution whole-atmosphere model with resolved gravity waves and specified large-scale dynamics in the troposphere and stratosphere. Journal of Geophysical Research: Atmospheres, 127, e2021JD035018. https://doi.org/10.1029/2021JD035018

1. Line 155: Please provide reference for the Savitzky-Golay (SG) filter

Typos etc.

1. Provide abbreviations appropriately:

Line 67: what does DW1 stand for?

Line 88: what does PW stand for (Planetary Waves is mentioned several times previously)

1. Line 84: “This gives….” – correct to, for e.g. This ‘manuscript/paper/study’ gives ….

1. Line 204: Typo in 40°W

This paper tackles an important issue: how to efficiently and accurately recover temperature fluctuations due to gravity waves that are masked by large scale planetary and tidal wave values in satellite data. It is particularly important to understand the strengths/limitations of new satellite instruments. The methodology/algorithm for using 2D spectral decomposition to remove the large-scale components due to planetary waves and tides is well described and tested using simulated data. The recovery of gravity wave fluctuations is convincing. However, like any technique there will be instrumental limitations that constraint the range of gravity wave scales that can be observed, as summarized in Appendix A for a range of techniques. It would help the reader to understand these limitations if there was a diagram similar to Fig 8 in Alexander et al QJRMS 136: 1103–1124 (2010) that describes observational constraints. More information is required on what GW scales can be recovered with these proposed new satellite measurements.

There are some minor issues:

1. Appendix A is not mentioned in the body of the text. Probably should be referenced in about line 31.
2. L 69: What does it mean that a tide is a ‘true resonant mode and propagating wave’?
3. L230 ‘date’ not ‘data’