Review of "Scale separation for gravity wave analysis from 3D temperature observations in the MLT region" by Björn Linder et al.

General comments

In this new study, Linder et al. propose and evaluate an approach for estimating gravity wave pseudomomentum flux from tomographic temperature measurements in the mesosphere and lower thermosphere, which are expected to be provided by the MATS satellite launched in November 2022. The study proposes the use of Savitzky-Golay filters for local separation of the background temperature and temperature perturbations of the MATS temperature measurements. The well-established S3D method is proposed to perform the spectral analysis to estimate the wave properties (wave amplitude and wavelength) from the temperature perturbations, which are input to the estimation of the gravity wave momentum flux.

The proposed methodology is evaluated using simulated temperature fields from the HIAMCM general circulation model, which provides realistic fields of temperature, winds, and other parameters from the surface to the thermosphere. The study compares estimates of gravity wave momentum fluxes estimated directly from the model wind fields with pseudomentum fluxes from model temperatures. It further compares ideal estimates of momentum flux with estimates derived with the SG filters and the S3D method applied to temperature fields sampled as MATS measurements, taking into account the satellite orbit, the retrieval resolution via expected averaging kernels, and the expected measurement noise.

The study has been carefully carried out and the results appear to be sound. The proposed methodology for estimating gravity wave pseudomentum flux from MATS measurements is convincing. The paper is exceptionally well written, clear and concise, in my opinion. I would recommend that the paper be considered for publication, subject to the correction of a few rather minor comments listed below.

Specific comments

Line 131: This study proposes to use the S3D spectral analysis method, but for completeness, the S-transform spectral method could be referenced as another commonly used method for analyzing the types of measurements to be provided by MATS.

Line 146: It is pointed out that the swath width of about 200 km of MATS is a bottleneck for properly estimating some of the gravity wave spectral characteristics. Why was the instrument built with such a small swath, assuming that the estimation of the gravity wave momentum flux in the MLT region is indeed a key objective of the MATS measurements?

Lines 148-150: Perhaps add the dimensions for clarity here, 600 km x 190 km x 10 km (along track x across track x vertical). It would be good to provide some rationale or reference as to why the vertical width of the S3D boxes was set to 10 km. It is pointed out that the length of the cuboids is 600 km, but the sampling would be done every 100 km. What would be the reason for this oversampling, since the results of neighboring boxes would be largely correlated?

Line 176: It is pointed out that the zonal wavenumber 18 corresponds to wavelengths of about 2200 km at the equator. If the reference method is to use zonal wavenumber 18 for scale separation, it looks like there would be some discrepancy with the measurements of the MATS instrument, which has a swath width of ~200 km, which in combination with the S3D could allow estimation of wavelengths up to ~600 km. Isn't there some kind of gap between 600 and 2200 km wavelength?

Lines 191-193: You might add that structured noise from something like stray light would also be very difficult and challenging to properly simulate and account for.

Lines 240-241: I may have missed it earlier in the paper, but for completeness you might want to mention whether the HIAMCM data is a boreal summer and austral winter case?

Lines 269-271: The proposed cuboids have an asymmetry in size along and across the track, which seems to lead to an anisotropy in spectral sensitivity of the gravity wave measurements along and across the track. Such an anisotropy can cause some difficulty in interpreting measurement results. This can be seen in the example presented here for the polar regions. Perhaps you could discuss and clarify why using such unbalanced cube sizes is still advantageous compared to e.g. using a cube size of 200 km x 200 km x 10 km?

Lines 286-287: When discussing vertical smoothing, it would be good to provide some information on the vertical resolution of the HIAMCM test data. The MATS measurements have a vertical resolution of 500 m, and averaging kernels with FWHMs of 1 km and 2 km are considered for the retrieval data. Is the HIAMCM vertical resolution comparable or better?

Technical corrections

line 201: Section -> Sect.

line 220: efficiently -> effectively (?)