Radiance assimilation usually assumes point observations, which is fine for global NWP models, while for high resolution regional NWP models (and future high resolution global NWP models), the footprint size is too large and the footprint operator needs to be considered together with observation operator (RTM).  The manuscript provides a comprehensive analysis and discussion on how such footprint operator can be developed and used. I have just one question and one suggestion.

Question: why the grided brightness temperature averaging is a straightforward one? is it possible to apply spatial response functions of AMSU/HMS channels? The standard deviation of OmB seems overestimated if the spatial response functions are not considered.

One suggestion:   it worth noting a related research using high spatial resolution AHI observation for studying the IR sounder sub-footprint moisture variation, Di et al. (2021) found that the current IR sounders (such as CrIS, IASI, GIIRS etc.) with spatial resolutions between 12 and 16 km have typical average sub-footprint brightness temperature variations (BTVs) between 0.8 and 1.5 K over land, a 1 K variation in 6.25 μm water vapor absorption band corresponds to a 10% – 20% upper tropospheric moisture variation depending on the atmospheric humidity. Such sub-footprint BTVs, without being accounted for, may introduce additional uncertainties in quantitative applications such as radiance assimilation.  Their study provides another evidence on the needs of footprint operator in data assimilation for high resolution NWP models.

Di, Di, Jun Li, Zhenglong Li, Jinlong Li, Timothy J. Schmit, and W. Paul Menzel. "Can current hyperspectral infrared sounders capture the small scale atmospheric water vapor spatial variations?." Geophysical Research Letters 48, no. 21 (2021): e2021GL095825.

Review of Mile et al. – Exploring the footprint representation of microwave radiance observations in an Arctic limited-area data assimilation system

The authors present a method to account for sub-FOV features in the forward model of a regional data assimilation system, applied to ATOVS microwave radiances in the Arctic. This paper is very well-written and relevant for publication in this journal. It is clearly laid out and was a pleasure to read through.

Minor revision is recommended to address some small clarifications. Two larger comments are offered for discussion and are not to be viewed as requirements of the revision, but could be addressed by the authors if they choose. These could also be viewed as potential avenues for future work, alongside the already-identified areas such as slant-path RT and accounting for the antenna response. The more general comments are given first, followed by the more detailed points by line number:

• The analysis focuses more on the surface emissivity inhomogeneities that can exist within a microwave FOV, but it is interesting to see that even higher-peaking channels like MHS-4 and non-surface-sensitive AMSU-A channels also exhibit reductions in OmB. This would suggest that sub-FOV inhomogeneities in the water vapour field (and possibly temperature) are significant, as has been suggested by some previous studies (e.g. https://doi.org/10.5194/amt-11-6409-2018) though of course a larger effect for all-sky simulations (https://www.mdpi.com/2072-4292/12/3/531). It would be interesting to quantify this, i.e. what is the contribution of reduced OmB from better surface representation vs. the atmospheric inhomogeneity. Whether or not the authors choose to elaborate on this aspect, it might be worth a little more discussion of the atmospheric element of sub-FOV inhomogeneity, particularly for Fig. 12 as it is currently not discussed much. It’s also maybe worth mentioning that sub-FOV inhomogeneity can be quite important for lowest frequencies especially such as for SST (e.g. Fig 2 here: https://amt.copernicus.org/articles/12/6341/2019/), and will be a key concern for using CIMR in LAMs going forward.
• The FOP spacing is justified in section 3.2, implemented at roughly the model resolution of about 2.5km, and of course there is computational cost to increasing the RT complexity. Did you test finer or coarser spacing of FOPs? The ‘trade-off’ mentioned in the last sentence of the conclusions is an important one for operational DA, and it might be worth quantifying whether 2.5km spacing is sufficient, or for example if 5km spacing still reduces OmB significantly but is much cheaper. Along the same lines, while Figs. 13-17 contain a lot of useful information, a simple statement of total OmB reduction for a characteristic channel (e.g. 4% for AMSU-A-5 or whatever) would be a good headline value to include either in the main text or even the abstract as a way to demonstrate the significance of your results.

L13 Does AROME not use channels 10-14 on AMSU-A? Or maybe these were also improved with the footprint representation? If not, consider changing to ‘tropospheric channels’ to clarify.

L21 ‘can be mentioned’? Not sure if this is a typo or it should be reworded, but it was unclear what this meant.

L30 ‘the sensitivity to the surface is relatively small.’ This is an odd wording. I’d suggest removing ‘due...small’ because plenty of surface-sensitive channels are also assimilated at many centres using FASTEM, such as the MW imagers.

L43 Probably okay to just cite one of the Bormann papers on slant-path RT

L49 Maybe worth mentioning that radiance assimilation is much more effective in the Arctic during summer (Lawrence et al. 2019), presumably because complexities such as sea-ice edge and snow-cover are detrimental to optimal assimilation of MW radiance in the Arctic wintertime, which is your study period.

L50 Suggest replacing ‘inadequately’ with the simpler ‘not’

L76-83 It would be good to cite where these values came from. Perhaps official NOAA documentation?

L104 Not sure what ‘increased assimilation cycle frequency’ means here? Please reword.

L121 Please reword ‘the neglected effects of the incorporated RTTOV in the observation operator’ – seems like it might be missing a word.

L160 What is meant here by ‘Earth’s frame’? Is that the surface or something else?

L190 Is the subscript ‘foop’ a typo here for ‘fop’?

L220 It’s a little confusing to say that it’s the retrieved emissivity for channel 6 in Figure 5, as presumably it is the surface-sensitive channel 3 that’s used for the emissivity retrieval of 50+ GHz channels; the same comment applies for L272, where I would’ve expected ch3 to be used rather than ch1 for the emissivity retrieval.

L222 Unfortunately most readers won’t know where Wahlbergøya and Wilhelmøya are within Svalbard, so if you refer to them in the text it would be helpful to label them on the map.

Fig 5 If it’s not too hard to do, rotation of panel (a) so that it matches the projection of panel (b) would facilitate more direct comparison of the two panels for readers.

Table 2 Are these performance values for the whole system minimisation (i.e. including full observing system) or only considering these instruments? Good to clarify this as it certainly will impact readers’ interpretation of the computational cost increase.

Fig 7 It would be helpful to add lat/lon values on these panels if possible.

Fig 8 Just a suggestion, but it might be nice to see a third panel in the middle with channel 5, as this might show a combination of the two sensitivities.

Fig 9 Would it be possible to combine Figs 8 & 9 into a four-panel plot? I found myself flipping back and forth to compare the two. The same applies to Figs. 10 & 11.

L295  Is this a cycling DA experiment, with bias correction etc. evolving in time? I would presume so as spin-up is mentioned.

Fig 10 The same comment as for Fig 8 – adding a panel with MHS-5 would be interesting to show the mix of surface and atmospheric sensitivity.