General comments:

This work by Panditharatne et al. reports on the adaption of the RAL Infrared Microwave Sounding retrieval processor to the evaluation of data from the far-infrared spectral range. The scheme is tested twofold: first by simulating FORUM-like observations and performing test retrievals of water vapour and temperature in comparison to IASI simulations. Second, simultaneous aircraft nadir measurements from two instruments covering the far- and mid-infrared are used as the input to the retrieval scheme. Results are discussed against vertical profiles of temperature and water vapour from dropsondes during the same flight.

This analysis clearly shows the applicability of the adapted retrieval scheme for the analysis of observations in the far-infrared spectrum. A second aim of the paper (I guess) was to show the improvement of using observations in the far-infrared with respect to pure mid-infrared retrievals (e.g. from IASI). However, I am not really convinced about the outcome of the study in this respect. E.g. assumptions on the measurement uncertainty of the two instruments (FORUM and IASI) are rather different with including all kind of instrumental errors for IASI while using only the spectral noise in case of FORUM. Also, the very different horizontal sampling/resolution between the two instruments has not been taken into consideration.

Still, I would support the publication of the manuscript in AMT after revision on basis of the comments and suggestions below.

Specific comments:

l.91-99:

Please explain a bit more about the species included in LBLRTM as well as the spectroscopy used. Has e.g. the N2-continuum at around 100 cm-1 been simulated? Which water-vapour continuum has been applied?

l.91-99:

It would also be important to know about the uncertainty in the following retrievals introduced by the spectroscopic errors (including errors in the continua). Some discussion about this should be included in the discussions.

l.73, ‘Retrieval Framework’:

Please add (e.g. in a Table) all elements and dimensions of the retrieval state vector, as well as their units. Additionally show (e.g. as supplement) the results and covariances of all parameters of the state vector (surface-temperature, surface emissivity).

In addition, information should be provided about the influence of other spectrally interfering trace gases (e.g. ozone) on the retrievals: e.g. which profiles are used and kept fixed (e.g. also for CO2, etc)? Have their uncertainty been considered for the selection of channels? What is the expected uncertainty introduced in the actual retrieval?

l.108:

Does the a-priori covariance of surface emissivity also contain correlations (off-diagonal elements) in spectral space?

l.111: ‘γi’:

I think i should be a subscript to gamma. Is gamma_i decreasing during the iterations?

l.130:

G, K_x, \hat{x} have not been defined. Please do so.

l.135: as you report for the RMSE the logarithm of specific humidity, has this quantity also been used in the retrieval state vector? Otherwise, why not reporting the RSME directly of what is in the state vector?

l.155:

Please explain more in detail which instrumental errors are considered in the S_y of FSI as well as of IASI and how these have been produced? Also mention the horizonal resolution on ground as well as measurement time related to the FSI versus IASI measurements those S_y values are valid for.

l.167:

Matrices of dimension (mxm) and (nxn) cannot be directly multiplied, please correct/modify.

Figure 5:

Are the water vapour biases plotted as the biases of the log()-values or the real wv-values in the retrieval state vector? If only the log(WV) is shown, please show also the ‘native’ ones.

l.227:

As the retrievals are performed with noise-free simulated ‘measured’ spectral radiances, can you explain more clearly what the median retrieval biases are significant for as a retrieval diagnostics?

l.235, ‘the partial derivatives of the forward model output against components of the state vector also contributes to the retrieval uncertainty’:

Why not writing ‘the Jacobian matrix K’? But why is this mentioned here at all? Is K strongly different between the instruments apart from the channel selection and the different spectral regions?

l.274:

It would be good to mention here also the maximum optical path difference of the interferometer for the measurements used here.

Figure 7, ‘taken from ERA5 around the path of each dropsonde’:

Please quantify what ‘around’ means (delta-time, delta-km)?

l.345:

Can you specify which single errors are included in the instrumental ‘Uncertainty’ curve in Fig. 9? Especially outline also possible errors due to spectral as well as radiometric calibration?

l.362-368:

I would be good to see these results as figures (e.g. in the appendix).

l.364, ‘looser’:

Clearer to say ‘smaller’ or do you mean ‘larger’ values?

l.385, ‘AK-treated’:

Please provide the formula used (including averaging kernel and a-priori profile).

Figure 12a:

Please also show the deviations of WV also as percentage as well as absolute (e.g. in a supplement) differences of WV (ppmv) from the ‘Drops_AK’. With always showing the log-scale plots, it is very difficult to follow the argumentation.

l.398, ‘This tightening of the a-priori temperature covariance also leads to an increase in the water vapour AKs’:

Can you make it plausible why this is the case?

l.436, ‘however this remains within the measurement covariance’:

Has the measurement error also been divided by sqrt(n) where n is the number of samples? Otherwise a direct comparison to the measurement error of one observation might be misleading.

Chapter 8 Conclusions:

Please discuss here (or before, e.g. in the introduction) the general differences in the method as well as the results between your analysis of the aircraft measurements and the work by Warwick et al., 2022 (https://doi.org/10.1029/2020JD034229).

l.484, ‘The performance of IMS was first assessed…’:

It is not clear to me what the aim of the paper is. Is it the assessment of the retrieval code or the assessment of the FORUM vs. IASI performance or the analysis of the aircraft observations? On l.63 it is written: ‘To validate this scheme in the far-infrared..’. However, I’m not convinced how retrieval test, with simulated as well as measured data ‘validates’ the processor? Please try to make this a bit clearer in the introduction and even in the title where the retrieval scheme validation is not mentioned.

l.491, ‘Because FORUM has not flown yet these aspects are not possible to quantify’:

However, there are requirement targets/threshold on the instrumental performance (e.g. calibration, etc) which could have gone into this analysis. Please explain why only the noise was used here.

Technical corrections:

l.110 and elsewhere, ‘Levenburg’:

Should be ‘Levenberg’.

Figure 4, caption:

‘degress of fredom’ -> ‘degrees of freedom’

l.257 and elsewhere, ‘8.8km’:

A space should be between number and unit.

l.325:

‘overlayed’ -> ‘overlaid’ (?)

l.341:

‘are’ -> ‘is’

l.383:

‘colocated’ -> ‘collocated’

l.421:

‘Figure 12’ -> ‘Figure 13’

The paper reports the adaptation of a retrieval code developed for IASI to the analysis of FORUM-like measurements. It is an interesting paper that can go ahead to be published.

However, I have some concern on the validity of the reached results and their application to the forthcoming FORUM instrument.

• The forward model used to simulate the FORUM measurements uses a 0.3 cm-1 sampling, but no mention is made to the spectral resolution. Is it the same as the spectral sampling? If so, the resolution of FORUM reported in ESA documentation is about 0.5 cm-1 and not 0.3 cm-1, and if the the spectral resolution used in this paper is 0.3 then this difference affects the conclusion reached in the paper, that cannot be directly applicable to FORUM.
• The simulated spectra are produced with a Norton Beer apodization, that makes the simulated channels signal spectrally correlated. However, in the retrieval, you use a diagonal covariance matrix, that neglects these correlations. This will affect the results of your retrievals. Moreover, since the covariance matrix is used to select the channels used in the retrieval, the whole process is not completely robust.
• The error used for the FSI includes only the NESR, while the one for IASI includes a lot of other components. Some of these could be deduced from the FORUM documentation (i.e. the required radiometric accuracy that can be used to deduce the expected calibration error) therefore the results presented here are biased in favor of the FORUM instrument
• The simulated retrieval are performed using the MERRA2 data. This is fine, but I think that, since the diverse profile dataset used in the development of the RTTOV code are relative to 2008, the use of any atmosphere of the more recent years could have been safely used for these tests.
• You do not retrieve ozone. No mention on which profile of ozone you use in the retrievals of the simulations is made in the text, while you correctly report the value for the retrievals of real observations
• You report all the equations of the optimal estimation (that are very well known) but you do not report any description of the used quantifiers (measurement cost per channel, State cost, cumulative degrees of freedom, hPa/DOF etc. I suggest adding few sentences describing what they represent
• You perform the simulated retrieval on noiseless simulated measurements. Why? No explanation for this is given in the paper
• The part of the paper describing the retrievals of the real observations (TAFT+ARIES retrievals) is extremely long and reports a lot of tests that are somehow redundant for the purpose of the paper. Moreover, the description of the tests is really confused, and it is very hard to follow. I suggest either to shorten it or try to report the results in a clearer way.
• When the dropsonde data are reported, you say AK treated drop-sonde. Which AK are you applying?

Specific comments

Line 119: why the convergence is reached when the change in the chi-square is less than 1?

Line 155: ‘FSI measurement covariance is smaller’, please quantify this

Lines 205-208 was the surface emissivity in the retrievals the same of the simulations?

Caption of Figure 5 ‘Dotted lines show the median absolute deviation (MAD) in the median

retrieval bias in each bin’ Since you use the optimal estimation this value is not significative, since if you have low information the results stay close to the a-priori and the MAD is very low

Lines 233-235. The sentence is really not clear, can you rephrase it?

The title of section 5.1.1 should be changed

Line 269 ‘is substantially less than’ please give estimates

The title of section 6.1 suggests that you describe how you treat TAFT and ARIES measurements to resemble FORUM but the section describes the way RTTOV simulates the measurements in the retrievals. Please change it