The authors have presented version 4 of the IASI NH3 product. In this version, they introduced total columns averaging kernels. With the averaging kernels, the IASI NH3 can be easier to be compared with model simulations and can be better implemented for the NH3 assimilations in the models. The improvement of HRI calculations makes the product more robust across the different IASI instruments. The manuscript is clearly written and well-structured and will be of interest to scientists using the IASI NH3 observations. I therefore recommend publishing this manuscript in AMT after addressing some minor comments below.

Minor comments:

L55:   eq (1) and (2) are used to calculate the HRI and estimate true NH3 total column.  According to the context, I guess that mean spectrum includes the NH3 background column B. Are they related? Maybe a short sentence to describe the relation between mean L and background B?

L75-77: eq (4).  Can you explain a little bit more on why you introduce the filter? After applying the filter, all low values will be removed and when averaging the product over a period, this will introduce a positive bias, which will affect a trend analysis of the NH3.  

L164: revise ‘ take care off’ to ‘take care of’

L281 you have mentioned ‘N’ here. This is the first time you introduced ‘N’. I guess this is the normalization factor. Please specify it.  Figure 3 shows the AVK normalization factors. Please mention that this is the ‘N’ variable in the caption.

L395 what do you mean by a larger here? Can you give a clearer explanation here?

Figure 8. Can you also add a sub-figure to show the difference of the two versions? It will be easier to see the distribution of the difference.   

Section 6.2 presented the intercomparison between ANNI v4 and results of an optimal estimation approach. Authors shows the consistency of both retrieval approaches. After reading the section, I am wondering why use the NN method instead of the optimal estimation approach? Maybe add some discussion about it.

The manuscript by Clarisse et al. describes a new NH3 retrieval from IASI, which has the improvement of including averaging kernels as well as fixing some other consistency issues. The introduction of averaging kernels for the standard IASI product is a welcome addition to the retrieval product that has been on the wishlist of potential users for more than a decade, as it allows for models to be fairly compared to the satellite retrieval data.  This is thus an important and significant step forward and will likely ensure that IASI NH3 data is used in more quantitative model-based studies in the future.  Overall, the article is very well written and logically sound.  The recapitulation of some theory is highly appreciated, as it provides a self-contained, consistent overview of DOAS and optimal estimation retrieval theory and notation.  My main request is that the article touch on, if only cursorily, how the updates made here are expected to impact comparisons of IASI data to in situ measurements (where not directly comparable, one can consider spatial gradients, season and annual trends, etc.).  Following the addition of such content, and addressing a few small issues below, the article is suitable for publication in AMT. 

Major comment: 

While it is interesting to compare to the v3 retrieval and an optimal estimation retrieval, there’s no comment on how the updates may address any comparison to in situ measurements. I recognize that column NH3 observations aren’t available from many in situ measurements, but ground-based surface concentration measurements can be used to evaluate gradients, seasons trends, and annual trends. Models can also be used as a transfer function to relate in situ measurements to satellite-observed column concentrations, as a means of evaluation. While a detailed comparison using models may be beyond the scope of a retrieval algorithm paper, some discussion of bias and error relative to in situ measurement is still warranted, and feasible.  Thus I’d request the following questions be addressed at a minimum:  based on all prior application studies with the IASA products, was there a suspected under-estimation of NH3, especially in more remote areas? Is v4 an improvement in this regard?  To what extent does the new temporal trend correction improve comparison of trends to in situ measurements? 

Minor comments and edits:

61: What is the reason for applying a scaling factor as 1/SF * HRI rather than SF * HRI? Is there a numerical benefit to this formulation? 

75-80: What is the origin / significance of the factors of 1.5 in the filtering criteria Eq. (4) and (5)?  Also, is my reading of the Eq. (5) filter correct in that negative column concentrations are allowed but only when HRI is not more than 50% above background?  Lastly, what is the background value, B? Is it actually zero or an arbitrarily small number? 

164: off —> of

As a user of DOAS and optimal estimation retrievals, I found Sections 3.3 and 3.4 very valuable, in terms of drawing similarities and differences between the two types of averaging kernels and how they are used.  The additional discussion of the two approaches for making “apples to apples” comparisons of modeled to retrieved values (and the note on when they are equivalent, as a ratio) is, while not new, extremely useful for new users to have laid out in a single paper with consistent and clear notation. 

287 and Fig 3: I agree the deviations of the overall set of samples from unity is small. It would though be interesting to see if there are regional biases. Showing only a single day makes it hard to discern any gradients between the missing values, and also for this day in particular many global hotspots are omitted.  Could the authors instead or additionally show means for normalization factors averaged across a much longer period?

Section 4.1: I think the authors means pseudo-inverse, not generalized inverse.  A generalized inverse is a more general, less restrictive, non-unique notion of matrix inverse. I don’t think that’s what they are using here. Rather, I note the way they are using a truncated eigenvalue decomposition to represent the inverse is the same as a truncated SVD decomposition (given that S is symmetric, and the eigenvalues position), which is based on the pseudo-inverse that omits all vectors associated with zero (or effectively zero, numerically) singular values.  I also note that Rodgers refers to this as a pseudo-inverse. I’m not familiar with their other reference. 

Fig 7: Are the v4 values here the final ones, after bias correction? Can the values <0 be shown as well? Are there more, or less, in v4 than v3?  The text says there are few <0 for v4 in a long term average, but as a user I’m more interested in the statistics of the daily data (otherwise I need to consider time-averaging the data prior to assimilation, and it’s not clear how to time-average the AVKs).  I see later in Fig 9 that v4 values < 0 are appreciable, so I think they should be shown here as well. 

Fig 7: Showing a slope fit to only a subset of values is a bit odd. Perhaps show a reduced major axis fit, or just report the correlation? 

Fig 8: I suggest adding labels to the lat/lon lines, or removing them.  Otherwise I’m not sure what purpose they serve. 

464: Remove the comma after separately 

467: errors —> error 

481: without an 

485: profiles, 

510: Having participated in several such studies, I would say these uncertainties strike me as considerably underestimated.