General Comments:

This paper focuses on optimizing the CEDS NH3 emission inventory using a top-down inversion system (4DEnVar) over South Asia. The authors have previously conducted a similar work in China (published in ERL), but they highlight several novelties in this study:

1. The application of the IASI averaging kernel to derive NH3 column concentrations;
2. A relatively high spatial resolution NH3 emission inversion over South Asia (0.5° × 0.625°);
3. The identification of a "double-peak" seasonal pattern difference between prior and posterior emissions.

Overall, while the study's scope aligns well with the journal ACP and contributes to advancing the field by improving top-down NH3 emissions over South Asia, I find that the analysis and discussion are not sufficiently thorough. Below, I provide suggestions to broaden and deepen the discussion and analysis:

1. Clarify the use of observations and simulations: The use of IASI and CrIS observations, along with GEOS-Chem simulations, should be more clearly outlined. For example, a table could be included summarizing the exact periods covered by each dataset (i.e., 2015-2023, 4 months in 2019), their respective roles in the study, and the purposes they serve. Additionally, the data filtering process for removing irrational values should be more rigorously justified, particularly regarding skin temperature and cloud fraction considerations. Comparisons between IASI, CrIS, or previous studies could help validate the dataset selection.

2. Present results in a logical sequence: The results section could benefit from a clearer structure. It might be more intuitive to first present the analysis of observed NH3 concentrations (Sec. 3.1.1 and 3.2) before discussing the spatial and temporal patterns of NH3 emissions. Then followed by the validation with the concentration inferred using the inversion.

3. Strengthen the discussion: The discussion should delve deeper into the reasons behind the changes in the seasonal patterns observed in the posterior emissions compared to the prior. Supporting this analysis with additional figures in either the main text or supplementary materials would be valuable. For instance, including information on:

• Seasonal fertilizer application timings for major crops like rice, corn, and wheat;
• Meteorological factors affecting NH3 volatilization and deposition, such as temperature and precipitation;
• Biomass burning patterns in 2019, as they may influence spatial and seasonal variations of NH3 emissions and concentrations.

Specific Comments

1. Abstract: One interesting point of this study is the different 'double-peak' seasonal pattern from the CEDS prior. I would expect to highlight this point in the abstract and briefly talk about the potential reasons for this.
2. Introduction:
   1. The effect of NH3 on climate change: inversed cause and effect, Sanderson et al., 2006 studied the effect of climate change on acid deposition. Consider reading more related and updated papers:
      • Gong, Cheng, et al. "Global net climate effects of anthropogenic reactive nitrogen." Nature 632.8025 (2024): 557-563.
      • Ma, Ruoya, et al. "Data‐driven estimates of fertilizer‐induced soil NH3, NO and N2O emissions from croplands in China and their climate change impacts." Global Change Biology 28.3 (2022): 1008-1022.
   2. NH3 level over South Asia, I would expect to see the number of NH3 concentrations or emissions here, as stated the highest in the world.
   3. Use NH3 instead of ammonia after the definition, which applies to the whole text.
   4. "the environmental impacts can be quantified" -> "enabling the quantification of environmental impacts"
   5. "However, these bottom-up estimates of NH3 emissions are generally considered uncertain (Xu et al., 2019), especially compared to other pollutants mainly derived from fossil fuel combustion" -> However, these bottom-up estimates of NH₃ emissions are generally considered as uncertain (Xu et al., 2019), particularly when compared to pollutants primarily originating from fossil fuel combustion, such as ...
   6. "limitations still remain": unclear what kind of limitations here.
   7. Add a citation about your emission inversion system.
   8. The description of emission inversion system and corresponding data could be shortened here and add more details in the data and method part.
   9. Clearly state the aims of this study, focusing on but not only the NH3 emission feature.
3. Data and method:
   1. IASI:
      • Which periods are used for MetOp A/B/C, respectively?
      • If you are using the L2 data, how do you aggregate it into the GEOS-Chem grid?
      • Except for the irrational values, have you detected any large outliers?
      • It is unclear how the B, A_z^a, and m_z coming from in the Eq. 1.
   2. Inversion:
      • I do not see the 'a' in Eq.3, where has it been used?
      • How is the parameter 'σ_integrated' calculated in Eq. 6?
   3. GEOS-Chem:
      • Add more information such as the boundary layer condition, the spin-up process, model version...
      • Sect. 2.3.1 and 2.3.2 can be combined.
      • Do you run the model for the whole year 2019?
      • The step that coarse-grained CEDS into 0.5 * 0.625 degs included in the GEOS-Chem or seperately?
      • What is the spatial resolution of the CEDS and is there any regional emission inventory with higher resolution over South Asia that you can use? Does CEDS contain both the anthropogenic and natural sectors?
   4. Figure 1:
      • Increase the size of the dots and change the color regime. I suggest using different point styles for different measurements.
      • Can you list these stations in the supplementary?
   5. Figure 2:
      • Row (b) seems useless and not mentioned in the text, consider moving to the supplementary.
      • The way you plotted the IASI and GC seems different.
4. Results and discussion
   1. Figure 3: I am curious why there are 0 values (grey area) in the CEDS prior and posterior, and how you deal with this 0 values or missing gap in the posterior. It may look confused since there are lots of grey area in (a) and (b) but not shown in (c)
   2. NH3 total column concentration:
      • "Four months": in 2019. Note all month are presented in Fig.4.
      • "Distributions for the rest months": could you provide timeseries or seasonal pattern of these two satellite observations?
      • "background error covariance matrix": does this refer to B in Eq.3 and 5?
   3. NH3 and PM2.5 ground concentration validation:
      • "The mismatch": specify which kind of mismatch, bias mismatch or spatial/temporal
      • Can also add the Bias in Fig. 4, 5 and 7.
      • Fig. 4 and 5 can be combined.
      • Fig. 2 and 6 can be combined.
      • "systematic biases": how do you define the systematic biases, which differentiate from the random error
   4. Seasonal and annual variation of ammonia concentration:
      • The peaks in NH3 posterior concentration (May) and emission (July) are different and interesting, can you elaborate to explain it?
   5. Spatial and Seasonal variation of ammonia emission:
      • No posterior data in Fig.S3.

General comments

The paper describes the application of an ammonia emission inversion system over South Asia. As emissions of ammonia are rather difficult to estimate by emission models, this approach is very useful to obtain insight in the actual emission strength. Especially the time period of the

seasonal emission peak(s) is difficult to model, but the described system seems able to provide a better estimate for that. The system uses IASI satellite observations to constrains the emissions; results are validated by comparing posterior simulations with observations from the CrIS  satellite instrument and observations from a ground network.

The temporal resolution of the emission estimates is monthly, which is rather course compared to the high frequency changes present in ammonia emissions. For the described study that seems a logical choice, as also the prior emission inventory is monthly. However, could the authors discuss the potential of their system for higher temporal resolution estimates? What are the current limitations for application on weekly or even daily scale? Is the availability and/or quality of the satellite observations a limitation, or simply the computing resources?

The inversion now uses IASI observations to constrain emissions, and CrIS observations for validation. Would it be possible to use instead the CrIS observations to constrain the emissions? The results show quite some differences between IASI and CrIS NH3 columns; would inversion of

CrIS data give very different results? A discussion on this would be useful.

Although the paper focusses on the application of the inversion system, the setup of the  inversion is described sufficiently well. For some parts a more detailed description could be useful, as described below in the Specific Comments. Overall, the paper is easy to read, and could be published after some minor modifications.

Specific comments

p 3, line 32: When the monthly averages over grid cells are calculated, is there any spatial or temporal weighting applied? For example, a spatial weight based on the overlap between a pixel footprint and the target grid cell, or a temporal weight based on the instrument error? 

p 4, line 14-15: What are the units of these variables? A more standard formulation of the kernel application would look like:

      Xm = Xa + A ( m - B )

  Could Eq (1) be rewritten to this actually?

How is the averaging kernel applied to the model data exactly? Is a monthly averaged kernel applied to  monthly averaged concentration? If so, how is the monthly averaged model concentration calculated, as an average over all ours, or using time of overpass only? Or are the individual

pixels simulated from the model first, and then averaged over grid cells and months?

Would it also be possible to not use monthly averaged observations, but simply all observations individually? The estimated emission state could still be monthly, so what is the reason for using monthly averaged observations?

p 4, line 3: Negative values are not necessarily wrong. The uncertainty of these values is probably high, so the "true" value is still a very likely outcome. By removing the negative observations, the monthly average will have a positive bias. Could this be discussed?

p6, lines 8-10: Why is this minimum value chosen, how often does it have this value? Are the gray values in Figure 2 "b" this minimum?

    Maybe better to move this part to Section 2.1 where the observation uncertainty is discussed.

p 14, section 3.2: Fig 9.a shows prior and posterior model columns, are these after application of averaging kernels? Then the lines should be different for IASI and CrIS.  If these are model columns, how well could these be compared to the satellite columns?

Technical corrections

p 2, line 13: "compared emissions of other pollutants"

p 2, line 2: Add a reference here?

p 4, line 16: The uncertainty assigned to the IASI measurements is also an essential"

p 4, line 24: Fig 2 is referenced before Fig 1, change order of figures?

p 5, line 22: Explain that the emission field is "f"; what are the units?

p 6, line 3: Shouldn't this be f_b ?

p 6, line 7: Shouldn't this be "observation representation errors are independent from each other" ?

p6 line 8: "as described in"

p8, line 19: "as well as manure from livestock, including cattle, ..."

p 8, line 25: "posterior result"

p 8, lines 26-27: mention 3.2 first, then 3.3

p 16, Figure 10 caption: (j) is a time series, not a scatter plot.  And the box plots represent yearly averages.