The manuscript “Improved constraints on ammonia emissions and deposition from co-assimilating NH3 and NO2 satellite observations over the Netherlands” investigates the impact of assimilating ammonia and nitrogen dioxide retrievals from satellite-borne instruments on ammonia emissions in the Netherlands using the local ensemble transform Kalman filter (LETKF) with the LOTOS-EUROS chemical transport model. The paper discusses the impact of assimilating different combinations of retrievals of NH3 from IASI, NH3 from CrIS, and NO2 from TROPOMI. Following describing the impact on the ammonia emissions, the paper then examines the impact of using the posterior NH3 emission on the atmospheric concentration of ammonia and on the deposition of NHx as well as comparisons to surface observations.

The authors show that the posterior ammonia emissions generally improve the agreement between the LOTOS-EUROS model and observations from the LML network, but degrades the comparison to observations from the MAN network. The authors attribute the degradation of the comparisons to the MAN observations to differences in representativeness of the MAN observations, the satellite retrievals, and the horizontal grid of the LOTOS-EUROS model.

As ammonia plays a significant role in particulate matter formation and nitrogen deposition, thereby important for human and ecosystem health, but bottom-up emission inventories of ammonia emissions are often poorly constrained, this paper provides relevant information. While a number of previous studies have examined using ammonia observations from satellites to improve ammonia emissions, few (if any) have expanded this to include observations of other chemical species (in this case NO2), and so provides a novel aspect to the work as well.

Overall, the paper is relevant and generally well written. The examination of the additional information provided by the NO2 retrievals from TROPOMI are particularly interesting. There are a few places where the clarity of the manuscript needs improvement. Also, many of the comparison statistics in the paper are presented without uncertainties and thus the reader cannot determine if differences in these statistics are statistically significant or not.

Major Comments:

• I think Section 2.1.1 needs to be revised to make the description of the assimilation system clearer.

For instance, on line 98, is only the beta parameters set via the LETKF or 3D gas concentrations are set with the LETKF as well? Please rewrite this sentence to more clearly differentiate between the inversion variables set by the LETKF and all other model variables.

Related to this, when the NO2 retrievals are assimilated and compared against the model output, are all differences attributed to mismatches in NH3 emissions or to other factors as well? If it is the case that the LETKF only adjusts the NH3 emissions, then is it a reasonable assumption to attribute all observed NO2 differences to the NH3 emissions instead of other factors?

What is the frequency of the analyses produced (i.e. t_k - t_{k-1})? How exactly are different times handled with respect to the temporal correlation in Eq. (1) and what is the assimilation window used? Is the assimilation window for time t_k set as from t_k – delta_t/2 to t_k + delta_t/2, where delta_t is the analyses frequency, and then there is some sort of formula that combines {x_k} for different times using Eq. (1) or does the assimilation window encompass multiple times {t_k} and Eq. (1) is used within a single analysis (or some other method)? Please clarify in the text.

Lines 102-104 describe the ensemble initialization, but at this point I don't think a definition of beta has been given, so I'm not certain what the stated standard deviation (of one) is the standard deviation of. At the start of the paragraph, it is stated that beta is a “perturbation factor”. Please give a precise definition of this. e.g. is this a multiplicative factor or some other type of perturbation. On line 104, it is stated that “The values of the mean and standard deviation for the ensemble can be adjusted if desired.” I don’t know what this means, please clarify.

• I’m less familiar with the specifics of the LETKF as compared to other ensemble methods, in which localization is done quite differently, so I was confused by some of the details in Section 2.1.2. I’m aware that for the ‘R localization’ that is typically used in the LETKF, the optimal localization length scale is often quite a bit smaller than that used in the ‘B localization’ used in many other ensemble systems (where the Schur product of the ensemble-based B matrix is taken with the localization matrix). However, I wasn’t aware that ‘R localization’ had anything to do with any of the properties of the observations like the instrument’s horizontal resolution (for ‘B localization’ these are unrelated). Could you add some references and maybe some more text explaining this, especially for readers less familiar with ‘R localization’.

At the beginning of this section, Shin et al. (2016) is referenced, in which they state that they choose a horizontal localization scale of 2*(10/3)^0.5 * 500 km ~ 1825 km. Although, the Shin et al. (2016) paper is for NWP instead of a relatively short-lived atmospheric gas, I’m surprised that the localization length scales between the two different applications would be so different (compared to the 15 km and 5 km used in for this work).

The ensemble size used in this work (12) is quite small compared to most (non-LETKF) ensemble systems. On line 100, the paper cites Van Der Graaf et al. (2022) as determining this number to be sufficiently large. Van Der Graaf et al. (2022) states  “A limited ensemble size of N=12 was found to be sufficient to describe the imposed model uncertainty, which is not too complicated due to short lifetime of NH₃ and therefore strong relation between concentrations and nearby emissions.” There doesn’t seem to be a more quantitative analysis of the dependency of the LETKF on ensemble size. If ‘B localization’ was used (in a non-LETKF system), the localization length scale would be much larger than 15 km or 5 km, and so N=12 would be a very small ensemble. N=12 would be sufficient to specify the error covariances within a 15 km x 15 km (or 5 km x 5 km) region, but I don’t have an intuitive understanding on why the ensemble size would need to be of very different sizes depending on whether B or R localization was used. Could you also add either some references or reasoning on why this is the case.

• On line 278, it is stated that “cases where the measured and modeled precipitation exceeded a mean absolute deviation of 1-sigma were excluded” from the evaluation statistics. I would have imagined that a 1-sigma cutoff would exclude quite a lot of observations and would have thought setting this at something like >= 2-sigma would be more appropriate. Could you either add a justification of the 1-sigma cutoff or change this to a higher cutoff.

• I don’t think Section 3.4 is necessary in the main text as I’m not sure it adds much to the conclusions of the paper. I think it would be best to move this section to the Supplement or an appendix and the authors can add a sentence or two in the main text to referencing the supplement/appendix. Also, I think Eq. (11) might be missing a trace on the right-hand side of the equation.

• There were insufficient details given about the uncertainties of the statistical values presented in Section 3.5. In Fig.7, the slope of the line of best fit has uncertainties associated with it, but the statistics in the lower-right corner (R, mu, sigma) do not. To properly compare these statistics between the base and optimized cases, uncertainties need to be added so the reader can determine whether the differences between these cases is statistically significant or not.

For instance, on lines 456-457, it states “The correlation in the temporal means also improved slightly from R = 0.84 to R = 0.85, and the slope of the regression also improved from 0.79 to 0.91”, but without uncertainties on these numbers the reader cannot tell if these changes are statistically significant or not (as with other subsequent comparisons done later in the paper).

Uncertainties for R, mu, sigma should be added to all scatter plots (Figs. 7, 8, 11-14, 16), Table 2 (also add uncertainties for the slope here), as well to the main text. So line 457 should read '...the slope of the regression also improved from 0.79 +/- 0.03 to 0.91 +/- 0.03' and similarly for whenever R, mu, or sigma values are stated in the main text. Also, in Fig. B2, the difference plot should show the uncertainties (i.e. the standard error) of the mean differences.

• For a lot of the comparisons between the model and surface observations in Section 3.5, scatter plots and their associated statistics were compiled for particular spatial and temporal average separately, for instance in Fig. 7 & 8, Figs. 11 & 12, and Figs. 13 & 14. I think there are more informative ways of computing and presenting these statistics to convey both spatial and temporal information, as well as the statistics overall. It is difficult for the reader to translate the information in the scatter plots of the temporal or spatial mean values into meaningful temporal or spatial information.

If scatter plots are used, I think they should only display the ‘raw’ (unaveraged) data. But its often hard for the reader to compare two different scatter plots that have more than ~10 data points, so I would redo all the scatter plots using the unaveraged data and put them in the supplement/appendix (for completeness) and copy the statistical values for R, mu, sigma, and the slope into a Table in the main text (something similar to Table 2, again make sure the uncertainties on each value are stated in the table).

For temporal information, I would plot the data on a time series. For spatial information, I would plot the data on a map, or for LML comparisons since there are only 6 stations, you could also do something like a box and whiskers plot (or something similar) with each station being at a different place on the x-axis. Plotting as a time series or on a map directly conveys the temporal or spatial information.

• On line 593, it is stated “whereas most MAN sites are located within Natura2000 areas” How many and what percentage are in these conditions? Can you recompute the comparison statistics excluding all of these stations? Or is doing this basically the same at the set of 6 stations colocated with the LML stations? Would it be possible to provide some sort of map showing the land use, maybe like the dominant land use in each grid point, to add support to the statement that LML stations are more representative of the model domain?

Minor Comments:

• Line 35: “increased oxidation of NO2 consumes HNO3” NO2 is a precursor to HNO3, so why does this consume HNO3? Please add more details here.
• Line 92: Is a ‘)’ missing somewhere on this line?
• Lines 99-100: “These are represented” What does ‘these’ refer to here? Later in the sentence it states that the ensemble “capture the uncertainties in both the model and observations”, why does the ensemble capture uncertainties in the observations? This sentence is a bit confusing, please consider rewriting.
• Line 107: Put the equation defining X^f inline with the text after “the state vector” in line 105. The lines 105 to 112 could be rearranged to make these sentences more clear.
• Line 111: “includes the application of the emissions perturbation factors,” Give more details about this.
• Lines 114-116: Would increase clarity if \bar{x} was renamed to \bar{x}^f.
• Line 128: Change “limit” to “approximation”.
• Line 132: Change “representing” to “represents”.
• Line 143: Looking at page 2558 of Shin et al. (2016), they say that they use the fifth order polynomial of Gaspari and Cohn 1999. Is there another part of Shin et al. (2016) where they use this Gaussian function? The Gaspari and Cohn is very similar to a Gaussian, so there would presumably be little difference between the two but was just confused about the reference here.
• Section 2.1.3: I think the paper would flow better if the information in this section was moved to Section 2.1.
• Section 2.2: I think the total column is being used from all three retrievals (IASI, CrIS, TROPOMI), but this is not clearly stated in the text. References are made to the total column in a few places in Section 2.2, but somewhere it should be clearly stated that the total columns are the observations being used in the LETKF.
• Figures 2, 4, 5: It's difficult to see the differences between rows (a) and (b), and while row (c) show the relative differences, there are several places where the base values are low, so that large percentage differences may correspond to small absolute changes. Can plots of the absolute differences be added as well, or some other way of presenting the results to show where substantial changes occur? The figure might also benefit from changing the units and making the panels larger (they are on the small size and are a bit hard to read).
• Lines 172-175: This paragraph should be moved to the beginning of Section 3.5, right before Section 3.5.1.
• Lines 407-408: Remove the sentence “Independent evaluation against ground-based observations … atmospheric conditions.”
• Lines 460-461: “This indicates that the spatial pattern ... without assimilation.” Is this sentence referring to Fig. 7 or Fig. 8? Its placement in the paragraph suggests that it is referring to Fig. 8, but would maybe make more sentence inferencing Fig.7? Please reword.
• 10: It is a bit hard to compare the three different sets (base, assimilation, observations) in these plots. Might be clearer with just 3 curves of the mean, maybe with a shaded standard error region around each curve, instead of the box and whiskers plot.
• Lines 472-474: “…even though only morning and afternoon satellite overpasses were used” I assume this is the case because the impact from the assimilation remains in the system for at least 6-12 hours. Could you add a sentence about this?
• 9: For the legend and the caption, I think 'base' and 'optimized' or a similar wording is better here than 'before' and 'after'. Also, why is the title of the legend 'Sites & Mean', i.e. why 'mean'?
• Line 492: “whereas the Kalman filter adjusts emissions uniformly without differentiating among source types.” But as long as emissions are adjusted on a per grid cell basis, does this matter? For whatever mix of emission source types within a grid cell, there will be a total diurnal pattern that will be a mix of the diurnal patterns of each source. But from the perspective of the assimilation, I would have thought that whatever sort of mix of diurnal profiles wouldn't matter since it is just trying to match the overall diurnal profile of that particular grid cell. Maybe some diurnal profiles are more difficult to capture than others, so maybe the assimilation will be more successful at matching the diurnal pattern from some sources over others, but I would not have thought that this is a feature of the Kalman filter not being able to differentiate between source types.
• Line 512: Remove “individually”.
• Fig 12: Is it a coincidence that the values for mu in Fig. 12 are identical (at least to 1 decimal place) to those in Fig. 11?
• Line 454: As with the comments above for Fig. 9, change ‘before’ and ‘after’ to something like ‘base’ and ‘optimized’ or something similar.
• 15: What does 'absolute' mean here (second row)? If referring to the absolute value, I would assume that there wouldn't be any negative values in panels (d) to (f). Please clarify what exactly is being plotted in the middle and bottom rows. Is panel (g) supposed to tell use which run (base or opt) is better depending on if the point is blue or red? Please clarify and make a reference to this in the main text.
• Lines 571-572: “This suggests that the assimilation enhances large-scale spatial and seasonal variability”. I don't follow where this comes from, please clarify.
• Line 575: “show similar behavior” Does this mean similar to the comparison of MAN sites in Fig. 15 or to the LML observations mentioned in the previous sentence?
• Lines 578-590: Starting with the sentence “Additionally, to support … LETKF simulations.” seems a bit out of order. Combine these two paragraphs and move this sentence to the end of the paragraph as a conclusion sentence.
• Table 2: Maybe add horizontal lines to separate each base/optimized pair so that it is easier for the reader to compare the numbers between the base and optimized statistics for each case.

This manuscript is well written and clearly organized, with detailed and thorough discussion throughout. I provide a few additional suggestions and minor comments to help correct errors and improve consistency. I recommend this manuscript for publication.

Review Report:

Title: Improved constraints on ammonia emissions and deposition from co-assimilating NH3 and NO2 satellite observations over the Netherlands

Authors: Tyler Wizenberg, et al.

This study presents a robust data assimilation framework using the LETKF (Local Ensemble Transform Kalman Filter) to co-assimilate multi-sensor satellite observations (IASI, CrIS, TROPOMI) of NH3 and NO2 into the LOTOS-EUROS chemical transport model. By focusing on the 2018–2022 period over the Netherlands and German, the authors aim to refine the representation of reactive nitrogen dynamics.

The study compared spatial distribution of emissions, deposition, and concentration  between the baseline version and the optimized version. Then the study further validated the concentration fields against two distinct ground-based in-situ measurements networks: the LML, representing urban, suburban, and rural environments, and the MAN (Measuring Ammonia in Nature), which monitors ammonia in sensitive natural reserves. The results demonstrate a clear improvement in post-assimilation fields, characterized by reduced mean bias and enhanced spatial correlation. The use of two complementary surface networks (LML and MAN) provides a rigorous "ground-truth" assessment across diverse land-use types, from high-emission agricultural zones to protected natural areas. Integrating both NH3 and NO2 observations allows for a more holistic understanding of nitrogen deposition than single-species assimilation. The application of the LETKF framework over a multi-year period (2018–2022) ensures the findings are statistically significant and not influenced by single-year meteorological anomalies.

Critical Recommendations for Revision

While the manuscript is technically sound and well-written, I recommend the following adjustments to increase its impact.

I recommend add in the introduction about why the modeled region including Netherland and German is an area of interest to study. Why NH3 emission is important for Netherland?

Figure 2 shows that the summer emission peak is much lower than the spring peak, even after optimization. In contrast, Lieven Van Damme et al. (2022) reported more comparable peaks between spring and summer. Do you have any interpretation for the cause of the double peaks in the seasonal cycle?

For the remain discrepancy in the emissions, I was look for analysis like Figures B2 and B4, when reading this part of discussion. However, they appears quite late. These plots demonstrate the temporal performance of the optimized run against independent observations in the concentration field. I feel these figures worth to show in the main manuscript.

In addition, the legends for Figures B2 and B4 introduce two new terms. Does “LE Background Run” correspond to the “base run,” and does “Analysis” refer to the “optimized run”? Please clarify these definitions and ensure consistent terminology throughout.

Similarly, in Figure 7, the labels begin to use “background” and “analysis.” Please clarify these terms in the manuscript or revise them to maintain consistency.

Finally, maps of emissions by source type (e.g., agriculture, anthropogenic) would help illustrate the spatial distribution of agricultural fields versus anthropogenic sources.

Minor Revision.

Section 2.1.1 Page 4 line 108, you mention time step t_k-1 and t_k but in equation 2 only used k and k-1.

Section 2.1.2 How is the weight of the additional observations applied to observations for spatial localization?

Section 2.1.3 Page 6 line 166, you only mentioned “For years after 2019, the 2019 emission totals are used as a baseline but are adjusted dynamically according to meteorological conditions.” The analyzed simulation covers 2018 to 2022. What about the emission for 2018? Why is 2019 but not 2018 used emission as baseline?

Section 2.1.3 Page 7 line 176 please provide a full name of TNO.

Section 2.2.1 page 7 line 185 “The IASI instruments onboard the MetOp-A, -B, and -C satellites are in Sun-synchronous orbits, passing locations twice daily with Equator crossing times at 09:30 and 21:30 local time, and with a time difference of approximately 45 minutes between them (Clerbaux et al., 2009).” It is unclear what does it mean for “45 minutes between them”? Do you mean since there are three IASI instruments onboard, around each day and night overpass, there are three IASI observations with 45 minutes apart? So each day, there are 6 observations? Maybe explain clearly.

Section 2.2.1 Page 7 line 195, please add reference for ‘HRI’.

Section 2.2.2 page 8 line 219, suggestion give a short sentence about what is “a quality_flag of ≥3”

Section 2.2.3 Page 8 line 230 you mentioned “horizontal resolution of 1◦×1◦” and described footprint size for IASI and CrIS. Please also mention the TROPOMI footprint size and swath width here as well.

Is the VCD product used in this study?

Page 10, “The locations of the sites within the Netherlands are shown on a map in Figure 1.” I recommend move this sentence forward to right after Table 1 was mentioned.

Section 3.1, Page 12 line 323, please define “MACC inventory”.

Section 3.1 compares emissions from pre- and post-assimilation and called them base and optimized. While in section 3.5.2, you discussed assimilations with choice of combinations of satellites. Please clarify at the beginning of section 3.1 if optimized run refer to the co-assimulations with all three satellite.

Does the optimal update of emission in southern part show in Figure 2 attributable to certain source types we can located with the emission maps?

Page 14 line 343 “As seen in Figure 2, 2020 shows the most significant emissions changes, with particularly large increases in the emissions (on the order of +70%) in the LETKF-optimized simulation between April and September.” Figure 2 can’t provide evidence of where increase in the emission up to 70%, while Figure 3 indicate optimal emission higher than base from April to September but maximized at 70%. Do you mean Figure 3 here?

Section 3.2 Page 14 line 365 “… in 2020 and 2021 with differences of +10.4% and +9.6%,” I think here you mean “2020 and 2022”.

Section 3.4, what’s the max DOFS in ideal case for your assimilation setup?

Section 3.4, Page 17, line 417: “Regions with high observation coverage” refers to areas with good spatial coverage. Moreover, high sampling density is an additional key factor that enhances the observational constraint.

Page 17, line 427: The statement “a positive relationship is observed” between observation density and DOFS is not clearly supported by Figure 6(a) and (b). The figure does not convincingly demonstrate a direct positive relationship; rather, it only appears that the higher DOFS in 2020 may be primarily associated with increased observation counts in that year.

Figure 8, if I understand correctly, it is the averaging across all sites from Figure 7 so it reduced the points to 60.

Page 22 Line 491 “scale mismatc” should be “scale mismatch”? Please also give estimate of what resolution of the grid-cell does the LOTOS-EUROS model output represents.

Does the optimized model run in Section 3.5.2 refer to the co-assimilation of IASI, CrIS, and TROPOMI (NO₂)? If so, has the name of this run changed, or is my understanding incorrect? Please clarify and ensure consistent terminology.