General Assessment

This study presents a robust local-scale inversion of agricultural ammonia emissions on the island of Schiermonnikoog in the Netherlands. The authors combine a high-resolution chemistry transport model (LOTOS-EUROS) with a Bayesian inversion framework, incorporating observational constraints from the MAN passive sampling network and synthetic LML-like measurements. The work is timely and relevant, especially considering the national nitrogen crisis and the need for fine-scale emission estimates to support policy and conservation efforts.

The manuscript is well structured and technically sound. It makes contribution by highlighting the limitations of existing monitoring networks and proposing practical strategies for observational enhancement. However, several aspects, including the inversion method, format of the manuscript, interpretation of the inversion results, treatment of uncertainties, and clarity of figures, require major revision before the manuscript can be considered for publication in ACP.

Major Comments、

1. Manuscript Structure: The current organization resembles a technical report rather than a research paper, especially the introduction section, and please consolidate the abstract into a single continuous paragraph.
2. Inversion Methodology (Lines 185-195): Clarify how Jacobian matrix K_N= ∂y/∂x is approximated within the iterative Levenberg-Marquardt framework for solving Eq. (3). Given its computational intensity, explicitly state which finite differences methods are used to compute the Jacobian. Additionally, conclusion's claim that the method "assumes a linear relationship between emissions and concentrations" as this contradicts the nonlinearity inherently addressed through iterative K-updating.
3. The inversion indicates a 51% reduction in ammonia emissions from 2019 to 2022, compared to a 23% reduction based on activity data (GVE and livestock). While the authors briefly acknowledge that the inversion might overestimate the reduction, the manuscript lacks a detailed discussion of possible reasons behind this discrepancy. Recommendation: (1)Test the inversion’s sensitivity to prior emission uncertainties (e.g., varying the prior error covariance β ). (2) Discuss confounding factors (e.g., unaccounted meteorological influences, changes in farming practices beyond livestock numbers, or biases in the "Other" category).
4. Sections 3.1.1 and 3.1.2: The model consistently underestimates peak concentrations near sources (e.g., Meteo Groenglop), attributed to coarse resolution (1.7 km × 2.15 km). However, Schiermonnikoog’s emissions are concentrated in a 275-ha polder, likely smaller than the model grid. Recommendation: Conduct a sub-grid sensitivity test (e.g., nesting a higher-resolution domain over the polder) to assess resolution impacts.
5. Monthly Inversion Performance (Section 3.3): Monthly inversions fail due to high MAN uncertainties and sparse data. The proposed solution (adding one LML-like site) improves results (Fig. 10) but lacks validation against independent data.

Minor Comments

1. Section 2.4.1: Define how "external influences" (Groningen, Friesland, etc.) were selected for the state vector. Why not include Denmark?
2. Section 2.2: Briefly justify the use of CAMS-REG v5.1 (2019) for both 2019 and 2022 prior emissions despite known livestock reductions.
3. 8b: Explain why monthly posterior uncertainties are asymmetric (e.g., wider in spring).
4. 9b: Include the location of the proposed Kooiduinen site on the map.

Review of “Local-Scale Inversion of Agricultural Ammonia Emissions: A Case Study on Schiermonnikoog, the Netherlands” by Li et al.

Li et al. present an inversion for ammonia emissions in the Netherlands.  They use the LOTOS-EUROS model in a flux inversion.  They use a network of surface stations measuring ammonia with a focus on improving the representation of agricultural emissions.  They include both real and synthetic inversions.  It is clear that the authors have done a lot of work.  My may comments revolve around the overall framing of the problem and the analysis of the results.  Only 6% of the ammonia is local to the island they are studying.  Therefore, most of what they measure is transported from distant regions.  It’s not clear to me that an inversion using 6 sites on the island is really necessary since little of what they measure comes from the island.  It seems like we are probably learning more about the upwind sources, but the discussion focuses on Schiermonnikoog.

This ties into my later comments (below) about their recommendations.  The authors recommend an additional measurement site on the island.  It feels like additional measurements in the upwind region would likely provide more value.  In their recommendation for the additional site they seem to disregard their own analysis (Fig 9b).  They reject three potential sites suggested by their analysis.  It does not seem like the conclusions do not follow from their analysis.

Overall, I think the authors have done a lot of good work.  I think the authors should reconsider the conclusions they draw and ensure they are supported by their results.  I would recommend major revisions for the manuscript.

Comments

1) Is this the right tool? 

The authors mention in Section 3.1.2 and show in Figure 6 that emissions from Schiemonnikoog only contribute 6% of observed concentrations.  The study is motivated by high spatio-temporal variability in ammonia emissions, yet that does not seem to be the case here.  This site is dominated by transport.  It seems like we would learn more about ammonia emissions from additional measurements in the regions with much larger emissions.

I think the authors can address this through some additional discussion.  I.e., justifying why these measurements are still valuable and why this framework is needed to address their questions.

2) Optimizing the network

The authors set up a nice framework to identify the most useful site on the island to improve the inversion.  However they seemingly disregard all of the information from that analysis.  It was unclear to me why they go through the effort if they are going to throw out the three most promising sites.  Their text is copied below:

“Although Fig. 9(b) indicates that the most informative location would be directly at the island’s main emission source, near the Schiermonnikoog-Meteo Groenglop site, this location is not ideal in practice. As discussed in Sect. 3.1.1, this site shows the least agreement between model and observation, likely due to unresolved spatial heterogeneity between reality and model. Moreover, measurement close to the source can lead to a large bias in regional misrepresentation of ammonia concentration (Schulte et al., 2022). The next model-suggested site is Schiermonnikoog-Om de West, at the western edge of the island. However, this site consistently records the lowest ammonia concentrations and is strongly influenced by sea winds, making it less suitable for detecting local agricultural emissions. Another candidate is the Schiermonnikoog-Paardenwei site, located in the north. While the model indicates it as a potentially useful location, this site is surrounded by dense vegetation, which in reality limits its sensitivity to nearby agricultural sources (see Sect. 3.1.1)”

I understand that there are practical considerations that need to be taken into account, but the conclusions don’t seem to follow from the analysis.

A minor point regarding Figure 9a and the associated discussion.  The observation error will also represent the errors due to the model.  I.e., it is more aptly thought of as the “model-data mismatch”.  I mention this because I wonder what the authors would consider the model error for LOTOS-EUROS.

Improving the instrument precision will eventually be limited by the ability of the model to represent the measurements.  Therefore, part of the parameter space in Figure 9a will likely be limited by the model error.  This is something that is discussed in Turner et al. (2016; doi:10.5194/acp-16-13465-2016) for a pseudo-data study of urban CO₂ emissions.

3) Description of the inversion

There are some key details in the inversion that seem to be lacking.  For example, it was not clear from the methods section what the temporal resolution of the inversion was.  Are the authors solving for 5 parameters (single scaling factors for their regions)?  From Section 3.2, it seems like the authors have two setups: an annual inversion and a monthly inversion.  I am not entirely sure though.

As an aside, it would be helpful to indicate where some of their different regions are in the Netherlands.  I would suggest adding that to Figure 1 or Figure 2.  I am not familiar with the geography of the Netherlands and do not know the spatial extent of Groningen, Friesland, etc.  This would be very helpful for understanding the actual setup of their inversion and interpreting the results.

Boundaries: It was not clear to me what the domain of the inversion was.  What domain is being simulated and where are the boundaries.  How are the boundary conditions specified?

Jacobian: How was the the Jacobian constructed?  Do you recompute K at each iteration in the LM method?  Is K being constructed from perturbations?  If so, is this a one-sided, two-sided, how big is the perturbation, etc.

Prior error covariance matrix: the description of S_a seems to be missing.  How large are the uncertainties in S_a?  Are there off-diagonal error covariances in the monthly inversion?  The authors mention that the monthly inversion performs poorly, but this strikes me as odd because a monthly inversion with temporal error correlations should give something similar.

Observational error covariance matrix: I appreciate that the authors have tried to develop an S_o matrix that they think is a better representation of their network.  However, it seems that they neglect off-diagonal terms in S_o.  This may be fine for the monthly inversion, but I think it could be problematic for the annual inversion.  The authors show seasonal biases in the simulation of ammonia.  This seasonal bias will manifest itself as a correlated error in the annual inversion because the model has errors in the seasonality (S_o is the model-data mismatch, and there is an error in the model as mentioned in the previous comment).  I think a justification for neglecting off-diagonal errors is needed or a test using off-diagonal errors.

Meteorology: How good is the meteorology for this region?  Getting the PBL height correct is likely important.  Is this well-represented at the site?  Models often times have difficulty getting coastal areas, is this an issue for your island?  Given the large contribution of distant sources, getting the transport correct seems critical.  Assessment of the meteorology seems important for this application.

4) Inversion evaluation

They claim the monthly inversion produces “unrealistically high” values in the spring (Line 358), but how was this assessed?  Evaluation against independent observations or k-fold cross validation are two common approaches for evaluating inversions, but it does not seem like the authors have done that.

5) Inversion discussion

The entirety of the discussion of the real inversion is half a page.  It seems odd to spend 17 pages discussing work and methods to estimate emissions of ammonia and then only discuss the results for half a page.

Specific comments

Abstract: Why is it broken into 4 short paragraphs?  The whole abstract is 10 sentences, why is it broken into 4 paragraphs?  Standard practice would typically be to have one paragraph.  Also a lot of superfluous intro.  Nearly half is intro/background (4/10 sentences).

Figure 1: How big is this island?  Some sort of scale would be important

Line 145: How many grid cells?  Maybe add to table 1

Line 175: Related, how is x defined?  Is it each pixel, time-dependent, etc?  Ah, see its defined on Line 208, would be good to explicitly state in a table somewhere or make sure its apparent.  Is it time-dependent or are you assuming temporally constant?

Lines 235+: I’m confused why they add to S_o.  If anything, having off-diagonal correlations in So would be more appropriate because the model could easily introduce correlated errors due to transport, the PBL, etc

Table 2 and Figs 4+: are these using the prior?  It’s a bit confusing because you describe the inversion and then start talking about the model performance but not clear if its prior or posterior.  It would be helpful to clarify that in the figure captions.