Review of Rubin et al., submitted to EGUsphere.

Gobal nitrogen and sulfur budgets using a measurement model fusion approach

This paper aims to make an improved estimate of global total nitrogen and sulfur deposition by fusion of measured and modelled wet and dry deposition. MMF is a powerful method for vastly improving budget of N and S in the atmosphere, and for estimating exposure to ecosystems of deposition. Thus, a paper on the subject, showing the power of the method is very much appreciated.

The manuscript is well written, however, the methods as explained have weaknesses and the final results of the MMF show too weak influence of the observations. The comparison to observations shows too large deviation and it is not clear if it is made with independent observations.

Thus, there is need for improvements to the methods before the manuscript can be accepted for publishing.

The causes for major revision are

1. In this work, observed wet deposition is fused with modelled wet deposition. The more common method is to fuse the concentration in precipitation, not wet deposition in itself. Precipiation and wet depositon has a larger variation in space compared to concentration in precipitation. Fusing the latter would allow for a longer length-scale in the fusion. Precipitation should be applied after the fusion of concentration in precipitation.
2. Here the grid resolution (1 degree) was used as maximum length-scale, which is very short (too short) and will cause for in principle only one or a few grid boxes to be influenced by the observation. There was no scientific explanation to the choice of this length-scale, which can be considered too short. The fusion method explained here, was rather used to estimate the observation error within the gridbox, but is that really how it should be done? Is the observation error dependent on the distans of the observation to the middle of the grid box? (answer is NO). The grid centre in the model is not the actual centre but an average of the whole grid.
3. The final product shows very little influence from the observations, which is not reasonable to my experience, and a result from the erroneous method. The figures show that the MMM (pure model) and MMF are very similar also in places with dense observations, and the MMF has a large deviation to observations (see e.g. the bias in deposition in China and US). 
4. The comparison to observations is not clear whether it is by independent or dependent observations, but in whichever case the comparison shows also too weak influence from the observations in the MMF product. It is strange that even in the specific grid box of the observations, the MMF deviate very much to the observed deposition.

For these reasons I recommend that the authors revisit their methods, to improve the MMF results before resubmitting.

For the updated manuscript please also note the following  suggestions:

Row 112-116. I suggest not to include datasets in the manuscript that are only promising. There are likely many promising national datasets in the global arena that potentially could be used, and to include all that are not used will be a paper in itself.

Row 136: title: please state MMF procedure

Row 165-166: change to “… include measurements from Asia, Europe and North America, and the dry deposition MMF surface includes measurements from the USA and Asia, …”. Explanation: many parts of the world are not covered for wet deposition either. The phrasing was now overenthusiastic about the coverage of wet deposition observations.

Table 1. row open oceans has values in “non-coastal” but not in “coastal”. This does not seem correct to me, it should be the other way around. Are the columns mixed up?

Figures: in general – please label panels a-f etc, it is easier to understand the description if all panels are referred to and labelled.

Global distribution of sulfur and nitrogen deposition is of great concern for atmospheric chemistry studies. Affected by precursor emissions and meteorological condition, the deposition varied greatly in different regions over the world, resulting in various ecological impacts. It is thus important to improve the understanding of deposition level and its spatial distribution and at the global scale. This manuscript applied a Measurement-Model Fusion Approach, to improve the estimates of global sulfur and nitrogen deposition for 2010. It incorporated available data from site measurement and chemistry transport modeling, and adjusted the total amount of deposition and spatial distribution. In general the manuscript provided quite useful information on relevant topic, and was organized and written clearly. As a scientific paper instead of data report, however, I have some concerns that need to be further stressed or clarified. Those mainly include the motivation, scientific findings and result evaluation. Details follow.

1. First of all, I feel the scientific motivation should be better stressed in the Introduction. What is the main purpose of the study? It should be clearly stated. Developing a new method for data fusion, or improving the estimation of global deposition (how to prove it then), or something else?
2. Similarly, could the authors justify their main findings (e.g., the changed estimation of total deposition?) How to demonstrate the numbers were more reasonable compared to existing ones?
3. Lines 97-100. I can understand that most of dry deposition were obtained based on this method. I am wondering, however, is it possible to collect some dry deposition data from direct observation instead of the inferential method. The latter actually bears some uncertainty from modeled dry deposition velocity.
4. The procedure part. It is unclear to me whether the authors applied the same IDW method as before, or they made some improvement on the methodology? More importantly, I feel an evaluation on the datasets should be made before conducting the data fusion. For example, how were the observation data compared with simulation applied in this study? Moreover, if there was big difference between observation and simulation, is it still reasonable to apply the current data fusion method?
5. Lines 202-203 (Figure 4). It is quite hard to read “higher observation in Asia are also better reproduced with MMF”. Could some quantitative numbers be given?
6. Similarly, lines 226-229. The analysis for the figures are quite descriptive and simple. Can you make more careful comparison and suggest the performance of the three modeling work compared to available measurements?
7. Figure 6. Why compare wet NH4+ only? It is necessary to provide the comparison for all the species and to make a judgment on data fusion quality.
8. Line 233-234. Does that mean TDep performed better than this work or the database was more reliable? Then what is the necessity of current work? Should think it over.

Minor issues:

The title could be quite confusing. “Budget ” might not be a proper word as current paper just focused on the deposition.

There is no need to repeat the reference when it is included in a sentence.

Figure 3: The x-axis and y-axis should be clearly labeled.

The language should be improved. Some clauses were not well organized.

General comment

The manuscript of egusphere-2022-873 presented the approach of MMF for global nitrogen and sulfur deposition. I will recognize this is important research to constrain depositions through fusion with measurements. However, my critical concern is how can we reinforce the usefulness of MMF. It will be a difficult and cumbersome task but independent evaluation by other measurements seems to be needed. Please address the following major concerns and specific comments.

Major concerns

• Independent evaluation: We find many statements of MMM status by HTAP2 within this manuscript; however, the independent evaluation supported by other measurements can increase the persuasion of this MMF result. I agree that MMF will be better in theory but we do not lead the proof that “MMF does give better deposition estimates by incorporating in-situ measurements” (P14, L262-263) without independent validations.
• The largest change over the ocean: I can follow that one of the reasons for coarse grid resolution will lead to the largest changes over oceans as listed in Table 1. However, because this was not helped by the observational fact (e.g., ship-borne measurements), how can we interpret this MMF result? Is it possible to only focus on the grid where the observation was available within the 1 by 1 grid in Table 1?

Specific comments

• P2, L18-19 (Abstract): Why sulfur trends were not stated? Moreover, according to my major concerns, please rewrite this abstract. It should be clarified the validation of this MMF result.
• P2, L45: It is ambiguous what “it” indicates. Is it ambient concentration or dry deposition?
• P3, L55: No need for the repetition of EANET.
• P4, L78-79: I noticed Tan et al.’s paper is updated recently (http://dx.doi.org/10.1016/j.scitotenv.2022.158007). What are the differences between this update and this study?
• P4, L86-88: This sentence is the result and is not appropriate to be stated in this introduction section.
• P4, L89: How about preparing table summarization for these available datasets? It will be kind to wide readers.
• P6, L137: It is one of an approach to use wet deposition itself, but their elements (concentration in precipitation and precipitation amount) could be the target of MMF. I can see some relevant discussion in Section 5, but for example, the project of MICS-Asia used the fusion for monthly-accumulated precipitation (https://doi.org/10.5194/acp-21-8709-2021). It will be better for readers why wet deposition is targeted as MMF in this study.
• P8, L183 (Table 1): It is kind to provide the region map for this analysis as a supplemental figure.
• P9, L189 (Figure 2): How about presenting the difference between MMF and MMM to clarify the difference driven by data fusion in this study? This result will clarify the impact of MMF compared to MMM, and can help to understand the result listed in Table 1.
• P10, L202 (Figure 3): But MMF used EMEP dataset itself, so this kind of comparison seems to be meaningless.
• P10, L202-203: I do not follow this sentence for East Asia. From this figure, MMF still underestimated the observational values.
• P12, L226-229: Within this context, TDep is regarded as truth?
• P12, L230: Why NH4 is only presented? In addition, because MMF uses NADP dataset itself, what is the meaning of this kind of evaluation?

Technical corrections

• P7, L169: In this figure 1, “concentration in precipitation” multiplied by “precipitation” should be “wet deposition”? Please confirm this illustration.