I found the paper highly interesting and well researched. I would only put forward to minor comments: 

1) In line 123, Gunnlaugsson and Rafnsson should be put within brackets, otherwise it sounds like they are the officials in question. 

2) Why is the article by Casey et al. from 2019 not cited? (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6456407/). This is not my field, but it looks like you might want to include it in the discussion. 

The authors pursue in their incredibly compelling paper the question what the cause was of human mortality in Iceland after the Laki eruption of 1783. In a very well-structured manner, they present the socio-economic situation of Iceland and the environmental impact of the eruption, followed by a data and method section. In their analysis part they look at the mortality data and later on how hunger and disease alone may explain the excess mortality in Iceland. After a short excursion about the impacts on the European mortality rate, they discuss the possibility of human death due to air pollution. In the final section they asses the possibility of wide-spread lethal fluorosis in humans, finishing with a concise summary.

The paper does address relevant scientific questions within the scope of NHESS as it examines previous research claims from the 1970s on about the contribution of fluorine poisoning towards human mortality after a natural hazard such as the Laki eruption of 1783.

Though the tools presented in the paper are well-established, it presents a vast amount of new data on Icelandic mortality for the late 18^th century. The historic data is presented up to international standards and the sources have interpreted and criticised according to historiography. The scientific methods and assumptions are outlined clearly and very extensively. The results support absolutely the interpretations, and the authors disprove fairly conclusively the mentioned previous research. All the results can be reproduced thank to the thorough explanation of the methodology, where the used functions are clearly defined, and due to the concretisation of the used data in the supplement.

The title of the paper clearly defines the content of the paper, i.e. what did the people die of after the Laki eruption of 1783, except for the that it doesn’t mention it mainly concerns the geographical region of Iceland. This could be added in the title. The abstract is a complete and concise summary of the research presented in the paper. Both – title and abstract – are targeted to a broad audience, especially working in an interdisciplinary field.

There are a few points to be said concerning some figures and their captions. In general, the figures are adequately used to facilitate and enrich the lecture of the paper. However, caption of two figures (Fig. 2 and Fig. 4) goes over the page numbers of pages nine (9) and thirteen (13).

Figures 1), 2a), 2b), 2c) and 5a) have identical issues. Too much information is presented in a single graphic. The numbers of each region could be presented as a separate graphic or a table. For the same images the resolution is subpar and could be enhanced. This would allow the preexisting graphs to show the full county titles, whereas for now the abbreviations are sometimes hard to detect.

In Figure 3 there is a mistake in the caption: In row 2, where it says “a value of 5 in December 1785 means that from January 1st 1783 till December 31st 1783”, it should be called “a value of 5 in December 1785 means that from January 1st 1785 till December 31st 1785”

The authors quite clearly give credit to previous work. This is done very precisely in the section where the problem of the previous research is presented. Another good example is the section where the mortality outside of Iceland is discussed by reference to research done by others. The number and quality of references are appropriate. There is no place where complementary references would be required. They are accessible to all scientists.

Whereas the overall presentation is very well structured, and the reader is guided towards the conclusions throughline, section 8 about fluorine poisoning might require some more specialized background knowledge to assess the final conclusions. Introduction and summary are supremely well and concisely written. A few other sections contain rather an extensive amount of information. Some part of the methodology section in 3.1. and 3.2 could be shortened and the still crucial but supplementary information could be placed into the annexe. Similarly, towards the end of the paper the methodology section in 8.2 could be pruned slightly and additional information be put likewise in the supplement.

The technical language is precise and understandable for sicentists from different fields. The English language is of high quality and presentable for a diversified audience.

The supplementary material serves deeper understanding and allows the repetition of research especially thanks to vast dictionary of Icelandic terminology.

Further notes:

Section 1 Line 41-50:

Concerning the eruption’s climate impact: Just because it is probabilistic that doesn’t mean it shouldn’t be considered. However, given their focus on mortality statistics not studying climate impact does not detract from the author’s conclusions.

Section 4.1 Line 203:

Concerning the small Pox epidemic unrelated to Laki: Question: Doesn’t hunger or lack of nutrition and migrating population, which the authors relate to Laki, worsen a smallpox epidemic?

Section 4.2 Line 274-275:

Concerning orthography: “were” is repeated

Section 6.1 Line 400:

Concerning orthography: “hey” should be “hay”

General comments

This paper by Wieners and Hálfdanarson is an excellent review and re-assessment of the causes of mortality in Iceland and Europe during and following the 1783-84 Laki fissures eruption. The analytical methods are thorough, robust and replicable. The findings are compelling and thoroughly explored. The paper is well written and structured, overall. I strongly recommend the paper to be published in NHESS after some minor corrections which are listed below.

Specific Comments

Of the corrections, the most important are:

• Consistently, the figures are of poor resolution and are hard to read. This especially applies to the maps which are especially challenging. I would strongly suggest that the authors remove all of the ‘columned’ numbers from the maps. It seems that most of these data are given anyway in the supplementary material. The reader cannot take in this level of information and it would be better for the maps to be used to clearly demonstrate the key points of the figures rather than trying to cram multiple parameters onto one map. The colour shading (blue to brown) is also not intuitive in terms of immediately understanding which means lower/higher values. Please also use a single font (ideally sans serif) and the key should not overlap with the map. See further detail in the list of comments, below.
• There are parts of the text which start to feel repetitive and are too detailed, particularly in relation to fishing/livestock ownership (see Section 5). Perhaps some of the detail could be moved to Supplementary Material as the ‘story’ is still compelling without it.

Technical corrections

• Add subscripts to molecular formulas like H₂SO₄ and SO₂ throughout the manuscript.
• Line 63 – ‘handled poor relief’ – what does this mean? Rephrase so that it is more intuitive.
• Line 64 – missing a bracket before ‘fig. 1a)’?
• Figure 1 is hard to read with so much text. My suggestion is to turn these two maps into two separate figures so that they can be larger. I don’t understand the key for Figure 1b at all (on the map, not the figure caption). It’s not clear what the colours in the pie charts mean and I can’t see the left and right columns that are referred to – I think it refers to the numbers but unclear. What are the colours on the map? Presumably they relate to the bar at the bottom right but what is that bar for? What is ‘national mean’? All of this is somewhat described in the caption but the map is overly crowded and hard to understand. It’s still not clear from the caption which colours in the pie charts refer to which level of fishing access. Even with explanation, the columned numbers are messy and do we really need this much information? Given that the info is already in the Supplementary Material, it does not need to be replicated here. Unless critical to the argument, I would remove Figure 1b or massively simplify it. Finally, it’s not clear to me why the county/regional names are different in the two maps. It is incredibly confusing and makes it hard to then follow the names in the paper.
• Line 96 – replace the word ‘subsidence’ with ‘gravitational settling and wind circulation’.
• Line 102 – was (fine) ash only produced in explosive episodes? Coarser ash would also have been produced by lava fountaining and might then have been abraded to finer ash by the wind. But the coarser ash would also have carried fluorine and would have been dispersed over much of Iceland in strong winds and when lava fountaining was at high effusion rates.
• Line 106 – it is not clear if the 450 mg/m2 refers to the mass of ash deposited on average or the mass of fluorine (I think the latter but this only became clear later in the paper). It’s also not clear why your figure is 450 mg/m2 when Thordarson and Self calculated 500 mg/(k)m2.
• Table 1 – what are the data in parentheses?
• Figure 2, Figure 5 – again, the numbers are not helpful on these figures. The maps are hard to read and messy. The text is too small to read.
• Line 274/5 – repeat of the word ‘were’.
• Line 293 – ‘Mortality in whole Iceland’ doesn’t make sense. The whole of Iceland? Same in Fig 4 caption.
• Figure 4 would be easier to interpret if the y axis were the same scale for a-i graphs. Fig 4j – I presume that the colours in graph j are the same key as graphs a-k but this isn’t explained in the caption.
• Line 308 – ‘the mort’ should say most.
• Line 376 – from here on there are mentions of ‘fugitives’. What is meant by this term? Usually it would mean a person who has escaped from captivity/prison/arrest. Is that the case here? Why were they captive? Do you just mean displaced people?
• Line 390 – what is ‘burthen’? Burden?
• Line 400 – ‘hey’ should say ‘hay’
• Especially because Figure1 is hard to read, it is really hard to follow the paper with all the mentions of locations. It would be much easier if these county/regional names came with ‘signposting’ as to their geographic location. This is sometimes done (e.g. mention of southwest regions) but not always.
• Overall section 5 feels repetitive of earlier information; the text becomes too detailed and rather confusing. The final summary paragraph of this section is excellent though – could the whole thing be shortened into a slightly longer summary?
• Line 493 and elsewhere - Lava ‘streams’ is not a commonly used term. Consider replacing with lava flows if this is what you mean.
• Line 496 – remove ‘health’ from ‘health volcanic pollution’
• Line 498 – ‘mortality Grattan et al’ missing punctuation or parentheses of some kind.
• Line 504 – Wakisaka et al. paper – are you sure this paper just looked at SO2 and aerosol? It’s impossible to separate these exposures from volcanic ash exposures which are the primary emissions from Sakurajima volcano.
• Line 561 – remove the rogue bracket after ‘mature’.
• Line 569 – ‘on 2004’ I think this should be ‘in 2004’.
• Table 3a – it is not clear in the table or caption that you are citing country regulations. It would be much better to cite the country authorities (e.g., US EPA) which have the least and most ‘strict’ guidelines rather than citing IVHHN as the source.
• Table 3, in general – I do not think that these sub-tables qualify as being labelled, together, as Table 3. They are separate and should be separately numbered.
• Table 3c – ‘IVHHN: Volcanic aerosol mostly in PM2.5 range, thus PM2.5=TSM.’ This is not correct – most of the PM from Sakurajima is volcanic ash so is larger than PM2.5. Additionally, see Horwell 2007 for comparison of PM10 and PM2.5 ratios for volcanic ash. https://pubs.rsc.org/en/content/articlelanding/2007/em/b710583p and Hillman et al. for an analysis of Sakurajima ash: https://doi.org/10.1007/s00445-012-0575-3
• Line 507 – replace the word ‘chapter’ with ‘section’.
• Line 686 – should there be ‘(?)’ in the text?
• References - Stewart et al. (x2) – please list all co-authors of these papers.
• There are also several other papers by Grattan’s group such as Grattan 1998 and Grattan & Pyatt 1999 which could be relevant to your analysis. Please also see Courtillot 2005.