Thank-you for your revised manuscript. Both reviewers asked for “major revisions” and expect to see it again. There follow here some suggestions or corrections of mine, to consider first please before I send it to the reviewers.

Page 2
Line 25. Better “. . data in nature and in wave channels . .”?
Line 33. Better “This paper . .”
Lines 39 and 48. What is the difference between “wave height above mean level . . h” and “surface height above mean level (η)”? See also page 3 line 2 and equation (3). If there is a difference, please explain clearly. If no difference, please use the same symbol everywhere (this was Referee 1 question).

Page 3
Lines 15-16. Better “. . (number of points in a single field multiplied by number of records in experiment multiplied by number of experiments). . .”
In equation (3), Ptilda could in principle be a probability of something independent of Hs and therefore a factor outside the integral. Then P(h) = Ptilda and ∫P(Hs)d Hs = 1. So I think P(Hs) is a probability distribution and hence:
Lines 19-20. Better “The probability of a wave exceeding a specific height h, if significant wave height is in a small range dHs around Hs, equals . . . multiplied by probability of significant wave height in this range (Ptilda(Htilda) ∙ P(Hs) dHs), by the standard definition . .”
Line 25. Better “where P(Hs) is the probability distribution of Hs for a specific point, . .”

Page 4 line 6. Better “. . found in areas of active navigation . .”

Page 6 line 5. Better “. . 60 degrees S. is characterised by probability > 10-7 of wave heights . .”

Page 7
Line 15. Better “. . monthly fields of cumulative wave-height probability”
Line 17. Omit “initial”. [Could be “chosen threshold” or something similar].
Line 18. Better “. . outside the range of validity for equation (2)”
Line 20. As referee 2 comment, if you mention “certain practical importance” you should give some example(s).
Line 21. “more” implies a comparison – with what? [Please state what or delete “more”.] Please quantify “minor”.

Dear Kirill Bulgakov
Thank-you again for your revised manuscript. Both original referees said they were willing to look at it again after “major revision” but only one has responded. Most of their comments are copied below but they are far from satisfied and do not want to see the manuscript again. In these circumstances I am adding some “Editor comments” of my own to reinforce some of both referees’ comments. I think major revision is still required, especially of section 2 (see below). Really then I should call on referees again, but this would mean new referees and “double jeopardy”. You might think it as well to withdraw this manuscript and start again with a new submission. Please note that any eventual publication will be accompanied by all comments, so that readers will be able to judge whether comments have been addressed satisfactorily.
Yours sincerely
John Huthnance

Referee comments on revised version.
< Page 1 – Abstract. Please add citation to “Chalikov and Bulgakov (2017)” (if this is the method the authors are describing and using). Please specify that long-term data are model data. Please add that you are applying the method to calculate the estimation of height of extreme waves of any given probability. Please add a short summary of your results and highlight their relevance.
Page 1 – Line 39 to Page 2 – Line 34: Probably this can be shorter, while it should be added what is(are) the state-of-art method(s) to estimate extreme waves? i.e. if this study is important for designing of engineering constructions or offshore activities in general, what is the method usually used to have an estimate of extreme waves nowadays? Max/average significant wave height or nothing? It would be good to compare with state-of-the-art estimates and to add at least a sentence in the conclusions to highlight why the proposed method is better.
Page 1 – Line 37: “M” change to “m”
Page 1 - Lines 37-38: “data are not enough to evaluate” change to “does not give information about”
[Editor comment. I think it would be better to change line 34 “does not provide any information on” to “is not enough to evaluate”]
Page 2 – Line 19: “no nonlinear” change to “linear”
Page 2 – Line 40: Please move here Page 3 Line 29-33
Page 2 – Line 48: “Each” change to “each”
Page 3 – Line 29: “data” change to “model data”
Page 3 – Line 33: reference needed, are the results of the validation good?
Page 3 – Line 35-36: “method 2-3” change to “Chalikov and Bulgakov (2017) method”, if this is correct. If the application of method 2-3 “for the estimation of height of extreme waves of any given cumulative probability” is the addition of this paper to the state-of-the-art, then it needs a bit more emphasis.
Page 4 – Figure 2: Would it be possible to add a panel with the maximum annual significant wave height? How does it compare with the probability distribution?
Page 4 – Line 11 & Page5 Lines 7-8: “calculated by data” change to “provided by the model”.
Page 5 – Line 8: remove ].
Page 7 – Line 19-20: If 10-9 corresponds to P(1.85), then to what does 10-7 correspond? Maybe this can help to explain why 10-7 has certain practical importance, otherwise a reference should be added to support the “practical importance”.
Page 7 – Line 29: “other purposes” is too vague.>>

Additional Editor comments.
Line 34. “does not provide any information” is too strong.
Lines 35-37. The point you want to make (lines 34, 37-8) is that the same Hs can give different extreme values. So you need two examples with the same Hs but different extreme wave height.

Page 1 line 39 to page 2 line 10. This is quite a lot of discussion which is not much related to what you do in this manuscript. Could be less? (c.f. referee comment)

Page 2 lines 11-23. Since in the end your manuscript is about wave height above mean sea level, there could be less here about trough-to-crest height. However, you might have more discussion somewhere about what applications want wave height above mean sea level (e.g. fixed platforms?) and which want trough-to-crest height (e.g. ships and tethered platforms?).

Page 2 lines 24-32. Please make clear whether this paragraph is about wave height above mean sea level or about trough-to-crest height; which?

Section 2. I think this needs re-writing and suggest you start with equation (3) including definition of the terms in (3) to give an overview of the calculations. Then you need to say how P~ and P(Hs) are obtained. Please also specify what is not already done in Chalikov and Bulgakov, 2017.

Page 2 line 41. Please explain “potential” waves.

Page 2 line 46. Does the initial JONSWAP spectrum affect the results? This is relevant to the other referee’s question about the limitations of formula (2).

Page 3 line 14. Does this mean that the maximum H~ anywhere in all 50 model runs was 1.85? “data” is too vague.

Page 3 line 19 refers to wind wave fields. But was wind applied in the model runs giving (2)? If “yes”, what wind? If “no”, how relevant is (2) for wind-forced conditions? This is relevant to the other referee’s question about the limitations of formula (2).

Page 3 line 20. “. . (swells) . . don’t influence extreme wave generation.” I disagree. Convergent long-wave currents can steepen shorter waves.

Page 3 line 29. I guess this should read “The model Hs data (Chawla et al., 2013) used for P(Hs) were calculated . .” The reader should not have to guess what you are referring to. I think the referee is saying that lines 29-33 here should be joined up with page 2 line 40.

Page 4 lines 13-14. To correspond to figure 2 this should read “. . As seen, the mean value . . does not exceed 5 m anywhere, while . .”. [You do not show any “maximum” Hs or even Hs when and where wave heights are extreme (cumulative probability 10**-7).]

Page 5 lines 7-8. Data do not calculate wave height nor do Chawla et al. 2013 according to section 2. Do you mean the field of wave height calculated as in section 2 via equation (3)?

Page 5 line 13. Better “. . less in the Northern Hemisphere winter, compared . .”

Page 7 lines 17-22. This could be part of a “Discussion” section.

“Conclusions” The first and last sentences are summary very much like the abstract. Only the middle sentence is a conclusion.

Thank-you for your revised manuscript. I still intend to seek another reviewer opinion since no reviewer has yet recommended less than major revision. However, before that there are some minor revisions that I would like to see.

Apart from matters of clarity, there is still some need for more discussion in my opinion, especially about how widely applicable are the results here. Any paper should have a discussion section for this purpose. A referee’s question about the significance of the JONSWAP spectrum as the initial condition still needs answering (you could look at how much the spectrum changes during the Chalikov and Bulgakov 2017 70,000 time steps). Might model resolution affect the relation between extremes and Hs? The calculations have wind energy input = dissipation; might the relation be different in a growing or decaying sea? What return period does 10-7 correspond to?

Detailed / specific comments (mainly for clarity, NB powers of 10 will not show as superscripts here).

Page 2
Line 21. Better “. . data considering that an extreme wave is a wave”
Lines 23-24. I do not understand “frequencies more then 2.5 10-5 Hz” in this context. All your waves have much higher frequency. Also should be “. . than 2.5 x 10-5” and “-5” should be superscript.
Lines 29-30. Better “(Chalikov and Bulgakov, 2017) compared with methods mentioned above is that Chalikov and Bulgakov (2017) is based . .”

Page 3
Line 9. Better “. . potential (irrotational) flow (the curl”. The expression is “potential flow”. “Potential” applies to the flow (pattern) NOT to the fluid or waves.
Lines 14-16. See comment above about discussion.
Line 21. “potential” -> “irrotational”
Line 31. Better “. . (the maximal value of Ȟ in all 50 experiments for (3)) . .”?
Line 36. “. . (number of points in single field multiplied by number of records in”
Line 39. Delete “on”
Line 40. Long-wave currents can steepen (or flatten) shorter waves according to the laws of physics. Physics applies always, not rarely!

Page 3 last two lines and page 4 first three lines. I think better “The spatial distribution of extreme wave probability was investigated, based on (3) from Chalikov and Bulgakov (2017) together with the spatial distribution of Hs from Chawla et al. (2013). We show global fields of wave height with cumulative probability 10-7 so calculated."

Page 5 line 4. Better “. . provided by a model (Chawla et al. 2013) is shown in Fig. 2. . .”

Page 6 top line. “-7” should be superscript.

Page 8
Lines 14-15. Better “. . based on (i) long wave-model runs for its relation to significant wave height (Chalikov and Bulgakov 2017) and (ii) Hs spatial distribution from a 16-year hindcast (Chawla et al. (2013).”?
Lines 17-18. Better “. . constructions. The approach here can be used to evaluate the height of waves . .”?
Line 20. Better “. . probability (10-7) for the main seasons illustrate the approach.”?

Dear Authors
I have received the last reviewer comments, recommending minor revision mainly relating to English usage. I converted your .pdf manuscript text to Word, edited it using "Track Changes" and converted it back to .pdf as the system requires. The figures and the content of equations (1) to (3) are missing but I am not suggesting any changes to those. I could not find your notation for cumulative probability and have used P~, H~ instead. But I hope that anyway you can find your way through my .pdf. Please check carefully that it says what you intend; I may have misinterpreted your manuscript and have probably made some mistakes. I think it best that I see your updated version.
Yours sincerely
John Huthnance

Thank-you for your revisions. I now have a very few "Technical Corrections" and one query (see "Comments" below). Then your final version should go direct to the Copernicus publication system with no further involvement by myself.
Thank-you for publishing in Ocean Science.
Yours sincerely
John Huthnance

Comments.
Page 2 lines 5, 21. "trough" (spelling)

Page 2 line 39. In "dHs" the "s" should be subscript.

Page 3 lines 39-40. This sentence "In these paper . . . considered." still puzzles me. Is it necessary? At least it needs correction. "In this paper" if you are referring to your own; "In these papers" if you are referring to Chalikov and Bulgakov (2017) and Chawla et al. (2013). "another approach" is really puzzling because you do not say what other approach. My best guess is that you might mean "In this paper results of an application of this method are considered."

Page 6 line7. ". . in spring, wave-height values . ."

Page 7 line 15. Not "peculiarities" which would not be "obviously connected" in the next line. Maybe "particularities" was intended but I think "features" would be easier English.