Dear Authors
Thank-you for your revised manuscript. In due course I shall be sending it back to both referees who asked to see it again after “major revision”. However, there are a few things which I would ask you to consider before that.

You have responded to (both) referees’ question about using SST rather than other variables (e.g. wind, runoff, tide-gauge records). However, I think that a few sentences on this question should be included in the final manuscript so that it is “self-contained” and eventual readers do not have to search the discussion to find answers.
I also wonder whether referee 1 will be happy with the large number of remaining abbreviations.

Here are a few more editorial-type details.
Page 3 lines 16-17. This sentence about the number of early tide gauges is not clear; are you saying that the first was in 1930 and this was the only one until 1950?
Page 3 line 19. Better “. . is proposing for the KP a new scheme . .”
Page 6 line after (4). “. . and the ε is random error. . .”
Page 8 line 2 Not “boundary”. Maybe simply “. . two years maximum lag. Using . .”
Page 8 line 27. Omit “of the linear trend”?
Page 8 line 29 “separate” (spelling)
Page 9 lines 10-11. “five TGs showed acceptable accuracies”. This seems to assume that all error is attributable to TGs. But the TG provide real and important data in the right place. It is the AVISO data that is in the wrong place.
Page 9 line 30 What are the “Six” reconstructions – please say clearly what they are.
Page 9 line 32. “. . there were only a few . .”
Page 10 lines 19-24 (Monte-Carlo) This is much the same as page 8 lines 5-9 except including sea-level trend. Probably these lines could be merged in one place.

Figure 2 caption. “gauge” (spelling, twice)
Figure 3, 4, 5, 7, 8, 15 captions. Replace “w/o” – “without”?
Figure 9 caption. “Cumulative variance of CSEOF modes . .”

Dear Authors
Thank-you again for your revisions. Both referees have now reported and for you convenience I include their comments below. Referee 1 would like to see the manuscript again after “major revisions” but I urge you please to take account of both sets of comments. I think what they want is clear and largely reasonable – and should not cause you too much difficulty.
Yours sincerely
John Huthnance

Referee 1
Cheon et al. “Reconstruction of sea level around the Korean Peninsula using cyclostationary empirical orthogonal function”

I appreciate that the authors have addressed my previous questions and concerns. But I really don’t see much improvements in presenting their new methodology and findings except that the quality of the figures have been improved much.

On the other hand, I do feel that the manuscript could contribute to the OS in understanding SL changes and SL reconstruction. Therefore I strongly suggest the Editor request the authors to revise the manuscript in focusing on their new method and reconstructed SL comparison. e.g. why your results are better than Hamlington even TG is not used in your reconstruction.

I recommend the Editor accept the manuscript after a major revision.

The manuscript developed a new method in a regional sea level (SL) reconstruction using CSEOF and its multi-regression between SL and SST PCTs. The reconstruction is extended back to 1900 while sparse TG observations are not included. The reconstructed SL is better than a similar SL reconstruction in comparison with TG observations.

Major comments
(a) I think there are too many figures for such a short manuscript. I suggest author considering delete Figures 3, 4, 9, 12, and 13. These figures do not provide much information and distract readers from your major findings and conclusions. In Figure 14, I suggest to delete the line “This study vs Hamlington”, which does not provide any information since you cannot use Hamlington as a reference. In Figure 15b, “this study” and Hamlington is hard to see. I suggest a dotted line in one of them, or apply a 3-12 month running mean filter. In Figure 16, I suggest replace the black color of the boxes in “this study” and Hamlington by blue and yellow so that the figure is more readable. I don’t see the reason why authors add Figure 16c without discussing it in the text.

(b) Writing needs improving.

Detailed comments (P=page, L=line)
P1L6, sea => seas?
P1L12, “ the reconstructed sea level in KP region has a better agreement with the tide gauge observations than previous…”
P1L16, it reads like there is no global impact. please consider revising.
P2L4, delete “even”?
P2L5, the KP region => the seas around the KP region or KP coastal regions
P2L16, accuracy of SLP reconstruction
P4L11, The mean values between what time periods?
P7L16, why to use square root of cosine, not cosine?
P7L18, lagged correlation?
P7L23-25, authors may want to extend their descriptions why GMSL is removed first and then random GMSL is added. What is the magnitude of random GMSL?
P7L3, what is 2-norm?
P8L14, “mean correlation”. I think the result is fine if there is no teleconnections within the seas around KP, but may have problem if teleconnection is strong. I suggest to calculate the averaged correlation within the domain of defined small scale (say 100-200km?)
P8L28-29, add the number of trend for AVISO (3.1mm/yr?)
P8L29-30, AVISO may have biases too.
P9L3, Change the order of Figures 10 and 9.
P9L9, I cannot agree that the first mode of 60% variance is less important. If the authors’ major focus is on the trends, the seasonal cycle should have been filtered out at the first place.
P9L33-34, Move the citation of Fig. 15 to the previous sentence?
P10L4, authors may want to address why Hamlington (2011) deviate more from TG.
P10L14-15, it looks a duplication with previous description in variance in L11-12.
P10L27, add the number of trend for AVISO.
P10L28-29, Does it mean that the impact of internal variability trends is larger in short time period and small in longer time period? Suggest revise.
P11L9, using Northwest Pacific sea level data?
P11L23, for the future work, I suggest authors consider using heat content in SL reconstruction, which may include more factors impacting the SL changes.


Referee 2
The new version of this paper has been much improved. It will make great contributions to studying sea level in the marginal seas of Asia. I suggest to accept it after minor revisions.

1. SST observations in early years have large uncertainties, which has been well documented. It will be good to clarify the reliability (limitations) of such reconstruction based on limited SST in early years. It may be worth just raising a note in main text (corresponding to the large spread in early years of Fig 18?) or conclusion. I still think this is very important for this paper.

2. I agree it is not easy to interpret the dynamics behind the SST-sea level correlations in this paper. However, as above, I would suggest to draw a sentence to make this up.

3. Figure 5. correlation of what?

Dear Authors
The reviewer is now much happier and has made these detailed comments (P=page, L=line) which I am forwarding as wanted minor revisions (so that I will look at the manuscript again)
Yours sincerely
John Huthnance

P1, L16, delete “and are happening now”
P1, L20, revise “Expensive decision”, “are already being made”. Can you revise it like this: Important decisions have to be made in both economic and societal activities.
P2, L1, after this TG => TG, hereafter
P2, L 4, “necessarily only”, delete one of the words. “weighted towards” => mostly in the NH.
P3, L28, delete “to center data”
P6, eq (6), how is d determined?
P7, L7, delete “system”
P7, L9, it is confusing in the value of what in “if the value”.
P7, eq (7), is (t-rou) a variable of PCT or a factor of multiplication? If it is a variable (most likely, based on equation (5)), the left side might be expressed as PCT(t). If it is a multiplication, you may have to explain why.
P7, L18, revise “Then using ..” as Using …, we can then extend …”
P8, L19, “that we assume” => to assume that
P8, L27, deemed => thought
P9, L5, Are “Eleven TGs” the location of eleven TGs, or eleven TG observations? It reads like TG observations, but the TG observations cannot be underestimated or overestimated.
P9, L14, Fig. 6a
P9, L17, Fig. 6b
Figure 6, what is the unit of the amplitude?
Figure 7, why the modes 1-2 are different from Figure 6?
P10, L3, delete “Normalized Root Mean Square Error;”
P10, L24, shows better agreement => shows a better agreement
P10, L26, for the reconstruction process (in Hamlington?)
P11, second paragraph, the comparison between the trend of 1900–2014 and 1993–2015 is not relevant. The trends over the same time period have to be used. This has to be revised.
P11, L13, altimeter data => altimeter data over 1993–2015.
Figures, a period “.” is needed at the end of the figure caption.
Figure 2 caption: two regions: one with high correlation coefficient (red-colored area in (a)) and the other with low correlation coefficient (blue-colored area in (a)).
Figure 6, move the figure legends to the middle of the figure?
Figure 10, optional: change yellow into red?
Figure 11, move the figure legend to the middle of the figure?

Thank-you for your revisions. I am now just asking you to consider “technical corrections” (below) after which it will go direct to the publishing process. This will include copy-editing; I expect there will be changes so you should check that they keep your intended meaning.
Thank-you for publishing in Ocean Science.

Page 1 line 18. Better “. . and higher storm surges causing severe damage on coastal structures . .”

Page 2.
Line 2. “TGs provide records . .” (omit “the”)
Line 14. Better “. . reduced-space . .”
Line 23. Better “. . past, reconstruction . . TGs was inaccurate . .”
Line 25. “gave” -> “give”.

Page 3.
Lines 10-11. Better “. . generally for any small region) from a globally reconstructed SLA has some problems. . .”
Line 18. “. . builds on Hamlington . .”
Line 25. Omit “a”

Page 4.
Line 4. “based on” -> “relative to” ?
Line 9. “Each dataset was trimmed . .”
Line 17. “. . until 1950. . .” (spelling)
Lines 22-23. “(greater than 7 mm/yr, likely owing to uncorrectable vertical land motions) being removed . .”
Lines 26-29 duplicate some of page 2 lines 14-18.
Line 29. Better “. . results. The Church and White (2000, 2011) dataset . .”

Page 5.
Line 6. “. . (2012a). Previous studies . .”
Line 7. Omit “they”.

Page 6
Line 6. Better “. . period d (called . .”
Line 15. Omit “following”

Page 7.
Line 3. “. . that each mode . .”
Line 11. “follows” (add “s”)
Equation (7). I think the superscript after PCT(subscript SST) should be “(i,n – ρ . .)” , i.e. “m” -> “i”.
Lines 15 and 17. “regression” (spelling, twice)
Lines 21-25. I think the order could be rationalised. “As a starting point, the AVISO was trimmed around the KP and the southeast sea of the Japanese islands was removed. GMSL and mean values were removed from AVISO at each grid point. Each SST dataset was trimmed to have the time span of 1891-2014 and cut into three regions: around the KP, the Northwest Pacific Ocean, and global (no trimming). In total, we made six different SST combinations (ERSST and COBESST2 for three regions). All grid points that were not continuous in time were removed for every dataset. Each data point was weighted by the square root of the cosine of latitude to consider the actual area of each grid.” [Here I have also added how there are six SST combinations].
Line 27. “. . nested period, because . .” [i.e. this would be a natural place to answer the referee question about the choice of nested period and help the general reader].

Page 8.
Lines 21-22. Better “. . while in other regions the linear trends were less than 1 mm/yr (Fig. 2). . .”
Line 30. “. . extreme trends and . .”
Lines 30-31. “. . The mean SLAs of the two regions agree well with each other . .”

Page 9
Lines 4-6. Better “. . In Fig. 4, 11 TG stations (square shapes) have an estimated linear trend at least 30% less than the AVISO, while 21 TG stations (diamond shapes) have an estimated trend exceeding AVISO by more than 30%. . .”
Line 17. “. . have a linear trend . .”
Line 29. “. . both of them through CSEOF (Hamlington”
Line 32. “. . comparison with our”

Page 10.
Line 15. “. . at each . .”
Lines 19, 21. “locations”
Line 24. “. . over the satellite era . .”
Line 30. “. . even using fewer predictors . .”