Dear Reviewer,

We would like to thank you for your remarks and your comments, which have helped us to correct and improve the manuscript. Please find below our answers (marked in bold).

General comments:  This study focuses on evaluating changes in significant wave height (swh) during the satellite altimeter period, making use of three different metrics:  (1) changes in mean swh, (2) changes in extrema, as measured by the 95^th percentile, and (3) changes in the 100-year return amplitude.  All of these show increases over the study period (2002-2020).  This study is not the first to tackle this issue. One of the lingering concerns with altimeter-based studies is that changes in the number of satellites or the quality of satellite observations could result in false trend.  The authors have addressed this topic in their Figure 4 by comparing trends that would be obtained with two satellites vs the multi-satellite results.

Overall, I think this analysis is a useful contributor to the swh climate change discussion and it should be published after revision.

1. The results in Figure 4 are extremely useful but perhaps miss an opportunity to clarify exactly what mechanisms account for the differences between two-satellite and multi-satellite analyses. The text explains that the availability of more satellites increases the probability of seeing extreme events.  I think the point that isn’t made clearly is that this difference occurs because swh has a non-Gaussian distribution, so that large extremes will alter the mean and 95^th percentile statistics much more than extremely small events.  Although the authors show that this effect is not the defining driver of swh trends, the differences between the black and red lines in Figure 4 are important, and the authors should emphasize that the 2-satellite trends are potentially a more accurate measure of the long-term trends than the multi-satellite trends. 

We've added the clarifications you suggested to the relevant paragraphs.

“For example, it is likely that more storms or extreme waves were sampled by the altimeters in the latter years of the period than in the former. The distribution of SWH is not Gaussian and is largely affected by extreme events, hence producing a spurious positive trend in SWH.”

“The mean SWH is not greatly affected by the number of satellites and the trends of mean SWH are almost identical. On the other hand, the P₉₅ daily maximum SWH is sensitive to the increase in the number of observations and the multi-mission product overestimates its trends compared with the two-satellite product. More importantly, the sign of the trend does not change, the spatial patterns of the trend are mostly consistent between the products and trends in the two-satellite product are contained within the uncertainty of trends in the multi-mission product. However, as the two-satellite product is more consistent over time, the long-term trends measured with it may be more accurate than those measured with the multi-mission product.”

1. There have been a number of studies on trends in significant wave height in recent years. This manuscript cites some altimeter-based analyses but also acknowledges some of the challenges in using a changing constellation of altimeters.  Another study by Bromirski et al (2023) that received some press took advantage of seismic data to show increasing waves and could corroborate these results.  The authors could consider whether to cite this: Bromirski, P. D. (2023). Climate-induced decadal ocean wave height variability from microseisms: 1931–2021. Journal of Geophysical Research: Oceans, 128, e2023JC019722. https://doi.org/10.1029/2023JC019722 I’ve noticed recent work has evaluated seasonality of wave climatology and that could be pertinent for the current study.

Thank you for the reference you sent us. Unfortunately, we decided not to include it because the comparison with the results presented could not provide a decisive conclusion.

The periods considered in this article are not the same as the one of the altimetric time series we use, and the regional patterns obtained in this article do not seem completely related to the patterns of SWH we obtained. The coarse spatial resolution of the altimetric time series may also take part in this conclusion.

1. The paragraph starting at line 143 appears to discuss Figure 3, but Figure 3 is not called out in the text. This should be clarified for readers.

The correction has been made.

1. Line 147. The contrasting trends of SWH and P95 of SWH are not entirely clear. I think the sentence should perhaps say, “In the North Atlantic in JFM, both SWH and P95 of SWH show decreasing trends.  However, the 100-year return trends are largely positive.”

The correction has been made.

1. Lines 158-161. This paragraph discusses calculations using ERA5 and AVERYS data that appear not to be included in the manuscript.  Either the paper should specify “(not shown)”, of the figures should be added to supplementary information and called out in the text.  Also true at line 218.

The figures are not shown in the manuscript. The mention “(not shown)” was added.

You can still find the figures associated with WAVERYS data in the supplementary information.

1. Line 171-177. I believe the figure references in this paragraph should be for Figure 4 rather than Figure 3.  It’s not clear to me why there are 5 boxes in Figure 4a, but only 3 highlighted in side panels, and I would suggest simplifying the figure to show only the 3 boxes that are included in time series analysis, or else add the additional panels in supplementary information and explain something about their significance.

The study of regional trends was initially carried out on all the 5 boxes plotted in figure 4a. However, the regional trends calculated did not, in the end, provide any additional information to the 3 boxes selected in the side panels, so we decided not to display all of them.

Figure 4a was simplified as suggested to show only the 3 boxes that are included in the side panels.

1. The discussion of Figure 4 indicates that the trends for the red and black lines agree within uncertainty estimates. I can see that this is true for the estimated trends, but I think the calculation would be more complete if the annual averages also included uncertainties.  Does each individual year agree within uncertainties?

Uncertainties on the annual averages were added on the figures with error bars (Bootstrap 95% confidence intervals).

On one hand, annual averages of daily mean SWH for both datasets (two-satellite in black and multi-mission in red) agree within uncertainties.

On the other hand, the annual average P95 of daily max SWH mostly agree within uncertainties. However, the bounds of the 95% confidence interval calculated for the average P95 of daily max SWH of the multi-mission product are systematically higher than the bounds of the confidence interval of the two-satellite product. It is especially true from 2008, when the multi-mission product merges more missions at the same time, until the end of the period. The multi-mission product contains greater extreme SWH than the two-satellite product for those years.

See the revised figure in supplements.

1. References are not in alphabetical order and include some items that are not cited in the text. These should be cleaned up.

The correction has been made.

1. Minor points of grammar/style

• line 8.  Remove "Indeed".  It doesn't make sense in this paragraph.
• lines 9-10.  Split the sentence into two.  "...several decades.  Such time series ..."  Otherwise "that" appears to reference "decades", which will confuse readers.
• line 20.  Change "such as" to "including"
• lines 21-22, 174-175.  Change “above” to “poleward of” or “north of”.  Change “below” to “equatorward of” or “south of”
• lines 22-23.  “As for” is not a clear construction.  Maybe “The 100-year return levels of the SWH have significantly increased in the North…”
• line 27.  Add comma after “variability”.
• Line 28.  Add comma after “changes”
• Line 33.  Split into two sentences, ending the first after “decades”.  Then “Thus far these records have only been available in global ….”
• Line 34.  Remove “using”
• Lines 53-54.  “is the value above which 5% of the values in the mean time series fall”.  This wording is not clear.  I would recommend rewriting, and in particular rewording “fall”.
• Lines 58, 102.  Change to “Timmermans et al. (2020)”
• Line 73.  Split into two sentences:   “before.  Thus”.  In English, this is called a “comma splice” and is not considered grammatically acceptable.
• Figure 2a labels.  “95e percentile” should be replaced with “95^thpercentile”
• Line 159.  Split into two sentences:  “datasets.  However,”
• Line 160.  It’s unclear whether “they” refers to “ERA5 and WAVERYS” or something else.  The word “they” should be replaced with the appropriate noun.  I also suggest removing “As for extreme values”, which is ambiguous.  I think the authors are using it to mean “Now we’re changing the topic to talk about extreme values”, but it can be interpreted as “Similar to extreme values”.
• Line 168.  Change to “The 100-year return levels have significantly increased in the North Atlantic and in the eastern North Pacific ….”
• Line 186.  Add comma after “former”.
• Lines 195-196.  Two consecutive sentences start with “However”.  That makes too many contrasts, so at least one “However” should be removed.
• Line 197.  Change “doesn’t” to “does not”.  (No contractions in formal writing.)
• Line 209.  Start a new sentence with “However” to avoid a comma splice.

Thank you for your careful proofreading. All minor points of grammar/style were corrected.

You shall find later the revised manuscript.

Dear Reviewer,

We would like to thank you for your remarks and comments, which have helped us to improve and clarify the manuscript. Please find attached in supplement our answers (marked in bold) as well as revised and supplementary figures.

You shall find the revised manuscript later.