The authors presented a study of MHWs in the Barents Sea, which is very interesting since the MHWs were less studied in the high-latitudes. However, the study cannot be published at the current form for the following major and minor comments:

Major comments:

(a) surface and bottom MHWs

It is very interesting to see the bottom MHWs in this study. My impression is that it might be better to have their focus on the comparisons of surface and bottom MHWs, and even change the title of the manuscript.

However, It is not clear whether the MHWs in the section using ROM data are for the surface or bottom. It might be good to compare both surface and bottom MHWs just as using the TOPAZ data,

(a) Baseline comparison

I don’t think this interesting, since the results are very intuitive at least qualitatively.

I don’t think this meaningful either, since this is just a way for scientists to redefine MHWs for a later period of baseline, but the ecosystem may not be able to get used to the new baseline quickly unless the authors can provide the physical evidence.

(b) MHW algorithm

It is not clear whether the MHWs were diagnosed from the entire time series from 1991 to 2021, or rather diagnosed year by year from January 1 to December 31, since the statement in L83-84 is not consistent with that in Olive et al (2018). See my detailed comments for L83-84.

(d) Heat budget analysis

It is glad to see the heat budgets were used to explain the changes in MHWs, but budgets should be closed. The increase of influx from the Atlantic may not be necessary in favor to MHWs, if the outflux is considered. Also, it is not clear whether theses heat fluxes can be used to explain both surface and bottom MHWs.

Minor comments:

L13-14, It is not clear for “surface and bottom expressions”

L18-19, the recent studies on the MHWs in the Arctic (Hu et al. 2020 and Huang et al. 2021) are worth citing here.

Hu, S., Zhang, L., & Qian, S. (2020). Marine heatwaves in the Arctic region: Variation in different ice covers. Geophysical Research Letters, 47, e2020GL089329. https://doi.org/10.1029/2020GL089329

Huang, B., Z. Wang, X. Yin, A. Arguez, G. Graham, C. Liu, T. Smith, H.-M. Zhang, 2021: Prolonged Marine Heatwaves in the Arctic: 1982-2020. Geophys. Res. Lett., 48, e2021GL095590, https://doi.org/10.1029/2021GL095590.

L23, I always has difficulty to understand why 90^th percentile was selected as an MHW criterion, since from statistics point of view the 90^th percentile is really too low.

L24, the impact of baseline is clear but this does not mean we need to change the base line since the ecosystem may need time to adjust the changes in baseline.

L29, Likewise, the removing of the linear trend does not make sense, since our scientists can remove the warming trend but the ecosystem cannot and it at least needs time to adjust the warming trend. It has not been unknown how long it will take for the ecosystem to get used to the new base line or warming trend.

L56, it may be better to say something why CTD data is used to your assessment.

L83-84, this is not consistent with the statement of Olive et al. (2018): “Note that when calculating the annual statistics of events which occur across several years, the duration and intensity are assigned to the start year of that event.” Authors need to check and verify the consistency between the python code and the statement of Olive et al. As the authors acknowledged that the frequency (maybe duration as well) may have been overestimated due to non-rational separation of MHWs across different years. More importantly, it is not clear whether MHWs are analyzed from the starting year (1991) to the ending year (2021). If yes, it is should be easy to fix the above problem. If not, I guess (based on the statement in the manuscript) the MHWs may have been analyzed every year from the January 1 to December 31. If this is the case, the MHWs may have been underestimated for those MHWs sustained from the end of year to the beginning of the next year. e.g. SSTs are above 90% over December 28-31 and January 1-4 of the next year, these SSTs may not be counted as an MHW if they are analyzed yearly, but should be counted as an MHW if they are analyzed for the entire period.

L98-100, it is easy to understand for the sea bottom MHWs if focuses are the ecosystem of the ocean bottom such as coral reefs. But this should be described much earlier in Introduction section and the Abstract.

L103, should “Table 1” be Table 2? Descriptions are needed for Table 2.

L111-115, it is not clear how these MHWs were diagnosed. Is it different from those based on Hobday et al. (2016) starting from L215?

Fig. 2., it is not very clear why the time series are from 2015 to 2018, as an example? How about the period from 1991-2014? Why the example of 2015-2018 was selected, and what are the implication for these MHWs. E.g. the connections from the 2015-16 El Niño event.

L129-130, since the negative trends of the bottom MHWs were not statistically significant, it might be safe to say “no significant trends were detected”.

L168-169, the heat is not directly related to the influx, but to the convergence of influx and outflux. What is the change of the outflux from Barents Sea to the Arctic?

L172, What is the “turbulent heat”, is it sensible, latent heat fluxes. How about solar radiation fluxes?

Fig. 5., Can the heat flux analyses be applied to both surface and bottom MHWs? What results the differences between surface and bottom MHWs?

Table 3, “Number of marine heatwave events per year during the period 1961-2020” is very confusing and out of context. I think the same period of 1991-2021 should be analyzed and compared with different baseline periods of 1961-1990 and 1991-2020, which can also be compared with the results presented in section 3.1.

Tables 3-5, I assume these are for the surface MHWs, what about the bottom MHWs?

L237-238, Does this imply that the ice may be melted at the bottom while remained at the surface?

L238, is this “sea-ice cover” the surface ice or bottom ice cover?

This is a study of the characteristics of marine heatwaves in the Barents Sea. It aims to investigate the occurrence of surface and bottom heatwaves in four different environments in the Barents Sea, to explore the differences in marine heatwaves characteristics when changing baselines, and to focus on the most severe MHW events in their study area.

Overall, I vacillated between rejecting the paper and accepting it with major comments and decided to give the authors another chance to improve their work. I have major and minor comments, such as the following:

Major comments:

• The language used to describe the results of this work is very general and has nothing to do with the MHW topic. To be more clear, there are some terminologies that are known to be used by researchers of different scientific topics, here in this paper they used different terminologies that are far from what should be used in a study like the MHWs, and this led to a lot of confusion when I read their paper. I doubt that the authors used some sort of paraphrasing software that caused these repeated mistakes in their manuscript. Here are examples of the mistakes to which I refer:

• Line 9: It was written “Determining the amplitudes and extent of marine heatwaves”. For MHWs, the term “intensity” was used to describe the level that the SST reached above the threshold climatology, while the term "amplitude" is usually used for ocean waves, sound waves, etc., not for MHWs. Also, the extent of the MHWs could be a vertical or spatial extent, so please specify which one you are referring to, and I think you mean vertical extent since you don’t have any spatial maps in your paper.

• Lines 13 – 14: The authors used the word “expression” in two different places and this word does not mean the same thing in the 2 places. The first time it said “to explore the frequency, intensity, and duration of marine heatwaves in the Barents Sea, as well as 13 their regional expression”, and I suspect they were referring to the regional occurrence of MHWs. The second place was, “We find that major marine heatwaves are rather coherent throughout the region and have comparable surface and bottom expressions”, and I believe using words like occurrences or events is more representative in this case. Please change it through the entire manuscript.

• Line 23: “temperatures above the 90th percentile based on a fixed baseline”, Hobday et.al., 2016 define an MHW when the SST exceeds either the 90^th percentile of the moving climatological average or a fixed threshold, so the above statement is not correct, please correct it. Also superscript the “th” that is after 90.

• Line 24: “Climate normal”, it is usually referred to as climatological average or climatological mean, please change it.

• Line 32: “When MHW are calculated for a whole region, regional heterogeneities will be lacking, thereby reducing the applicability of such an index” ??? which index???????

• In the introduction: you refer to other studies in the literature (e.g., line 37 (see e.g., Jakobsen and Ozhigin (2011) for a comprehensive overview)). Instead, try to make your introduction richer and like a story that gives the reader an idea of the topic you are studying. There are so many studies on MHWs and one of them deals with the Barents Sea (https://doi.org/10.3389/fmars.2022.821646). So you can use their work to introduce yours, and the authors should also mention how their work differs from the previous one. Also, you have a very unique area of study. I would have expected you to describe it in more detail in your introduction. This will help the reader to know more about the circulation in the Barents Sea, the physical properties and the atmospheric conditions, so that later when you talk about it, they can compare the normal and the extreme conditions.
• Lines 70 - 73: “We choose these periods to examine the effect on MHW statistics of using different baseline periods. The first period, 1961-1990, was a relatively cold period in the Barents Sea region, whereas the period 1991-2020 has been relatively warm (e.g., González-Pola et al., 2020)”. I don’t really see any logic in comparing the MHWs defined by these two baselines, because the result is easy to expect. It was a cold period from 1961 to 1990, so this baseline will result in longer and more intense MHWs compared to the warm period baseline (1991-2020). If the author wants to study the results of MHWs using different baselines, I suggest you try to take a longer or shorter period for climatology, e.g. 25 or 35 years, but within the same period (warm or cold) so that you can check whether using less or more than 30 years of climatology could be reflected in the characteristics of MHWs or not. This will be very helpful for the studies examining the composite events of the MHWs and, for example, low chlorophyll-a events, since the available data for chlorophyll-a start from 1998.
• Lines 101-102: “Here, we compare modelled and observed near-bottom temperatures averaged in time (monthly) and space (see sub-regions, Fig. 1).” How did you manage to define the MHWs using the monthly data?  According to the definition you use, it is a daily phenomenon.
• Lines 111 – 114: “We first estimate MHW statistics based on the TOPAZ reanalysis for the full Barents Sea region (see Fig. 1 for area definition). Two distinct MHW events are identified in both the surface and bottom temperature time series. While the strongest MHW, in terms of cumulative effect (degree days), appeared in 2016 both near the surface and near the bottom, the second strongest MHW appeared in 2013 near the surface and in 2012 near the bottom”.
• Does it make sense that you find only 2 MHW events over 31 years ( 1991 – 2021)? Especially the other study (Mohammed et.al., 2022) stated that over the 39 years (1982- 2020) In total, 72 MHWs were recorded in the whole Barents Sea over the 39-years study period with a total of 1,068 MHW days.

• How is it possible to find MHWs on the bottom (2012) that cannot be seen on the surface? Especially your area is very shallow (maximum depth about 400 m), where does the heat come from?

• Line 115: “When applying the MHW definition provided by Hobday et al. (2016)” . So what was the method used to define MHWs in lines 111 – 114?
• I would like to ask you if you have studied the role of the sea ice cover cycle in the region for the occurrence of MHWs?

Minor comments:

• In your data section please specify the periods that you used for each dataset
• Lines 151 - 152 rephrase it to be “In the Bear Island Trench and Pechora Sea, the maximum intensities of MHW near the surface are about twice the maximum intensities near the bottom”.
• The figures: Put labels (A, B, ….etc) on the panels so it easier to be easier to be interpreted.