Dear authors,
thanks for the detailed responses. Both referees found that there exist severe technical shortcomings in the computation of the transports. Please incorporate this into the revised ms.
What I have not understood from your response is that it is very hard to include all NEMO components derived from ORAS4 to close the budget.
Related to the budgets, please check if your conclusions are robust along with the new calculations.

Please revise the manuscript following the suggestions of the referees. There will be another round of reviews.
Kind regards
Gerrit Lohmann

Dear authors,

The manuscript has improved but still has several major and many minor issues.
However, the referees are confident that the paper can get much closer to acceptance after another round of revisions.
Compared to the first version, some major problems in the computation of the
transports have been corrected. There is however a number of smaller issues
remaining as you will see in the detailed comments.

Finally, the paper needs to be edited to improve English.

Regards,
Gerrit Lohmann

Dear authors,
the paper can become acceptable with relatively minor revisions. The only major comment of the referee is that "the authors still make a very uncommon choice for the latent heat of vaporization (namely that at 100°C), which is more than 10% lower than more standard values. This shall be corrected, possibly including recomputation of the results if this wrong value was really used and not only stated in the text."
I agree. Please check also the minor things and suggestions to the figures.
Kind regards
Gerrit Lohmann

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Third review of „Synthesis and evaluation of historical meridional heat transport from midlatitudes towards the Arctic “ by Yang Liu et al.

The manuscript has substantially improved compared to earlier versions. There are still a few minor issues that I recommend to address before the paper can be accepted for publication. The only major comment is that the authors still make a very uncommon choice for latent heat of vaporization (namely that at 100°C), which is more than 10% lower than more standard values. This must be corrected, possibly including recomputation of the results if this wrong value was really used and not only stated in the text.

Specific comments:
P2L31: There is an additional, more recent reference for this statement: Mayer, M., Tietsche, S., Haimberger, L., Tsubouchi, T., Mayer, J., & Zuo, H. (2019). An improved estimate of the coupled Arctic energy budget. Journal of Climate, 32(22), 7915-7934.
P3L1: “point” --> “point to”
P3L32: remove “as a result”: your choice is not a result of the statements before.
P5L3: “old” is relative. One could view ORAS4 as “old” as well, given ORAS5 is available already. Maybe better say “predecessor”
P5L6: the forcing changed to operational forcing in 2010, see Balmaseda et al. (2013)
P6L14: remove “the” before “produced”
P7L13: I understand now the reason for the confusion. The authors provide Lv at the boiling point of water, where Lv is significantly lower than at lower temperatures: see graph at https://www.engineeringtoolbox.com/water-properties-d_1573.html
This is a very unusual choice. Usually, Lv at 0°C is used as this is a much more typical air temperature. See, for example, the description of ECMWF’s IFS part IV: physical processes. See chapter 12: the choice in the IFS is 2.508e6J/kg.
P9L14: add °C to “0”
P10L25: change sentence to something like “One possible explanation…”
P11L11: please state here whether you did check surface fluxes and OHC changes
P11L15: “source” --> “sources”
P11L19: remove “With linear regression,”
P12L26: The fact that OGCM does not assimilate ocean data and still agrees well with observations suggests that the surface forcing is a very important driver of OMET variability. You should explicitly state this.
P12L26: The sentence “To conclude, the heat transport at 26:5N is too low in these products” is right, but you could add a statement that two products appear to have reasonable variability.
P12L29: I suggest to remove “quite”
P13L6: How can the OHC of OGCM be almost twice as high as those of the other products? This would suggest twice as high column-average temperatures in OGCM. This cannot be right. There must be an inconsistency in the choice of integration depth or land-sea masking. Please check and correct.
P13L6ff: Figure 8 shows quite consistent OHC increases in the different products. What prevents you from computing a warming rate from this (in Wm-2) and compare the results to global mean warming rates? This could be used as a measure of AA in Arctic OHC increase.
P13L30: I suggest to add “of the relationships” after variability.
P14L18: the different results in MERRA2 likely stem from its shift in AMET around 2000. This should be mentioned.
P14L23: Does “one month lag” mean that you basically correlate NDJ OMET with DJF fields? Also, I find it hard to imagine that OMET at 60N affects Barents Sea sea ice within one month. What is the typical propagation time for a temperature anomaly from 60N to the Barents Sea? I suggest to make more careful statements.
P15L12: “aspect” --> “respect”
P15L14: should mention that reanalyses do not assimilate direct observation of the TOA and surface energy budgets.
P16L23: Could you provide an example of variables that should be used with care?
P16L26: add “interannual variability of” before “AMET”
P16L32: “large” --> “long”
P16L32-33: You find that the annual cycle of the products agrees well, but interannual (five-yearly filtered) variability not. What is the maximum time scale that can be viewed as robust? How about annual means anomalies?
Figures 9 and 10: Having only lines and no stippling, it is sometimes hard to see what areas are significant. For example, in the SIC regressions I cannot tell which areas are significant and which not. I recommend to improve the plots to make this clearer. A standard way would be to stipple significant areas.

Thanks for the revised paper. It is accepted
Gerrit