Dear Authors,

Thanks you very much for your updated manuscript that answers the referee's comments. But before publishing the manuscript, I would ask you to consider the following additional comments:

-Regarding the density compensation discussed on p.12, it is not clear to me how you got to S+0.253psu. In the footnote, can you also give the equation, not only the parameter values? Also in your reply to referee 2, you wrote "this seems to readily maintain density compensation"; can you be more precise how you got to that conclusion and give some details in the paper?

-On p. 19, L1, please change "units of HPa" for units of "m/HPa" (I think)

-In Figure 10 captions, please described the thick green line (and maybe add "is" before "plotted"?)

-In section 4, please refer to section 7, when you mention "from the web" and/or when you discuss the recommended data output.

-In section 6, you need to specify the version of the code used here.

Minor comments

- The first sentence of section 2.2.2 needs to be reformulated; without the text between hyphens and in parentheses, it gives: "Ideal observables are integrated quantities should be constrained by observations, indicative of underlying mechanisms and of climatic relevance" which does not look right to me. Please rephrase this sentence.

-In the captions of Figure 6 & 7, please replace "4mb" by "4Hpa"

-On figures 6, 7 and 8, please use either the abbreviations everywhere or the full expressions. For example, the Fresh Water Content appears as FWC but the heat content is spelled out. It could be useful to consistently give the full expressions in the captions and only the abbreviations on the figures per se.

-on p.22 L 23, please change "depends of the eddy field" for "depends on the eddy field"

With best regards

Dear Author,

Thank you very much for these final revisions.

With best regards