My comments are somewhat similar to Henri's actually, and mostly writing ones.  

==== major comments ====  

* The article content reads back-to-front to me: having read through it, what I was expecting to see at the front is nested in the middle and the back. The slight result is that (to me at least) it is not entirely clear what the scientific question or motivation is as written relating to the two AMOC diagnostics. In this sense I guess I am biased because I roughly know what the article would be about because I use \rho-AMOC quite often (although I don't claim to be in the "serious people" group mentioned by Henri), but the framing is not entirely helpful for the more general audience in my opinion.

The article currently reads like "we did this and we got this", when it could read more "we think this so we did this and we got this", because some of the content to demonstrate the "we think this" part is actually in the middle/end of the article. The fix is then relatively easy: copy/move/anticipate some of the relevant text discussion up to abstract, introduction and/or section 2. This would help re-balance the article, because section 1 could do with a stronger or more concrete problem statement/hypothesis, and section 2 as the theoretical/scientific foundation stone for the article is also a bit short.  

I am also of the strong opinion the authors need to stress that z-AMOC and \rho-AMOC are different "diagnostics" and not "AMOCs": there is the model AMOC somehow nested in the diagnosed variables, but there are different representations of it. (cf. a "vector" is the mathematical object, but there are different "representations" of it depending on the choice of basis, and some representations are more useful than others depending on the context.) Following on from that then:  

- The model AMOC is exposed to the same drivers, but this driving is represented differently in the different diagnostics.

- The fact they have different distributions and/or magnitudes are not surprising, since they are different diagnostics and measure different things.  

The article text needs a change of tone and some content to reflect that. The results are fine, but it is a little oversold at the moment to me at least, although I think the referees agree. See "minor comments" of where I think text can be changed/moved/copied/anticipated.  

* As mentioned by the other referee, most MOC calculations use meridional velocity v, so why is w used, particularly when it can be noisy and contribute to uncertainties? Please comment accordingly.  

* Following on from that and as mentioned by the other referee, how is convection represented in the model? Because if it is explicit then it would manifest as a w, but if it is as an enhanced vertical mixing then would one convert a diffusive flux into an effective velocity, or something else? It is thus not clear what w_\rho actually includes, and is therefore not entirely clear what \psi_\sigma is measuring, which is kind of important since that definitions of those are the scientific foundations of the present article. Please clarify accordingly.  

* At this resolution some sort of GM scheme is used presumably, then is w* included in these calculations (probably in \psi_z because GM is supposed to be adiabatic)? This needs clarifying (if GM is not used then please just say so).  

* The maths presentation in text and in some of the figures is inconsistent and needs fixing, see below.  

==== minor comments ====  

* line 58: Remove comma  

* line 79: Weird sentence and probably missing the word "unstructured" (because you can't assume people know about details of FESOM). Reword accordingly, e.g. "The unstructured mesh is such that there are approximately 127,000 mesh nodes at the ocean surface." or similar  

* line 84: 89 density bins seem a bit small in terms of numbers, and are the bin sizes uniform? Normally I do about 160 to 200 and above uniformly spaced (a bit less if I have it unevenly spaced), but I don't to do averaging in density space online unless I am using MITgcm. Any comments on the dependence/sensitivity to the choice of bin numbers.  

* line 95 + 96: Probably swap colon for a full stop and start a new paragraph as is done already, or follow on straight away (doesn't really matter).  

* Remove all instances of "Eq. X below:", because this is forward referencing and the arguably that text is redundant anyway (don't really need it).  

* Eq 1 and 2: Need to be clear that these are cumulative integrals in y and full integrals in x. In that sense the integral limits need to be \int_West^y.  

* Eq 1 and 2: Why are these flipped from the usual orientation? Would have expected South to North and West to East (which introduces two minus signs that cancel I suppose).  

* Eq 1 and 2: Because of the unstructured mesh one presumably needs to do something in order to do zonal/meridional integrals, so what is actually done? There is a citation to Sidorenko et al (2020a) but this is not that helpful in that there could also be a brief description of what is actually done, because there is unnecessary ambiguity. (Re-interpolation? If so, nearest nearbour, linear or something else? Evaluation of basis element even though this is finite volume?)  

* Equations: Need punctuation to go after them as they should be regarded part of the sentences. So full stops after the symbols at Eq. 1, 3, 5, and commas in Eq. 2 and 4.  

* line 102 + 110: Remove indentation, this is not a new paragraph (don't give it an extra blank line after \end{equation})  

* Sec 3 first paragraph: "Averaging in time" is implied but no mention of time window, although this  is in Fig 1 caption. This is not entirely helpful, so should mirror that detail around here in the text.  

* Fig 1 axis labels and elsewhere: Rather than "kgm-3" it should be "kg m-3" and similar. To do this in LaTeX I guess you would do something like "$kg\ m^{-3}$" (as is done in the text). Degrees symbol is slanted here and is inconsistent with how it is used in text; try ${}^\circ$ if that isn't already what is used (if it is then I don't know what the problem is).  

* line 142: The two AMOC measures differ in their "spatial distribution" but the comparison shown in Fig 1 is not evidence to support that, because the vertical co-ordinates are completely different. Either

- say they differ in the meridional distribution

- remap the z-AMOC into density co-ordinates

- remap the \rho-AMOC into depth co-ordinates if you have a mean isopycnal depth variable computed  

* line 143 + 144: "Distinct driving mechanisms" make no sense to me, because your model is "driven" by the same thing, while the AMOC diagnostics are just that, diagnostics computed from the model variables. Probably lessen or remove related text. Relates to the above point that it is not clear that the two diagnostics are just that, different measures.  

* line 155: The "annual and 15 year means" are out of place / unbalanced if there is no "50 year" mean mentioned when talking about the AMOC at the beginning of the section.  

* paragraph beginning line 160: As above, the two AMOC diagnostics are just measuring different things so the differences are not that surprising. They measure different physical effects, so in this case you probably care more about \rho-AMOC so just say that.  

* line 181 to 187: Would recommend some of this text to be copied/moved up to introduction or section 2 to frame the article more concretely.  

* line 199: Don't need the "AMV" acronym because it's never used again anyway.  

* line 219 + 220: Analogously worded sentence should be up in introduction and/or section 2.  

* Fig 6 caption (but do this also in text): Over what depth/density classes and averaged how? (full depth?)  

* line 263: Either "w_\rho" is meant, or need to state why "w_p" is different to "w_\rho"  

* line 280: The model AMOC weakens by the same mechanism presumably but these are projected differently onto the different AMOC diagnostics. Reword accordingly.  

* line 300 to 302: Analogously re-worded sentence should be up in introduction and/or section 2 to anticipate this sentence coming up here.  

* line 338 to the end: Analogously re-worded paragraph should be up in introduction and/or section 2.Comment on egusphere-2025-2326