Dear Antonio Manjón and Maxim Ballmer,

both reviews of your manuscript were very positive, and I think you addressed most of the reviewers' comments very well. Looking through the paper, I noticed several points where the clarity of the manuscript could be improved or reviewer questions weren’t fully answered. I have listed them below, but they should require only very minor changes to the manuscript.

Best regards,
Juliane Dannberg


You write that you use the extended Boussinesq approximation, which does include adiabatic heating. But then you impose potential temperatures at the boundaries. Can you clarify this? Both reviewers had questions about this, and I think it is still not quite clear. Do you use the Boussinesq approximation and additionally include shear heating, but not adiabatic heating? Or do the models include adiabatic heating and have an adiabatic gradient, but the temperature you show in the figures is only the potential temperature? Since Reviewer 2 asked about it, I think it would also make sense to explicitly state that you do include latent heat of melting.

Figure 2, Figure A2: Please add an indication (such as a vertical red line) into the color bar for F where the slope changes at 0.2, to make that clear to the reader.

Line 70: Reviewer 2 asked about phase changes, so I think it would make sense to clarify that in the manuscript as well and explicitly state that no phase changes are included.

131 I find the description of the rheology a bit confusing. The text says that the viscosity is constant along the adiabat, but for T = Tref the viscosity profile in B shows that the viscosity changes with depth. Can you clarify this paragraph? Your overall viscosity profile is consistent with what we know about Earth’s viscosity profile, so this is only a matter of clearly explaining what you did and why. I would also refer to Appendix B in this paragraph, so that readers can have a look at the viscosity profile.

In the rheology section, you say “We do not consider the effects of compositional (e.g. pyroxenite vs. peridotite, water-dependent) rheology in this work”, but Appendix B discusses theological stiffening. I would refer to Appendix B in that part of the methods section.

In general, Reviewer 2 had a number of questions about the setup. If this is not clear to this one person, there may be other readers who have the same questions, and so I think it would be very useful to add this information from your reply letter to the manuscript (in the cases where you haven’t already done so; for example the difference between depleted and enriched peridotite).

I think it might also be useful to briefly discuss the implications of using a diffusion creep (rather than a dislocation creep dominated) rheology. I see that as one of the major limitations of this study (which is otherwise really comprehensive and includes many effects in a self-consistent manner). I know that you reduce the activation energy to mimic this effect, but I wonder if dislocation creep would have the potential to enhance EDC specifically, because it reduces the viscosity in regions of strong deformation.

Before you start the results section (or before you discuss the model for the Canary Islands in line 234), I think it could be useful to remind the reader of the age of the plate (at the onset of volcanism) and duration of volcanism in the Canary Islands, just so that it is easier to understand which of the results you present are most relevant for this application. This would also help address Reviewer 1’s comment “Does the model really apply to the Canary Islands, given that lithosphere older than 50 Myr in your models leads to instabilities?”. I believe part of the point of the question was to compare the age of the plate at the time when EDC occurs, and the age of the Atlantic Plate where Canary Islands volcanism occurs.

Figure 3: It would be instructive to illustrate the magnitude of the velocity (i.e. by placing a labelled arrow with a length that corresponds to a characteristic velocity, like 2cm/yr, next to the color bar)

Line 150: You probably want to remove the “therefore”

Line 172: You refer to figure 4c for cases with η 0≤3.83·10^18 Pa·s, but the caption of figure 4c only mentions a change in activation energy, and no panel in Figure 4 shows a widespread distribution of melting, as mentioned in the text.

Based on the description of Figure 4, I think it would be really insightful for the readers to see animations of the time evolution of these models (this would illustrate the processes you describe in the text, like the different onset and vigor of EDC, and the late wide-spread melting). This is just a suggestion, but I think it would make the results much more accessible.

Line 211 “unless the pyroxenite component melts at a lower temperature than peridotite” Do you mean as long as (or something to that effect) instead of unless? Because in your models, pyroxenite does melt at lower temperatures.

Line 235: You still use the notation 48+40 Myr pointed out by Reviewer 2 (and from your reply letter it looked like you wanted to make that consistent throughout the paper). But I thought it was very useful to have the addition of the initial plate age pointed out here, especially when as you compare the onset of SSC to observations.

Discussion following line 307: I find this paragraph a bit confusing. The way I read it, your results generally show a similar behavior as Kaislaniemi and Van Hunen (2014): Increased radiogenic heat production increases the temperature, and this increases melt production. In your models, the cause for this is slightly different (since you include the self-consistently calculated the initial oceanic lithosphere depletion profile), but I did not quite understand the use of the words “However” and “by iteself”.

Line 375: Reviewer 2 pointed out a melting parametrization with CO2, and I realize that this doesn’t fit well into your modelling framework. But to account for that, I would rephrase the sentence slightly to say something like “Existing melting parametrizations that include the effect of CO2 parametrize lithologies in a different way than done in our study, and there is no parametrization that we could efficiently include in our models.”

Line 323: Generally, the discussion should not introduce new results. So rather than referring to the results of Appendix B only in the discussion, I would find it more intuitive to make the “Effects of dehydration stiffening” (or something along those lines) an extra subsection in the results section.

Line 403: The models now do take into account a composition-dependent rheology, so I would slightly rewrite that sentence.

Code and data availability: I think it would help the reproducibility of the study a lot to make the code and input files freely available together with the manuscript. This is not a requirement of Solid Earth, but I think it would make the study much more useful to the community. Solid Earth recommends to provide access to data is by depositing them (as well as related metadata) in FAIR-aligned reliable public data repositories, assigning digital object identifiers, and properly citing data sets as individual contributions.

Appendix A, Figure A2 caption
As far as I understand, there are 97% peridotite everywhere in the model (so this is involved in EDC). Is what you mean here that *depleted* peridotitic components are barely eroded and entrained by EDC, this is not true for the PX component?

Reviewer 2 asked a number of questions about the setup of the mid-ocean-ridge models you answered in your reply. I think it would be useful for the reader (and also for reasons of reproducibility) to add this description to Appendix A.

Appendix B: 436 “rheology-dependent viscosity” → you probably mean composition-dependent viscosity or depletion-dependent viscosity

Figure B2 caption: “melting rates are also less important” Do you mean *lower* instead of less important?

Dear Antonio Manjón and Maxim,

thank you for incorporating all my comments, I think the manuscript is much clearer now.
I am especially glad to see you made your code and input files available!

Best regards,
Juliane Dannberg

Dear authors,

We are pleased to accept your manuscript for publication in Solid Earth. Many thanks for submitting your work to the journal.

With best wishes,
Susanne Buiter