Both reviewers regard this contribution as very interesting and support that it be published in ESURF. I concur with this and suggest that the authors prepare a revised version of the manuscript that I am happy to read and, potentially, send back to one of the reviewers. Going through the replies to the reviews by the authors, I acknowledge that most of the points raised by the authors appear to be addressed by the author.

However, I did not see them addressing the important (second) point raised by the second reviewers, that the authors should try to find a better, more general framework to discuss their findings (and not limit their discussion to the PETM and its recording in the Pyrenees as a case example); this would greatly improve the impact of their work.

I appreciate that they seem to have improved the flow of the manuscript by moving some of the material from the appendices so that the important assumptions and limitations of both models are appreciated by the reader. I agree that the flow of the manuscript is interrupted by having to go through the appendices to understand the reasons for what could appear as restrictive choices in the range of model parameters.

Personally, I find also that, in many parts of the paper, the discussion of the results is focused on the comparison between two models and how these can be explained from a mathematical point of view. It would be good if the authors could more often come back to the underlying processes, approximations and hypotheses on which the models are based.

Many thanks for this revised version which has addressed most of the points raised by the two reviewers. I also wish to thank the reviewer who is suggesting a few minor points be addressed to improve the clarity and, in my opinion, impact of the manuscript. I concur with this opinion and suggest that the points raised by the reviewer be addressed and/or responded to.

Many thanks for your thorough response to the reviewer's comments

Dear John & co-authors,
I am delighted to inform you that you paper has been accepted for full publication in ESurf. I would like to thank you all for all the work in making the changes requested - the Associate Editor noted how these greatly improved the clarity and impact of the manuscript.
All the best,
Tom Coulthard