Dear Kristofer and co-authors,

I can accept your manuscript for publication once you attend to the minor comments of Referee 1 (copied below), to my satisfaction.

Best regards,
Bob Marsh

I am happy to see that the authors have incorporated most of my suggestions, and think that this manuscript is now nearly ready for publication. I only have a few minor comments standing out

- Page 2, line 7: “Their” should be “The” as first word
- Page 2, line 13: This statement about reversibility of the flow not being possible in RK4 is somewhat mysterious. Are the authors here talking about a fundamental mathematical property of RK4? Because as far as I know the RK4 scheme is commutable under dt -> -dt. Or are they talking about numerical noise and accumulation of round-off errors? Because in that case the statement essentially says that the TRACMASS scheme has no (or far less) numerical noise than RK4. I’d like to see evidence for that, if that’s what the authors mean.
- Page 3, line 10: I think it would be good if the statement “since it does not satisfy the discretised continuity equation in a GCM” would be a bit more expanded. Why is this the case? Is this easy to derive? if so, please show, or otherwise provide references
- Figures 5, 6 and 7 would be easier to comprehend if they have latitude and longitude ticks. While the Eurasian continent in Fig 7 is probably recognisable to most readers, I doubt whether the Agulhas region in Figures 5 and 6 is so recognisable too. Latitude and Longitude ticks will help readers orientate themselves.

Dear authors,

Can you clarify to me how you originally responded to the reviewers, in particular reviewer 2, so that I can proceed with a decision.

Regards, Bob

Dear Kristofer and co-authors,

Thank you for responding to all the comments of Stephen Griffies. Just for clarification, in response to his point 3, you respond that you have "added a figure" - although there are no extra figs in v5 compared to v4, I think you are referring to Fig. 4 - which did not appear in earlier versions, but which does indeed summarize the different methods as Griffies requested. Also, when you supply the production files, can you cite van Sebille et al. (rather than van Sebille) at line 35, and of course check on the status of this m/s.

Otherwise, it just remains to say well done on a fine paper!

Regards, Bob