Dear authors,
Please revise your MS by thoroughly considering the previous comments of both reviewers. One of the reviewers posed comments. To speed up the review process I return the MS to you now for your further revision.

"The authors have not responded truthfully to the previous round. They claim to have updated the manuscript, but on several accounts they demonstrably have not. No change to G Nurser's request for a correction to the stress on p 3, line 87, can be seen, even though they claim so. Also, they claim to have included Wu et al (2019), but it is not to be found in the list of references. I refuse to review sloppy work. I would want to see a version with tracked changes before I proceed, and I will not review this version"

Best wishes
Qiang Wang

Dear authors,
Some minor revisions are required before the paper will be accepted. See the comments from the reviewer.
Best wishes
Qiang Wang

The paper is substantially revised and I am satisfied now to see that my comments and the comments by George Nurser have been answered.

There is one equation which I believe the authors must check before the paper is acceptable for publication. On Line 180 is says that $u_s \partial_z = \partial_z u_s + \partial_z(u_s)$. I believe the sign in front of the first term on the RHS should be negative. How has this affected your implementation?

I have a few minor corrections:
l 45: Not Van Roekel, but Valcke 2012, I believe
l 115: weater -> weaker
l 195: S_oce? Should it not read S_ds?
Fig 2: The lowest panel has a title US=f(tau) which sits atop the numbers 600 and 800. A little more space is neeed to make it more readable. I don't think this is a problem with the rendering as the authors claim - I also use a Mac.
l 295: rugosity -> roughness?
l 180: Wrong sign in front of $$? As mentioned above
l 434: reminder -> remainder
Fig 9: southern and northern hemisphere, not south and north
l 464: retroactions -> interaction?