Dear Authors

Thank you for preparing a reply to the comments by both reviewers. Based on the comments by the reviewers, your reply, and the original manuscript, I kindly invite you to submit a suitably revised version of your manuscript that takes into account the review comments as outlined in your reply.

Thank you for submitting your work to Biogeosciences.

With kind regards, Fortunat Joos

Dear authors

Your revised manuscript has been assessed by one of the original reviewer. Unfortunately, the reviewer still finds major shortcomings which prevent the publication of your manuscript in its current form.

The review comments are generally very clear and of substance. The issues raised by the reviewer need to be thoroughly addressed before publication in BG can be considered.

To mention a few examples, the apparent mismatch between the air-sea pCO2 gradient and air-sea carbon flux in the North Atlantic (Fig. S3 and S4) is worrisome (review comment 2.1.2). Please follow the reviewer’s recommendation (comment 2.1.3) and give figures for the weathering fluxes. I also suggest that you compare these figures to data-based estimates. Please carefully explain your finding regarding the experiments with fast and slow gas exchange rates on page 7 (comment 2.2.1; I guess the reviewer refers to page 7 and not to page 4) and improve the analysis of the nutrient depletion experiment (comment 1.2). Regarding the description of the results in section 3.3.1 on air-sea gas exchange, a rewrite of this section is necessary as many statements in this section are incorrect. I suggest that you consider Figure 1 and in particular the inset in Menviel et al., 2015; this inset may be helpful to clarify your arguments.

It is well known that 13C in the ocean is changing on multi-millennial time scales in response to ocean-sediment and weathering interactions. The reviewer recommends that you prolong your simulations beyond year 2000. He made this point already in his first review. I agree that it appears peculiar that most runs extend for 2000 years only given the paleo focus of this work and the cost-efficiency of your model with an annual time step and 11 layers only. However, I do not insist on this point and leave the decision on the duration of simulations to you. In any case, you need to be more specific in the figure captions of Figure 3 and following and provide information on the time of results (e.g., after how many years differences in results are taken). Further, it would be useful to refer to the equilibration time scale for the surface-to-deep 13C gradient (line 9/10 on page 5 of marked-up version) as this is the focus of your study

Please address all comments and submit your reply together with a manuscript version where your changes are highlighted as well as a revised manuscript. I urge all three authors to carefully consider their presentation of results.

Thank you for submitting your work to Biogeosciences.

With kind regards,

Fortunat Joos

Further comments:
Page 6, line 19ff (of marked-up MS): The text on the equilibration time is not very precise and the explanation for the longer equilibration time scale of 13C compared to oxygen is in my opinion not correct. Probably you would like to address how long it takes to equilibrate the atmosphere and ocean surface layer by air-sea gas exchange (not considering surface-to-deep exchange) for O2, DIC, and 13C(DIC) after a small perturbation in surface ocean O2, DIC and d13C(DIC), respectively. The equilibration time depends on how fast the tracer amount in the surface layer is replaced by air-sea gas exchange as further moderated by the Revelle factor for DIC.
(For this you may solve the according differential equations:
d/dt x(s) = F(x(s), x(a)) and d/dt x(a) = - F(x(s), x(a))
to extract the exponential time scale associated with the re-equilibration. F is the net air to sea flux and x(s) and x(a) the perturbation in the atm. and surface layer) )

p6, line 25: suggest to delete this sentence as unclear and not precise. (The surface ocean d13C is not in equilibrium with the atmosphere in many region due to the slow equilibration time scale for d13C with respect to gas exchange with the atmosphere.)

p6, line 29: It is highly misleading to state that air-sea equilibrium would be 2 permil as the equilibrium depends strongly on temperature and varies greatly with latitude

Dear authors

Your manuscript has again be assessed by one of the reviewer. I am happy to accept your manuscript for publication in Biogeosciences based on the recommendations by the two reviewers and my own reading.

The second reviewer noted an inconsistency in your reply regarding the supplementary figures. This concerns the reply, but not the manuscript itself.

Thank you for submitting your manuscript to Biogeosciences.

With kind regards, Fortunat Joos