Dear authors

Thank you for your reply to the comments by the two referees and by Keith Rodgers. Both referees suggested that your manuscript requires major revisions before a potential publication in Biogeosciences. Both referees kindly agreed to review a revised manuscript.

Based on these recommendations, your reply, and my own reading, I invite you to submit a revised manuscript. I will send out the revised manuscript to the two referees for further evaluation.

Please follow the instruction given on the journal's website when preparing your revised manuscript and your response. The author's response should be structured in a clear and easy-to-follow sequence: (1) comments from referees/public, (2) author's response, and (3) author's changes in the manuscript. Regarding author's changes, a marked-up manuscript version (track changes in Word, latexdiff in LaTeX) converted into a *.pdf including the author's response must be submitted.

Thank you for submitting your work to Biogeosciences.

With kind regards, Fortunat Joos

Dear authors

Your revised manuscript has been evaluated by the two reviewers. Both find your manuscript a useful contribution to the field and suggest publication after minor or technical revision. Based on their recommendations and my reading, I ask you to further revise the manuscript before a potential publication.

My own comments and suggestion are added below. Most notably, I find the terminology regarding the “gradient effect” misleading. The effect termed “gradient effect” arises, in my understanding, from the time-varying evolution in atm. CO2 and its deviation from an exponential curve. This should be reflected in the name for this effect. Section 2.3 is, in my opinion, not very clear and requires further improvement. I also suggest renaming “one dimensional model” to Impulse Response Function (IRF) model throughout the manuscript. As noted by one of the reviewers, there is some confusion regarding the representation of gradients in the IRF model and how this is described in the manuscript.

Thank you for submitting your work to Biogeosciences. I am looking forward receiving your revised version.

Yours sincerely,

Fortunat Joos

Major Comments

1) The terminology of the attribution of Canth to mechanisms is confusing and misleading:
The CESM and IRF model results for Canth are compared to a historical scaling approach. The deviations of ocean uptake are attributed to “carbonate chemistry” and “a vertical gradient effect” (Eq. 11).
The historical scaling is taken as a reference to discuss mechanisms that lead to deviations from these scaling results. The assumptions of the historical scaling to work are (i) the system is linear, i.e. no change in carbonate chemistry and circulation, and (ii) the forcing of the system is exponential, i.e. the atmospheric CO2 follows an exponential curve. Given this, it seems natural to attribute deviations to (i) carbonate chemistry (as done by the authors), and (ii) to deviations from exponential forcing – an atmospheric pCO2 history effect.
The deviation in the vertical gradient between Canth estimated from historical scaling and simulated by CESM (Fig. 3 and 4) arises both from the carbonate chemistry (changes in buffer factor) as well as due to deviations of the atmospheric pCO2 evolution from an exponentially increasing curve. (In addition, there may be changes in circulation, wind speed and air sea gas transfer coefficient and in the marine biological cycle that also may affect the simulated vertical gradient in Canth in CESM – albeit these effects are likely of minor importance here as postulated by the authors).
The problematic notation is evident when comparing section 3.3 and 3.2. On line 300 it is stated: “These two effects reduce the ocean carbon sink by a total of 31% from the historical scaling, with approximately 1/3 of the effect due to the vertical gradient and 2/3 due to carbonate chemistry.” In section 3.2 and Fig. 3 the deviation in the Canth gradient between the historical scaling and as simulated by CESM is shown. It is clear that the integral of these deviations (shown by gray shading) must equal the difference in cumulative air-sea flux of Canth for the historical scaling and for CESM. Thus, about 2/3 of the difference between the vertical gradient in Canth as simulated by CESM and the historical scaling is due to ocean chemistry and not due to the “vertical gradient effect”.
What is termed “vertical gradient” effect in this paper, reflects, in my opinion, rather the effect of a time-varying CO2 evolution which deviates from an exponential curve. Thus, I find it misleading and conceptually confusing to talk about a “gradient effect”. The terminology should be changed.

2) Please replace the term “one dimensional model” with “Impulse Response Function model “ and “IRF model”. Reason: The IRF model is not a 1-d model and may represent 3-d, 2-d, as well as 1-d models. The IRF model does not resolve a 1-d, e.g. vertical, gradient.

3) Assumptions for the diagnostic framework and the IRF should be clearly stated.
a) It seems that you apply the response function from the HILDA model and adjust mixed layer depth to emulate the anthropogenic carbon uptake by CESM. Thereby it is assumed that the time scales of anthropogenic carbon removal from the mixed layer and thus of ocean overturning are the same (or at least scale in some sense) in the HILDA model and in CESM- POP2. The IRF model does nicely emulate CESM over the 21st century. However, I doubt that this is true on longer time scale as the ventilation of the deep Pacific and Indian is much too sluggish in POP2 as evident from radiocarbon simulations. It should be noted that the IRF model may not equally well represent CESM results on longer time scales.
b) In section 2.5, it is assumed that the gas exchange velocity k_gas is time invariant. Again this may not hold under future climate change in CESM and in reality. Similarly, changes in the marine biological cycle are neglected.
c) ocean circulation is assumed to be time invariant and not affected by global warming. This is stated. However, it also applies to Eq. 14 where the last term only reflects the impact of warming on carbon chemistry, but not on ocean transport and stratification.

4) There is technically nothing wrong with section 3.4 and and Fig. 6. However, I do not see that this discussion and analysis adds any particular insight. I suggest to delete this text and figure from the MS.
It is well established that the surface ocean pCO2 equilibrates quickly with the atmospheric pCO2 (typical time scale of 1 yr, see e.g. Broecker and Peng, Tracers in the Sea, 1984) and that the air-sea disequilibrium in pCO2 is small relative to the absolute pCO2 value. Correspondingly, the gross air-to-sea and the gross sea-to-air CO2 flux are very comparable. This fact needs not to be iterated.

Further Comments

Line 17: I find the number of 39% misleading. Ocean uptake should be related to total anthropogenic emissions, including those from land use. LUC emissions are substantial over the historical period. A more conventional estimate is that the ocean has taken up between 25 to 30 percent of anthropogenic emissions.

L30: effective surface diffusivity: The term “surface” seems misleading. It is a vertical diffusivity applied to operate over the upper and deep ocean

l. 38: natural sink – suggest deleting “natural”

l40: expand to say: “are strictly exponential and the system is linear”. As this holds only for linear systems.

L124: historical period: 1920 to 2006: Should this not read 1820 to 2006? Starting the simulation in 1920 would lead to a massive cold start problem. I think the RCP simulations started in 1820.

Section 2.3: I found this section somewhat unclear and confusing.
It is not clear to me what is done. I guess that you use the IRF function of HILDA from Joos et al. and adjust the mixed layer depth h to 109 m to match the anthropogenic carbon uptake as simulated by CESM for the historical period. Eq. 7 and Eq. 10 (together with the chemistry described in the appendix) are then used to compute ocean uptake. If this is correct then please state this explicitly. It would also help to bring Eq. 10 next to Eq. 7.
It is also my interpretation that Eq. 8 and 9 are not applied in this study, but added for illustration and to conceptually separate mechanisms. I recommend moving these two equations and the related text to section 2.5 to keep the description of the IRF model strictly separate from the description of the separation into individual terms.

L145: typo: in -> on

L145: Change “one dimensional” to “reduced form” or to “substitute”.

L160ff, eq. 8: Eq. 8s represents rather a conceptual than an operational description and the text on l.160 is in my opinion not correct. Even in the case of 1-d box diffusion model, many ocean layers are used to determine the carbon flux at the base of the mixed layer. Here it is not clear how the gradient dC_ant^ML/dz would be derived. I suggest rewriting the text to read something like “The convolution integral (Eq. 7) may be conceptually linked to the following tendency equation of anthropogenic carbon in the surface ocean mixed layer:”
Eq. 8
The change in the mixed layer carbon concentration results from the air-sea flux (F_anth) and from the flux between the mixed-layer and the deeper ocean, here formally written as a diffusive flux.
Suggest deleting “The one-dimensional model’sKz;eff must match that of the ocean component
of the ESM being emulated (Gnanadesikan et al., 2015).” as this sentence is not needed and rather confusing given that it remains unclear how the gradient is determined.
L 167: Please specify from what the “diffusive flux term” is estimated. I first guessed from the air-sea flux and the change in surface layer concentration as simulated by CESM. However, then in section 2.4 it becomes clear that the separation is done using the IRF model.

L198: only true under the assumption of a constant k_gas and in a spatially-averaged framework. These assumptions may not necessarily hold for CESM. Please clarify the limitation.

Line 207: expand to read: “impact of warming on the carbon chemistry”

Line 259: typo: fro -> from

Section 3.2: The deviations in Canth between the historical scaling and POP2 are due to changes in the buffer factor and due to deviations from an exponential forcing in the scenarios. Correct? I suggest to state this for clarity and to avoid confusion with the attribution done in the next sections.

Line 318: two verbs: “acts increases”

L 324: typo: around

L385 to 391: This paragraph is misleading and should be deleted. An IRF model is applied and not a 1-d diffusion-advection model.

L457 ff: Suggest to use the term Impulse Response Function model instead of 1-d model throughout the MS.

Dear authors

Thank you for submitting a revised version. I have read your reply and your revised manuscript and I am happy to accept your MS subject to the corrections listed below.

Thank you for submitting your work to Biogeosciences.

With kind regards, Fortunat Joos

Line numbering is from the version with track changes:
1) Line 2: It is incorrect to say “UNFCC Paris Agreement, committing to mitigate global anthropogenic carbon emissions so as to limit global mean temperature increase to no more than 1.5_C.” Please see the Paris Agreement and change the text accordingly.

2) Line 450: “Cwarm only accounts for the impact of warming on solubility “. In my understanding, this should read here and elsewhere (e.g., in the caption of Fig. 5) in the MS: “Cwarm only account for the impact of warming on solubility and inorganic carbonate chemistry” as chemical equilibrium constants also change with temperature.

3) Fig. 5: The present coloring is inconsistent with the attribution presented in Tab. 1. Please color the difference between the run with constant chemical capacity (Cccc) and the historical scaling always by light green. Now this difference, denoting the “transport effect” according to Tab. 1 is colored by light blue if the “transport effect” is positive. As evident in Fig. 5, the “transport effect” as determined with the IRF model is positive under RCP8.5 and also partly positive under the other two scenarios. Please make the color scheme in Fig. 5 consistent with the attribution as described in the main text and in Tab. 1 and with the text on line 389 to 392.

4) “..transport to begin to play a role after 2060” suggest to rewrite to “..transport effect to begin to play a role after 2060” and similar on line 561