The ms addresses an interesting question, if changes in ocean pH will affect the oxygen and carbon isotope composition of marine organisms. If yes, our interpretation of the isotope composition of fossil shells will be biased due to past changes in ocean chemistry and atmospheric pCO2. Koehler and Mulitza (K&M) present a compilation of glacial/interglacial stable isotope data for G. ruber and G. sacculifer and compare the data to the output from a carbon cycle model, to determine if the isotope data are affected by glacial changes in ocean pH.

The data presented in the ms are probably of fair to good quality and relevant; the conclusions are probably valid and supported by the data. However, the text is badly organised and it is often difficult/impossible to understand what exactly the authors are trying to say. The phrase "probably" is used because the poor presentation leaves room for misinterpretation.

Carbon isotope data - foraminifera. Spero et al (1999) use equations for the relation between d13C and [CO3=] in G. ruber and G. sacculifer to suggest that the offset between the two species in glacial sediments can be used to trace changes in oceanic pH. K&M seem to take these equations as an established fact, only to find that the predicted response cannot be reproduced based on a much larger suite of data. This negative outcome is mentioned immediately at the end of the data section (section 2.3 (not the right place)), which implies that actually there is no real purpose to continue with the modelling part of the study. This is poor salesmanship. I suggest to rewrite the text, emphasising that Spero et al (1999) presented a reconstruction based on a single core, the validity of which can be tested with the current much larger data set. However, there are some points to keeps in mind:

1. K&M are focussed mainly on only two papers, Spero et al (1997) and Spero et al (1999). Spero et al (1997) present the famous experiment in which Orbulina and G. bulloides were grown under a wide range of [CO3=] concentrations, after which the d18O and d13C of the test was measured. Spero et al (1999) is not as well documented: the paper is based on "published" experimental results for G. ruber and G. sacculifer, the two species used by K&M. However, the only citation for the actual experiment is a conference abstract, the data are not available as far as I'm aware.
2. Bijma et al (1999) presented a re-evaluation of data in Spero et al (1997), focussing on pH instead of [CO3=]. They showed that within the range of normal, open-ocean pH there is actually very little variation in isotope composition of Orbulina and G. bulloides. This may well be true for G. ruber and G. sacculifer as well, but this cannot be checked.
3. The range of variation in d13C observed by Spero et al (1997) is too large to explain as a chemical equilibrium reaction (Zeebe, 1999); vital effects related to symbiont activity can explain part of the trend but not the entire magnitude (Zeebe et al., 1999). So something mysterious is going on, if this is relevant for glacial oceanography remains to be seen.

references (if not cited in K&M)

Bijma, J., Spero, H. J., & Lea, D. W. (1999). Reassessing foraminiferal stable isotope geochemistry: Impact of the oceanic carbonate system (experimental results). In G. Fischer & G. Wefer (Eds.), Use of Proxies in Paleoceanography: Examples from the South Atlantic (pp. 489–512). New York: Springer-Verlag.

Zeebe, R. E. (1999). An explanation of the effect of seawater carbonate concentration on foraminiferal oxygen isotopes. Geochimica et Cosmochimica Acta, 63(13-14), 2001-2007. doi:10.1016/S0016-7037(99)00091-5

Carbon isotope data/model - atmosphere.

The authors write (lines 350-351; my emphasis in bold): "... More interesting is how simulated changes in atmospheric d13CO2 compares to simulated changes in various marine d13CDIC time series (Figure 7)." However, model version C1 is forced with measured d13C-CO2atm; which means it is input, not output. This raises the question what the modelling contributes - please address this explicitly. The measured isotope data in Figure 3 all show similar trends (with some lead/lags). The modelled d13C-DIC in figure 7 shows, after forcing with atmospheric d13C-CO2, pretty much the same trend, i.e., non-polar d13C-DIC is in equilibrium with the atmosphere. Is this new?

More in general, there is a lot of description of the variables/parameters taken into account, but it is not clear which time-series the model is forced with explicitly. There is a reference to a previous version of BICYCLE, but please repeat this information.

Lastly, the authors choose model version C1CO2 as their final version, even though this version "violates mass conservation" (line 335). As far as I can see there is little difference between C1 (forced with measured d13C-CO2) and C1CO2 (both CO2 and d13C-CO2 prescribed) - why not stick with C1 as the version with fewer assumptions?

Correlation coefficients. Linear correlation coefficients are not well suited to determine if two time series are correlated. A significant correlation (table 2) means that the time series show similar long-term cycles, i.e., the 100 kyr. That this is the case can be seen visually by inspecting figures 3 and 7. However, the presence/absence of shorter cycles (20 kyr, 40 kyr) cannot be addressed with linear correlation coefficients; neither can leads/lags.

The more appropriate way to test for similarity between time series is to use Fourier Analysis or related methods. I suggest that the authors calculate coherence spectra, to test if the 20 kyr and 40 kyr cycles are present in the isotope data and model input and output. At the very least, Table 2 should go the supplement - it takes up a lot of space, and the essential message (similar long term trends in d13C in the atmosphere, surface ocean, and deep ocean) can be seen in figure 3.

The distinction between 20/40 kyr and 100 kyr cycles is important for the evaluation of Fig. 7. In the basic version of the model (SEi) the modelled d13C shows rapid fluctuations which closely follow those in the atmospheric pCO2 records, at least visually. Only when the model is forced with observed d13C-CO2 does it reproduce the long-term trend (100kyr). It needs coherence spectra to determine what happens with the shorter fluctuations.

Further comments. - see also attached .pdf:

• words like "interesting" and "surprising" should not be used in a scientific manuscript;
• K&M use the label "non-polar" to describe their isotope data (e.g., fig. 3), however all marine cores in the data set are located between 40°N - 40°S; this leaves a very wide zone (40-66°) unaccounted for in both hemispheres.
• The first part of section 3.1 has been copied literally from Koehler and Munhoven 2020; this counts as plagiarism. Please check the rest of the text and modify where necessary.

Review

The authors present a study of the cycling of carbon-13 over the past glacial cycle. They compile sediment data from two species of planktonic foraminifera and compare the results with box model simulations focusing on the Carbonate Ion Effect (CIE), which has been observed in the lab and proposed to affect paleorecords. However, the authors do not find evidence that the CIE affects paleorecords. To the contrary, the similarity of the two different species records and comparisons with model simulations suggest minimal or no CIE.

I think the paper is well written, nicely illustrated and comes to a conclusion backed up by the evidence provided. I don’t have major issues and recommend publication with minor revisions. Below I list two specific points that could be addressed in a revision.

1. In the abstract (line 13) the authors claim that the model results agree with sediment-data-based reconstructions of d13C_DIC. I don’t agree. Fig. 7 shows that the model overestimates the variations in d13C_DIC. However, the comparison does not include the CIE. I suggest to estimate the CIE based on deep ocean model simulated CO3 and include it in the model-data comparison. Does it make a difference?
2. The authors suggest a temperature dependence of fractionation during photosynthesis, based on observed trends in d13C or organic matter. However, previous formulations of fractionation during photosynthesis proposed it depends on pCO2 (Popp et al.,1989; Rau et al.,1996). Couldn’t this also explain the observed trend?

Popp, B. N., Takigiku, R., Hayes, J. M., Louda, J. W., and Baker, E. W.: The post-paleozoic chronology and mechanism of 13C depletion in primary marine organic-matter, Am. J. Sci., 289, 436–454, 1989.

Rau, G. H., Riebesell, U., and Wolf-Gladrow, D.: A model of photosynthetic 13C fractionation by marine phytoplankton based on

diffusive molecular CO2 uptake, Mar. Ecol.-Prog. Ser., 133, 275–285, 1996.

Technical comments:

• Line 49 “these” should be “this”
• 3: For T1 there is a higher resolution record from Bauska et al. (2016; www.pnas.org/cgi/doi/10.1073/pnas.1513868113) available.
• Line 82: replace “ten boxes large ocean” with “ocean with 10 boxes”
• Line 198: explain acronym AOBM
• Line 253: replace “In” with “At”
• Lines 255-258: see point (2) above. This also applies to the meridional gradient (e.g. Fig. 8 in biogeosciences.net/10/5793/2013/)
• Line 296-297: how?
• Line 300: typo replace “uncertainties” with “uncertain”
• Line 387: “not too far away from the truth” It is unclear if the different processes are correct. E.g. you assume large changes in SO ventilation with a big effect on CO2, whereas Khatiwala et al. (2019; doi: 10.1126/sciadv.aaw4981) suggest small effect of ocean circulation.
• 481-482: related to point (2) above, what is the effect of this assumption on the simulated surface d13C_DIC in the case of prescribed atmospheric d13C_CO2?