Leloup and Paillard present a new model to link astronomical forcing with multi-million-year oscillations in Earth’s carbon cycle. I will immediately admit to not being an expert on astronomical forcing of Earth’s surface environment or the mathematical modelling of how different modulations may have influenced surface processes. As such, it is difficult for me to make detailed comments about the modelled approach. However, I do have some general thoughts on the assumptions made by the model.

The authors are very open about the fact that this is a very simple model and that they have been unable to include several processes that may complicate the relationship between astronomical forcing and the carbon cycle. I am the first to acknowledge that any model of geological processes has to make simplifications, and that it is impossible to consider every possible control. However, I do worry that there are some potentially major factors that have not been considered, and whose exclusion from the model makes it potentially unrealistic.

Firstly, and very importantly, whilst the rate of organic-carbon burial is indeed related to global oxygen levels, the reverse is also true. Several studies have highlighted that a large increase in organic-matter deposition will cause surface oxygen levels to rise (see e.g., Lenton and Watson, 2000, Global Biogeochemical Cycles; Berner, 2004, Oxford University Press; but there are many others). It’s not clear whether the authors have considered this as a two-way process. On the subject of oxygen, at the moment the model seems to consider surface oxygen as a single inventory of oceanic and atmospheric oxygen levels, but the reality is that different parts of the marine realm can be very oxygen depleted regardless of overall oxygen levels. This is particularly the case for for small restricted epicontinental basins, and these varied in abundance due to tectonic configuration at various times in Earth’s past, and were highly influenced by local processes and sea level changes, both of which are related to astronomical forcing. Also, the authors consider oxidation of non-carbon elements as an important control, but not the potential reduction of these elements, which I find curious. And what about sulfur and phosphorus?

I also wonder if the authors have considered the potential role of terrestrial organic-matter burial in their model. Of course, organic carbon burial in the ocean will typically be the more important sink, but there are times in Earth’s history when terrestrial burial is thought to have had a massive influence on the global cycle, most famously during the Late Devonian–Carboniferous, but also in the Mesozoic (e.g., Valanginian; see Westermann et al., 2010, EPSL). This is important because the terrestrial sink is likely controlled by very different factors (not directly linked to surface oxygen) than the marine sink.

If it isn’t possible to incorporate these factors into the model, then at the very least there needs to be more open consideration of them (as well as other processes which will vary over time). But as things stand, I worry that the list of missing controls is so long at present that the model cannot really be a strong representation of reality, and that at least some of them need to be included as separate terms regarding the sources and sinks of carbon and oxygen etc.

Minor comments:

Line 51: Here ‘favour’ is written. Elsewhere it is ‘favor’. Be consistent.

Line 99: A constant fractionation factor of -25 per mil for organic matter is a probably a big assumption given the differences in different organisms, and especially following the rise of C4 plants in the Cenozoic (considering that this paper discusses that time interval).

Line 117: How is the carbon cycle forced astronomically? Simply invoking an unnamed link feels rather vague to me.

Lines 132–133: Yes, but this will not be evenly distributed and even when surface oxygen levels rise, there can still be places in the ocean that can be very anoxic.

Line 154–155: This will then cool the climate and reduce organic-matter oxidation, raising surface oxygen levels, both of which will act to mitigate the organic-carbon burial.

Lines 162–168: What are ‘lower’, ‘intermediate’, and ‘higher’ carbon values defined as? What range?

Line 175: ‘…we place ourselves here in one of the simplest case possible.’ is rather casual language for me.

Line 201: I assume that the organic-matter burial being referred to here is oceanic. What about terrestrial organic-carbon burial?

Line 258: What about reduction of other elements?

Line 422: I’m not sure a mechanism is being proposed per say. It’s been assumed that astronomical forcing influences carbon supply vs burial and oxygen levels, and that long-term cycles can be reproduced for a certain set of parameters. But this is all very theoretical still and there isn’t a cause-and-effect link proposed for how the astronomical forcing is influenced these carbon and oxygen sources and sinks. For me, that would be the mechanism.

Peer review of „Multi-million year cycles in modelled d13C as a response to astronomical forcing of organic matter fluxes”.

In this paper, the authors built a simplified numerical representation of the carbon cycle, assuming a mass balance without carbon reservoirs (and hence no lag-times there), unlimited nutrients (otherwise organic burial B would also depend on weathering W), and with constant [Ca²⁺] concentration in the ocean. Without applying any forcing, their model evolves into steady-state equilibrium when the oxidation of other elements than organic carbon (Ox) increases steeply with oxygen content (O). When the Ox term increases less steeply with O, the model produces oscillations in d13C without any astronomical forcing. Finally, the authors add an eccentricity forcing to the burial of organic carbon and they observe that the resulting d13C is oscillating with preferential periodicities of 2.4, 4.8 and 7.2 Myr. The authors thus built a model that is prone to oscillate at multi-million-year timescales between multiple equilibria, and by adding the forcing they are making sure that the model resides around one equilibrium value until the astronomical forcing becomes strong enough to push the system towards the second equilibrium. Finally, the authors compare their model results to the Westerhold et al. (2020) benthic d13C compilation and point out to the reader that the multi-million-year oscillations in this record could be the result of self-sustained oscillations in the Earth system.

Major concern.

This is a nice “back-of-the-envelope” carbon cycle exercise, but I do not see the immediate merit in this paper. The authors set the model variables such that it is prone to produce multi-million-year cycles. They force it with an eccentricity cycle (including the 2.4 Myr component) and come back home with a simulated d13C signal that emphasizes these same 2.4 Myr cycles, as well as multiples of that cycle. I would be interested to read why the authors believe their approach provides additional insights into the behavior of the carbon cycle in addition to other previous attempts to simulate the global carbon cycle. I am especially thinking about Bachan et al. (2017), who reports on carbon cycle stabilization pathways in response to a sinusoidal forcing.  

I also feel that some simplifications in the model need to be more clearly justified. It seems contra-intuitive to de-couple silicate weathering from the organic carbon flux (B does not depend on W). The ocean cannot recycle the same nutrients ad infinitum. You have to introduce new nutrients to compensate for the ones lost to mineralization and burial. Those nutrients come from terrestrial weathering. Moreover, that weathering also modulates the availability of alkalinity, which balances out the atmospheric CO2, and allows for calcification. One ends up with a triangle of calcification (take alkalinity and nutrients, releases CO2), weathering (take CO2, releases alkalinity and nutrients) and organic matter burial (take CO2 and nutrients). But these three are not in phase with each other, which in itself already results in an oscillatory pattern.

Bachan, Aviv, et al. "A model for the decrease in amplitude of carbon isotope excursions across the Phanerozoic." American Journal of Science 317.6 (2017): 641-676.

Minor concern.

The y-axes in Figures 2 and 3 are incorrectly labeled.

• In Figure 2, the y-axis represents B, not dC/dt. My suggestion would be that the authors hatch the area in-between the organic and inorganic terms and label them with dC/dt>0 when the inorganic term is larger than the organic term, and vice versa.
• In Figure 3, the y-axis represents B for the green curve and Ox for the blue curve. Not dO/dt. Again, here the authors could hatch