the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Aug 2026
Modeling the response of the marine carbon cycle to extreme CO2 injection events
Abstract. We explore how the response of a conceptual model of the marine carbon cycle depends on the way in which carbon is injected from the atmosphere. We find that, for single-injection pulses, the threshold amount required for a large response of the excitable system depends on pulse duration but not on its specific form. We do, however, see differences in the number of large transient responses in carbon and, correspondingly, the duration of the response for different pulse shapes. These differences are magnified as the system is pushed towards increased excitability and can be understood in terms of the geometry of an increasingly winding heteroclinic orbit. Inspired by Large Igneous Provinces (LIPs), we also consider random sequences of injection pulses. We find a wide range of possible responses for a given overall amount of injected carbon and duration, depending on the mean characteristics of the individual pulses. We also identify a resonance-like "Goldilocks" zone, in which intermediate pulse durations or arrival frequencies produce the largest number of repeated transients, and we test the framework with illustrative scenarios motivated by the Siberian Traps and Columbia River Basalt Group.
Status: open (until 01 Oct 2026)
- RC1: 'Comment on egusphere-2026-4694', Anonymous Referee #1, 04 Sep 2026 reply
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RC2: 'Comment on egusphere-2026-4694', Anonymous Referee #2, 08 Sep 2026
reply
Publisher’s note: a supplement was added to this comment on 11 September 2026.
Gandhi et al use an existing conceptual model by Rothman to evaluate to what extent the rate and time of (LIP-like) C emissions affect carbon cycle feedback responses. The model consists of two feedbacks coupled to a simplified ocean with a (DIC) dampening timescale for air-sea exchange and ocean mixing. In certain parameter space, bistability exists which produces a non-proportional response to emissions when a threshold is met. Gandhi et al interrogate how the threshold changes with emissions rates with an ensemble of varying idealized and LIP-inspired emission scenarios.
General recommendation:
Rothman 2019 already demonstrated (by interrogating equations) that fast emission rates can lead to excitation of the system, amplifying the system response. Gandhi et al illustrate the implications with tested examples, i.e. a parameter sweep in mass-time space, this is hence a useful supplement to Rothman’s study. The methods and use of the model are sound, but the structure of the text could be improved. Authors mostly (not always) use appropriate citations. Figures are generally informative but somewhat difficult to interpret without context. The idealized scenarios to demonstrate patterns are useful but the LIP-inspired scenarios need improved justification. I believe the study fits the scope of ESD and contributes new insights though some critical points [see attached for full document] should be addressed, mainly improving readability and providing more, or better integrated, real-world application context.
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General comments
The manuscript "Modeling the response of the marine carbon cycle to extreme CO2 injection events" by Gandhi et al. reviews a conceptual model of the marine carbon cycle originally formulated by Rothman (2017,2019), and studies the response of this excitable system to forcing pulses. The underlying motivation is extreme volcanic activity known as Large Igneous Provinces and its impact on the planet. The topic is scientifically relevant and within the scope of ESD. The authors review the model introduced by Rothman and discuss how three types of pulse perturbations affect the response of this excitable system. We note that the transient behaviour of the model against square injection pulses (one of the three types of perturbations considered in this work) had already been treated by Rothman (2019) as the authors correctly mention in their manuscript. The most (maybe only) innovative point seems to be the discussion of repeated random perturbations for a cumulative mass of injected CO2 showcasing three different dynamical behaviours depending on the mean size of the injection pulses, which also affects the injection frequency. The authors suggest to use the number of windings of the heteroclitic orbit as the measure of response of the system bringing into the discussion resonances and Goldilocks zones. The conclusions reached are of qualitative nature and do not go beyond the discussion of some numerical simulations. In other words, no rigorous dynamical analysis of the system is carried out beyond reviewing the autonomous case already presented by Rothman. The simulations are thoroughly described and therefore reproducible. Previous work is correctly referenced throughout. The title reflects the content of the paper and the abstract provides a complete and concise summary.
Specific comments
In my opinion the paper looks written a bit in a hurry, more similar to a collection of notes and results rather than trying to enhance the clarity for the reader's benefit. For example, I encourage the authors to (at least) review the following points:
1) the different notations for derivatives df/dt, f' and \dot f are interchangeably used, to the detriment of the manuscript's clarity.
2) The model is introduced rather quickly without providing enough context to understand its dynamics beyond referring to Rothman 2019 and plotting a bifurcation diagram. I encourage the authors to provide a more detailed presentation, possibly in appendix if they feel that this would disrupt the flow of the text. The same holds true for the reduction and its equilibrium (c*,w*), heteroclinic orbit, limit cycles, which are presented without any explanation.
3) On multiple occasions, the authors literally quote Rothman (2019), sometimes out of the blue, without any context (see for example third sentence after Figure 1, the end of page 9, the first sentence of Section 3.5, Section 3.7). The reader is inevitably forced to study Rothamn (2019) before being able of reading this manuscript.
4) Reading the introduction, I had the impression that the most innovative accomplishment of this manuscript was to discuss bifurcation-,noise-induced- and rate-induced tipping for the model by Rothman. However, Sections 3.5 and 3.6 seem completely superfluous as they are limited to few sentences directing the reader towards other papers and the phenomena of bifurcation- and noise-induced-tipping are never mentioned again in the text. Also Sections 3.7 and 4 on rate-induced tipping are respectively limited to reporting previous statements by Rothman, and setting up the ramp function and discussing one experiment in Figure 4.
Since seven people are listed as authors of this manuscript, I encourage a collective discussion on how to privilege the reader's perspective and make the paper clearer and more self-contained.
Technical corrections
- The constant C_p is used but not introduced in Section 2. The definition appears only in Table 1 without any discussion.
- At the end of page 3 the acronym DIC is used before being introduced in the following line
- At the end of page 4 the role of the variable c in determining an equilibrium is discussed before introducing the variable c.
- After formula (2b) it would be beneficial to write "where, for $\alpha>0$ we define," so that it is clear that in the ensuing formulas alpha is an exponent and not a super index. Otherwise there might be confusion on what S_\beta and \overline S_\gamma are.
-First line of subsection 3.3. The authors might want to write "In the (R_\theta,C_X) plane as this is consistent with the notation of Figure 2(b)
- End of page 9. The authors write "for the slice c_x=0.5 in panel a". However, it is not clear to which Figure they are referring to. If Figure 2, there is no c_x in panel a.
- Last sentence of Section 2.1. "summarized IN Table 1"