The Rapid Communication manuscript by Verbitsky and Omta describes the relaxation behavior when an idealized model of the ocean’s alkalinity budget is subjected to idealized orbital forcing, documenting spontaneous changes in the dominant periodicity of the model response. The manuscript draws an interesting comparison to the Mid-Pleistocene Transition from obliquity-pacing of climate to a saw-tooth pattern with ~100kyr dominant periodicity, but it offers little discussion why the dynamic behavior of the idealized model should apply to the real Earth System. Because of the abbreviated format of the manuscript it is difficult to assess the significance of the work.

Detailed comments:

Orbital forcing of the calcification rate constant as the primary driver of CO2 change is a highly unusual model to use, and simulating the ocean’s alkalinity budget completely independent of seawater carbonate saturation state is questionable. This model may be suitable if the point of the manuscript is simply to document “a remarkable physical phenomenon”, but drawing any conclusions about the paleoclimate record based on these results would require detailed justification of the model and discussion of its applicability.

The authors draw attention to the fact that the model remains phase locked to the forcing frequency for millions of years before spontaneously settling on oscillation with a dominant period that appears to be an integer multiple of the forcing period. The authors should explain how their finding is similar or different to the notion of skipping obliquity cycles advanced by Wunsch and Huybers. Is this simply a case of non-linear phase locking?

Given the emphasis on the million-year persistence of influence from the model initial values it is worth noting that the model does not include any stochastic “white noise” term that would over time erode in initial value information. It would have been helpful if Figure 1 included a small set of identically forced simulations with different initial conditions, to assess if they relax onto the same long-term solution. Also, it would have been helpful if the manuscript included power spectra and phase space portraits for the different solution groups indicated in Figure 2b.

The conclusion takes a major leap from the identified behavior of the model to claiming that “thus MPT exhibits a remarkable physical phenomenon” [line 188]. In absence of any significant discussion on the applicability of the model to the MPT this leap seems rather speculative. Further, it would have been helpful if the manuscript had elaborated  on the implications for the interpretation of the dynamic mechanism yielding obliquity-paced  iNHG and presumably preconditioning the system to experience some type of MPT. For example, if the model dynamical behavior is applicable then climate change should always lag CO2 change, which always lags orbital forcing by thousands of years.

Summary:

The Rapid Communication article by Verbitsky and Omta presents a sensitivity study carried out on a simple conceptual ocean chemistry model. The underlying model used in this study is the calcifier-alkalinity (CA) model, as described by Omta et al. (2013, doi: 10.1002/gbc.20060). The authors apply an obliquity-paced orbital forcing to the calcifier growth parameter and demonstrate that the system exhibits long equilibrium times, with transitions from an initial dominant period to an asymptotic one that can occur abruptly. The authors find that this transition in the period can be highly sensitive to the initial conditions and that this sensitivity depends on the amplitude of the orbital forcing. Based on their results, the authors state that the MPT could be the result of a relaxation process resulting in a sharp transition in the dominant period and that it could have resulted from different sets of initial values and orbital forcing amplitudes. Therefore, the observed 41-kyr to 100-kyr shift in the periodicity just resembles one specific instance, but different initial values or an altered orbital forcing amplitude could have led to a completely different pattern in this period shift.

In my view, this article presents an interesting view on the MPT. Especially demonstrating that the C-A model can produce abrupt, MPT-like jumps in periodicity purely driven by orbital pacing alone, without the need for any change in parameters, is significant. Furthermore, the result that the sensitivity of the asymptotic state depends on the amplitude of the orbital forcing is very interesting. My primary concern with this work lies in the very conceptual view of the model, and how the results relate to the MPT and the real world. Strengthening the link between the modelled relaxation processes and the real climate system would enhance the significance of the results for the MPT.

Major comments:

• Please comment on why it is justified to consider T, k0, I0, M and C(0) as constant. For me it is not obvious why P/τ should only depend on α and A(0)/F, but not on Mτ or C(0)/F 
• In Fig. 3: is there any physical justification for the used parameter bounds? Can some of the areas in the parameter space be ruled out due to constraints from observations? Based on this analysis, the authors claim that “[...] the MPT could have been not just of the 40 – 80 kyr type, as we observe in the available data, but also of a 20 – 40, 80 – 100, 40 – 120, or even 80 – 40 kyr type” (L.18 f.). Especially the 80-40 kyr scenario, which means a reduction in periodicity, seems to occur very rarely in the simulations. It mainly appears in the lower left and upper left parts of Fig 3a) and 3b), where the blue-coloured areas transition to green-coloured areas. Are these scenarios realistic?
• Fig. AC1-1 shows that the time until equilibrium is reached is highly variable and for the three shown simulations ranges from ~2 - 6Myr. While this article mainly focuses on the periodicity, the timing until the asymptotic period is reached is important for a full view on the MPT and it would be interesting to include some insights on the mean equilibrium times of the ensemble simulations
• Large parts in Fig.3 do not change in colour. Does this imply that a large quantity of the simulations reach the asymptotic period within the first 1Myr of simulations? Hence, the mentioned shifts in period are only occurring for very specific sets of initial values and forcing amplitudes?

Minor comments:

• Point a) in the abstract (L. 15 f.): actually if  α < 0.002, the period becomes completely insensitive to the initial parameters. Therefore, please change the wording of point a), s.t. it is clear that the sensitivity to the initial parameters increases with α
• A potentially nicer way of depicting the change in frequency over time would be to use a wavlet scalogram (e.g. Pyleoclim package in Python), instead of the presented time-averaged power spectra in Fig. 1b and 1c. But this is just a suggestion
• L.48: just want to highlight that there is also other recent work on this topic, e.g. Ma et al. (2024, doi: 10.1016/j.gloplacha.2024.104526) who link the MPT to successive changes in the annual mean insolation
• L. 94: please add the GitHub link
• L.116, L. 123 and thereafter: the naming “pre-MPT” and “post-MPT” is a bit misleading, since some of the ensemble simulations do not necessarily represent realistic MPT-like scenarios, but rather just some relaxation/equilibrium simulations with an initial and an asymptotic period. Therefore, I suggest to just use the term “initial” and “asymptotic” for these periods there.
• Fig. 3: are T, k0, I0, M, C(0) kept constant at the same values presented in Fig. 2 and above? If so, please add the values to the caption, or to L. 146
• L. 233: DOI doesn’t work. Please update to https://doi.org/10.1002/gbc.20060