An improved conceptual model of Quaternary global ice volume and the Mid-Pleistocene Transition

Pollak, Felix; Parrenin, Frédéric; Capron, Emilie; Chase, Zanna; Jong, Lenneke; Legrain, Etienne

doi:10.5194/egusphere-2025-2233

Preprints

https://doi.org/10.5194/egusphere-2025-2233

Preprints

05 Jun 2025

| 05 Jun 2025

An improved conceptual model of Quaternary global ice volume and the Mid-Pleistocene Transition

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

Abstract. During the Quaternary period, spanning the last 2.6 million years, the characteristic frequency and amplitude of glacial-interglacial cycles evolved from low-amplitude 41,000-year cycles to high-amplitude 100,000-year cycles. This transition occurred around 1.2 to 0.8 million years ago and is referred to as the Mid-Pleistocene Transition (MPT). While the 41 kyr cycles are driven by changes in Earth’s obliquity, which largely affect the incoming solar insolation, no apparent change in external orbital forcing during this period could explain the shift towards 100 kyr cycles. Several theories have been put forward to explain this shift, including scenarios of both gradual and abrupt changes in the internal climate system throughout the Pleistocene. In order to test which theory best matches the observations, we have constructed a conceptual model capable of simulating changes in the global ice volume over the past 2.6 Ma and accurately reconstructing the MPT and its associated change in amplitude and frequency. Four different forcing scenarios are implemented, ranging from a purely orbitally driven model to a ramp-like change in internal forcing. The model is in favour of a ramp-like forcing scenario, where the gradual change in internal forcing is limited in time and started around 2 Ma. These findings imply that the climate system had already undergone major changes in the early Pleistocene and support the idea of a long-term climatic shift as a cause of the MPT. For the best-performing model, we included an ice volume dependency in the state thresholds, demonstrating that glacial terminations during the past 900 ka are mainly driven by precession rather than obliquity.

Received: 15 May 2025 – Discussion started: 05 Jun 2025

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Journal article(s) based on this preprint

27 Mar 2026

Simulating global ice volume across the Mid-Pleistocene Transition with a ramp-like increase in the deglaciation threshold

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

Clim. Past, 22, 675–688, https://doi.org/10.5194/cp-22-675-2026,https://doi.org/10.5194/cp-22-675-2026, 2026

Short summary

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

Interactive discussion

Status: closed

RC1:
'Review on egusphere-2025-2233', Anonymous Referee #1, 03 Jul 2025

This paper improves an exisiting conceptual model on global ice volume changes as function of orbital forcing and some internal feedbacks which is then applied to the last 2.6 Ma in order to understand the Mid-Pleistocene Transition (MPT).
In my view this is a solid piece of work, but misses one important piece of discussion. All sea level (=global ice volume) reconstructions used here as target are some sort of deconvolution of the LR04 benthic d18O stack into sea level and temperature. However, a most recent approach by Clark et al., published some weeks ago in Climate of the Past (doi: 10.5194/cp-21-973-2025) doing the same thing supported by SST and deep ocean data comes to a significantly different deconvolution with larger glacial/interglacial amplitudes in the sea level component throughout the Quaternary than the sea level records used here.
In an ideal world, this new record (data to figure 10b in Clark et al., 2025 available in the SI there) would as an alternative be used here as tuning target, but I understand that this would be a major effort and leave it up to the authors if they want to jump on this challenge. However, I noted that the authors referred to another discussion paper (Scherrenberg et al., 2024), so it is not clear to me why they not also included in their discussion of the MPT the Clark et al paper, whose discussion version was also available since September 2024. What should be and needs to be done is that this difference between the sea level component in the new Clark et al 2025 paper and those used here needs to be discussed. This is in my view important for two reasons.

1. The Clark paper is simply one of the newest papers published on MPT sea level changes (although only indirectly contained in the contribution to the benthic d18O stack) and should be considered/discussed in any upcoming paper on the same topic.

2. The regolith hypothesis, formulated some decades ago, also by Clark and others, was trying to explain that there were ice sheets in North America, that were reaching as far south as 39-40°N around 2.5 Ma ago (e.g. Balco & Royery, 2010, doi: 10.1130/G30946.1). However, more complex models are not yet able to simulate these ice sheet extends. The Utrecht model (in the version of de Boer et al 2014, doi:10.1038/ncomms3999) was failing to do so, as has been shown in Köhler & van de Wal 2020 (doi: 10.1038/s41467-020-18897-5), which plotted in their Fig. 2b the latitudinal ice sheet extend of the Utrecht model as function of time.

(Side note: Köhler & van de Wal 2020 is to some extend a reinterpretation of Tzedakis et al 2017 on the appearance of interglacials during the Quaternary and might for that content also be discussed here as one recent study on the understanding of the MPT.)

The sea level of Berends et al (2021) used here is a follow-up study of the de Boer et al 2014, both using a model to deconvolve benthic d18O into sea level and temperature, thus both results differ in detail, but rely on the same approach and give in principle comparable results. Also the 3 Ma long simulations of the CLIMBER model (Willeit et al., 2019, doi: 10.1126/sciadv.aav7337), which is a more complex climate model than in the Utrecht approach, and which does not use benthic d18O as input, do not get large ice sheets down to 40°N at 2.5 Ma BP.

That said, these interpretations of the benthic d18O stack are still failing to explain the terrestrial evidence of Balco and others. These shortcomings are also worth mentioning in the discussion.
With this two contrasting deconvolutions of the benthic d18O stack - one based on ice sheet model, one based on an ocean temperature data compilation - such a simple model as used here might be able to give ideas how to understand them. Eg if completely different conceptual models are necessary to satisfy both data sets, but again, maybe this is a task for a future study, especially since a final interpretation of the sea level related changes in benthic d18O from Clark et al is still not published. Nevertheless, I would say it is a missed opportunity if the authors decide not jump on this issue here and now.

Minor issues:

- Barker et al. 2025, explaining the role of orbital parameters for the 100k-world after the MPT also gives a glimpse on their roles in the 41k-world (their SI Figure 8). Thus, I believe this paper is one of the most recent studies discussing underlying processes of the MPT and should already be discussed widely in the introduction.

- Please update the reference to Scherrenberg et al., 2024 to the now available final version: https://doi.org/10.5194/cp-21-1061-2025).

- Figure 4: purple and red dots look the same. Make one symbol differently, eg squares.

- lines 520ff: Somehow now „glacial inception“ is shortened to „gl. inception“. Please use full words.

- line 614: The most recent review on MPT SST changes is in Clark et al. 2024 (doi:10.1126/science.adi1908). please revise your discussion here based on that paper, instead of using the older study by McCymont et al 2013.

- line 618: d^{13}C instead of d_{13}C

- Section 4.5. The starting sentence should already say that such a future exercise would be one which would ignore anthropogenic impacts.

- line 688:“… would reach a maximum rate“. A rate of what? Glacial inception can hardly be a rate.

- The content of the Appendices (Tables A1-A2, Figures B1-B6) are in my view actually Supplementary Figures which should appear in an SI (in the final format an extra PDF) and not as Appendices (added extra figures in the main PDF).

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC1
- AC1: 'Reply on RC1', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC1
RC2:
'Comment on egusphere-2025-2233', Andrey Ganopolski, 04 Jul 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC2
- AC3: 'Reply on RC2', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC3
RC3:
'Comment on egusphere-2025-2233', Tijn Berends, 11 Jul 2025

Review of Pollak et al., 2025: “An improved conceptual model of Quaternary global ice volume and the Mid-Pleistocene Transition”
By Tijn Berends

Summary
The Mid-Pleistocene Transition (MPT) remains one of the most important unexplained phenomena in the Earth’s climate system of the past few million years. Explanations for the observed change in glacial cycle periodicity often involve interactions between different components of the Earth system. Explicit physical models of these physical systems are often too computationally expensive to feasible simulate the multi-million-year timescales involved. This means that conceptual models, while by necessity less detailed than physical models, can provide valuable insights.
The authors present results from a simple conceptual, zero-dimensional model of the cryosphere, where the net ice mass balance is determined by insolation, plus some generic climate feedback terms which depend on the total ice mass. It additionally includes an artificial switch between “glacial” and “deglacial” states, which allows the model to reproduce the general features of the Pleistocene glacial cycles, including the MPT. The authors performed some experiments where they include a temporal change in some of the model’s parameters, which could be interpreted to represent both the hypothesized change in subglacial substrate (i.e. the regolith hypothesis), as well as the background CO2 concentration (i.e. the gradual cooling hypothesis). They show that this increases the match between their model results, and different d18O-based sea-level reconstructions.
While I think this work has potential, I believe it requires some substantial revisions.

Major comments
My main issue with this manuscript is that it is a continuation of the work by Legrain et al. (2023), but it is difficult to understand from the manuscript how the new model and its results differ from those by Legrain et al. Right now, a reader who is not familiar with Legrain et al. could be given the false impression that the model and the experiments are entirely novel. (In fact, even for me it is difficult to spot the differences, and I actually reviewed the Legrain et al. paper!). To prevent this, when presenting the model equations, it should be made clear how and why they are different from those already published. Similarly, since three of the four experiments (ORB, ABR, and GRAD) were also performed by Legrain et al., the results of those experiments with the earlier model version should be shown for comparison, to illustrate the effect of the changes to the model.

My second issue regards the way the performance of the different model versions is assessed, namely by comparing to the sea-level curve from my 2021 paper (Berends et al., 2021a). I hesitate to call it a reconstruction (despite the rather optimistic title of that publication!), because, as I cautioned readers in that paper, that curve is based on a model-based deconvolution of the LR04 benthic d18O stack, and includes major uncertainties. For example, at the last glacial maximum, I simulated a sea-level drop of only ~100 m, well below the accepted value of ~130 m. As I stated in the discussion section of that paper, the results presented there “…should not be interpreted as a realistic reconstruction of what the world looked like in terms of global climate, ice-sheet geometry, sea level, and CO2 during these periods of geological history. Rather, … they should be viewed as scenarios which can help in interpreting an expected new ice-core record.” Considering the magnitude of the errors and uncertainties in this curve (i.e. up to 30 m), I do not think it can be used to (in)validate the results of the conceptual models presented here, which all lie well within this uncertainty (i.e. RMSE’s of less than 20 m). Given that other sea-level curves (like the different ones from Rohling et al., which are also cited in the manuscript) suffer from similar uncertainties, in my view this means that the currently available sea-level data is insufficient to choose one of the author’s models over another. This implies that the conclusion of the manuscript should be that, “until more accurate observations become available, both abrupt and gradual changes in the Earth system can explain the available (inaccurate) observations equally well”. Of course, that does not mean it is not worthwhile to study the implications of abrupt vs. gradual changes, or of introducing non-linearities such as the ice-volume feedback in the RAMP-l model. But at present, such studies are, by necessity, exploratory in nature.

The authors also apply their different model versions to the future. I do not immediately see the relevance of such experiments, given that present-day CO2 concentration far exceeds the Pleistocene range. The results presented here should, as far as I understand, be interpreted as “possible future patterns of glaciation in the absence of any anthropogenic CO2 emissions” – i.e., a thought experiment. Since such a thought experiment lies quite far from the scope of the rest of the manuscript, I think it might be best to leave it out altogether.

Lastly, I believe that, with thirty pages of body (plus ten pages of bibliography and appendices) the manuscript is too long, especially considering the rather simple model and limited number of experiments. There is a lot of repetition going on, with e.g. the nature of the four different experiments being described in the experimental set-up, in the results, and then again in the discussion. A lot of text could, and therefore should, be removed without losing information or coherence.

Minor comments

Sect. 2.1: Please add a few lines explaining why it is physically justified to assign different weights to the different orbital signals (eccentricity, obliquity, and precession) in the different experiments. A flake of snow lying on top of an ice sheet cannot know the eccentricity of Earth’s orbit or the tilt of its axis; it can only feel how much solar heat it is receiving at that moment (which is a simple mathematical result of those orbital parameters, with no room for “optimization”). Of course, it has to do with the asymmetry in the sensitivity of the mass balance to summer vs. winter changes; that fact deserves to be mentioned.

Fig. 2: it looks like the ORB and ABR models produce higher-than-present sea levels between 2.6 and 2.2 Myr. Should I interpret this as retreat of the Antarctic ice sheet? How does your model handle negative values for the ice volume?

Fig. 3 and other places: I’d like to suggest again (as I did to Legrain et al. before) to use a wavelet transform (or something similar) to show the temporal changes in frequency content. This is much more intuitive and informative than showing time-averaged power spectra for two different blocks of time.

Table 2: Please explain why running the models over different lengths of time (2.0 Myr, 2.6 Myr, or 3.6 Myr) can yield such different results. Are the models also optimized separately?

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC3
- AC2: 'Reply on RC3', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC2

Interactive discussion

Status: closed

RC1:
'Review on egusphere-2025-2233', Anonymous Referee #1, 03 Jul 2025

This paper improves an exisiting conceptual model on global ice volume changes as function of orbital forcing and some internal feedbacks which is then applied to the last 2.6 Ma in order to understand the Mid-Pleistocene Transition (MPT).
In my view this is a solid piece of work, but misses one important piece of discussion. All sea level (=global ice volume) reconstructions used here as target are some sort of deconvolution of the LR04 benthic d18O stack into sea level and temperature. However, a most recent approach by Clark et al., published some weeks ago in Climate of the Past (doi: 10.5194/cp-21-973-2025) doing the same thing supported by SST and deep ocean data comes to a significantly different deconvolution with larger glacial/interglacial amplitudes in the sea level component throughout the Quaternary than the sea level records used here.
In an ideal world, this new record (data to figure 10b in Clark et al., 2025 available in the SI there) would as an alternative be used here as tuning target, but I understand that this would be a major effort and leave it up to the authors if they want to jump on this challenge. However, I noted that the authors referred to another discussion paper (Scherrenberg et al., 2024), so it is not clear to me why they not also included in their discussion of the MPT the Clark et al paper, whose discussion version was also available since September 2024. What should be and needs to be done is that this difference between the sea level component in the new Clark et al 2025 paper and those used here needs to be discussed. This is in my view important for two reasons.

1. The Clark paper is simply one of the newest papers published on MPT sea level changes (although only indirectly contained in the contribution to the benthic d18O stack) and should be considered/discussed in any upcoming paper on the same topic.

2. The regolith hypothesis, formulated some decades ago, also by Clark and others, was trying to explain that there were ice sheets in North America, that were reaching as far south as 39-40°N around 2.5 Ma ago (e.g. Balco & Royery, 2010, doi: 10.1130/G30946.1). However, more complex models are not yet able to simulate these ice sheet extends. The Utrecht model (in the version of de Boer et al 2014, doi:10.1038/ncomms3999) was failing to do so, as has been shown in Köhler & van de Wal 2020 (doi: 10.1038/s41467-020-18897-5), which plotted in their Fig. 2b the latitudinal ice sheet extend of the Utrecht model as function of time.

(Side note: Köhler & van de Wal 2020 is to some extend a reinterpretation of Tzedakis et al 2017 on the appearance of interglacials during the Quaternary and might for that content also be discussed here as one recent study on the understanding of the MPT.)

The sea level of Berends et al (2021) used here is a follow-up study of the de Boer et al 2014, both using a model to deconvolve benthic d18O into sea level and temperature, thus both results differ in detail, but rely on the same approach and give in principle comparable results. Also the 3 Ma long simulations of the CLIMBER model (Willeit et al., 2019, doi: 10.1126/sciadv.aav7337), which is a more complex climate model than in the Utrecht approach, and which does not use benthic d18O as input, do not get large ice sheets down to 40°N at 2.5 Ma BP.

That said, these interpretations of the benthic d18O stack are still failing to explain the terrestrial evidence of Balco and others. These shortcomings are also worth mentioning in the discussion.
With this two contrasting deconvolutions of the benthic d18O stack - one based on ice sheet model, one based on an ocean temperature data compilation - such a simple model as used here might be able to give ideas how to understand them. Eg if completely different conceptual models are necessary to satisfy both data sets, but again, maybe this is a task for a future study, especially since a final interpretation of the sea level related changes in benthic d18O from Clark et al is still not published. Nevertheless, I would say it is a missed opportunity if the authors decide not jump on this issue here and now.

Minor issues:

- Barker et al. 2025, explaining the role of orbital parameters for the 100k-world after the MPT also gives a glimpse on their roles in the 41k-world (their SI Figure 8). Thus, I believe this paper is one of the most recent studies discussing underlying processes of the MPT and should already be discussed widely in the introduction.

- Please update the reference to Scherrenberg et al., 2024 to the now available final version: https://doi.org/10.5194/cp-21-1061-2025).

- Figure 4: purple and red dots look the same. Make one symbol differently, eg squares.

- lines 520ff: Somehow now „glacial inception“ is shortened to „gl. inception“. Please use full words.

- line 614: The most recent review on MPT SST changes is in Clark et al. 2024 (doi:10.1126/science.adi1908). please revise your discussion here based on that paper, instead of using the older study by McCymont et al 2013.

- line 618: d^{13}C instead of d_{13}C

- Section 4.5. The starting sentence should already say that such a future exercise would be one which would ignore anthropogenic impacts.

- line 688:“… would reach a maximum rate“. A rate of what? Glacial inception can hardly be a rate.

- The content of the Appendices (Tables A1-A2, Figures B1-B6) are in my view actually Supplementary Figures which should appear in an SI (in the final format an extra PDF) and not as Appendices (added extra figures in the main PDF).

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC1
- AC1: 'Reply on RC1', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC1
RC2:
'Comment on egusphere-2025-2233', Andrey Ganopolski, 04 Jul 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC2
- AC3: 'Reply on RC2', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC3
RC3:
'Comment on egusphere-2025-2233', Tijn Berends, 11 Jul 2025

Review of Pollak et al., 2025: “An improved conceptual model of Quaternary global ice volume and the Mid-Pleistocene Transition”
By Tijn Berends

Summary
The Mid-Pleistocene Transition (MPT) remains one of the most important unexplained phenomena in the Earth’s climate system of the past few million years. Explanations for the observed change in glacial cycle periodicity often involve interactions between different components of the Earth system. Explicit physical models of these physical systems are often too computationally expensive to feasible simulate the multi-million-year timescales involved. This means that conceptual models, while by necessity less detailed than physical models, can provide valuable insights.
The authors present results from a simple conceptual, zero-dimensional model of the cryosphere, where the net ice mass balance is determined by insolation, plus some generic climate feedback terms which depend on the total ice mass. It additionally includes an artificial switch between “glacial” and “deglacial” states, which allows the model to reproduce the general features of the Pleistocene glacial cycles, including the MPT. The authors performed some experiments where they include a temporal change in some of the model’s parameters, which could be interpreted to represent both the hypothesized change in subglacial substrate (i.e. the regolith hypothesis), as well as the background CO2 concentration (i.e. the gradual cooling hypothesis). They show that this increases the match between their model results, and different d18O-based sea-level reconstructions.
While I think this work has potential, I believe it requires some substantial revisions.

Major comments
My main issue with this manuscript is that it is a continuation of the work by Legrain et al. (2023), but it is difficult to understand from the manuscript how the new model and its results differ from those by Legrain et al. Right now, a reader who is not familiar with Legrain et al. could be given the false impression that the model and the experiments are entirely novel. (In fact, even for me it is difficult to spot the differences, and I actually reviewed the Legrain et al. paper!). To prevent this, when presenting the model equations, it should be made clear how and why they are different from those already published. Similarly, since three of the four experiments (ORB, ABR, and GRAD) were also performed by Legrain et al., the results of those experiments with the earlier model version should be shown for comparison, to illustrate the effect of the changes to the model.

My second issue regards the way the performance of the different model versions is assessed, namely by comparing to the sea-level curve from my 2021 paper (Berends et al., 2021a). I hesitate to call it a reconstruction (despite the rather optimistic title of that publication!), because, as I cautioned readers in that paper, that curve is based on a model-based deconvolution of the LR04 benthic d18O stack, and includes major uncertainties. For example, at the last glacial maximum, I simulated a sea-level drop of only ~100 m, well below the accepted value of ~130 m. As I stated in the discussion section of that paper, the results presented there “…should not be interpreted as a realistic reconstruction of what the world looked like in terms of global climate, ice-sheet geometry, sea level, and CO2 during these periods of geological history. Rather, … they should be viewed as scenarios which can help in interpreting an expected new ice-core record.” Considering the magnitude of the errors and uncertainties in this curve (i.e. up to 30 m), I do not think it can be used to (in)validate the results of the conceptual models presented here, which all lie well within this uncertainty (i.e. RMSE’s of less than 20 m). Given that other sea-level curves (like the different ones from Rohling et al., which are also cited in the manuscript) suffer from similar uncertainties, in my view this means that the currently available sea-level data is insufficient to choose one of the author’s models over another. This implies that the conclusion of the manuscript should be that, “until more accurate observations become available, both abrupt and gradual changes in the Earth system can explain the available (inaccurate) observations equally well”. Of course, that does not mean it is not worthwhile to study the implications of abrupt vs. gradual changes, or of introducing non-linearities such as the ice-volume feedback in the RAMP-l model. But at present, such studies are, by necessity, exploratory in nature.

The authors also apply their different model versions to the future. I do not immediately see the relevance of such experiments, given that present-day CO2 concentration far exceeds the Pleistocene range. The results presented here should, as far as I understand, be interpreted as “possible future patterns of glaciation in the absence of any anthropogenic CO2 emissions” – i.e., a thought experiment. Since such a thought experiment lies quite far from the scope of the rest of the manuscript, I think it might be best to leave it out altogether.

Lastly, I believe that, with thirty pages of body (plus ten pages of bibliography and appendices) the manuscript is too long, especially considering the rather simple model and limited number of experiments. There is a lot of repetition going on, with e.g. the nature of the four different experiments being described in the experimental set-up, in the results, and then again in the discussion. A lot of text could, and therefore should, be removed without losing information or coherence.

Minor comments

Sect. 2.1: Please add a few lines explaining why it is physically justified to assign different weights to the different orbital signals (eccentricity, obliquity, and precession) in the different experiments. A flake of snow lying on top of an ice sheet cannot know the eccentricity of Earth’s orbit or the tilt of its axis; it can only feel how much solar heat it is receiving at that moment (which is a simple mathematical result of those orbital parameters, with no room for “optimization”). Of course, it has to do with the asymmetry in the sensitivity of the mass balance to summer vs. winter changes; that fact deserves to be mentioned.

Fig. 2: it looks like the ORB and ABR models produce higher-than-present sea levels between 2.6 and 2.2 Myr. Should I interpret this as retreat of the Antarctic ice sheet? How does your model handle negative values for the ice volume?

Fig. 3 and other places: I’d like to suggest again (as I did to Legrain et al. before) to use a wavelet transform (or something similar) to show the temporal changes in frequency content. This is much more intuitive and informative than showing time-averaged power spectra for two different blocks of time.

Table 2: Please explain why running the models over different lengths of time (2.0 Myr, 2.6 Myr, or 3.6 Myr) can yield such different results. Are the models also optimized separately?

Citation: https://doi.org/10.5194/egusphere-2025-2233-RC3
- AC2: 'Reply on RC3', Felix Pollak, 29 Aug 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2233/egusphere-2025-2233-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2233-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (03 Sep 2025) by Lorraine Lisiecki

I’d like to thank the reviewers for their insightful and thorough recommendations to improve this manuscript. Additionally, I thank the authors for providing detailed plans to address the reviewers’ concerns. After reviewing these plans, there are a couple additional concerns I want to ensure are addressed in the revised manuscript.

Specifically, the authors plan to change the target used for tuning the model by replacing the sea level reconstruction of Berends et al (2021) with a detrended benthic d18O stack. (This stack was originally published by Ahn et al (2017). Recently, Clark et al (2025) proposed long-term detrending of the d18O values based on possible diagenetic artifacts.) The new tuning target is meant to address the reviewers’ concerns that the manuscript address a recently proposed an alternate deconvolution of carbonate benthic d18O into its two main components: deep-sea temperature and the d18O of seawater (a proxy for ice volume) by Clark et al (2025). However, benthic d18O itself is not an improved proxy for ice volume compared to the Berends et al (2021) sea level reconstruction; the benthic d18O stack makes no correction for deep-sea temperature changes (or incorrectly assumes temperature varies synchronously and proportionally with ice volume) whereas the Berends reconstruction makes more physically based assumptions about the relationship between temperature and ice volume change. The point I wish to emphasize here, as the reviewers did, is that any estimate of ice volume variations over the past 3 Myr (or even the past 100 kyr) has very large uncertainties. Whichever target the authors choose to use, the revised manuscript must describe the magnitude of ice volume uncertainty and potentially significant biases that affect the chosen target record and how this might impact the model tuning and evaluation.

The authors should also avoid calling the stack “Clark et al (2025) benthic d18O” and instead refer to it as “Prob-Stack benthic d18O (Ahn et al, 2017) as detrended by Clark et al (2025).” Prob-Stack provides updated d18O values and corresponding 95% confidence intervals using more core records than the LR04 stack (Lisiecki and Raymo, 2005), but it essentially replicates the LR04 age model. The Berends et al (2021) sea level reconstruction also uses the LR04 stack. Thus, the manuscript should mention that the ice volume target used (whichever the authors select) is impacted by the orbital tuning applied to the LR04 stack which could may affect the parameter values optimized to fit the target.

I look forward to reviewing a revised manuscript by these authors that addresses all reviewer concerns as well as those mentioned above.

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AR by Felix Pollak on behalf of the Authors (13 Oct 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (24 Oct 2025) by Lorraine Lisiecki

RR by Anonymous Referee #1 (05 Nov 2025)

Suggestions for revision or reasons for rejection

I focus in this 2nd round of reviews mainly on the aspect if the applied changes have improved the draft.

Having that in mind I have to say that in my view the draft has not improved, when it comes to also discussing what we know about the MPT from the new data on temperature, d18O_sw, and sea level from recent papers of Clark et al. (2024, 2025). Unfortunately, there was also bad luck with the timing of the submission, since on 16th October 2025 a new 4.5 Ma long record of global mean sea level change has been published by Clark et al in Science, DOI: 10.1126/science.adv8389, which were not yet considered here. This new paper of Clark et al. takes into account how temperature might influence d18O of land ice, and therefore how sea level was calculated in detail out of the previously published d18O_sw.

My main critics, the shortcoming of Pollak et al. so to say, is that the authors indeed took up the challenge to also test their approach against the new d18O_sw aka sea level of Clark et al (thanks for jumping on the challenge!), which is fundamentally different from all other sea level reconstructions, since the MPT now only contains a change in frequency (41 ka to 100 ka), but not anymore an increase in the sea level (or ice volume) amplitude. Thus, we has to speak about a new paradigm of how to understand the MPT. However, the authors in their revised draft do not even mention in the introduction that there are now two fundamentally different interpretations of the MPT out there (not citing Clark et al. 2025 at all in the introduction). The new interpretation of Clark - although not completely understood (e.g. no model explained the new reconstructions) - is for the first time able to explain paleo data, that suggest a large Laurentide ice sheet existed 2.5 Ma, something which all other approaches fail to explain. I mentioned this deficit already in round one of the reviews, but if I am not wrong, the authors did not include it in their revision. Finally, my suggestion to also test models against the new Clark et al data was based on the variety of model which had been applied in version 1 (4 models). My idea was, that testing different models against structural completely different data would give the authors arguments which model works best for which data set. Unfortunately, in the revision the authors have chosen to restrict their zoo of models to one - without any support from data for this choice. This is somehow making a conclusion before the analysis was performed. Thus, they choose from the beginning how the model should perform and with no surprise the new data disagree most with the chosen RAMP model. In doing so, this whole excersice of including the Clark data in the test is more or less meaningless.

So how to continue? If the authors insist on testing only one model (RAMP), the test to the Clark data should be deleted again for the reasons given above. If so, they nevertheless need to explain in intro and discussion, that they choose to sample only a subset of available data. Whatever they decide, they need to state on the existence of the Clark et al papers and that they are superior in explaining certain paleodata (large ice sheets at 2.5 Ma), which all approaches looked into here were not able to tackle. Check the new Clark et al paper on sea level in Science on more details of independent support for such large ice sheets. Alternatively, they revise the revision to again apply several models from which we then see which approach is explaining best which data set.

Minors:
- page 4, line 117: „In the RAMP model, we only use a linear combination of precession and obliquity.“ This is not correct, Equation 1 contains also eccentricity (e).
- page 5, line 124ff: I(t) has as units m/kyr. Therefore, I(t) cannot be an „orbital forcing“ (which has as units W/m^2), it is more „a system response in terms of sea level change per time to the orbital forcing“. Please revise throughout the draft.

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RR by Andrey Ganopolski (20 Nov 2025)

ED: Reconsider after major revisions (05 Dec 2025) by Lorraine Lisiecki

I thank the authors for their revisions and invite them to submit further revisions based on reviewer comments. The authors chose to address previous comments about uncertainty in the ice volume target by tuning their model to four different targets. However, both reviewers and the editor have concerns about how these additional records were incorporated into the revised manuscript. First, I want to emphasize that it is not necessary that this manuscript include application of the model to all of these targets. It would be sufficient for the authors to simply discuss that ice volume reconstructions are uncertain and some of the reasons why -- for example, due to assumptions about the temperature component of benthic d18O. Three of the targets are very similar because they estimate that temperature and ice volume change approximately proportionately through time (thus, correlating strongly with benthic d18O). Because these 3 targets are very similar, it is unsurprising (although reassuring) that the model reaches similar findings for all 3. In contrast, the d18Osw reconstruction of Clark (and the recently published sea level curve based on it) uses a different approach to estimate temperature and generates a dramatically different estimate. The current version of the manuscript doesn’t sufficiently explain why 4 different tuning targets are used and why this model would even be applicable to simulating detrended benthic d18O since it is designed to simulate ice volume. At a minimum, I would recommend removing the optimization to benthic d18O.

The next revision of this manuscript should carefully incorporate responses to all of the reviewers’ critiques, those discussed above as well as other concerns including the model’s variables for time and the reconstruction/forecast of the Holocene and next glacial maximum (if this remains in the revision). I’d also like to see a different title for the next revision: The model doesn’t actually “reveal” a ramp-like change as the “cause” of the MPT because its only one possible conceptual model, it doesn’t explore all alternate hypotheses, and there’s uncertainty about the appropriate ice volume signal that should be reproduced. Thank you in advance for your attention to these details.

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AR by Felix Pollak on behalf of the Authors (15 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (28 Jan 2026) by Lorraine Lisiecki

RR by Anonymous Referee #1 (03 Feb 2026)

Suggestions for revision or reasons for rejection

3rd round of review of

# egusphere-2025-2233
Title: Simulating global ice volume across the Mid-Pleistocene Transition with a ramp-like increase in the deglaciation threshold
Author(s): Felix Pollak et al.
Journal : Climate of the Past

2026.0204

(line numbers are from the version with tracked changes)

Slowly evolving improvement…
I hope we are finally getting to a publishable version in the near future.

From the performed changes in the draft I am still not entirely happy with the way the new Clark et al. (2025) global mean sea level (GMSL) record is treated. It is now mentioned as contrasting / alternative view in the introduction, which is great. However, the reader is then completely left alone with that information. Why has it not been taken up for further analysis? The introduction misses a statement why the authors are focusing on the other two alternatives GMSL versions. The introduction should also include the information that a modified version of the RAMP model has been applied to the Clark GMSL with all details contained in the SI (which is ok) and that these results are discussed in section 4.

In the SI it is said that various parametrizations were tested in order to reconstruct the Clark GMSL. Maybe this can be more specific. Did you only test alternative versions of the RAMP model or also others? From the initial draft version I remember there was the model ORB which was only using the orbital parameters and no further thresholds. I would imagine that this model might also help here. Furthermore, the modified model RAMP-2 that was fitted to the Clark GMSL is still a model that simulates a rise in glacial amplitudes over time. Does this make sense if this rise in amplitude is not seen in the Clark GMSL data (or do yoo see such a rise in the data somehow, then some more details on this would be needed)? Or was RAMP-2 chosen to have a model that can also successfully be applied to one of the other GMSL curves?

The values of the two additional threshold model parameters v_1(1) and I_0(t) are never mentioned or showed, Figs S4c contains only v_0(t). And if we add now v_1,1, v_1,2, I_0,1 and I_0,2, is this not + 4 parameters ending in a total of 9+4=13 (not 12) parameters?
line 169 in SI: x1 in {} appears twice, but x2 in {} is missing.

Furthermore, the part in the discussion dealing with the Clark GMSL to a large extent copies text already given in the introduction. Please delete the repeating part in the discussion and focus only on the results.

The alternative view of GMSL from Clark (and what you found here with RAMP-2) should also briefly be mentioned in abstract and conclusions and what this new time series would imply for future studies.

Orbital parameters: As already mentioned before there are 3 orbital parameters (eccentricity, precession, obliquity) and all three appear here, but the authors repeatedly talk about 2 orbital parameters (e.g. line 136 or the title of section 4.3), probably coming from the fact, that eccentricity and precession are combined in the precession parameter.

Technical:
- line 158: the dimensionless orbital forcing I(t)^tilde needs to be defined. Somehow this definition was deleted here but not replaced with an alternative.
- line 168: „Time is given in physical units (kyr).“ I believe this formulation was chosen due to comments of rev#2. However, I think you might use „physical units“ in the response letter, but this is not necessary here in the text.
- Figure 2: x axes labels and titles are missing
- line 352, Title of section 4.1: Please use word instead of symbols for v_0
- Entries in the reference list contains very often the publisher, which is not needed.
- SI line 150: typo in „cruves“

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RR by Andrey Ganopolski (16 Feb 2026)

Suggestions for revision or reasons for rejection

I appreciate the author's efforts in revising the manuscript to address the recommendations of different reviewers, which were not always consistent. I believe there is a limit to how much a paper of this kind can and should be improved, and I would recommend its publication after minor revision. Therefore, I only have a few relatively minor comments:

L.12. 'The identified orbital forcing differs from the widely used insolation at summer solstice at 65° N, as it exhibits a larger precession signal'. This sentence does not make it clear which of the two has the stronger precessional component. Please clarify that this refers to solstice insolation.

L.122: I still do not understand what the authors mean by 'Hence, selecting a specific insolation metric can pose a bias to the model, since this determines the strength of the precession and obliquity signals in the model'. Selecting a single metric for the real latitudinal and seasonal redistribution of insolation caused by variations in the Earth's orbital parameters is obviously subjective. One option is to choose a physically meaningful metric for orbital forcing, such as solstice insolation, and then tune the model with this forcing. Alternatively, one can tune the forcing and the model together. In the latter case, there are more 'tunable' parameters, so it is not surprising that the fit between the modelling results and the target should be better. This does not mean, however, that the 'orbital forcing' chosen in this way is less 'biased' than solstice insolation, for example. However, apart from the toy world of conceptual models, there are physically based Earth system models that allow us to analyse the relative importance of the processional and obliquity components of orbital forcing during glacial cycles. The results of such an analysis clearly show that, although the response of ice sheets to orbital forcing is complex and non-linear, it is beyond doubt that the processional component is much more important than the obliquity component during the late Quaternary (see, for example, Ganopolski et al., 2010).

4.2 'Model extrapolation'. 'Extrapolation' is an odd term for these kinds of models, as they are not actually 'extrapolating' but simulating the future. However, the main problem is not with 'extrapolation'. The problem is that the RAMP model simulates glacial inception 6,000 years ago. Thus, this is not 'extrapolation' but a simulation of past ice sheet evolution, which we know well, unlike the future, which we do not. This is why the fact that Imbrie and Clader (with all due respect to these researchers) who also simulated a glacial inception in the recent past is irrelevant. What is relevant is that the glacial inception did not happen in reality and thus this is an obvious failure of the RAMP model.

L.3832 and L389. The term 'caloric summer insolation' does not exist because what does 'summer' mean? If summer is JJA or even MJJA, as I demonstrated in my 2024 paper, the insolation during this period is still dominated by precession. The correct term, introduced by Milankovitch and also used by Tzedakis, is 'caloric summer half-year insolation'. Indeed, six-month 'summer' insolation is dominated by obliquity.

Supplementary information

The RAMP-2 model results are shown, but the model itself is not presented properly. SI is a part of the paper, and the same rules apply: if a new model is used, it should be described properly, including the numerical values of all 12 of its parameters.

Line 169. There is a typo here: it should be x, x₁ and x₂.

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ED: Publish subject to minor revisions (review by editor) (05 Mar 2026) by Lorraine Lisiecki

AR by Felix Pollak on behalf of the Authors (13 Mar 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (17 Mar 2026) by Lorraine Lisiecki

AR by Felix Pollak on behalf of the Authors (19 Mar 2026) Manuscript

Journal article(s) based on this preprint

27 Mar 2026

Simulating global ice volume across the Mid-Pleistocene Transition with a ramp-like increase in the deglaciation threshold

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

Clim. Past, 22, 675–688, https://doi.org/10.5194/cp-22-675-2026,https://doi.org/10.5194/cp-22-675-2026, 2026

Short summary

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

Model code and software

Conceptual-Model-Pollak-et-al-2025 Felix Pollak https://doi.org/10.5281/zenodo.15421084

Felix Pollak, Frédéric Parrenin, Emilie Capron, Zanna Chase, Lenneke Jong, and Etienne Legrain

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The Mid-Pleistocene Transition (MPT) marked a shift towards extended glacial periods and amplitudes, while its underlying mechanisms are still disputed. Here, we present a new conceptual model capable of simulating the global ice volume over the last 2.6 Ma and reconstructing the MPT. We find that a long-lasting, gradual trend in the climate system is most favourable in reconstructing the MPT and that for the last 900 ka, precession was more important for glacial terminations than obliquity.


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