Estimating breakpoints between climate states in the Cenozoic Era

Bennedsen, Mikkel; Hillebrand, Eric; Koopman, Siem Jan; Larsen, Kathrine By

doi:https://doi.org/10.48550/arXiv.2404.08336

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https://doi.org/10.48550/arXiv.2404.08336

Preprints

19 Nov 2024

| 19 Nov 2024

Estimating breakpoints between climate states in the Cenozoic Era

Mikkel Bennedsen, Eric Hillebrand, Siem Jan Koopman, and Kathrine By Larsen

Abstract. This study presents a statistical time-domain approach for identifying transitions between climate states, referred to as breakpoints, using well-established econometric tools. We analyze a 67.1 million year record of the oxygen isotope ratio δ¹⁸O derived from benthic foraminifera. The dataset is presented in Westerhold et al. (2020), where the authors use recurrence analysis to identify six climate states. Fixing the number of breakpoints to five, our procedure results in breakpoint estimates that closely align with those identified by Westerhold et al. (2020). By treating the number of breakpoints as a parameter to be estimated, we provide the statistical justification for more than five breakpoints in the time series. Further, our approach offers the advantage of constructing confidence intervals for the breakpoints, and it allows for testing the number of breakpoints present in the time series.

Received: 07 Nov 2024 – Discussion started: 19 Nov 2024

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Journal article(s) based on this preprint

05 Nov 2025

Estimating breakpoints in the Cenozoic Era: an econometric approach

Mikkel Bennedsen, Eric Hillebrand, Siem Jan Koopman, Kathrine By Larsen, and Rachel Lupien

Clim. Past, 21, 1981–2008, https://doi.org/10.5194/cp-21-1981-2025,https://doi.org/10.5194/cp-21-1981-2025, 2025

Short summary

Mikkel Bennedsen, Eric Hillebrand, Siem Jan Koopman, and Kathrine By Larsen

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-3443', Anonymous Referee #1, 20 Dec 2024
General Comments:
This paper is a useful contribution to paleoclimate literature. The authors present the usage of a novel breakpoint analysis technique on a record of Cenozoic climate from Westerhold et al. (2020), and adequately support the usage of this technique on said data via sensitivity tests.
My major piece of feedback is that this paper currently lacks substantive earth science/paleoclimate motivation, and is far too terse. While it’s an impressive piece of work on the application of this changepoint technique to CENOGRID, additional context is necessary for broader application in the paleosciences. That is, as a methods paper that is designed to introduce a new approach to changepoint analysis within the paleosciences, further work is necessary to show where and when this method can be used to answer other paleoclimate questions. For example, some discussion of age uncertainty is essential, as this is an issue of fundamental importance in paleoclimate. Additionally, CENOGRID is an interesting dataset, but its length and completeness aren’t typical of paleoclimate records, which complicates its being the sole non-synthetic example used in demonstrating the application of a novel technique. Additional explanation of the choice of CENOGRID as well as potential edge cases not covered by CENOGRID needs to be done. As a data scientist I’m left feeling confident that this technique is useful, and I’m intrigued by the idea of applying this method to my own work. However, as an earth scientist I’m left not quite understanding the breadth of problems that it is well suited for, nor what the significance of the additional breakpoints that were identified in the Cenozoic is.
Specific Comments:
The need for this method in particular within paleoclimatology should be discussed in more detail. This paragraph “Our approach contributes to the existing breakpoint detection methods in paleoclimate research by applying well-established econometric tools in the time-domain, developed in Bai and Perron (1998, 2003), to identify climate states in the paleo record. It enables the estimation of multiple breakpoints along with confidence intervals and provides procedures to estimate the number of breakpoints” should be built upon. I see how confidence intervals might be useful, but what are the other strengths and weaknesses of this approach when compared to other methods? Some discussion of other approaches is offered in the preceding paragraph, but it is somewhat superficial. As a reader, I need better context for breakpoint analysis in paleoclimate studies: its historical usage, current applications, and future potential.
This sentence “The paleoclimate variable δ18O measures the ratio of 18O to 16O in the shells of benthic foraminifera obtained from ocean sediment cores, relative to a standard sample.” is incorrect (or at least misleading), as δ18O is not exclusive to benthic forams, which the sentence seems to be suggesting.
This sentence “The weight difference between the oxygen isotopes leads to an inverse relationship between δ18O and ocean temperatures; see for instance Epstein et al. (1951) and Shackleton (1967).” is an inadequate description of benthic δ18O. Mention of other factors (seawater composition, ice sheet volume, etc.) needs to be included. CENOGRID is composed of many integrated signals, the makeup of which will determine what detected breakpoints are telling us about the climate.
As the reader, I’m left wondering why only oxygen isotopes were considered. Carbon isotopes are also available, why not include carbon isotopes in the analysis, as was done in the original Westerhold publication?
The authors discuss the varying resolution of the time series at length, which is helpful. However, I would be curious as to whether or not the resolution impacted the detection of break points. Is there any correlation between the detection of new breakpoints (discussed later in the manuscript) and the resolution of the time series? For example, just by visual comparison, it seems to me that the breakpoint observed in Coolhouse 1 in later sections might be related to a large change in resolution that occurs nearby. While this breakpoint isn’t heavily interpreted here, this is an important point to understand if other researchers are to apply this method to their own data.
This sentence “Furthermore, we recommend using binning frequencies 10 and 25 kyr as they result in the most consistent outcomes.” strikes me as rigid and somewhat unhelpful, as many records will not share the general time axis properties of CENOGRID. Is there a different way to describe your binning recommendation that’s more flexible and/or applicable to other datasets?
Certain technical choices need to be better explained given the audience of this journal. For example: “To address these issues, we use the autocorrelation and heteroscedasticity consistent (HAC) covariance matrix estimator with prewhitening in our implementations.”. Perhaps this is standard fare in breakpoint analysis literature, but most paleoclimatologists won’t be familiar with this procedure. Some explanation as to why this approach is suitable for this data is warranted here, as is mention of alternatives that were considered. In the same vein, it would be helpful to spend a little bit more time explaining information criteria. That is, expand upon “We use information criteria to estimate the number of breakpoints”. What does this mean, why are they used, have they been used in paleoclimate contexts before, etc.
Age uncertainty needs to be addressed somewhere in this paper. It doesn’t need a full treatment, in that the method doesn’t need to be modified to account for it, nor does it need to be included in the analysis, but discussion of how to include it in future studies is essential. Specifically I would be curious as to how this technique might be expanded to include the usage of age ensembles and how choice of age modeling method might impact breakpoint detection. However, discussion of including age uncertainty directly would also be acceptable here.
The simulation study is a particular strength of this work. The authors thoroughly test their method across different data-generating processes, demonstrating its robustness to various forms of non-stationarity and serial correlation. This kind of rigorous testing is essential for establishing the reliability of statistical methods in paleoclimate contexts. I just wanted to make a note of that.
When analyzing the possible presence of multiple breakpoints, I’m left desiring some kind of prescription as to how I should set the number of breakpoints. Certainly the claim that there are more than 5 statistically significant breakpoints in CENOGRID seems robust. However, the current analysis feels somewhat hand-wavy, with seven breakpoints being settled upon in a rather arbitrary way. In particular this statement needs to be expounded upon: “The estimation results based on information criteria justify dividing the climate states Warmhouse II and Coolhouse II into two substates each at approximately 39.7 Ma and 10 Ma, respectively. This is supported by the presence of breakpoints estimated approximately at these time stamps in the estimations with seven or more breakpoints.”
The ending of this manuscript is far too abrupt. Potentially new breakpoints are discovered when varying numbers of breakpoints are allowed, but what do they mean? A few climate events are referenced, but events themselves may or may not justify entirely new regimes. Much context is needed here, interpreting and explaining the presence of these novel breakpoints. While the authors are free to choose how to address this comment, I might suggest including a “Discussion” section, in which the primary results are emphasized, and an explanation/interpretation of these results is offered. Some of my other comments could probably be folded into this section as well.
Technical Comments:
The paper currently is a bit undercited. I suggest the authors go back through with a fine toothed comb and make sure they’re citing existing literature wherever possible. In particular, all sections discussing δ18O interpretation should be thoroughly cited, particularly regarding ice volume effects, temperature relationships, etc. A couple of other key spots (non-exhaustive) that need citations include:
“The climatic transitions contain important information about variations in Earth's climate system” (here Tierney et al. 2020 is referenced, but some explanation of what is contained in that review along with additional citations is called for)

“Our approach contributes to the existing breakpoint detection methods in paleoclimate research” (cite breakpoint analysis in paleoclimate literature)

“This breakpoint aligns with the Middle Eocene Climatic Optimum, a known climatic event” (cite original papers describing this event)

“Some of these breakpoints coincide with other climatic events, for instance, the Latest Danian Event at 62.2 Ma and the onset of the Miocene Climatic Optimum at 16.9 Ma” (cite original papers describing these events, not just Westerhold 2020)
Citation: https://doi.org/10.5194/egusphere-2024-3443-RC1
- AC1: 'Reply on RC1', Kathrine By Larsen, 14 Mar 2025
  
  We sincerely appreciate the reviewer's constructive and insightful comments, which have helped us improve our manuscript. Please find our point-by-point response to each comment in the attached file. The reviewer's comments are in black text, and our responses are highlighted in blue.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3443-AC1
RC2:
'Comment on egusphere-2024-3443', Anonymous Referee #2, 30 Jan 2025
The authors apply a statistical approach to a reference paleoclimate dataset to evaluate shifts in climate states across the Cenozoic. They review existing methods and highlight the advantages of the breakpoint method and apply this approach on the Westerhold et al. 2020 dataset. They review the model and the impact of model parameterization on determined number of breakpoints. Ultimately, they established a similar number of breakpoints to Westerhold et al 2020 paper using this new approach and summarize their methodological approach and findings.
The application of new statistical approaches to assess time series and breakpoints is an important field of study but this contribution lacks significance beyond the application and usefulness of the method used. Although the paper is organized in structured manner, it is lacking background on other statistical assessments applied to assess Cenozoic or long-term changes in past climates and inclusion of a breath of paleoclimate specific references. Overall, this contribution mostly focuses on method development and application rather than implications of findings. Based on the above, it is difficult to see how it has led to a deeper understanding of Cenozoic climate.
I would suggest that this contribution needs to expands its discussion to outline how its findings enhanced our Cenozoic climate knowledge. Further there is a lack of background information needed to fully characterize the dataset evaluated, its attributes and limitations, and age model considerations.
Below I have made some comments to develop the paper and give its finding wider significance.
General comments:
Introduction lacks information on Earth’s history and significance of these various climate states. A review of existing methods is useful but does not link to wider significance of work and importance for paleoclimate field or mention how this analysis could provide new understanding or concepts for workers.

Justification for use of Westerhold et al. 2020 dataset needs to be developed further. More information on benthic foraminifera used to construct record, limitations associated with age model differences, and potential interpretation of d18Ob record from past work. There is limited mention of d18Ob and its use to pinpoint climate states and whether these states align when using other similar datasets or depending on inclusion or exclusion of individual/regional d18Ob records does it impact the breakpoint determinations

The contribution needs to consider its finding and whether it has led to a deeper knowledge of Cenozoic Science. For instance, what framework can the climate transitions of the Cenozoic be categorized and how is this related to dynamics of the climate system? This will allow for the novelty of the method application to be developed in more detail. A thorough review of other approaches used to assess climate change in Cenozoic would be useful to include, going beyond this method, including tipping point analysis and frequency analysis to showcase how this co-eval alongside of the breakpoints.
Citation: https://doi.org/10.5194/egusphere-2024-3443-RC2
- AC2: 'Reply on RC2', Kathrine By Larsen, 14 Mar 2025
  
  We are grateful for the time and effort the referee has dedicated to evaluating our manuscript, as well as the constructive feedback that has helped us strengthen the paper. Please find our responses to the referee’s comments in the attached file. The referee's comments are in black text, and our comments are highlighted in blue.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3443-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-3443', Anonymous Referee #1, 20 Dec 2024
General Comments:
This paper is a useful contribution to paleoclimate literature. The authors present the usage of a novel breakpoint analysis technique on a record of Cenozoic climate from Westerhold et al. (2020), and adequately support the usage of this technique on said data via sensitivity tests.
My major piece of feedback is that this paper currently lacks substantive earth science/paleoclimate motivation, and is far too terse. While it’s an impressive piece of work on the application of this changepoint technique to CENOGRID, additional context is necessary for broader application in the paleosciences. That is, as a methods paper that is designed to introduce a new approach to changepoint analysis within the paleosciences, further work is necessary to show where and when this method can be used to answer other paleoclimate questions. For example, some discussion of age uncertainty is essential, as this is an issue of fundamental importance in paleoclimate. Additionally, CENOGRID is an interesting dataset, but its length and completeness aren’t typical of paleoclimate records, which complicates its being the sole non-synthetic example used in demonstrating the application of a novel technique. Additional explanation of the choice of CENOGRID as well as potential edge cases not covered by CENOGRID needs to be done. As a data scientist I’m left feeling confident that this technique is useful, and I’m intrigued by the idea of applying this method to my own work. However, as an earth scientist I’m left not quite understanding the breadth of problems that it is well suited for, nor what the significance of the additional breakpoints that were identified in the Cenozoic is.
Specific Comments:
The need for this method in particular within paleoclimatology should be discussed in more detail. This paragraph “Our approach contributes to the existing breakpoint detection methods in paleoclimate research by applying well-established econometric tools in the time-domain, developed in Bai and Perron (1998, 2003), to identify climate states in the paleo record. It enables the estimation of multiple breakpoints along with confidence intervals and provides procedures to estimate the number of breakpoints” should be built upon. I see how confidence intervals might be useful, but what are the other strengths and weaknesses of this approach when compared to other methods? Some discussion of other approaches is offered in the preceding paragraph, but it is somewhat superficial. As a reader, I need better context for breakpoint analysis in paleoclimate studies: its historical usage, current applications, and future potential.
This sentence “The paleoclimate variable δ18O measures the ratio of 18O to 16O in the shells of benthic foraminifera obtained from ocean sediment cores, relative to a standard sample.” is incorrect (or at least misleading), as δ18O is not exclusive to benthic forams, which the sentence seems to be suggesting.
This sentence “The weight difference between the oxygen isotopes leads to an inverse relationship between δ18O and ocean temperatures; see for instance Epstein et al. (1951) and Shackleton (1967).” is an inadequate description of benthic δ18O. Mention of other factors (seawater composition, ice sheet volume, etc.) needs to be included. CENOGRID is composed of many integrated signals, the makeup of which will determine what detected breakpoints are telling us about the climate.
As the reader, I’m left wondering why only oxygen isotopes were considered. Carbon isotopes are also available, why not include carbon isotopes in the analysis, as was done in the original Westerhold publication?
The authors discuss the varying resolution of the time series at length, which is helpful. However, I would be curious as to whether or not the resolution impacted the detection of break points. Is there any correlation between the detection of new breakpoints (discussed later in the manuscript) and the resolution of the time series? For example, just by visual comparison, it seems to me that the breakpoint observed in Coolhouse 1 in later sections might be related to a large change in resolution that occurs nearby. While this breakpoint isn’t heavily interpreted here, this is an important point to understand if other researchers are to apply this method to their own data.
This sentence “Furthermore, we recommend using binning frequencies 10 and 25 kyr as they result in the most consistent outcomes.” strikes me as rigid and somewhat unhelpful, as many records will not share the general time axis properties of CENOGRID. Is there a different way to describe your binning recommendation that’s more flexible and/or applicable to other datasets?
Certain technical choices need to be better explained given the audience of this journal. For example: “To address these issues, we use the autocorrelation and heteroscedasticity consistent (HAC) covariance matrix estimator with prewhitening in our implementations.”. Perhaps this is standard fare in breakpoint analysis literature, but most paleoclimatologists won’t be familiar with this procedure. Some explanation as to why this approach is suitable for this data is warranted here, as is mention of alternatives that were considered. In the same vein, it would be helpful to spend a little bit more time explaining information criteria. That is, expand upon “We use information criteria to estimate the number of breakpoints”. What does this mean, why are they used, have they been used in paleoclimate contexts before, etc.
Age uncertainty needs to be addressed somewhere in this paper. It doesn’t need a full treatment, in that the method doesn’t need to be modified to account for it, nor does it need to be included in the analysis, but discussion of how to include it in future studies is essential. Specifically I would be curious as to how this technique might be expanded to include the usage of age ensembles and how choice of age modeling method might impact breakpoint detection. However, discussion of including age uncertainty directly would also be acceptable here.
The simulation study is a particular strength of this work. The authors thoroughly test their method across different data-generating processes, demonstrating its robustness to various forms of non-stationarity and serial correlation. This kind of rigorous testing is essential for establishing the reliability of statistical methods in paleoclimate contexts. I just wanted to make a note of that.
When analyzing the possible presence of multiple breakpoints, I’m left desiring some kind of prescription as to how I should set the number of breakpoints. Certainly the claim that there are more than 5 statistically significant breakpoints in CENOGRID seems robust. However, the current analysis feels somewhat hand-wavy, with seven breakpoints being settled upon in a rather arbitrary way. In particular this statement needs to be expounded upon: “The estimation results based on information criteria justify dividing the climate states Warmhouse II and Coolhouse II into two substates each at approximately 39.7 Ma and 10 Ma, respectively. This is supported by the presence of breakpoints estimated approximately at these time stamps in the estimations with seven or more breakpoints.”
The ending of this manuscript is far too abrupt. Potentially new breakpoints are discovered when varying numbers of breakpoints are allowed, but what do they mean? A few climate events are referenced, but events themselves may or may not justify entirely new regimes. Much context is needed here, interpreting and explaining the presence of these novel breakpoints. While the authors are free to choose how to address this comment, I might suggest including a “Discussion” section, in which the primary results are emphasized, and an explanation/interpretation of these results is offered. Some of my other comments could probably be folded into this section as well.
Technical Comments:
The paper currently is a bit undercited. I suggest the authors go back through with a fine toothed comb and make sure they’re citing existing literature wherever possible. In particular, all sections discussing δ18O interpretation should be thoroughly cited, particularly regarding ice volume effects, temperature relationships, etc. A couple of other key spots (non-exhaustive) that need citations include:
“The climatic transitions contain important information about variations in Earth's climate system” (here Tierney et al. 2020 is referenced, but some explanation of what is contained in that review along with additional citations is called for)

“Our approach contributes to the existing breakpoint detection methods in paleoclimate research” (cite breakpoint analysis in paleoclimate literature)

“This breakpoint aligns with the Middle Eocene Climatic Optimum, a known climatic event” (cite original papers describing this event)

“Some of these breakpoints coincide with other climatic events, for instance, the Latest Danian Event at 62.2 Ma and the onset of the Miocene Climatic Optimum at 16.9 Ma” (cite original papers describing these events, not just Westerhold 2020)
Citation: https://doi.org/10.5194/egusphere-2024-3443-RC1
- AC1: 'Reply on RC1', Kathrine By Larsen, 14 Mar 2025
  
  We sincerely appreciate the reviewer's constructive and insightful comments, which have helped us improve our manuscript. Please find our point-by-point response to each comment in the attached file. The reviewer's comments are in black text, and our responses are highlighted in blue.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3443-AC1
RC2:
'Comment on egusphere-2024-3443', Anonymous Referee #2, 30 Jan 2025
The authors apply a statistical approach to a reference paleoclimate dataset to evaluate shifts in climate states across the Cenozoic. They review existing methods and highlight the advantages of the breakpoint method and apply this approach on the Westerhold et al. 2020 dataset. They review the model and the impact of model parameterization on determined number of breakpoints. Ultimately, they established a similar number of breakpoints to Westerhold et al 2020 paper using this new approach and summarize their methodological approach and findings.
The application of new statistical approaches to assess time series and breakpoints is an important field of study but this contribution lacks significance beyond the application and usefulness of the method used. Although the paper is organized in structured manner, it is lacking background on other statistical assessments applied to assess Cenozoic or long-term changes in past climates and inclusion of a breath of paleoclimate specific references. Overall, this contribution mostly focuses on method development and application rather than implications of findings. Based on the above, it is difficult to see how it has led to a deeper understanding of Cenozoic climate.
I would suggest that this contribution needs to expands its discussion to outline how its findings enhanced our Cenozoic climate knowledge. Further there is a lack of background information needed to fully characterize the dataset evaluated, its attributes and limitations, and age model considerations.
Below I have made some comments to develop the paper and give its finding wider significance.
General comments:
Introduction lacks information on Earth’s history and significance of these various climate states. A review of existing methods is useful but does not link to wider significance of work and importance for paleoclimate field or mention how this analysis could provide new understanding or concepts for workers.

Justification for use of Westerhold et al. 2020 dataset needs to be developed further. More information on benthic foraminifera used to construct record, limitations associated with age model differences, and potential interpretation of d18Ob record from past work. There is limited mention of d18Ob and its use to pinpoint climate states and whether these states align when using other similar datasets or depending on inclusion or exclusion of individual/regional d18Ob records does it impact the breakpoint determinations

The contribution needs to consider its finding and whether it has led to a deeper knowledge of Cenozoic Science. For instance, what framework can the climate transitions of the Cenozoic be categorized and how is this related to dynamics of the climate system? This will allow for the novelty of the method application to be developed in more detail. A thorough review of other approaches used to assess climate change in Cenozoic would be useful to include, going beyond this method, including tipping point analysis and frequency analysis to showcase how this co-eval alongside of the breakpoints.
Citation: https://doi.org/10.5194/egusphere-2024-3443-RC2
- AC2: 'Reply on RC2', Kathrine By Larsen, 14 Mar 2025
  
  We are grateful for the time and effort the referee has dedicated to evaluating our manuscript, as well as the constructive feedback that has helped us strengthen the paper. Please find our responses to the referee’s comments in the attached file. The referee's comments are in black text, and our comments are highlighted in blue.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3443-AC2

Peer review completion

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

ED: Reconsider after major revisions (19 Mar 2025) by Julien Emile-Geay

AR by Kathrine By Larsen on behalf of the Authors (29 Apr 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (12 May 2025) by Julien Emile-Geay

RR by Anonymous Referee #1 (03 Jun 2025)

RR by Anonymous Referee #2 (16 Jun 2025)

Suggestions for revision or reasons for rejection

Bennedsen et al. resubmission tackles applying econometric methods to estimate breakpoints. The previous version lacked context for wider paleoclimate science and was hard to discern the impact/importance of the new method for undersanding Cenozoic clmate better. They have modified the manuscript across all sections to deepen the context and implications of the work.

Specifically the authors have improved the manuscript however more details are needed to justify some changes and include additional references/previous work to make this contribution exhaustive. Some aspects are related to additional references related to recurrence analysis, Cenozoic d18Ob records, use of econometric methods in time series analysis, and impacts of age uncertainty on findings.

Although the authors now have added a discussion to provide wider paleoclimate context which expands the application more, there is additional work needed to refine this section including restructuring and a summary figure.

With these revisions completed, this would make a good contribution for this journal.

Major comments:
Discussion section hints at potential additional break points however this is alongside of methods aspects. I would recommend adding a section in the results around ‘additional breakpoints’ to highlight method/criteria used, number of additional breakpoints identified, and then leave the implications of this for the discussion. Info about binning and regime length in discussion make it difficult to digest. I also recommend making a new figure to go along with this section.

Authors highlight there are potential additional breakpoints detectable in the time series. This section refers to Figure 5 only but highlights changes in carbon cycle, cooling and wider climate systematics. It would be useful to make an additional figure which includes d18Ob, d13Cb, relavant SST or BWT records with stages of cryosphere development + C3/C4 to showcase timing of possible new breakpoints and wider features. This could have the initial westerhold points and the new potential ones.

Specific comments:
-title has changed to include ‘econometric’ methods-however this term is not known in paleoclimate field and only mentioned at the end of the introduction very briefly defining it (line 83). I would recommend reconsidering title change or expanding on the use of these types of methods more widely or explaining why applying this from another field is worthwhile or novel or beneficial.
-lines 30-33 it is worth mentioning that there are not only shifts in data set but the resolution is varying as well and reference accordingly
-line 33- there are more recent publications to include as well (Mudelsee et al 2014) in addition to Zachos
-ine 45 are there other applications in the field of climate science that can be summarized used using recurrence analysis (e.g Liang et al 2025). It would be useful to provide exhaustive background on application of recurrence analysis and metrics used in this analysis in addition to westerhold
-line 81 sets out the study but does not mention Westerhold dataset, could be useful to say this work applies approach on climate stack
-line 89 here the econometric framework is then then referred to as the Bai-Perron framework and using this term for the remaining. It is useful to introduce both econometric and Bai-Perron framework?
Line 101- ‘weight difference’ consider defining as ratio of heavy to light for instance
Line 110-can you provide example resolution across key time intervals, the average resolution is only so useful as there are few records in early Cenezoic with orbital resolution
-line 113- age model uncertainty is mentioned but also said it is not accounted for, can you add the biggest drivers of uncertainty here? It is later mentoned but would be worth to introduce reader to the issues here broadly also it is useful to highlight why it does not need to be addressed in this study. See lines 327-330.
-line 336-337 it is stated that the authors ‘expect our main findings to be robust’ despite age uncertainties across the Westerhold. Are the authors able to conduct a sensitivity test in some way to showcase this?
-line 355- the authors mention the post-MECO cooling and refer to Bohaty & Zachos, 2003, however there are additional insights into the MECO and carbon cycle and temperature trends since this publication.
Line 368-denote average resolution for the record
-Figure 1 and 3-add the geological time scale for reference as well as the climate states for reader context. This would help also understand changes in data density/resolution with time.
-Figure 3-caption should include more description of the data for instance including time interal, data resolution and number of core sites.

Heading 3.1-consider changing to ‘breakpoint number sensitivity tests ‘or more general than current

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ED: Reconsider after major revisions (18 Jun 2025) by Julien Emile-Geay

Dear authors,

I am now in receipt of two reviews of your revised manuscript. Reviewer is satisfied with the work and supportive of immediate publication, while Reviewer 2 suggests additional work.

I must agree with Reviewer 2 that the implications of additional breakpoints need to be more carefully discussed. From a methodological standpoint, it comes as no surprise that estimating the number of breakpoints from information-theoretic criteria would lead to additional breakpoints compared to those identified previously in Westerhold et al (2020). This begs the question of the geological significance of these new breakpoints. As such, Reviewer #2’s suggestion of incorporating different lines of evidence (in addition to benthic d18O, “d13Cb, relavant [sic] SST or BWT records with stages of cryosphere development + C3/C4” (the ratio of C3 to C4 plants)), is very well taken, and could shed light on whether transitions identified solely in d18O are geologically meaningful, or whether they are simply a methodological artifact. It may also be worth discussing how to integrate the Bai-Perron detection of breakpoints across multiple data streams (e.g. the ones cited above), though a formal investigation of this type is clearly out of scope for this paper.

Reviewer 2 also makes a number of useful, specific suggestions regarding additional references that would make the manuscript more current to the present state of the scholarship.

Finally, I agree that the choice of title could be improved, though for a different reason: while there is nothing wrong with using the mainstream word “econometric”, the issue I see is with the plural form “methods”. This is misleading as only one such method (the Bai-Perron framework) is really used. Thus it would seem more truthful to choose the title “Estimating breakpoints in the Cenozoic Era with the Bai-Perron framework”, or “Estimating breakpoints in the Cenozoic Era — an econometric approach”, to avoid giving the impression that a whole array of econometric methods have been applied to the question.

In revising your manuscript, please make sure to observe the revisions checklist provided by the editorial office.

Best of lucks for your final revisions,

Julien Emile-Geay

Hide

AR by Kathrine By Larsen on behalf of the Authors (13 Aug 2025) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (29 Aug 2025) by Julien Emile-Geay

After reading the manuscript, I am satisfied that the revisions have addressed the concerns and suggestions of the reviewers. I only recommend a few minor changes prior to publication:

L197+: “aucorrelation occurs when current values correlate with past values, which is common in paleoclimate data due to long-term persistence in climate dynamics.” Here it should be added that taphonomic processes such as bioturbation also add to this aucorrelation in the proxy record.

L304+: “a few paleoclimate studies use information criteria for model selection, for example Valler et al 2024 show we can be beneficial”. This statement seems gratuitous as Valler et al 2024 were far from the first to use an IC in paleoclimatology. I recommend removing it altogether.

L318-319: “six and 12” and “ seven and 14”. Please use either numeric or textual representations, but do not mix and match.

L374-376: This argument is circular; you cannot use the Bai-Perron framework to validate the recurrence network analysis of Westerhold et al (2020), and use Westerhold et al (2020) to validate the Bai-Perron framework. Given that this framework is actually rooted in statistical theory and econometric practice, it seems like it would help buttress the results of Westerhold et al (2020). The intersection with the tipping points identified by Rousseau et al (2023) is also relevant here.

L387: “Five of these breakpoints closely match the five major transitions identified by Westerhold et al (2020).” Please clearly mark those transitions on Fig 7.

L430: “which Clark et al (2006) describe as a gradual transition occurring between 1.25 and .7 Ma” —> See also James et al (2024, 10.1029/2023PA004700) for a dynamical argument about a gradual transition.

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AR by Kathrine By Larsen on behalf of the Authors (04 Sep 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (04 Sep 2025) by Julien Emile-Geay

AR by Kathrine By Larsen on behalf of the Authors (11 Sep 2025) Manuscript

Journal article(s) based on this preprint

05 Nov 2025

Estimating breakpoints in the Cenozoic Era: an econometric approach

Mikkel Bennedsen, Eric Hillebrand, Siem Jan Koopman, Kathrine By Larsen, and Rachel Lupien

Clim. Past, 21, 1981–2008, https://doi.org/10.5194/cp-21-1981-2025,https://doi.org/10.5194/cp-21-1981-2025, 2025

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Mikkel Bennedsen, Eric Hillebrand, Siem Jan Koopman, and Kathrine By Larsen

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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Our study presents a statistical approach for identifying transitions between climate states in the Cenozoic Era. We analyze a temperature proxy record covering the period from 67.1 million years ago to present time. Our analysis corroborates the transitions previously identified in the literature and provides statistical justification for additional transitions. Our approach allows for constructing confidence intervals, offering measures of uncertainty.


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