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)

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.