Review of the manuscript “The Paleochrono-1.1 probabilistic model to derive optimized and consistent chronologies for several paleoclimatic sites” by Parrenin et al., submitted to Geoscientific Model Development

General comment:

This is an interesting, well-written paper presenting a new probabilistic model (Paleochrono-1.1) to derive a common and optimised chronology for several paleoclimatic sites with potentially different types of archives. This is an important modelling question, which definitely fits within the scope of GMD. The new model builds on a previous model (IceChrono), but has substantial advantages compared with its predecessor (computational efficiency, ease of use, accuracy), which are clearly outlined and discussed in the paper, and can thus be considered as a substantial advance in terms of age modelling (in particular to combine different types of information from several archives).

All methods and assumptions appear valid and are clearly outlined, and the detailed description enables the reader to reproduce the results. The results of the example presented in the paper nicely demonstrate the general potential of the model. All conclusions are supported by the results.

The authors mention several aspects of the model (e.g., that it can also be used to construct age models for individual sites, the risk of choosing incorrect values for error bars and correlation lengths, etc.). The paper (and in particular the non-expert readers, who should use the model later) would strongly benefit from a more detailed explanation how to choose these values and their effect on the modelling results. Thus, I recommend to either present more examples or to calculate the same example with different choices of the parameters (see below for further details).

In summary, I highly recommend publication in GMD, but I am convinced that the paleoclimate community would benefit from a more detailed illustration based on several examples. Below, I also list some other minor comments that may be useful to further improve the paper.

Detailed comments:

It may be good to modify the title to better illustrate the potential of the model to the general reader. The current title – in my opinion – does not illustrate that the model derives a common, combined age model from several sites using stratigraphic links, etc.

Line 49: I would not consider speleothems as an archive with a continuous deposition process. We meanwhile know that many speleothems show various hiatuses (ranging from a few years to tens or hundreds of ka), and their growth thus rather needs to be considered as episodic. Later, it becomes obvious that the authors are aware of this, but it may be useful to state this major difference to, e.g., ice cores right at the beginning.

Line 58 ff.: Maybe mention the various, very sophisticated methods used in dendrochronology here.

Line 127: “Paleochrono-1.1 does not integrate information regarding hiatuses, …” Even if this is true, as mentioned further down, hiatuses can be included: “If there is a known hiatus in the archive, the sections before and after the hiatus should be considered as two different sites in Paleochrono-1.1.” This means that hiatuses will not be detected by the model, but they can be included. This should be clarified and may be very important for archives like speleothems (see above).

Line 134: “… simple archives, with one unique depth age relationship …” This is not clear to me. What does unique mean in  this context. Please clarify.

Line 151 ff.: “Uncertainties on the prior estimates and on the observations are assumed to be Gaussian …” This may be problematic for old (i.e., > 200 ka) U-series ages, where the errors become asymmetric. This should be included later, when, e.g., non-Gaussian uncertainties of 14C ages are mentioned.

Line 308 ff.: “We assume also a correlation length of 1,000 yr for the deposition rate of both speleothems, assuming higher frequency variations are absent.” This is OK for this paper, but it may be noteworthy that the Asian speleothem d18O records often show a correlation on the precession time scale. Would this have an effect of the results?

Line 317 ff.: “We assign a constant uncertainty (1σ) of 100 yr to these synchronisation horizons. 100 yr is a rough estimate of the synchronisation error during DO transitions.” This is not clear to me. What is the effect of this uncertainty in the end? What would happen if the chosen value was too small? It may be interesting to demonstrate and discuss the effect for different values. Alternatively, more information should be provided to assist the readers how to choose this value.

Line 331 ff.: “Figure 4 shows that Paleochrono-1.1 is able to reconstruct a variable deposition rate from the chronological information, in particular the dated horizons along the MSL speleothem. It is also able to estimate an uncertainty on this posterior reconstruction, which will depend mainly on the uncertainty of the U/Th dated horizons, the depth resolution of the U/Th dates and the assumed growth-rate variation that affects interpolation uncertainty.” It is clear to me that the main scope of the paper is to demonstrate that the model can generate a common, combined model for different archives. However, since the model can also be used to calculate individual age models for single archives (e.g., speleothems) and will probably also be used for this purpose, it may be good to present the results for this as well. If so, it would be interesting how the results compare with other published age models (for speleothems, see, for instance, Comas-Bru et al., 2020).

Line 381 ff.: “… whereas the NGRIP ice core provides very accurate relative ages (i.e.,

durations) from counting of annual layers across intervals.” Even if the relative accuracy of such layer counted chronologies is very high, the counting uncertainty sums up to considerably (e.g., for GICC05). How is this included in the model?

Line 407 ff.: “Additionally, the models for combining all the information may grow to be so comprehensive that most users will not be able to maintain an overview of the data employed, and operating the model will entail sometimes implicit and important choices, e.g. on how to estimate the error bars of the prior and of the observations, how to set the correlation lengths for the prior, etc.” I completely agree with that and would like to encourage the authors to demonstrate the effect of, e.g., incorrect choices for error bars and correlation lengths of the prior. This would not only be helpful to avoid such mistakes, but also improve the applicability of the model.

Line 427 ff.: “In conclusion, optimal chronologies are practical for users who want to use the best possible common chronology, but it absolutely does not replace the need to compare and improve the chronologies of individual sites. The compromises involved in the modelling entail a risk that wrong chronological information or insufficiently quantified uncertainties will influence the resulting time scale negatively in a non-transparent way.” This is a very important point, and - again – I think, it would be very useful to better demonstrate the mentioned effects in the paper. One way would be to (i) construct an individual age model for one of the speleothems (and compare with one of the published models in SISAL), then (ii) construct the common model, and then (iii) construct a (iii) model using wrong chronological information or insufficiently quantified uncertainties to demonstrate the effect.

Conclusions: This is mainly a repetition of the previous sections and could be shortened.

Comas-Bru, L., Rehfeld, K., Roesch, C., Amirnezhad-Mozhdehi, S., Harrison, S.P., Atsawawanunt, K., Ahmad, S.M., Ait Brahim, Y., Baker, A., Bosomworth, M., Breitenbach, S.F.M., Burstyn, Y., Columbu, A., Deininger, M., Demény, A., Dixon, B., Fohlmeister, J., Hatvani, I.G., Hu, J., Kaushal, N., Kern, Z., Labuhn, I., Lechleiter, F.A., Lorrey, A., Martrat, B., Novello, V.F., Oster, J., Pérez-Mejías, C., Scholz, D., Scroxton, N., Sinha, N., Ward, B.M., Warken, S., Zhang, H. and SISAL Working Group Members (2020) SISALv2: A comprehensive speleothem isotope database with multiple age-depth models. Earth System Science Data 12, 2579–2606.

This paper describes the Paleochrono (1.1) model, which is intended to allow the construction of consistent age models for different sites and archives.  This is likely to be a very important tool, particularly for the ice core community but potentially for other palaeoclimate communities. It carries out an important task that has not been accessible in an available program before. The methodology is carefully described, and appears logical, even if one could questions some aspects of the way errors are combined.  The program’s application is illustrated with a nice cross-archive example, and the computing performance is clearly described. Overall, I found this an important paper that should be published with only minor corrections.

Most of my comments are very minor single word clarifications. I have just two broader issues to raise.

In lines 310-320, the mid-point of DO transitions is synchronised with an uncertainty. This rests on the assumption that there are no or minimal lags between DO onsets in different sites and archives. For speleothems from different regions this is precisely what was shown by Corrick et al 202, using U/Th dates from different speleothems.  However while they inferred it as likely, Corrick et al did not specifically demonstrate synchroneity between DO events in spelothems and in Greenland ice (or methane in Antarctic ice). This was rather done in Adolphi et al 2018. This illustrates a point that needs to be made more generally: that it is only OK to use tie points between archives if there is an a priori reason (mechanism (volcanic eruption), independently verified dates (U/Th dates in spelothems), or linkages (cosmogenic nuclide wiggle matching between ice and speleo)) to assume they are synchronous, and if the limit of synchroneity is specified (as it is at 100 years for speleo-ice at DO events). I know the authors know this but I think it needs spelling out, and the justification from the Adolphi and Corrick papers emphasised, to avoid the danger that genuine asynchroneity is falsely ignored by future users.

I cannot claim to understand the details of how the cost function is calculated. I understand that each marker or correlation comes with an uncertainty. However I would have appreciated some discussion of how the priors are weighted compared to the age markers etc. Possibly this is a parameter inside the model?

Minor comments

Line 67. “an event dated by radiometric analysis”. Shouldn’t this be a “layer dated by radiometric analysis”?

Line 101. needs a “)” after “surface”.

Line 133. Maybe mention reversals as well as hiatuses (reversals occur in deep Greenland ice for sure, and in some Antarctic ice).

Line 165. “𝐷 is the (dimensionless) relative density of the snow/ice material”. Clarify that this is relative to pure bubble free ice, not to (for instance) water.

Line 350 and line 487. Neither m nor mn seem like good abbreviations for minutes. I suggest spelling out or using “mins”.

Line 400. I know you refer to it later but here would be a good place to reference Mulvaney et al 2023.

Figure 1. I found the legend on the right confusing for the diouble-headed blue and purple arrows, because they are labelled as ice-air or ice-ice links, but could equally refer to speleo-air or speleo-ice links. I assume that was the meaning of putting ice in () but this is nowhere stated. It perhaps should be for clarity (ie add a statement that (ice) should be taken to refer to whatever sediment is used, eg speleothem or marine sediment as well as ice).