Broken 206Pb/238U carbonate chronometers and 207Pb/235U fixes

Vermeesch, Pieter; McLean, Noah; Vaks, Anton; Golan, Tzahi; Breitenbach, Sebastian F. M.; Parris, Randall

doi:https://doi.org/10.5194/egusphere-2025-432

Preprints

https://doi.org/10.5194/egusphere-2025-432

Preprints

13 Feb 2025

| 13 Feb 2025

Broken ²⁰⁶Pb/²³⁸U carbonate chronometers and ²⁰⁷Pb/²³⁵U fixes

Pieter Vermeesch, Noah McLean, Anton Vaks, Tzahi Golan, Sebastian F. M. Breitenbach, and Randall Parris

Abstract. Carbonate U–Pb dating has become a key tool for Quaternary palaeoclimatology and palaeoanthropology beyond the ∼800 ka age limit of Th–U disequilibrium dating. U–Pb geochronology is based on the paired radioactive decay of ²³⁸U to ²⁰⁶Pb and of ²³⁵U to ²⁰⁷Pb. Current carbonate U–Pb data processing algorithms rely mostly on the ²⁰⁶Pb/²³⁸U clock and attach little weight to the ²⁰⁷Pb/²³⁵U data. A key weakness of this approach is the need to correct the ²⁰⁶Pb/²³⁸U data for initial ²³⁴U/²³⁸U disequilibrium, which may cause an excess (or deficit) in radiogenic ²⁰⁶Pb compared to secular equilibrium. We introduce a new disequilibrium correction algorithm, using matrix exponentials. This algorithm can be used to undo the effects of U-series disequilibrium using either an assumed initial composition, or a measured set of modern ²³⁴U/²³⁸U (and optionally ²³⁰Th/²³⁸U) activity ratios. Using a deterministic Bayesian inversion algorithm, we show that disequilibrium corrections work well for relatively young samples but become unreliable beyond 1.5 Ma and impossible beyond 2 Ma. Using theoretical models and real world examples from Siberia, South Africa and Israel, we show that the uncertainty of the disequilibrium correction of such old samples exceeds the correction itself. Previous ‘Monte Carlo’ error propagation methods underestimate these uncertainties by up to an order of magnitude. We advocate the use of the ²⁰⁷Pb/²³⁵U isochron method as a more accurate and precise alternative to²⁰⁶Pb/²³⁸U geochronology for >2 Ma carbonates that are suspected to have experienced significant levels of initial ²³⁴U/²³⁸U disequilibrium.

Received: 29 Jan 2025 – Discussion started: 13 Feb 2025

Competing interests: Pieter Vermeesch and Noah McLean are associate editors of Geochronology.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Pieter Vermeesch, Noah McLean, Anton Vaks, Tzahi Golan, Sebastian F. M. Breitenbach, and Randall Parris

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-432', Perach Nuriel, 13 Mar 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-432/egusphere-2025-432-RC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-432-RC1
- AC1: 'Reply on RC1', Pieter Vermeesch, 13 May 2025
 
 The reviewer requests some additional information, including references and further background. Most of this information was covered in a book chapter on the Taung Child that was accepted for publication a few months ago (Vermeesch et al, 2025). However, since this book chapter is locked behind a paywall, we agree that it would be useful to repeat some of its content in the 'Broken chronometers' paper.
 "It is important to mention in the introduction previous contributions that mentioned this problem and used the ²⁰⁷Pb/²³⁵U isochron approach (e.g., Mason et al., Parrish et al. and more)."
 We apologise for the oversight. The references, which are covered in the book chapter, will be added to the revised manuscript.
 "It would be nice if the author could explain in the introduction the issue of disequilibrium correction from a geological point of view. For example, variations in ²³⁴U/²³⁸U and Th/U ratios in natural systems, the notion of correction of the initial ratio for the whole system (isochrone) and not for each spot analysis (which shows variations in initial U concentrations)."
 This is a useful comment, which is addressed in our response to the community comment by Dr. Timothy Pollard. We will summarise the consequences of initial U heterogeneity in the revised discussion of model-3 regression (Figures 8c and 8a).
 “I am also interested to know if variation in initial ²³⁴U/²³⁸U could also lead to variations in initial ²⁰⁷Pb/²⁰⁶Pb?”
 Geochemical/isotopic conditions can always co-vary. However, the reduction of the scatter around the Botovskaya isochron from the right to the left of Figure 9a suggests that (for this particular sample at least), the initial ²⁰⁷Pb/²⁰⁶Pb ratio is not substantially correlated with heterogeneous initial disequilibrium. We will draw attention to this in the revised manuscript.
 “It will be good to frame the issue of disequilibrium correction in the geological context, such as the age range and initial value range that are most critically affected. For example, the section in the conclusion, line 360 onwards, should be in the introduction. It is very important that the reader understand that this problem is not affecting only young ages.”
 We agree to move line 360 to the introduction. The practical age range and initial value range for the ²⁰⁶Pb/²³⁸U method are discussed in some detail in the aforementioned book chapter, which includes an elaborate figure (Figure 3 of Vermeesch et al., 2025) to illustrate it. Reproducing this figure would create excessive duplication of content. However, we will refer the reader to it in the revised manuscript.
 “I think there should be a section dedicated to variations in Th/U ratios as it seems like more critical for example in the case of Ash15 sample. Section 7.2 show that uncertainties in initial 230/238 are more crucial for this scenario. Would be good to discuss why 230/230=1 is more appropriate than 0 in that case?”
 We will follow the reviewer's suggestion and include another reference to the paper by Vermeesch (2020), which explicitly deals with the problem of U-Th-Pb isochron regression.
 “Please indicate if possible that ASH15 ID-TIMS data was used for reference material and therefore the corrected age was not needed, only the measured value.”
 The fact that ASH15 is a reference material was already mentioned in the first sentence of Section 7.2. However, we will add a second note to clarify that the possible existence of initial disequilibrium does not compromise its use as a reference, with the caveat that the excess scatter of the data around the ²⁰⁶Pb/²³⁸U isochron may be caused by that disequilibrium.
 “It is important to mention the fact that measuring ²⁰⁷Pb/²³⁵U on ID-TIMS will always be much better than on LA-ICPMS, so the comparison should be between LA-ICPMS ²⁰⁷Pb/²³⁵U and ²⁰⁶Pb/²³⁸U. The former will always have larger uncertainties because of problems to measure 207Pb in young carbonates. The question is then, will uncertainties from variations in initial values be larger than uncertainties in ²⁰⁷Pb measurements?”
 The tradeoff in accuracy between ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²³⁵U is the same for ID-TIMS and (LA-)ICPMS. However, it is true that the precision differs. This is why Section 7 of the paper is divided in three sections, for ID-ICPMS, ID-TIMS and LA-ICPMS, respectively. Whether the ²⁰⁷Pb/²³⁵U isochron works depends on the sample. See our response to the next comment.
 “If precipitation is from large reservoir such as meteoric, sea water, lake water etc. we could estimate initial values and provide uncertainties which will be perhaps better than using imprecise ²⁰⁷Pb measurements?”
 Indeed. IsoplotR allows the user to pre-specify an initial ²³⁴U/²³⁸U activity ratio. However, the manuscript deals with the alternative situation where the initial ²³⁴U/²³⁸U activity ratio is unknown and must be estimated from the sample. The ability to specify an assumed initial ²³⁴U/²³⁸U ratio is mentioned in line 7 of the abstract. Whether the precision of the ²⁰⁷Pb/²³⁵U isochron is sufficient is up to the user to decide. The counter example of Figure 9d was specifically added to make the point that the ²⁰⁷Pb/²³⁵U method is no panacea.
 “It is also important to discuss potential problems of using ²⁰⁸Pb as a common lead (instead of ²⁰⁴Pb). In particular when ²³²Th are high? What will be a limiting concentration from which you will not recommend using it as a common lead? And for what age range (<5 Ma?), or even better, a calculation of concentrations + age combinations?”
 The presence of ²³²Th can be accounted for using the total-Pb/U-Th isochron regression algorithm of Vermeesch (2020). As mentioned earlier in this response, we will draw attention to this paper by adding further references to it in the revised manuscript. The sensitivity of ²⁰⁸Pb-normalised U-Pb isochrons to the presence of Th is highly sample-specific, but can be assessed in IsoplotR by changing the ²³²Th/²³⁸U ratio.
 References
 Vermeesch, P., 2020. Unifying the U–Pb and Th–Pb methods: joint isochron regression and common Pb correction, Geochronology, 2, 119-131, doi: 10.5194/gchron-2-119-2020.
 Vermeesch, P., Hopley, P., Roberts, N. and Parrish, R. 2025. Geochronology of Taung and other southern African australopiths. In: "One hundred years of Australopithecus africanus", Wood, B.A., Grine, F.E. and Smith, H.B. Eds., Springer (in press).
 
 preprint available at: https://pieter-vermeesch.es.ucl.ac.uk/papers/VermeeschSpringer2025.pdf
 
 Citation: https://doi.org/10.5194/egusphere-2025-432-AC1
CC1:
'Comment on egusphere-2025-432', Timothy Pollard, 07 May 2025

Please see the attached document.

Citation: https://doi.org/10.5194/egusphere-2025-432-CC1
- AC2:
  'Reply on CC1', Pieter Vermeesch, 13 May 2025
  Some of the questions in the community comment have an unequivocal answer. Others are a matter of opinion. All are important, so we thank Dr. Pollard for his useful contribution. We will respond to the comments in their original order, using the same headers.
  Monte Carlo approach
  “Line 90 states incorrectly that Isoplot (Ludwig, 2003b) implements a Monte Carlo approach for estimating uncertainties in disequilibrium-corrected U–Pb ages that incorporate a measured [34/38] value”
  Ludwig (2003a) describes a Monte Carlo approach for estimating uncertainties in U-series disequilibrium dating. Ludwig (2003b) implements this algorithm, as well as another Monte Carlo algorithm for concordia intercepts. The reviewer is correct that Isoplot does not join the two algorithms together. We will change the wording of the sentence to reflect this. Importantly, Ludwig (2003a)’s U-series disequilibrium algorithm is subject to exactly the same limitations as the U-Pb algorithm used by DQPB. Therefore, the references to Ludwig (2003a,b) remain relevant to the ‘broken chronometer’ discussion.
  “Section 3 also provides a misleading description of the Monte Carlo approach implemented in DQPB. Prior to beginning the Monte Carlo simulation, DQPB checks that the measured [34/38] value provided by the user is statistically distinguishable from secular equilibrium.”
  We were aware of DQPB’s disequilibrium check. In fact, this ‘patch’ was added to DQPB after a review from Vermeesch (2022, https://doi.org/10.5194/gchron-2022-24-RC1). It protects the user against the worst misbehaviour of the Monte Carlo (MC) algorithm but does not fundamentally fix the problem. If a sample is statistically indistinguishable from secular equilibrium, then the MC algorithm effectively throws its arms in the air and gives up. The Bayesian algorithm does not. We will make this difference more explicit in the revised manuscript.
  The matrix exponential approach
  We thank the author for pointing out the Oak Ridge National Laboratory report by Bell (1973), and the book chapter by Albarède (1995). We were not previously aware of these publications but will cite them in the revised manuscript.
  Maximum range of measurable [²³⁴U/²³⁸U] disequilibrium
  The reviewer takes issue with our decision to assume a value of 4‰ (at 2σ) for the reproducibility of the modern ²³⁴U/²³⁸U activity ratio measurements. This value was obtained from a South African speleothem analysed by Walker et al. (2006). The reviewer points out that this dataset represents not one but three different samples from the same speleothem, and therefore represents a ‘pessimistic’ point of view. The reviewer claims that we have made a “logically flawed argument”:
  “They assert that because, according to their assessment, the [34/38]_m data from Walker et al. (2006) are overdispersed relative to analytical uncertainties, then all speleothem [34/38]_m ratios are likely to be similarly overdispersed, rendering U–Pb ages and uncertainties derived from measured [34/38]_m values inherently unreliable. However, this reasoning relies on an extreme extrapolation from a single dataset to the global population of speleothems.”
  We used the dataset of Walker et al. (2006) out of necessity. It contains ten ²³⁴U/²³⁸U activity ratio measurements. Most other published speleothem U-Pb datasets include fewer than four measurements, which is insufficient to quantify the dispersion of ²³⁴U/²³⁸U activity ratios. The reviewer is correct that the true extent of the ²³⁴U/²³⁸U-overdispersion is unknown for nearly all published disequilibrium-corrected U-Pb datasets. This undermines their position more than it does ours. Absence of evidence (for dispersion) does not equal evidence for absence (of dispersion). Less harm is done by overestimating the dispersion than by underestimating it. Therefore, we prefer to call our approach ‘cautious’ rather than ‘pessimistic’. The burden of proof is on those who use the analytical precision of 0.02‰ in their calculations to demonstrate that their ²³⁴U/²³⁸U-ratios are reproducible. Perhaps the estimate of 4‰ is overly cautious. Perhaps it is not cautious enough. In the absence of systematic ²³⁴U/²³⁸U surveys, this is a matter of opinion.
  Bayesian approach
  The manuscript acknowledges that the uniform prior for the initial ²³⁴U/²³⁸U activity ratio is unrealistic, and could be replaced by “a more informative local or regional prior”. The reviewer requests that the influence of such an informative prior be discussed in more detail.
  We will revise the manuscript to argue that, if the choice of prior has a detectable effect on the posterior distribution, then this is a sign that the ²⁰⁶Pb/²³⁸U method should be abandoned in favour of the ²⁰⁷Pb/²³⁵U method. This message can be conveyed using the existing figures. For example, Figures 4c and 4d would look the same for any choice of prior, whereas Figures 5b and 5c would not. Therefore, the ²⁰⁶Pb/²³⁸U method can be safely applied to the Corchia dataset of Figure 4, but not to the Hoogland dataset of Figure 5.
  Limits of the U-Th dating method
  The limit of the U-series disequilibrium dating method is not sharp but fuzzy. The reviewer writes that the manuscript uses two cutoffs (800 ka and 1 Ma, respectively). The 800 ka value was taken from the U-series literature (Cheng et al., 2013). The 1 Ma value is an approximate value for the U-Pb method. The reviewer is correct that the age limit is sample dependent. For oceanic corals ([34/38]_i = 1.15), the age limit for the U-Th method is less than 800 kyr. On the other hand, for southern African speleothems ([34/38]_i > 2), the U-Th dating limit is similar to that of the ²⁰⁶Pb/²³⁸U method, i.e. closer to 1 Ma. The revised manuscript will emphasise the fuzziness of the applicability cutoff.
  ²⁰⁸Pb normalization
  See our response to reviewer 1. We add the suggested references to the revised manuscript.
  ASH-15 isochron fit
  The reviewer’s final question relates to the mathematical treatment of the ASH-15 TIMS U-Pb dataset. The ²⁰⁶Pb/²³⁸U isochron for this dataset is overdispersed with respect to the analytical uncertainty. As discussed by Vermeesch (2024) and mentioned by the reviewer, there are three ways to model this uncertainty. The excess dispersion can be attributed to (1) the y-intercept (non-radiogenic Pb composition, ‘model 3a’), (2) the x-intercept (the age, ‘model 3b’), or (3) both x- and y-intercept. Figure 8 uses the second option, for three reasons:
  For ‘ordinary’ 2-dimensional (Rb-Sr, Lu-Hf, …) isochrons, the first two methods are mathematically tractable but the third one is not. For 3-dimensional U-Pb datasets (²³⁸U/²⁰⁶Pb, ²⁰⁷Pb/²⁰⁶Pb and ²⁰⁸Pb/²⁰⁶Pb), only the second approach is feasible. This is the reason why IsoplotR currently does not implement model-3a regression for U-Pb data.
  
  Model-3a data exhibit more excess scatter near the y-intercept than the x-intercept. Model-3b produces the opposite type of trend (Figure 2 of Vermeesch, 2024). The Botovskaya data of Figure 9 are clearly more consistent with the latter model. Admittedly, the situation is not so clear-cut for ASH-15, but even there the evidence for model-3a is not any stronger than that for model-3b.
  
  As pointed out by reviewer 1, any spatial variability in initial ²³⁴U/²³⁸U activity ratio would cause similar patterns of excess scatter as model-3b isochron regression. Under this scenario, model-3b would still be the statistically most sensible solution, although the reviewer is correct that the dispersion estimate would not have any real geological meaning. The revised manuscript will be amended to clarify this subtle but important point.
  
  The ASH-15K data are available through the online supplement of Nuriel et al. (2021). The R code to fully reproduce Figure 8 will be added to the supplementary information.
  References
  Albarède, F. (1995). Introduction to Geochemical Modeling. Cambridge University Press. https://doi.org/10.1017/CBO9780511622960
  Bell, M. (1973). ORIGEN: the ORNL isotope generation and depletion code (No. ORNL-4628). Oak Ridge National Laboratory (ORNL), TN, USA. https://inis.iaea.org/records/mpm97-77602
  Cheng, H., Lawrence Edwards, R., Shen, C.-C., Polyak, V. J., Asmerom, Y., Woodhead, J., Hellstrom, J., Wang, Y., Kong, X., Spötl, C., Wang, X., & Calvin Alexander, E. (2013). Improvements in ²³⁰Th dating, ²³⁰Th and ²³⁴U half-life values, and U--Th isotopic measurements by multi-collector inductively coupled plasma mass spectrometry. Earth and Planetary Science Letters, 371–372, 82–91. https://doi.org/10.1016/j.epsl.2013.04.006
  Ludwig, K. R. (2003a). Mathematical–Statistical treatment of data and errors for ²³⁰Th/U geochronology. In B. Bourdon, S. Turner, G. M. Henderson, & C. C. Lundstrom (Eds.), Uranium-series geochemistry (Vol. 52, pp. 631–656). Mineralogical Society of America.
  Ludwig, K. R. (2003b): User’s manual for Isoplot 3.00: a geochronological toolkit for Microsoft Excel, Berkeley Geochronology Center Special Publication, 4.
  Nuriel, P., Wotzlaw, J.-F., Ovtcharova, M., Vaks, A., Stremtan, C., Šala, M., Roberts, N. M. W., & Kylander-Clark, A. R. C. (2021). The use of ASH-15 flowstone as a matrix-matched reference material for laser-ablation U − Pb geochronology of calcite. Geochronology, 3(1), 35–47. https://doi.org/10.5194/gchron-3-35-2021
  Vermeesch, P. 2024. Errorchrons and anchored isochrons in IsoplotR. Geochronology, 6, pp.397-407. https://doi.org/10.5194/gchron-6-397-2024
  Walker, J., Cliff, R. A., & Latham, A. G. (2006). U-Pb isotopic age of the StW 573 hominid from Sterkfontein, South Africa. Science, 314(5805), 1592–1594. https://doi.org/10.1126/science.1132916
  
  Citation: https://doi.org/10.5194/egusphere-2025-432-AC2
RC2:
'Comment on egusphere-2025-432', Robyn Pickering, 13 May 2025
Vermeesch et al present a manuscript titled “Broken ²⁰⁶Pb/²³⁸U carbonate chronometers and ²⁰⁷Pb/²³⁵U fixes” in which they question the validity of the widely used 238U-206Pb chronometer as applied to carbonate rocks, and propose an alternative and better way to date these is by using the 235U-207Pb decay chain. They argue that the main issue with the 238-206 chronometer is the need to address the initial 234-238U conditions of the carbonate being dated, and that this brings so much uncertainty that it renders the technique unusable. They provide three case studies, relooking at published data, to illustrate their argument. They also offer what they claim is a new calculation program to produce U-Pb carbonate ages.
I am unable to recommend this manuscript for publication. My main reasons for rejecting the manuscript follow the guidelines from GChron given as follows:
It is not often that a reviewer is placed in a position where the answers to questions like “are the scientific approach and applied methods valid?” and “are the results discussed in an appropriate and balanced way (consideration of related work, including appropriate references)?” are no and no.
Here are my reasons for saying this:
1. The title of the manuscript is not acceptable, it is inflammatory and overstates the authors perception of both the problem and their solution. To suggest that the entire 238-206 carbonate chronometer is ‘broken’ is a very bold claim and asks the geochronology community to throw out the last almost 20 years of work in this field, starting from Woodhead et al., 2006 but arguably 28 years of work if you start with Richards et al., 1998. This means disregarding a huge body of well-respected work on dating carbonates, mainly in this case speleothems, from around the world. Such a claim requires remarkable evidence, which this manuscript fails to deliver.
While yes, in theory, they are not wrong that 234-238U is an issue, but to argue that this is such a big issue that the entire chronometer needs to be viewed as ‘broken’ is not substantiated by what they present here. The basis of their argument for the extent of the 234-238 issue is based on a single U-Pb age from a single layer of speleothem from one cave site in South Africa, Hoogland. So, they appear to be attempting to discredit an entire field and over 20 years of work, based one a single ‘bad’ sample. The authors also refer to another piece of theirs, a book chapter in press, which is made out to contain more issues with the 238-206 method, but this is also based on this single Hoogland sample. So, from my reading of this manuscript, they are advocating for the entire 238-206 carbonate chronometer to be discounted based on a single sample.
It is worth noting that the handling of this single Hoogland data here contains an error too. On line 112, the authors use the published data from the Hoogland sample and writes: “[34/38]m = 1.0016 ± 0.001 (1SE)”. However, in the methods section of the original publication (Pickering et al., 2019), all uncertainties are given as 2SE. This is standard practice, all U-series ratios are quotes at 2SE. This means that the Hoogland 234-238 data, so pivotal to this manuscript, are still outside 3 standard deviations from secular equilibrium and their figures 2 and 3 are flawed.
Further to this, Adams et al (2010) present palaeomagnetic data and a biochronological faunal analysis of Hoogland cave, which place the basal flowstone at ~3.12 Ma, so the later Pickering et al (2019) direct dating of this same flowstone to 3.1 Ma is in complete concordance with the existing and independent geochronological data. So, basing the rubbishing of the entire 238-206 carbonate chronometer off this one sample is not only unwarranted but incorrect.
So, in summary, this title is incorrect, misleading and something of an insult to the speleothem U-Pb community:
206/238 is not broken → sure, there are important things to consider, and they point out some valid concerns, but in many cases 206/238 works fine and the title suggests otherwise, basically entirely discrediting previous speleothem U-Pb work.

207/235 is not a perfect fix → it only works older samples and then only for samples with high U concentrations and low common Pb, even their own attempt to date the lower flowstone at Taung did not work for these reasons (Section 5, last sentences, Vermeesch et al. in press). Also, though it can be more accurate but is often less precise, as they acknowledge:

Quoting from their own manuscript:
Line 44: “…the 207Pb/235U method is more accurate than the 206Pb/238U method, whilst being less precise for young samples.”

Lines 206-207: “Although the 207Pb/235U method outperforms the 206Pb/238U method at 1 Ma in terms of accuracy, its poor precision means that its potential benefits do not materialize until 2 Ma.’ → not a perfect fix and 206/238 not broken; and also, now suddenly 206Pb/238U breaks down at 1 Ma?

Lines 234-236: “The 207Pb/235U age uncertainty is invariably larger than the 206Pb/238U age uncertainty. In fact, below ~1 Ma, it could be argued that the 207Pb/235U age uncertainties are unusably imprecise.”. → again 206Pb/238U not broken.

Lines 291-293: “…SB-72-8 produces a well defined linear array in 206Pb/238U isochron space, but fails to do so in 207Pb/235U isochron space. Unfortunately, such cases are not rare. The 207Pb/235U approach only works in samples that are sufficiently rich in U and sufficiently poor in common Pb.”
2. To further support their case for using the preferential use of 235-207 chronometer, at the expense of the 238-206 chronometer, three case studies are presented: data from some of the co-authors from Siberian speleothems, both ID and LA data and a new matix matched carbonate standard.
For the ID Siberian data, the authors here recalculate the 238-206 ages, using the published data for over 70 speleothem samples, and present matched 235-207 ages (their Figure 7). The 235-207 ages certainly do overlap with the corrected 238-206 ages but the errors on the 235-207 ages are huge by comparison, which is a serious detractor from this method. So yes, in this case, speleothems from this karst region have 238 and 235 ages which are coeval, but this is not a surprising nor novel results, we would expect this. The much larger errors on the 235 ages are a strike against this approach vs making an argument to use it in favour of the 238 ages.
The LA Siberian data is also looked at, as an example where measuring residual 234-238 was not done, as this is not really possible with LA (ID is the only way to get solid 234-238 measurements), so they argue that their 235 age is better, as it does not need this 234-238 ‘correction’, which was not possible given that this is a LA dataset. There are several issues with this case study. To be clear, the 234-238 measurements are not used by the U-Pb carbonate community as a ‘correction’ but part of the age calculations. The word ‘correction’ implies that this is used as an afterthought, and that the 238-206 ages need ‘correcting’. The 234-238 measurements are a routine part of U-Pb age determinations, and are part of how the final age is calculated. The same is true doing U-Th dating. So this is another almost meaningless case study, and to me shows the lack of familiarity these authors have with the routine work of U-series dating, rather than an intrinsic issue with the method.
The new standard, ASH-15, does not record any initial 234-238 disequilibrium, so unsurprisingly, the 238-206 and 235-207 results are in near perfect agreement. This is not a useful case study here and not does illustrate in any way how the 238-206 chronometer is ‘broken’.
3. So, none of these three case studies present compelling evidence to abandon the 238 chronometer in favour of the 235 one. Further to this point, in this case study they go on to that the 235 chronometer only works in speleothems with very high U concentrations, the Siberian speleothems are reported to have between 30 and 170ppm of U, which is very high. Engel and Pickering (2022) look at the concentration of U in a much bigger dataset of geographically spread U-Pb ages (South Africa, Australia and Italy) and find much much lower U concentrations are the norm. Again, this speaks to these authors lack of familiarity with the norms and strategies of the U-Pb carbonate community.
4. Another example of this lack of familiarity with the norms and standards of U-series carbonate dating, is the repeated reference to a limit of 800 ka, or even up to 1 Ma for U-Th dating (with no reference). The accepted limit in the community is 600 ka, beyond this depending on the age calculator used, ages are resolvable but are in the ‘dead’ space beyond the infinite line on the U-Th isochron, and are not regarded as reliable or useful by the community. The authors go on to say that 238-206 breaks down at 1 Ma, and thus that U-Th and U-Pb have the same maximum age limit. All of this is incorrect. I have never seen an 800-ka U-Th age, let alone 1 Ma. And as for 238-206, their “magical number” of 1.5 Ma is based on assumed measured 234-238U uncertainty of 2 permil 2SE and the question is whether that is realistic or not. With lower uncertainties, you get a very different outcome of their Table 1 and I’m not sure if it’s helpful to the community to provide such hard numbers. Instead, people should look at their measured 234/238 and assess how far or close it is from secular equilibrium.
Here are a few examples from their text:
Line 22: “206Pb/238U dating is the default method for older (>800 ka) rocks…” → wrong, we can date much younger material quite well too with 238-206, its just a lot of work (multiple analyses to build an isochron vs a single U-Th analysis) so it is not a common practice. Pickering & Kramers 2010 explore this in some detail.
Lines 203-205: …whereas the 206Pb/238U is more accurate for samples younger than 1 Ma. Note that the latter is similar to the applicability range of the 230Th/U method. So one could argue that the 206Pb/238U method 205 is of limited use to carbonate U–Pb geochronology (except to infer [34/38]i; Engel et al., 2019).” 238-206U does NOT have the same applicability range as the U-Th chronometer.
Saying that it is safe to assume there is no detrital Th in ‘clean’ samples is another example – it is standard practise to apply a 232-230 correction to all U-Th age data and to use these as the final ages, regardless on the appearance of the sample.
5. The first line in section 6 is also misleading (line 176): “In the previous section, we showed that the accuracy of the 206Pb/238U method is undermined by the extreme 234U-enrichment that is observed in some ground waters…”
–this is a massive overgeneralization, as we do not in fact see such enrichment that often. The Hoogland example is a case but this is literally just one case in what is now a huge, global U-Pb carbonate dataset and is not typical to what we normally see. So where they “show” that the accuracy is undermined is based on data that is not necessarily representative of a typical speleothem. This is yet another example of how unfamiliar these authors are with the standards and norms of this field.
6. Leading on from this last point, and indeed related: it is worth also noting, that none of the authors are themselves U-Pb carbonate specialists; there are certainly expertise in Ar-Ar data, geochronological data handling, U-Pb zirchon data, stalagmites and some lab technical skills but to make such a big claim about the 238 chronometer to have some validity, one would need to see it coming from experts in the field. This is a small observation but last authors surname is misspelled (Parris vs Parish) which is not a good look.
Further to this point, in all the published work by these coauthors, they all rely on the 238 chronometer for their carbonate/speleothem dating. So if this method was so problematic, why have they themselves used it for years?
7. These authors go onto the argue that there they provide a better, faster new way of calculating U-Pb carbonate ages. Again this is not a strong argument and is based on their perception of an issue, which is not shared by the U-Pb carbonate community. The speed of the current age calculators is not an issue, no one is looking for a ‘faster’ method. Their only other argument for their method is that the existing routine by Engel (2019) ‘can be written out more succinctly’, which is an observation but not the basis on which to argue that we need a new method.
In summary, none of the arguments presented here are compelling and I can see no value in this manuscript being published, there is potential to do more harm than good here.
Some minor comments
Previous work should be better cited, particularly for the use of 207Pb/235U and normalization with 208Pb

Figure 5 caption: typo “206Pb/206U”
Citation: https://doi.org/10.5194/egusphere-2025-432-RC2
- AC3:
 'Reply on RC2', Pieter Vermeesch, 29 May 2025
 Before addressing the reviewer’s comments, we would like to note that we specifically requested Dr. Pickering as a reviewer because her work provides several examples where our conclusions differ markedly from those of the original authors. We were hoping for a critical review from Dr. Picking, because critical reviews are useful. Our paper makes strong and far-reaching claims. As the reviewer points out, extraordinary claims require extraordinary evidence. If there were any flaws in our thinking, then we wanted the reviewers to find them.
 As an established leader in the field of disequilibrium-corrected carbonate U-Pb geochronology, Dr. Pickering is well equipped to assess the merits of our highly technical paper. In her detailed review, Dr. Pickering did indeed find a few minor mistakes which we will correct (see below). However, none of these mistakes change the conclusions of our paper. In fact, we believe that the corrections only strengthen our message.
 We have divided our response into two parts. In this main document, we will focus on the constructive parts of Dr. Pickering’s review. Unfortunately her review also included some personal attacks, which distract attention from the scientific discussion. We have addressed those comments in a separate attachment.
 I. The title
 The reviewer does not approve of our paper’s title ("Broken ²⁰⁶Pb/²³⁸U carbonate chronometers and ²⁰⁷Pb/²³⁵U fixes"). More particularly, she takes issue with the word 'broken'. This eye-catching word was meant to draw attention to the important implications of a technical paper that might otherwise be overlooked. It was not our intention to suggest that carbonate ²⁰⁶Pb/²³⁸U geochronology never works. In fact, our paper makes it quite clear that the ²⁰⁶Pb/²³⁸U method can work well for very young samples (such as the Corchia example of Figures 1 and 4, where the disequilibrium correction is precise); for very old samples (where the relative uncertainty of the disequilibrium correction is small); for samples with known initial ²³⁴U/²³⁸U activity ratios such as marine carbonates; and for areas where average initial ²³⁴U/²³⁸U activity ratios are close to secular equilibrium.
 Southern Israel (where ASH-15 was collected) is one example where ²⁰⁶Pb/²³⁸U dating can be reliably used beyond the Quaternary. Chaldekas et al. (2022) show that 904 speleothem samples dated in southern and central Israel have an average initial ²³⁴U/²³⁸U activity ratio of 1.081 ± 0.138 (2s). Similarly, Markowska et al. (2025) report an average value of 1.013 ± 0.178 (2s) from Arabian speleothems (N = 39), and also collated all speleothem dates (N = 1300) from Arabia and groundwater activity ratios and report that these values fall mostly between 1.0 and 1.1. In these areas, it is probably safe to use the ²⁰⁶Pb/²³⁸U method. However, even then it is useful to check the consistency with the ²⁰⁷Pb/²³⁵U method if possible (e.g., Engel et al., 2019).
 To address the reviewer’s comment, we will change the title to "Carbonate ²⁰⁶Pb/²³⁸U chronology problems and ²⁰⁷Pb/²³⁵U fixes". We will also add a reference to Chaldekas et al. (2022) and draw attention to the small difference between the ²⁰⁷Pb/²³⁵U and ²⁰⁶Pb/²³⁸U ages of ASH-15. These changes should avoid any confusion about the implications of our paper.
 II. "Throwing out 28 years of established work"
 The reviewer points out that our paper:
 "[...] asks the geochronology community to throw out the last almost 20 years of work in this field, starting from Woodhead et al., 2006 but arguably 28 years of work if you start with Richards et al., 1998."
 Further on, she writes:
 "[...] in all the published work by these coauthors, they all rely on the 238 chronometer for their carbonate/speleothem dating. So if this method was so problematic, why have they themselves used it for years?"
 As far as we know, our findings do not undermine any of the published work of Dr. David Richards (who reviewed the book chapter of Vermeesch et al., 2025) nor that of co-authors Vaks, Golan, Breitenbach or Parrish. However, even if it did, then this would not weaken the scientific credibility of these people. As a case in point, the first author (Vermeesch) would like to draw attention to some changes in opinion that have occurred in his own publication record. Vermeesch (2012)’s paper on Kernel Density Estimation (KDE), which is featured prominently in Pickering et al. (2019), proposes KDEs as a statistically more sensible alternative to a ‘broken’ visualisation technique called a Probability Density Plot (PDP). PDPs were used for many years and in hundreds of geochronological studies, including Vermeesch (2010), before Vermeesch (2012) realised that they were wrong. In a similar vein, co-author McLean employed the same Monte-Carlo-with-rejection approach criticized here in a GSA presentation (McLean et al., 2014), but now acknowledges that it can yield inaccurate ages. We hope that by highlighting scenarios where established methods can yield inaccurate interpretations, we can advance the field and science more broadly.
 III. 'Hoogland'
 The reviewer asserts that our concerns about the ²⁰⁶Pb/²³⁸U method are based on a single sample, the 'Hoogland' speleothem of Pickering et al. (2019). She writes that we “discredit an entire field and over 20 years of work, based on a single ‘bad’ sample”. This is not the case. We could have used any other sample from Pickering et al. (2019). In fact, 'Hoogland' is not the worst affected sample. Bolt’s Farm (particularly AV01), Drimolen (DN19A and DMK5), Malapa (M6) and other samples are even more problematic than Hoogland. The reasons why we chose ‘Hoogland’ are as follows:
 Hoogland is the oldest of Pickering et al. (2019)’s samples, requiring the largest disequilibrium correction. The difference between its corrected and uncorrected age estimates is more than 100% (3.14 Ma vs. 7.4 Ma). This makes it the best example to illustrate the sheer magnitude of the problem at hand.
 
 The Hoogland sample forms a well-behaved isochron. Unfortunately, the same cannot be said about all the other data reported by Pickering et al. (2019). In fact, we have found some inconsistencies in the supplementary information of this paper, which render many of its data (such as Cooper’s Cave, Sterkfontein, Malapa) unsuitable for reanalysis. We will clarify this statement in the next point of this response.
 
 To refute Dr. Pickering’s comment, we will replace the Hoogland example with another one. We could have used data from other studies as well, such as Polyak et al. (2008), who present ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²³⁵U data from the Grand Canyon. Unfortunately, the supplementary data for that study use ²⁰⁴Pb as a common denominator without specifying error correlations. This makes it less than ideally suited for reanalysis.
 IV. Inconsistencies in the supplementary information of Pickering et al. (2019)
 Dr. Pickering points out that we wrongly assumed 1-sigma errors for the ²³⁴U/²³⁸U activity ratio uncertainties of Pickering et al. (2019), whereas in reality they were reported at 2-sigma. We thank the reviewer for pointing out this unintentional mistake and will adjust the calculations in the revised manuscript accordingly. However, before doing so, we feel obliged to report some issues with the supplementary information of Pickering et al. (2019), which partly explains why we made the mistake in the first place. We think that it is important to point out these issues here, for the benefit of Dr. Pickering and any other users of her data.
 The Pb/U and Pb/Pb ratio uncertainties are labelled as “% err”, except for the Sterkfontein and Swartkrans samples, whose uncertainties are labelled as “2SE”. The analytical uncertainties exhibit a tremendous degree of variability. The Pb concentrations and Pb/Pb ratios for Cooper’s Cave (“% err”) are similar to those of Drimolen (“% err”). Yet their uncertainties differ by three orders of magnitude (“0.003” vs. “3”). We suspect that the uncertainties are a mixture of absolute and relative values, and that at least some of the labels are wrongly reported.
 
 The error ellipses for several samples (including Cooper’s Cave and Sterkfontein) are infinitesimally small, resulting in MSWD values of as much as 100,000. To solve these problems, we were forced to choose the uncertainty levels (relative, absolute, 1-sigma, or 2-sigma) that produced the most credible appearing concordia diagrams and most reasonable looking MSWD values.
 
 The error correlations between the ²³⁸U/²⁰⁶Pb and ²⁰⁷Pb/²⁰⁶Pb ratios are close to -1 for most samples, except for Sterkfontein, where they are close to +1.
 
 The error correlations for Malapa sample M1_2 spill over into mathematically impossible values of less than -1.
 
 The above problems explains how the 1-sigma vs. 2-sigma confusion arose, and why we chose Hoogland as an example and not Malapa, Sterkfontein or Cooper’s Cave.
 V. ‘3-sigma’-level disequilibrium of ‘Hoogland’
 Dr. Pickering points out that, by changing the ²³⁴U/²³⁸U activity ratio of the Hoogland sample from 1-sigma to 2-sigma, the sample is three standard errors removed from secular equilibrium. This assessment is based on a single ²³⁴U/²³⁸U measurement with an analytical precision of 0.01‰ at ~95% confidence level. Our response to the two other reviews explains why this small uncertainty is unrealistic:
 Reviewer 1 (Dr. Perach Nuriel) pointed out that the ²³⁴U/²³⁸U activity ratio can exhibit significant levels of spatial variability, easily exceeding 0.01‰. A single ²³⁴U/²³⁸U activity ratio measurement is unable to capture this natural variability, which may exist between the different aliquots of a single isochron.
 
 Our response to the community comment by Dr. Timothy Pollard explains why we prefer to use a value of 4‰ for the reproducibility of ²³⁴U/²³⁸U activity ratio measurements, more than two orders of magnitude higher than the value of Pickering et al. (2019). Perhaps our preferred value is overly cautious. However, any reasonable compromise between the two proposals would still render the ²⁰⁶Pb/²³⁸U method unusable for the Hoogland sample.
 
 To address the reviewer’s comment, we will use the reported 2-sigma uncertainty value as a ‘best case scenario’. However, we will also add our preferred reproducibility of 4‰ to the posterior distributions as a ‘worst case scenario’. We will leave it up to the reader to decide which scenario is more realistic.
 VI. The ²⁰⁷Pb/²³⁵U method is no panacea
 The reviewer argues that the ²⁰⁷Pb/²³⁵U is not a clear-cut solution to the alleged problems of the ²⁰⁶Pb/²³⁸U method. We never claimed that it was. In fact, Dr. Pickering quotes several sentences from our paper, in which we explicitly state that the ²⁰⁷Pb/²³⁵U method is often unusably imprecise. It is unclear what the reviewer wants us to do. However, we will try to address her comment by explicitly stating that some carbonates are, unfortunately, undateable by the U-Pb method. This may be an inconvenient message, but it is true.
 VII. Inconsistency of the ‘applicability cutoff’ of the U-Th method
 The reviewer laments “the repeated reference to a limit of 800 ka, or even up to 1 Ma for U-Th dating (with no reference)”.
 As explained in our response to the community comment, the 800 ka value comes directly from Cheng et al. (2013), who state in their abstract: “The isotopic composition of a sample with an age <800 ka can clearly be resolved from the isotopic composition of a sample in secular equilibrium, assuming closed system behavior”
 The 1 Ma value does not refer to the U-Th method, but is an approximate cutoff value for the U-Pb method. We have already addressed this issue in our response to the community comment. There is no hard cutoff. Instead, there is a fuzzy zone that is highly sample specific. In our response to the review by Dr. Pollard, we referred to the book chapter of Vermeesch et al. (2025) for further details. The addition of Dr. Pickering’s comment has prompted us to go one step further. We will modify Figure 3 of Vermeesch et al. (2025) and add it to the revised manuscript. This should remove any notion of a hard cutoff.
 References
 
 Chaldekas, O., Vaks, A., Haviv, I., Gerdes, A. and Albert, R., 2022. U-Pb speleothem geochronology reveals a major 6 Ma uplift phase along the western margin of Dead Sea Transform. GSA Bulletin, 134(5-6), pp.1571-1584.
 Cheng, H., Lawrence Edwards, R., Shen, C.-C., Polyak, V. J., Asmerom, Y., Woodhead, J., Hellstrom, J., Wang, Y., Kong, X., Spötl, C., Wang, X., & Calvin Alexander, E. (2013). Improvements in ²³⁰Th dating, ²³⁰Th and ²³⁴U half-life values, and U-Th isotopic measurements by multi-collector inductively coupled plasma mass spectrometry. Earth and Planetary Science Letters, 371–372, 82–91.
 Engel, J., Woodhead, J., Hellstrom, J., Maas, R., Drysdale, R., and Ford, D.: Corrections for initial isotopic disequilibrium in the speleothem U-Pb dating method, Quaternary Geochronology, 54, 101 009, 2019.
 Markowska, M., Vonhof, H.B., Groucutt, H.S., Breeze, P.S., Drake, N., Stewart, M., Albert, R., Andrieux, E., Blinkhorn, J., Boivin, N. and Budsky, A., 2025. Recurrent humid phases in Arabia over the past 8 million years. Nature, pp.1-8.
 Pickering, R., Herries, A. I., Woodhead, J. D., Hellstrom, J. C., Green, H. E., Paul, B., Ritzman, T., Strait, D. S., Schoville, B. J., and Hancox, P. J. (2019) . Nature, 565(7738):226.
 Polyak, V., Hill, C. and Asmerom, Y., 2008. Age and evolution of the Grand Canyon revealed by U-Pb dating of water table-type speleothems. Science, 319(5868), pp.1377-1380.
 Vermeesch, P., Fenton, C.R., Kober, F., Wiggs, G.F.S., Bristow, C.S, and Xu, S. (2010). One million year residence time of Namib dune sand from cosmogenic nuclides, Nature Geoscience, 3, 862-865
 Vermeesch, P. (2012). On the visualisation of detrital age distributions. Chemical Geology, v.312-313, 190-194, doi: 10.1016/j.chemgeo.2012.04.021
 Vermeesch, P., Hopley, P., Roberts, N. and Parrish, R. (2025). Geochronology of Taung and other southern African australopiths. In: "One hundred years of Australopithecus africanus", Wood, B.A., Grine, F.E. and Smith, H.B. Eds., Springer (in press).
 
 Citation: https://doi.org/10.5194/egusphere-2025-432-AC3

Pieter Vermeesch, Noah McLean, Anton Vaks, Tzahi Golan, Sebastian F. M. Breitenbach, and Randall Parris

Data sets

Data files and R code for testing Pieter Vermeesch https://github.com/pvermees/supplements

Pieter Vermeesch, Noah McLean, Anton Vaks, Tzahi Golan, Sebastian F. M. Breitenbach, and Randall Parris

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Short summary

U-Pb dating of cave sediments has provided important new time constraints on the evolution of cave-dwelling organisms (including early humans), and of Earth's climate during the past 5 million years. This paper shows that the most common type of U-Pb dating, which uses ²³⁸U and ²⁰⁶Pb, can be inaccurate beyond 2 million years ago. It proposes an alternative type of U-Pb dating, using ²³⁵U and ²⁰⁷Pb, as a more accurate alternative.


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