the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: Pblossaware Eruption/Deposition Age Estimation
Abstract. Interpreting overdispersed crystallization and closure age spectra has become a problem of significant import in highprecision geochronology. While Bayesian eruption age estimation appears to provide one promising avenue for the statistical interpretation of such dispersed datasets, existing methods critically hinge on an assumption of fully closedsystem behavior after the time of eruption. However, given the presence of two independent decay systems with distinct responses to opensystem behavior, the U/Pb system provides in principle the possibility of quantifying and potentially even constraining the timing of Pbloss. Here we present a method for Pblossaware eruption age estimation, that explicitly models not only the duration of crystallization but also the timing and magnitude of Pbloss given accurate ^{206}Pb/^{238}U and ^{207}Pb/^{235}U isotopic ratios and covariances, leading to eruption age estimates that are potentially robust to posteruptive Pbloss. Further applications to detrital zircon data are considered.
C. Brenhin Keller
Status: open (until 17 Jun 2023)

RC1: 'Comment on gchron20239', Pieter Vermeesch, 01 Jun 2023
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This manuscript modifies the eruption age estimation algorithm of Keller et al. (2018) to accommodate Pbloss. The Keller et al. (2018) model uses a Markov Chain Monte Carlo (MCMC) inversion algorithm to estimate the onset (saturation) and termination (eruption) of zircon crystallisation, as parameterised by either a theoretical or an empirical magma evolution model. The new paper adds a third parameter to the inversion, namely the time of partial Pb loss. The topic of the manuscript is suitable for a technical note in GChron. However, I do have a number of substantive comments.
The manuscript provides surprisingly little technical detail for a technical note. It does not contain a single equation. Perhaps this is because the maths are similar to Keller et al. (2018)? Nevertheless, the lack of detail left me unable to answer a number of important questions.
From the examples, it appears that the algorithm works in “Wetherill space”, and does not use 204Pb or 208Pb as a proxy for common Pb. Is this correct? If so, why is the full Pb composition not taken into account?
Line 60 of the manuscript explains that the algorithm “Project[s] along a Pbloss array from your proposed time of Pb loss, through each analysis, back to Concordia”. This does not look right to me. It implies that the measured isotopic ratios are equal to the true ratios. In reality, the true isotopic ratios are unknown and must be estimated from the data. As a counter example, suppose that:
a) the crystallisation sequence follows a uniform distribution between 1050 and 1000 Ma.
b) we set the prior distribution for the crystallisation history equal to this true solution (in the real world this is impossible, but in a thought experiment we should be able to do so).
c) 50% of the radiogenic Pb was lost at 0 Ma.
then the true Pb207/U235 and Pb206/U238 ratios of the youngest (syneruptive) age should be 0.8387 and 0.0839, respectively. Now suppose that the measured Pb207/U235 and Pb206/U238 ratios are 0.8380 and 0.0839. Then a line through these measurements and the origin of the Wetherill diagram (t=0 Ma) would project outside the prior distribution. In other words: the measurements are impossible! As a result, the true geological history would be excluded from the collection or posterior solutions.
My intuition tells me that any mixing line between any point within the prior distribution of Pb loss and the prior distribution of zircon crystallisation should be allowed. In the counter example, a mixing line between the origin and the composition at 1000 Ma would not go right through the measurement, but it would pass by it close enough to be retained within the posterior ensemble of solutions.
Other comments:
Line 8: I would suggest changing “covariances” to “(co)variances”.
Line 9 of the abstract should be expanded. To paraphrase K.K. Landes: an abstract is not an outline but a summary of a paper.
Figure 1: there are duplicate tick marks on the concordia line. Figures 2a and 4a have the same problem.
Figure 1, third line of the caption: typo (“uncertaities”)
Lines 4445: “While a traditional discordia array could be fitted to the entire dataset, potentially eliminating the problem of Pb loss, this would be as statistically invalid as a traditional weighted mean given the geologic dispersion of the data”
> this comment does not apply to “nontraditional” discordia regression. For example, IsoplotR implements a “model3” regression model that parameterises overdispersion using an excess variance component of the lower age intercept. A similar solution could be formulated for the partial Pbloss problem.
Line 66: it would be useful to show the actual likelihood function, perhaps in an appendix.
Line 68: please remove the double brackets here and elsewhere in the manuscript.
Line 71: missing references for Julia and Isoplot.jl
Lines 9697: duplication of “broad”.
Line 114: are decay constant uncertainties accounted for in the MCMC model?
Line 144: “in summary”?
Figure 5: This case study raises all kinds of new questions:
1. I am not sure if this is the best example, as there is hardly any discordance visible in it.
2. What does a “Normal prior of 0 +/ 30% Pbloss extent” mean? Is it possible that some grains have gained 30% Pb?
3. The cloud of discordia lines implies that only the youngest grains experienced Pb loss. Why would this be?
4. Following up on 3, if all grains are allowed to have experienced Pb loss, then each should be allowed to have a different commonPb loss intercept. This problem is unsolvable. If only modern Pb loss is allowed, then the MCMC solution is no different than projecting the data onto concordia and applying a conventional MDA algorithm to the projected data.
In conclusion, I do not think that the MCMC algorithm is ready to be used in detrital geochronology.
Line 150: should be “interpreted by Karlstrom et al. (2018)”
Citation: https://doi.org/10.5194/gchron20239RC1 
RC2: 'Comment on gchron20239', Ryan Ickert, 06 Jun 2023
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Review of “Technical Note: Pblossaware Eruption/Deposition Age Estimation” by Keller for Geochronology.
This review by Ryan Ickert (Purdue University)
This short manuscript is an extension of the Keller et al. (2018; hereafter K18) method for estimating age distributions from geochronological data (most often UPb IDTIMS zircon). The portion of the age distribution that is typically of interest is the end of zircon crystallization (“eruption” age). In K18, the model required the ages and uncertainties, and some way to estimate the relative crystallization distribution (e.g., a uniform, truncated normal, saturation, bootstrapped distribution etc.). However, in some UPb datasets there is evidence for unmitigated Pbloss, even after chemical abrasion.
The novel extension in this technical contribution is that the model now can take into account singlestage Pbloss for the coupled ^{238}U^{206}Pb and ^{235}U^{207}Pb systems. This likely is relevant for only a small subset of UPb data, but nevertheless it is an important one. The technique is straightforward and relatively flexible, hopefully amenable to most datasets with small amounts of Pbloss.I like that this is a short contribution, though it can be tightened a bit, and I have some concerns about one critical element that is only lightly addressed. These are detailed below, followed by more minor points that are detailed linebyline.
Length:
For reasons detailed below, the entire detrital zircon section can probably be eliminated. Multistage Pbloss is probably common in discordant DZ data. I don’t think that hurts the manuscript.
The figures can be significantly condensed. Figure 3 is not necessary – the typical reader of Geochronology will trust the author if he says the Markov chain has a short burn in and is usually stationary. Figure 1, 2a, and 4 are almost identical and could easily be condensed into one, physically larger, figure. This would have the added benefit of a reader being able to more easily see the differences (or lack thereof) instead of having to flip back and for, as I did.
Choice of decay constants:
This is given very short treatment in the manuscript. I think this needs to be expanded, for two reasons.
 This model will generate inaccurate results with the Jaffey decay constants, and this is not clearly stated in the paper. Highprecision zircon UPb datasets almost always generate UPb data that clusters to the right of the Jaffeyconcordia central estimate, but within uncertainty. Although not often made explicit, the interpretation is generally that these represent accurately measured, closedsystem domains, and the systematic offset is simply because highprecision UPb data provides a more precise measurement of the decay constant ratios than those in Jaffey. If this is true, then using the Jaffey decay constants, this model will infer that *every* zircon dataset that is currently interpreted as closed system has had a small but consistent amount of Pbloss, and (if I understand the model correctly) will increase the amount of apparent age dispersion by “overprojecting” the data through the concordant cluster back to the Jaffey concordia. I’m not sure if this is significant or not, but it certainly is inaccurate, assuming our understanding of zircon UPb systematics is correct (ie, that there is no other reason for the offset).
 Despite the well documented datasets from the Schoene et al. and the Mattinson papers, no one uses the revised decay constant ratio and this may generate confusion. A large part of the reason is that we can’t get away from Jaffey – we only have information on the ratios, so we either need to pin one on the other or use some combination of both Jaffey constants and the ratio, and Jaffey is indistinguishable from the geochronologically determined ratio (just less precise) so the dates change very little, if at all. Most recommendations are to keep the lambda238, so very few ages actually change. Adding this changed suite of decay constants into the mix threatens to throw UPb geochronology into the chaos that Ar/Ar geochronology seems to relish. I don’t object to it, but it certainly warrants some discussion in the manuscript because this is something that many geochronologists will be wary of.
 (I repeat myself below but it’s worth emphasizing that there is little or no evidence that the Jaffey decay constants are inaccurate. Evidence suggests that highprecision UPb data can measure the decay constant ratios at a higher precision than Jaffey, but the quantity estimates are indistinguishable. If Jaffey were inaccurate, then the ratios would differ outside of uncertainty. I’m 100% sure that the author knows this and perhaps wrote inaccurately (hah!) due to length constraints. That should be made more clear in the manuscript because it’s easy for someone to misunderstand.)
L8: “Covariance” alone is probably not correct because it does not include the variances? (Maybe it’s short for covariance structure or covariance matrix, but some readers may find this confusing)
L8: I’m not sure what “potentially robust” means here? Perhaps just eruption age estimates for which Pbloss is explicitly accounted for?
L26: For consistency with line 19 use U/Th instead of UTh.
L30: Consider mentioning that the weightedmean is the gold standard of geochronological statistical tools.
L33: This is a rather bold statement that requires some evidence. There’s plenty of suspicion in the community that unmitigated Pbloss might be responsible for some overdispersion and it is very hard to test.
L53: What does “dispersed” mean here? Typically one would refer to data being either overdispersed and underdispersed, which implies “dispersed” means the analytical uncertainties account for the scatter in the data. But I don’t think that’s the meaning implied?
L111: Here, the term “accuracy” is used in a way that is confusing. The Jaffey, Mattinson, and Schoene decay constant ratios are all mutually consistent. The Jaffey decay constant ratios are less precise, but as far as I’m aware, there is no evidence to suggest that they are inaccurate. Obviously, this is not a misunderstanding by the author – who himself has worked on improving the decay constants  but I think the problem is that the issue here is rather nuanced and is done a disservice by condensing it into a short 7 line paragraph.
L114: Please also cite Mattinson (2010) for the decay constant ratios.
L115: Following Holden et al., (2011), please use a consistent unit for time (preferably Ma). Please also specify the confidence level.
Section 3: I appreciate the effort here but I’m not sure this is the right tool for detrital zircon. For chemically abraded IDTIMS zircon dates from igneous rocks with simple histories, most sample suites tend to be very close to concordant and in many cases (particularly very old ones) have consistent “zero age Pbloss 207/206 dates” that are consistent with the unmitigated Pbloss being consistent with a singlestage event. However, this is not the case for grains that are not chemically abraded. My experience is that many unabraded zircon from the Proterozoic and Archean of northern Canada have multistage Pbloss, and I expect that to be the case for Pbloss in many suites of detrital grains, violating the assumptions in the model here. I recommend this section be eliminated.
Citation: https://doi.org/10.5194/gchron20239RC2
C. Brenhin Keller
Model code and software
Isoplot.jl C. Brenhin Keller https://doi.org/10.17605/OSF.IO/Z37WE
C. Brenhin Keller
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