General Comments for Moser et al manuscript:

This manuscript critically examines the assumptions underlying the calculation of ²³⁰Th/²³⁸U zircon isochron model ages and explores how these crystallization ages can be used to estimate eruption ages. The authors specifically test previously established models for estimating eruption ages from U-Pb zircon datasets, applying them to U-Th datasets. While the manuscript also suggests the introduction of a new U-Th-Pb methodology, I recommend de-emphasizing this aspect, as it detracts from the primary focus and main contribution of the work, which is age modeling. Additionally, this is not the first study to propose LA-ICPMS U-Th-Pb dating (see Ito publications). If the authors intend to present this as a methods paper, more substantial documentation of the method development would be needed. Throughout the manuscript, I found myself seeking more detailed explanations of the methods and model parameters, which I have outlined below. The manuscript would also benefit from editorial improvements, including clearer terminology, improved sentence structure, additional context for arguments, and more detailed figure captions.

Specific Comments:

As currently written, the manuscript devotes the vast majority of its discussion (approximately 95%) to ²³⁰Th/²³⁸U, with only minimal attention given to ²⁰⁶Pb/²³⁸U, which appears as an afterthought. Therefore, I find it an overstatement to claim that the paper presents a new U-Th-Pb dating technique, as the primary focus is clearly on age modeling. Positioning this as a methods paper diminishes its more significant contribution: refining the calculation of isochron ²³⁰Th/²³⁸U model ages. I recommend removing U-Pb from the title, de-emphasizing the methods aspect in the introduction, and revising the third section of the discussion accordingly. Furthermore, the claim of being the first to propose simultaneous U-Th-Pb dating is inaccurate, as similar approaches have been published previously (see Ito, 2014; Ito, 2024). It could be worthwhile commenting how your methods compare to Ito. I also noticed some circular reasoning in the use of U-Th and U-Pb ages, where the selection of an appropriate DTh/U for the initial ²³⁰Th disequilibrium correction appears to be based on achieving consistency between the resulting U-Pb and U-Th ages. Similarly, the choice of melt composition model is determined by whether the U-Th ages match the U-Pb ages.

Given the presence of multiple U-Th and U-Pb chronometers, it would be helpful to clearly specify which chronometers (²³⁰Th/²³⁸U and ²⁰⁶Pb/²³⁸U) are the main focus of this paper. You could either use the full isotope notation consistently throughout or define each chronometer at the outset and use abbreviations thereafter. This distinction is important, as you also use U/Th to refer to elemental ratios, and in the methods section, "U-Th" refers to multiple isotopes of each element. The manuscript would benefit from a stronger introduction outlining the necessary corrections for U-Th and U-Pb dating. One major challenge in U-Pb dating of zircon in this age range (< 1 Ma) is the correction for initial ²³⁰Th disequilibrium. The text does not adequately explain why this correction is needed, how it is performed, and why it is particularly important for young zircon (<1 Ma). In your discussion (pg. 11), you note that variability in the initial ²³⁰Th/²³²Th ratio, extrapolated from glass measurements, can significantly affect zircon crystallization ages. It would be useful to clarify whether variability in the initial ²³⁰Th/²³²Th ratio or analytical precision has a greater impact on age variability, and whether this effect changes depending on the age of the zircon.

There are a couple of instances where references are light or predominantly cite co-authors or researchers affiliated with ETH Zurich, while overlooking significant contributions from other individuals and laboratories. Including a broader range of references would more accurately reflect the breadth of work in this field and acknowledge the efforts of the wider scientific community. I made note in a few places, but I would check all of your citations. It is generally preferable to include more citations rather than risk omitting important contributions, as this helps foster inclusivity and ensures proper recognition of prior research.

Throughout the manuscript, the authors use several vague terms that could be clarified to improve the overall readability. For instance, phrases such as “zircon signal,” “crystallization bloom,” “zircon subsets,” and “melt anchor point” are ambiguous. I am unsure of the intended meaning for most of them and recommend either replacing these terms with more precise language or providing explicit definitions upon first use. The term “melt anchor point” should be rephrased to “initial ²³⁰Th/²³²Th ratio” for clarity. Additionally, the manuscript frequently uses “techniques,” “methods,” and “approaches” interchangeably, which sometimes makes it unclear whether you are referring to age modeling or analytical procedures. This issue is compounded when the text shifts between these concepts within the same paragraph (for example, in line 60). I suggest reviewing the manuscript for terminology consistency throughout.

In the Samples section, please clearly specify which samples were analyzed using LA-ICPMS and which published datasets were selected for age modeling. Currently, this information is only apparent after reviewing the raw data tables, which makes it difficult for readers to follow. Furthermore, it appears that some of the published data used for age modeling were generated by SIMS, while others were obtained via LA-ICPMS. Additionally, a brief explanation of the rationale for including both LA-ICPMS and SIMS data to test your models would be helpful. For reference, Barboni et al. (2016) also includes SIMS ²³⁰Th/²³⁸U zircon dates for the Belford dome, which may be relevant to your discussion.

There a several studies that suggest the importance of applying chemical abrasion treatment to zircon before LA-ICPMS U-Pb dating (e.g., Crowley et al., 2014; Von Quadt et al., 2014; McKanna et al., 2023; Donaghy et al., 2024). Although Pb loss is very unlikely in < 1 Ma zircon, the zircon standards in this study are quite old and will have experienced significant radiation damage. How did the authors handle this issue?

The Methods section would benefit from additional detail and clarification. Since in-situ techniques depend on sample-standard bracketing, it would be helpful to describe how standards were run, including the frequency of standard measurements (e.g., were standards measured only at the start of each run, or throughout?). Please provide information on how corrections were made for abundance sensitivity, relative sensitivity, and drift, or cite previous methods if these were followed. If 91500 was used to quantify concentrations, please specify the assumed concentrations for this standard. Additionally, clarification on how low 230Th counts were handled would be useful. I noticed that the 230Th background increases progressively for both unknowns and standards during each LA-ICPMS session; any insight into the cause of this trend would be appreciated. In some cases (for example, lines 86–98 in the table for 91500), the 230Th background is higher than for the standard, yet the corrected 230Th value remains positive—could you explain how the corrected 230Th is calculated in these instances? The (230Th)/(238U) ratios in your secular equilibrium standards show considerable variation, although the uncertainties (7–12%, 2 sigma) mean they still overlap with secular equilibrium. A brief discussion of this variability and its implications would strengthen the Methods section. Please also provide a similar discussion or relevant citation for your U-Pb analyses. Additionally, if authors want to emphasize new approaches to the U-Th-Pb LA-ICPMS technique, there needs to be more details about how uncertainties are propagated.

It was unclear from the Methods section which samples were analyzed in this study and which were sourced from the literature. Explicitly stating which samples were analyzed by LA-ICPMS and clarifying which were measured using the U-Th-Pb method versus the U-Th method would improve clarity. Additionally, please describe how errors were propagated (e.g., quadrature, linearized uncertainty propagation, or Monte Carlo methods), and provide details on sample preparation for LA-ICPMS analysis (such as sticky mount or epoxy mount). Finally, I only discovered at the end of the manuscript that the raw data are available in a separate repository. It would be helpful to mention this in the Methods section. Including the raw data spreadsheet in the supplementary materials would also be beneficial, though I am not certain of the GChron guidelines regarding supplementary files if the data has been posted in a separate repository.

Several studies have highlighted the importance of applying chemical abrasion treatment to zircon prior to LA-ICPMS U-Pb dating (e.g., Crowley et al., 2014; Von Quadt et al., 2014; McKanna et al., 2023; Donaghy et al., 2024). While Pb loss is unlikely to be a significant issue in <1 Ma zircons, the zircon standards used in this study are considerably older and likely to have experienced substantial radiation damage and associated Pb loss. Could the authors clarify whether chemical abrasion was applied to the standards, and if not, how potential Pb loss was addressed in the analytical protocol? This information would help readers assess the reliability of the standardization and the resulting age determinations.

The Eruption Age Calculation Methods section (pg. 8) is currently difficult to follow due to its organization. Much of the confusion arises from switching back and forth between weighted means and Bayesian models. I recommend reorganizing this section so that you present the weighted mean and Bayesian model approaches in separate paragraphs. For each, begin by discussing the current status quo for that calculation type, including common pitfalls, and then describe the specific models you will test. Abbreviations should be used sparingly; for example, I suggest not using “WM.” Also, since your weighted mean models are not proper nouns, they should be capitalized only as appropriate (e.g., “young” and “acceptable”). Additionally, please define the “I” in i-MSWD—I assume it stands for “iterative.” For the i-MSWD approach, clarify how other ages are added to the population: how many older ages are included at each step? Providing these details will make the methodology much clearer for readers.

All the figure captions could use addition detail. Whenever possible, a figure and its caption should be able to stand-alone to improve comprehension. Most of the figure captions lack mention of

All figure captions would benefit from additional detail. Ideally, each figure and its caption should be able to stand alone, providing enough information for readers to understand the figure without referring back to the main text. Since KPT is the only sample measured using the U-Th-Pb method, figure S1 should be moved from the supplementary materials into the main text to improve clarity and accessibility. For the U-Th isochron plot, the error ellipses appear to represent 1 sigma uncertainties, even though the caption states they are 2 sigma (in Fig S1). Please double-check all isochron plots to ensure the error ellipses accurately reflect the stated uncertainties (1 sigma vs. 2 sigma). I also note that most figures do not specify what the plotted uncertainties represent. Clearly stating whether uncertainties are 1 sigma, 2 sigma, or another value is essential for proper interpretation of the data.

In the outlook section, you mention the asymmetric nature of your model ages and how they are not used in your models. It would be worthwhile to provide some text in the discussion about how this might bias your models and the eruption age estimates.   

Technical Corrections:

Line 20: delete magmatic (repeated twice in sentence)

Line 27: delete an

Line 30: It is a stretch to say that U-Pb is widely used for >150 ka. I can only think of a few SIMS or LA-ICPMS ²⁰⁶Pb/²³⁸U zircon studies for samples < 1 Ma. Add citations

Line 41: You only list zircon (U-Th)/He for dating eruptions. How about ⁴⁰Ar/³⁹Ar? Throughout the paper you use crystallization but sometimes you use crystallisation. Be consistent.

Line 46: This sentence is awkward, consider rephrasing. Replace “Instead of dating the eruption directly” with Alternatively. Should “through” actually be “from”?

Line 48: Replace “Typical extended” with “Protracted”. Consider using a different phrase from global. Global weighted mean and global isochron ages are vague terms so they need to be defined or use a different term.

Line 49: Refs. Bachmann et al., (2007) is not the only group to make this observation. See general comment above about reference issues throughout this paper.

Line 51: What are weighted ages of zircon subsets?

Line 52: Include Keller et al., 2018 in the list of refs and check the order of refs.

Line 55: What do you mean by low variability in uncertainties? I think you might be trying to say that there is no systematic change in ²⁰⁶Pb/²³⁸U age uncertainties with time but that is not necessarily true. Young zircons (< 10 Ma) typically have larger age uncertainties given there has been much time for radiogenic ²⁰⁶Pb ingrowth.

Line 56: It is worth mentioning in the text that the large ²³⁰Th/²³⁸U age uncertainties are driven by the uncertainties in determining the isochron slope when it is close to unity.

Line 60: Most of the body of work is focused on using ²³⁰Th/²³⁸U zircon crystallization ages to determine an eruption age. There isn’t much discussion about quantifying eruption frequencies and timescales, consider rephrasing or add text in the discussion to this point.

Line 62: Define LA-ICPMS at first use. By “methods,” are you referring to ²³⁰Th/²³⁸U vs ²⁰⁶Pb/²³⁸U or age modeling?

Line 64: Check citation order? Oldest first?

Line 65: Do age determination techniques refer to analytical or modeling?

Line 67: Define typical LA-ICPMS uncertainties (at 1 vs 2 sigma?).

Line 72: Do different methods refer to analytical methods? See comments above about “developed new dating routine”

Line 76: I don’t really understand what you are trying to say in the sentence “Given that…” Is U-Pb dating better understood than U-Th dating? Probably also depends on the time period you are talking about. How is it better understood? Rephrase sentence. Also check refs.

Lines 78-80: Sentence “ Using addition” is awkward. Rephrase. You alternate between analyze and analyse. Be consistent.

Line 83 (and elsewhere): use ⁴⁰Ar/³⁹Ar. Also this sentence is a run-on. Rephrase.

Line 91: Change to beginning of sentence to: The LA-ICPMS measurements were conducted at ETH Zurich using 193 nm….

Line 92: change “to a” to and

Line 94: Did you calculate a ACF at the start of each run? Or what is a common ACF value?

Line 98: What is a zircon blank?

Lines 104-106: What do you mean by “independent of the measuring method”?

Paragraph starting at Line 112: I think it would be better to use the term partition coefficient than fractionation factor. This paragraph might be easier to read if it was summarized in a table. Factionation is misspelled (line 125).

Line 145: List which primary reference zircon you are referring to? 91500? Which statistically robust methods do you suggest? Expand on this statement. (What are physically robust methods?)

Line 147-148: “To finally…” is an awkward sentence, rephrase. Also define DQPB abbreviation. Change to “Initial ²³⁰Th disequilibrium” in the next sentence. You alternate between D_Th/U and f_U/Th. Be consistent. Why did you select 0.2 for D_Th/U? Based on glass measurements that you collected (mean value? or n of 1?)? How much do your ²⁰⁶Pb/²³⁸U change if you vary the D_Th/U?

Paragraph starting at line 153: Quantify your parameters of your synthetic dataset. How many zircons and duration of zircon crystallization (did you do a literature review to pick a duration)? What is your analytical uncertainty?

Line 157: Remove “First,” redundant with (1). Change to: representing crystallization from the time of zircon saturation until eruption. Should you reference Fig. 2C somewhere in this paragraph?

Lines 168-169: Change to constant zircon production to continuous zircon crystallization. Define the sampled time interval? What is a crystallization bloom? Like an algae bloom?

Line 208: You previously mention using 0.2 (line 149).

Line 212: Can you quantify “higher uncertainties”? Also, rephrase “For the method” sentence. It is a run-on sentence.

Line 214: Which model age assumptions are you referring to here? Providing an actual value or range is more useful than descriptors like “infinitely high uncertainties”?

Line 216: Unclear if “their lower reported uncertainties” refers to U-Pb or U-Th.

Line 223: Awkward sentence. Rephrase.

Line 226: What does “dilution of the signal” mean? Be very specific with you are trying to say.

Line 231: Here you say that a constant fractionation factor is incorrect though at the beginning of the paragraph you say that assuming a constant factor permits spatial and temporal heterogeneity in the melt. I don’t follow the contradiction. Expand on both arguments and in which situations these would matter.

Line 232: What do you mean by boundary layers of other mineral phases?

Line 237: Include more refs

Paragraph stating at line 238: Paragraph could use some restructuring. I’m not exactly sure the point you are trying to make in this paragraph. Change “might be even more complicated” to “is complex”. Define CL. It feels like you are rushing to make a series of statements, without providing some context for each statement or a way to tie it altogether into a coherent paragraph.

Line 256: Awkward sentence, rephrase. What do you mean by measure glass accurately? Analytical precision? Or would it be worthwhile measuring different shards of glass?

Line 262: Reference a figure. Figure 3?

Line 268: Rephase “This is potentially…” sentence.

Line 276: Define enhanced 232Th counts (counts > XX)

Line 279: Awkward sentence, rephrase. Are there inclusions in the glass? “Fall well above” could be rephrased to older than

Line 286: Change to zircon-bearing crystal mush. I think you should circle back to your observation above that the youngest zircon ages are older than the independently observed eruption based on your arguments here. It is not uncommon for the crystal mush (including zircon crystals) to be scorned from deeper parts of the magmatic system just prior to eruption, which could explain why you don’t see overlapping ages between zircon and eruption ages (i.e., the recharge melt didn’t reach zircon saturation conditions). I think you could expand and emphasize that point.

Line 293: Change intercept to y-intercept.

Line 310: Was data with high Th concentrations excluded from the figures and age modeling?

Figures/Tables

Figure 1: Use “constant melt composition” as opposed to constant glass composition. The glass composition is a proxy for the melt composition. Are uncertainties 1 or 2 sigma?

Figure 2: Are you showing 1 or 2 sigma uncertainties? (a) Add ²³⁰Th/²³⁸U to y-axis. What is a “true eruption age” in a synthetic dataset? Also mention what the typical LA-ICPMS uncertainties that were used (e.g., 10%, 2 sigma). (b) Define the different weighted mean models that are represented by the three colored symbols in caption. (c) There is no explanation for what the different lines (solid and dashed) mean. What are tested zircon age subsets? (d) Provide a more detailed explanation of both axes in the caption. I think x-axis refers to time though I’m not sure if the dash means subtraction or from.

Figure 3: The error bars and light gray circles are nearly impossible to see if you print them. Is it possible to make use a different color or shape for the light gray symbols. Could you also make these figures bigger? The x-axis for (a-d) is misleading. It also looks like the they are the partition coefficients. Either add the  x-axis labels back in or increase the space between the two rows and mention in the caption that they all have the same x-axis. I’m not sure what the difference between the two RMS-Z means (the values not in parentheses).  You mention normalized age difference, what are you normalizing to?

Figure 4: How is the “true eruption age” determined? Mention in caption. Add error ellipses are 1 sigma uncertainty. There are some ages younger than the visual near-zero isochron line. What criteria did you use to make your near-zero isochron line? There is no mention in the caption what the colored symbol.

Figure 5: I think the dashed lines should be removed. I’m not sure they add much to the figure. Just FYI, Barboni et al, 2016 also has U-Th data for the Belfond Dome too. What are the red lines in the inset (c).

Figures 6: define colored symbols (MSWD and bayesian models). The three symbols on the right side of the (b) are very small and hard to see. Are there no constant melt circles in (b). Define uncertainties.

Table 1: What is the difference between the U-Th-Pb zircon and U-Th zircon columns? I thought all your zircon analyses represent simultaneous U-Pb and U-Th analysis? (It was not clear to me until I looked at your raw data tables that U-Th-Pb measurements were only conducted on The KPT samples. This should be clearly stated in the methods section.)

The problem Moser and coauthors address is a difficult and rather statistically complicated one, of a type that is becoming increasingly common in geochronology -- that is, how to interpret dispersed mineral crystallization age datasets with complicated uncertainty structures, in this case from two different systems (U/Th and (U-Th)/Pb) at once.  While there is probably (as usual) more that could be done, I think this manuscript presents a generally reasonable approach to the problem, and should make a good contribution to the literature.

I agree with just about all of the comments made in the very thorough review by Reviewer 1, so will not belabor the point by repeating them. If the authors wish to continue to emphasize the analytical methods aspect of joint U/Th and (U-Th)/Pb measurement, I don't object in principle but would ask for more information in the main text about the technical details of this joint measurement, and how it compares to previous attempts at such the Ito papers mentioned by Reviewer 1. 

Beyond what has already been covered by Reviewer 1, my main request would be to include more discussion of the magnitude and treatment of systematic uncertainties (which generally should be excluded during Bayesian age estimation, and then re-applied to the result), particularly in the context of combining U/Th and (U-Th)/Pb measurements which have quite disparate systematic uncertainty structures. Doing this perfectly is a hard problem which I don't expect the authors to solve completely, but I think some additional consideration is warranted.