the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The Geometric Correction Method for zircon (UTh)/He chronology: correcting systematic error and assigning uncertainties to alphaejection corrections and eU concentrations
Abstract. The conventional zircon (UTh)/He (ZHe) method typically uses microscopy measurements of the dated grain together with the assumption that the zircon can be appropriately modeled as a geometrically perfect tetragonal or ellipsoidal prism in the calculation of volume (V), alpha ejection correction (F_{T}), equivalent spherical radius (R_{FT}), effective uranium concentration (eU), and corrected (UTh)/He date. Here, we develop a set of corrections for systematic error and determine uncertainties to be used in the calculation of the above parameters for zircon, using the same methodology as Zeigler et al. (2023) for apatite. Our approach involved acquiring both “2D” microscopy measurements and high resolution “3D” nanocomputed tomography (CT) data for a suite of 223 zircon grains from nine samples showcasing a wide range of morphology, size, age, and lithological source, calculating the V, F_{T}, and R_{FT} values for the 2D and 3D measurements, and comparing the 2D vs. 3D results. We find that the values derived from the 2D microscopy data overestimate the true 3D V, F_{T}, and R_{FT} values for zircon, with one exception (V of ellipsoidal grains). Correction factors for this misestimation determined by regressing the 3D vs. 2D data range from 0.81–1.04 for V, 0.97–1.0 for F_{T}, and 0.92–0.98 for R_{FT}, depending on zircon geometry. Uncertainties (1σ) derived from the scatter of data around the regression line are 13–21 % for V, 5 %–1 % for F_{T}, and 8 % for R_{FT}, again depending on zircon morphologies. Like for apatite, the main control on the magnitude of the corrections and uncertainties is grain geometry, with grain size being a secondary control on F_{T} uncertainty. Propagating these uncertainties into a real dataset (N = 28 ZHe analyses) generates 1σ uncertainties of 12–21 % in eU and 3–7 % in the corrected ZHe date when both analytical and geometric uncertainties are included. Accounting for the geometric corrections and uncertainties is important for appropriately reporting, plotting, and interpreting ZHe data. For both zircon and apatite, the Geometric Correction Method is a practical and straightforward approach for calculating more accurate (UTh)/He data, and for including geometric uncertainty in eU and date uncertainties.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
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RC1: 'Comment on egusphere20233046', Florian Hofmann, 06 Feb 2024
This is an excellent paper showing a large dataset of nanoCTscanned zircon grains to improve the alphaejection correction and eU concentration calculations for (UTh)/He dating. This study uses and expands on their proven approach from a previous study on apatite. They find that 2D alphaejection corrections in zircon are fairly accurate when compared to 3D estimates. This is in contrast to their previous study in apatite which found significant differences between these approaches and proposed correction factors for 2D measurements. The authors provide a detailed analysis of their data and a rigorous assessment of the propagation of uncertainty to the calculated ages and eU concentrations. They also clearly lay out strategies and workflows for classifying grains and applying corrections, as well as assessing and propagating uncertainties. This study will be helpful to users of the (UTh)/He method and can provide a template for sample processing workflows to help standardize these procedures between different laboratories. As such, it is a perfect fit for GChron.
Overall, this manuscript is wellwritten and organized, and the text and figures are presented in a highly polished form. The methodological approach, data analysis, and recommendations are welldocumented in the main manuscript as well as the appendices. The authors clearly incorporated the feedback received on a similar previous study into this manuscript. My comments below mainly concern minor formatting details that can be addressed in copyediting, and would, in my opinion, not require any revisions. I, therefore, recommend this manuscript be accepted in its present form.
Detailed Comments:
Line 78: Do the numbers for the resolution (0.840.92 μm) refer to the voxel size or the smallest possible distance between two objects that can be resolved?
Table 1: The formatting makes it hard to read, especially the second column. It’s not immediately apparent which lines belong to which sample. I suggest adding horizontal lines or additional space to separate the rows from each other.
Line 399: Insert spaces between number and unit to make it consistent with the rest of the text: “100μm” > “100 μm”. Also change elsewhere (Figure C1, Line 138, etc.).
Lines 434441: This might be beyond the scope of this paper to discuss, but I’m wondering how the 2D and 3D volumederived masses would compare to ICPMSderived Zrbased masses for zircon grains. Some labs measure Zr routinely and use that for calculating grain mass (e.g. Guenthner et al., 2016, G3). Using those two approaches concurrently could be used to derive the average density of the zircon grains, which correlates to the amount of crystal damage. The difference in density between pristine and highly metamict zircons of around 16% (as mentioned in Line 530) should be resolvable given the uncertainties mentioned in this manuscript.
Citation: https://doi.org/10.5194/egusphere20233046RC1 
AC1: 'Reply on RC1', Spencer Zeigler, 21 Mar 2024
We are grateful for Florian’s kind and thorough review. We agree with his suggestions, made the associated modifications to the manuscript, and include our responses in bold below.
Detailed Comments:
Line 78: Do the numbers for the resolution (0.840.92 μm) refer to the voxel size or the smallest possible distance between two objects that can be resolved?
They refer to the voxel size. We have added language to clarify this point to the introduction (see L78).
Table 1: The formatting makes it hard to read, especially the second column. It’s not immediately apparent which lines belong to which sample. I suggest adding horizontal lines or additional space to separate the rows from each other.
We have made changes to this table to increase legibility. Further changes to legibility will be made during the proofing process if necessary (see attachment).
Line 399: Insert spaces between number and unit to make it consistent with the rest of the text: “100μm” > “100 μm”. Also change elsewhere (Figure C1, Line 138, etc.).
Thank you. We have made this change throughout the text and in Figures: 2, 7, and C1.
Lines 434441: This might be beyond the scope of this paper to discuss, but I’m wondering how the 2D and 3D volumederived masses would compare to ICPMSderived Zrbased masses for zircon grains. Some labs measure Zr routinely and use that for calculating grain mass (e.g. Guenthner et al., 2016, G3). Using those two approaches concurrently could be used to derive the average density of the zircon grains, which correlates to the amount of crystal damage. The difference in density between pristine and highly metamict zircons of around 16% (as mentioned in Line 530) should be resolvable given the uncertainties mentioned in this manuscript.
This is an interesting idea, but we agree that this is beyond the scope of this paper. We have added mention of the stoichiometric approach described by Guenthner et al. (2016) for zircon mass determination and how those outcomes compare with our results. As you point out, both our approach and the stoichiometric approach require assuming the density of zircon, which is another source of uncertainty.

AC1: 'Reply on RC1', Spencer Zeigler, 21 Mar 2024

RC2: 'Comment on egusphere20233046', Anonymous Referee #2, 12 Feb 2024
This is a very nice contribution that aims to assess systematic errors and uncertainties of alphaejection corrections and eU determinations that stem from commonly used “2D” microscopy measurements by comparing a series of measurables derived from highresolution nanoCT “3D” data and the conventional “2D” data. The authors did an excellent job in providing rich information regarding the overall approaches they used including sample selection, data acquisition, and statistical analyses. The conclusions made by the study are important for users of the ZHe method in offering quantified potential errors and additional uncertainties of conventional data and a retroapplicable geometric correction method. I find both the significance and quality of this work fit the scope of GChron, and I highly recommend publication with only minor revisions or clarification. Below I illustrated a few minor concerns/confusions, followed by linespecific comments.
In section 3.2, the authors assumed a zircon Th/U ratio of 0.87 and no Sm contribution owing to a lack of parent isotope measurements. Is it possible to perform some kind of supplementary analysis or offer more reasoning to demonstrate that the use of the assumed values (as opposed to samplespecific parent isotope measurements) would not lead to a significant difference in a series of calculated results presented later, nor the major conclusion?
The collapsed clarity dimension. I do enjoy reading the discussions of how zircon clarify is related to eU, which is a critical proxy for radiation damage accumulation and annealing, and the density of zircon. However, I am a little confused about the way the authors delivered their reasonings about abandoning the clarity dimension in the GEM (section 2.4, around lines 160168). My understanding is that the manuscript is centered on the assessment of error and uncertainty in zircon dimensions, therefore one should be able to exclude the contribution of clarity in terms of the role of varying eU before performing analyses. However, as the author pointed out, zircon clarity is also related to its density, so I think this part of the role of zircon clarity should only be either retained or abandoned after showcasing the analyses presented later on. Therefore, does it make more sense to not abandon this dimension at this point of the manuscript? Moving on, it seems that the authors use 1, 2, or 3 as a numerical index for grain clarity if I understood correctly. Could the clarity be treated as a continuum (through some methods like a grayscale image?) and would a different conclusion on the importance of grain clarity?
Line 78: Is there a reason that the resolution of the CT data is presented as a range? I am not sure if additional information is beneficial though. Regardless, at this scale, would it make sense to simplify it as ~1 µm for ease of reading?
Line 100: Table 1 might look clearer if (1) more space is allowed between rows separating different sample suites or (2) adapting a similar formatting to tables 24.
Line 138: additional space between number and unit.
Line 179181: Minor comment. The first sentence of section 3.1 is a bit repetitive. However, this starting sentence, whether or not in a revised form, seems to be a more explicit way to introduce the firstorder goal of this study if placed in the Intro section.
Line 266268: Would it be better if the definition of the corrections for systematic error could be more explicitly defined here? (e.g., incorporate details from Table 2 footnotes).
Citation: https://doi.org/10.5194/egusphere20233046RC2 
AC3: 'Reply on RC2', Spencer Zeigler, 21 Mar 2024
We thank the anonymous reviewer for their detailed review which will improve our manuscript. We have included replies (in bold) to each of their points and suggestions below.
In section 3.2, the authors assumed a zircon Th/U ratio of 0.87 and no Sm contribution owing to a lack of parent isotope measurements. Is it possible to perform some kind of supplementary analysis or offer more reasoning to demonstrate that the use of the assumed values (as opposed to samplespecific parent isotope measurements) would not lead to a significant difference in a series of calculated results presented later, nor the major conclusion?
The value for the Th/U ratio comes from the average of 736 zircon analyses in the CU Boulder TRaIL. We used this value mainly for illustrative purposes (i.e., to calculate the combined FT and RFT shown in Figure 7). However, the Th/U ratio is also used to calculate the correction and uncertainty for the combined FT and RFT. But, because the ratio is used in the calculation of both the 3D and 2D values for each parameter, the actual value of the correction and uncertainty are not impacted by the choice of Th/U (i.e., the choice of Th/U “cancels out” during the regression). The actual measured elemental concentrations are used to calculate combined FT and RFT when the corrections and uncertainties are applied to real grains. We have added language to clarify this point.
The collapsed clarity dimension. I do enjoy reading the discussions of how zircon clarify is related to eU, which is a critical proxy for radiation damage accumulation and annealing, and the density of zircon. However, I am a little confused about the way the authors delivered their reasonings about abandoning the clarity dimension in the GEM (section 2.4, around lines 160168). My understanding is that the manuscript is centered on the assessment of error and uncertainty in zircon dimensions, therefore one should be able to exclude the contribution of clarity in terms of the role of varying eU before performing analyses. However, as the author pointed out, zircon clarity is also related to its density, so I think this part of the role of zircon clarity should only be either retained or abandoned after showcasing the analyses presented later on. Therefore, does it make more sense to not abandon this dimension at this point of the manuscript? Moving on, it seems that the authors use 1, 2, or 3 as a numerical index for grain clarity if I understood correctly. Could the clarity be treated as a continuum (through some methods like a grayscale image?) and would a different conclusion on the importance of grain clarity?
Thanks for this comment. We wanted to emphasize that noting clarity when picking is important given its relationship to radiation damage and density. But we see your point and have downplayed the discussion of the clarity axis by making edits to section 2.4 and moving the discussion about the GEM design to Appendix B.
We use 1, 2, and 3 as a numerical index for grain clarity due to the unreliability between analysts categorizing clarity into any finer of bins. We favor treating clarity as a qualitative proxy for radiation and therefore retain that axis on the GEM presented in Appendix B. For analysts who prefer more categories to reflect intrasample variation in visual metamictization, we refer the readers to Armstrong et al. (2024) (and have included this citation in our manuscript).
Line 78: Is there a reason that the resolution of the CT data is presented as a range? I am not sure if additional information is beneficial though. Regardless, at this scale, would it make sense to simplify it as ~1 µm for ease of reading?
We originally present the CT resolution as a range because the actual resolutions measured by the CT varied as a function of scan time, magnification, voltage, and power (see Appendix Table B1). We agree that for readability it would be simpler to report the resolution as “sub1 µm” and have made this change throughout the text (3 instances).
Line 100: Table 1 might look clearer if (1) more space is allowed between rows separating different sample suites or (2) adapting a similar formatting to tables 24.
We agree and have made changes to improve readability. Further changes to legibility will be made during the proofing process if necessary (see attachment).
Line 138: additional space between number and unit.
We have made this change.
Line 179181: Minor comment. The first sentence of section 3.1 is a bit repetitive. However, this starting sentence, whether or not in a revised form, seems to be a more explicit way to introduce the firstorder goal of this study if placed in the Intro section.
Thank you for your comment, ee will assess how to incorporate a similar statement into the introduction.
Line 266268: Would it be better if the definition of the corrections for systematic error could be more explicitly defined here? (e.g., incorporate details from Table 2 footnotes).
We define the systematic error in line 53 and will add a clarifying note from the Table 2 footnotes to L266268.

AC3: 'Reply on RC2', Spencer Zeigler, 21 Mar 2024

RC3: 'Comment on egusphere20233046', William Guenthner, 28 Feb 2024
This manuscript by Zeigler and coauthors examines discrepancies between 2D (microscopy) and 3D (nanoCT) computed geometries in zircon grains. Zircon geometric measurements propagate into a number of different metrics (volume, alphaejection correction, eU concentration) that are important for generating and interpreting zircon (UTh)/He data sets. I found the article to be very well written, the data to be high quality, and the scope to be appropriate for the readership at Geochronology. I have three general comments. I would suggest that addressing the first one would encompass some new calculations from existing data. The other two could largely be addressed with additional discussion text. As such, I think these are “moderate” revisions.
 I am wondering how the Ft error would be different if a different set of 2D geometry equations were used. Both Hourigan et al. (2005, https://doi.org/10.1016/j.gca.2005.01.024) and Reiners et al. (2005, American Journal of Science v. 305, p. 259311) derive a set of Ft equations that take into the account the specific dimensions of the two pyramidal terminations in a given zircon grain. Specifically, see equations 13 in the Reiners et al. (2005) article. The Ketcham et al. (2011) equations do take the pyramid heights into account, but only as a uniform approximation, whereas the Hourigan et al. equations, further derived by Reiners et al., are grain specific. My question then is, is the magnitude of the errors that result from the 2D and 3D comparison of volume and Ft in figure 7 somewhat mitigated by using equations that incorporate metrics for the terminations? The authors seem to suggest as much at line 390. I would encourage the authors to examine this by measuring tip heights directly from their collected images. This is significant in so far as the authors are proposing a general correction that could be applied to previously published datasets, and I know from experience that all zircon (UTh)/He data sets generated at the University of Arizona (of which there are a bunch in the published literature at this point) use the Reiners et al. (2005) correction and not the Ketcham et al. (2011).
 There is little mention in the current version of the manuscript concerning U and Th zonation and its influence on the Ft correction. The authors have defined the scope of the current work to focus on corrections to potential systematic error introduced by relying on a 2D geometric approximation only, and this is fine and appropriate. A full consideration of this influence plus the zonation effect would likely be a separate study. However, again, given that the authors propose a generaluse error assignment for all zircon grains with only 2D measurements, my concern is that this correction could still give false confidence in what the actual, true Ft error correction should be. For example, common scenarios of U and Th zonation in zircon can lead to Ft correction errors of ~30 % (Hourigan et al., 2005), which is far greater than the errors discussed here. How do the authors consider their findings in comparison to those of Hourigan et al. (2005) and their recommendations for Ft error correction? Zonation is admittedly a pernicious issue, and so there might not be a great answer to this question without resorting to timeintensive in situ approaches, but the authors do need to elaborate more on the error discrepancies here.
 How do the results here compare with the Zr stoichiometric approach of Guenthner et al. (2016)? A comparison of Figure 4a in Guenthner et al. (2016) and Figure 7a seems to suggest that there might be good firstorder agreement between the 3D approach and the stoichiometric approach. Have these zircon grains already been dissolved? A useful followup would be a direct comparison among the 3D, 2D, and stoichiometric approach. This is likely outside the scope of the current study, but some additional discussion along these lines is warranted in the current text.
Willy Guenthner
UIUC
Citation: https://doi.org/10.5194/egusphere20233046RC3 
AC2: 'Reply on RC3', Spencer Zeigler, 21 Mar 2024
We thank Willy for his helpful review that will improve our manuscript! We address each of his points and suggestions below, with our replies in bold
 I am wondering how the Ft error would be different if a different set of 2D geometry equations were used. Both Hourigan et al. (2005, https://doi.org/10.1016/j.gca.2005.01.024) and Reiners et al. (2005, American Journal of Science v. 305, p. 259311) derive a set of Ft equations that take into the account the specific dimensions of the two pyramidal terminations in a given zircon grain. Specifically, see equations 13 in the Reiners et al. (2005) article. The Ketcham et al. (2011) equations do take the pyramid heights into account, but only as a uniform approximation, whereas the Hourigan et al. equations, further derived by Reiners et al., are grain specific. My question then is, is the magnitude of the errors that result from the 2D and 3D comparison of volume and Ft in figure 7 somewhat mitigated by using equations that incorporate metrics for the terminations? The authors seem to suggest as much at line 390. I would encourage the authors to examine this by measuring tip heights directly from their collected images. This is significant in so far as the authors are proposing a general correction that could be applied to previously published datasets, and I know from experience that all zircon (UTh)/He data sets generated at the University of Arizona (of which there are a bunch in the published literature at this point) use the Reiners et al. (2005) correction and not the Ketcham et al. (2011).
Thank you for this excellent point. We will add clarifying language around our decision to use the Ketcham (2011) equations over alternative approaches. We will also emphasize that the use of the Reiners et al. (2005) or Hourigan et al. (2005) geometry equations do not preclude the application of our corrections and uncertainties to previously published data. The mean length and width can be derived from measurements of the trunk and tip height and can be incorporated into the Ketcham et al. (2011) approach. We will add language to emphasize this fact.
We agree that it would be interesting to see how these different 2D methods impact the corrections and we would be happy to discuss sharing our grain images if you would like to collaborate on a technical note!
 There is little mention in the current version of the manuscript concerning U and Th zonation and its influence on the Ft correction. The authors have defined the scope of the current work to focus on corrections to potential systematic error introduced by relying on a 2D geometric approximation only, and this is fine and appropriate. A full consideration of this influence plus the zonation effect would likely be a separate study. However, again, given that the authors propose a generaluse error assignment for all zircon grains with only 2D measurements, my concern is that this correction could still give false confidence in what the actual, true Ft error correction should be. For example, common scenarios of U and Th zonation in zircon can lead to Ft correction errors of ~30 % (Hourigan et al., 2005), which is far greater than the errors discussed here. How do the authors consider their findings in comparison to those of Hourigan et al. (2005) and their recommendations for Ft error correction? Zonation is admittedly a pernicious issue, and so there might not be a great answer to this question without resorting to timeintensive in situ approaches, but the authors do need to elaborate more on the error discrepancies here.
We acknowledge that zonation can have a large influence on the magnitude of corrections and uncertainties. We stated at multiple places in the original paper that our corrections do not account for zonation, but to combat the real issue of “false confidence” we will add language to emphasize this more strongly in the introduction.
We will also explain in the introduction that our strategy in this study and some of our other work has been to compartmentalize and characterize different sources of uncertainty. This study is aimed at characterizing the geometric uncertainties associated with ZHe dates. Additional work could characterize the uncertainty arising from zonation, and then that uncertainty could additionally be propagated into the ZHe data. We see this paper as part of an ongoing effort in the thermochronology community to carefully characterize the different uncertainty components in (UTh)/He dates.
How do the results here compare with the Zr stoichiometric approach of Guenthner et al. (2016)? A comparison of Figure 4a in Guenthner et al. (2016) and Figure 7a seems to suggest that there might be good firstorder agreement between the 3D approach and the stoichiometric approach. Have these zircon grains already been dissolved? A useful followup would be a direct comparison among the 3D, 2D, and stoichiometric approach. This is likely outside the scope of the current study, but some additional discussion along these lines is warranted in the current text.
These grains have not been dissolved. This is a good idea and we also have previously discussed such a follow up study as part of setting up the stoichiometric method in our lab. Our lab has explored the stoichiometric approach several times since 2012 but have not felt comfortable implementing it without a way to independently “ground truth” the results. We agree that these zircon grains provide the opportunity to carry out a rigorous comparative study. We will also add mention of how the masses and volumes determined in this study compare with the results of Guenthner et al. (2016).
Citation: https://doi.org/10.5194/egusphere20233046AC2 
AC4: 'Reply on RC3', Spencer Zeigler, 05 Apr 2024
We appreciate the excellent suggestion by the AE to include the zircon photomicrographs in our data repository so that anyone can use the data to develop geometric corrections and uncertainties for any approach, including for the Reiners et al. (2005) and Hourigan et al. (2005) methods. We simply had not thought of this. We have now added the photomicrographs to the repository and updated our data availability statement accordingly.
Citation: https://doi.org/10.5194/egusphere20233046AC4
Interactive discussion
Status: closed

RC1: 'Comment on egusphere20233046', Florian Hofmann, 06 Feb 2024
This is an excellent paper showing a large dataset of nanoCTscanned zircon grains to improve the alphaejection correction and eU concentration calculations for (UTh)/He dating. This study uses and expands on their proven approach from a previous study on apatite. They find that 2D alphaejection corrections in zircon are fairly accurate when compared to 3D estimates. This is in contrast to their previous study in apatite which found significant differences between these approaches and proposed correction factors for 2D measurements. The authors provide a detailed analysis of their data and a rigorous assessment of the propagation of uncertainty to the calculated ages and eU concentrations. They also clearly lay out strategies and workflows for classifying grains and applying corrections, as well as assessing and propagating uncertainties. This study will be helpful to users of the (UTh)/He method and can provide a template for sample processing workflows to help standardize these procedures between different laboratories. As such, it is a perfect fit for GChron.
Overall, this manuscript is wellwritten and organized, and the text and figures are presented in a highly polished form. The methodological approach, data analysis, and recommendations are welldocumented in the main manuscript as well as the appendices. The authors clearly incorporated the feedback received on a similar previous study into this manuscript. My comments below mainly concern minor formatting details that can be addressed in copyediting, and would, in my opinion, not require any revisions. I, therefore, recommend this manuscript be accepted in its present form.
Detailed Comments:
Line 78: Do the numbers for the resolution (0.840.92 μm) refer to the voxel size or the smallest possible distance between two objects that can be resolved?
Table 1: The formatting makes it hard to read, especially the second column. It’s not immediately apparent which lines belong to which sample. I suggest adding horizontal lines or additional space to separate the rows from each other.
Line 399: Insert spaces between number and unit to make it consistent with the rest of the text: “100μm” > “100 μm”. Also change elsewhere (Figure C1, Line 138, etc.).
Lines 434441: This might be beyond the scope of this paper to discuss, but I’m wondering how the 2D and 3D volumederived masses would compare to ICPMSderived Zrbased masses for zircon grains. Some labs measure Zr routinely and use that for calculating grain mass (e.g. Guenthner et al., 2016, G3). Using those two approaches concurrently could be used to derive the average density of the zircon grains, which correlates to the amount of crystal damage. The difference in density between pristine and highly metamict zircons of around 16% (as mentioned in Line 530) should be resolvable given the uncertainties mentioned in this manuscript.
Citation: https://doi.org/10.5194/egusphere20233046RC1 
AC1: 'Reply on RC1', Spencer Zeigler, 21 Mar 2024
We are grateful for Florian’s kind and thorough review. We agree with his suggestions, made the associated modifications to the manuscript, and include our responses in bold below.
Detailed Comments:
Line 78: Do the numbers for the resolution (0.840.92 μm) refer to the voxel size or the smallest possible distance between two objects that can be resolved?
They refer to the voxel size. We have added language to clarify this point to the introduction (see L78).
Table 1: The formatting makes it hard to read, especially the second column. It’s not immediately apparent which lines belong to which sample. I suggest adding horizontal lines or additional space to separate the rows from each other.
We have made changes to this table to increase legibility. Further changes to legibility will be made during the proofing process if necessary (see attachment).
Line 399: Insert spaces between number and unit to make it consistent with the rest of the text: “100μm” > “100 μm”. Also change elsewhere (Figure C1, Line 138, etc.).
Thank you. We have made this change throughout the text and in Figures: 2, 7, and C1.
Lines 434441: This might be beyond the scope of this paper to discuss, but I’m wondering how the 2D and 3D volumederived masses would compare to ICPMSderived Zrbased masses for zircon grains. Some labs measure Zr routinely and use that for calculating grain mass (e.g. Guenthner et al., 2016, G3). Using those two approaches concurrently could be used to derive the average density of the zircon grains, which correlates to the amount of crystal damage. The difference in density between pristine and highly metamict zircons of around 16% (as mentioned in Line 530) should be resolvable given the uncertainties mentioned in this manuscript.
This is an interesting idea, but we agree that this is beyond the scope of this paper. We have added mention of the stoichiometric approach described by Guenthner et al. (2016) for zircon mass determination and how those outcomes compare with our results. As you point out, both our approach and the stoichiometric approach require assuming the density of zircon, which is another source of uncertainty.

AC1: 'Reply on RC1', Spencer Zeigler, 21 Mar 2024

RC2: 'Comment on egusphere20233046', Anonymous Referee #2, 12 Feb 2024
This is a very nice contribution that aims to assess systematic errors and uncertainties of alphaejection corrections and eU determinations that stem from commonly used “2D” microscopy measurements by comparing a series of measurables derived from highresolution nanoCT “3D” data and the conventional “2D” data. The authors did an excellent job in providing rich information regarding the overall approaches they used including sample selection, data acquisition, and statistical analyses. The conclusions made by the study are important for users of the ZHe method in offering quantified potential errors and additional uncertainties of conventional data and a retroapplicable geometric correction method. I find both the significance and quality of this work fit the scope of GChron, and I highly recommend publication with only minor revisions or clarification. Below I illustrated a few minor concerns/confusions, followed by linespecific comments.
In section 3.2, the authors assumed a zircon Th/U ratio of 0.87 and no Sm contribution owing to a lack of parent isotope measurements. Is it possible to perform some kind of supplementary analysis or offer more reasoning to demonstrate that the use of the assumed values (as opposed to samplespecific parent isotope measurements) would not lead to a significant difference in a series of calculated results presented later, nor the major conclusion?
The collapsed clarity dimension. I do enjoy reading the discussions of how zircon clarify is related to eU, which is a critical proxy for radiation damage accumulation and annealing, and the density of zircon. However, I am a little confused about the way the authors delivered their reasonings about abandoning the clarity dimension in the GEM (section 2.4, around lines 160168). My understanding is that the manuscript is centered on the assessment of error and uncertainty in zircon dimensions, therefore one should be able to exclude the contribution of clarity in terms of the role of varying eU before performing analyses. However, as the author pointed out, zircon clarity is also related to its density, so I think this part of the role of zircon clarity should only be either retained or abandoned after showcasing the analyses presented later on. Therefore, does it make more sense to not abandon this dimension at this point of the manuscript? Moving on, it seems that the authors use 1, 2, or 3 as a numerical index for grain clarity if I understood correctly. Could the clarity be treated as a continuum (through some methods like a grayscale image?) and would a different conclusion on the importance of grain clarity?
Line 78: Is there a reason that the resolution of the CT data is presented as a range? I am not sure if additional information is beneficial though. Regardless, at this scale, would it make sense to simplify it as ~1 µm for ease of reading?
Line 100: Table 1 might look clearer if (1) more space is allowed between rows separating different sample suites or (2) adapting a similar formatting to tables 24.
Line 138: additional space between number and unit.
Line 179181: Minor comment. The first sentence of section 3.1 is a bit repetitive. However, this starting sentence, whether or not in a revised form, seems to be a more explicit way to introduce the firstorder goal of this study if placed in the Intro section.
Line 266268: Would it be better if the definition of the corrections for systematic error could be more explicitly defined here? (e.g., incorporate details from Table 2 footnotes).
Citation: https://doi.org/10.5194/egusphere20233046RC2 
AC3: 'Reply on RC2', Spencer Zeigler, 21 Mar 2024
We thank the anonymous reviewer for their detailed review which will improve our manuscript. We have included replies (in bold) to each of their points and suggestions below.
In section 3.2, the authors assumed a zircon Th/U ratio of 0.87 and no Sm contribution owing to a lack of parent isotope measurements. Is it possible to perform some kind of supplementary analysis or offer more reasoning to demonstrate that the use of the assumed values (as opposed to samplespecific parent isotope measurements) would not lead to a significant difference in a series of calculated results presented later, nor the major conclusion?
The value for the Th/U ratio comes from the average of 736 zircon analyses in the CU Boulder TRaIL. We used this value mainly for illustrative purposes (i.e., to calculate the combined FT and RFT shown in Figure 7). However, the Th/U ratio is also used to calculate the correction and uncertainty for the combined FT and RFT. But, because the ratio is used in the calculation of both the 3D and 2D values for each parameter, the actual value of the correction and uncertainty are not impacted by the choice of Th/U (i.e., the choice of Th/U “cancels out” during the regression). The actual measured elemental concentrations are used to calculate combined FT and RFT when the corrections and uncertainties are applied to real grains. We have added language to clarify this point.
The collapsed clarity dimension. I do enjoy reading the discussions of how zircon clarify is related to eU, which is a critical proxy for radiation damage accumulation and annealing, and the density of zircon. However, I am a little confused about the way the authors delivered their reasonings about abandoning the clarity dimension in the GEM (section 2.4, around lines 160168). My understanding is that the manuscript is centered on the assessment of error and uncertainty in zircon dimensions, therefore one should be able to exclude the contribution of clarity in terms of the role of varying eU before performing analyses. However, as the author pointed out, zircon clarity is also related to its density, so I think this part of the role of zircon clarity should only be either retained or abandoned after showcasing the analyses presented later on. Therefore, does it make more sense to not abandon this dimension at this point of the manuscript? Moving on, it seems that the authors use 1, 2, or 3 as a numerical index for grain clarity if I understood correctly. Could the clarity be treated as a continuum (through some methods like a grayscale image?) and would a different conclusion on the importance of grain clarity?
Thanks for this comment. We wanted to emphasize that noting clarity when picking is important given its relationship to radiation damage and density. But we see your point and have downplayed the discussion of the clarity axis by making edits to section 2.4 and moving the discussion about the GEM design to Appendix B.
We use 1, 2, and 3 as a numerical index for grain clarity due to the unreliability between analysts categorizing clarity into any finer of bins. We favor treating clarity as a qualitative proxy for radiation and therefore retain that axis on the GEM presented in Appendix B. For analysts who prefer more categories to reflect intrasample variation in visual metamictization, we refer the readers to Armstrong et al. (2024) (and have included this citation in our manuscript).
Line 78: Is there a reason that the resolution of the CT data is presented as a range? I am not sure if additional information is beneficial though. Regardless, at this scale, would it make sense to simplify it as ~1 µm for ease of reading?
We originally present the CT resolution as a range because the actual resolutions measured by the CT varied as a function of scan time, magnification, voltage, and power (see Appendix Table B1). We agree that for readability it would be simpler to report the resolution as “sub1 µm” and have made this change throughout the text (3 instances).
Line 100: Table 1 might look clearer if (1) more space is allowed between rows separating different sample suites or (2) adapting a similar formatting to tables 24.
We agree and have made changes to improve readability. Further changes to legibility will be made during the proofing process if necessary (see attachment).
Line 138: additional space between number and unit.
We have made this change.
Line 179181: Minor comment. The first sentence of section 3.1 is a bit repetitive. However, this starting sentence, whether or not in a revised form, seems to be a more explicit way to introduce the firstorder goal of this study if placed in the Intro section.
Thank you for your comment, ee will assess how to incorporate a similar statement into the introduction.
Line 266268: Would it be better if the definition of the corrections for systematic error could be more explicitly defined here? (e.g., incorporate details from Table 2 footnotes).
We define the systematic error in line 53 and will add a clarifying note from the Table 2 footnotes to L266268.

AC3: 'Reply on RC2', Spencer Zeigler, 21 Mar 2024

RC3: 'Comment on egusphere20233046', William Guenthner, 28 Feb 2024
This manuscript by Zeigler and coauthors examines discrepancies between 2D (microscopy) and 3D (nanoCT) computed geometries in zircon grains. Zircon geometric measurements propagate into a number of different metrics (volume, alphaejection correction, eU concentration) that are important for generating and interpreting zircon (UTh)/He data sets. I found the article to be very well written, the data to be high quality, and the scope to be appropriate for the readership at Geochronology. I have three general comments. I would suggest that addressing the first one would encompass some new calculations from existing data. The other two could largely be addressed with additional discussion text. As such, I think these are “moderate” revisions.
 I am wondering how the Ft error would be different if a different set of 2D geometry equations were used. Both Hourigan et al. (2005, https://doi.org/10.1016/j.gca.2005.01.024) and Reiners et al. (2005, American Journal of Science v. 305, p. 259311) derive a set of Ft equations that take into the account the specific dimensions of the two pyramidal terminations in a given zircon grain. Specifically, see equations 13 in the Reiners et al. (2005) article. The Ketcham et al. (2011) equations do take the pyramid heights into account, but only as a uniform approximation, whereas the Hourigan et al. equations, further derived by Reiners et al., are grain specific. My question then is, is the magnitude of the errors that result from the 2D and 3D comparison of volume and Ft in figure 7 somewhat mitigated by using equations that incorporate metrics for the terminations? The authors seem to suggest as much at line 390. I would encourage the authors to examine this by measuring tip heights directly from their collected images. This is significant in so far as the authors are proposing a general correction that could be applied to previously published datasets, and I know from experience that all zircon (UTh)/He data sets generated at the University of Arizona (of which there are a bunch in the published literature at this point) use the Reiners et al. (2005) correction and not the Ketcham et al. (2011).
 There is little mention in the current version of the manuscript concerning U and Th zonation and its influence on the Ft correction. The authors have defined the scope of the current work to focus on corrections to potential systematic error introduced by relying on a 2D geometric approximation only, and this is fine and appropriate. A full consideration of this influence plus the zonation effect would likely be a separate study. However, again, given that the authors propose a generaluse error assignment for all zircon grains with only 2D measurements, my concern is that this correction could still give false confidence in what the actual, true Ft error correction should be. For example, common scenarios of U and Th zonation in zircon can lead to Ft correction errors of ~30 % (Hourigan et al., 2005), which is far greater than the errors discussed here. How do the authors consider their findings in comparison to those of Hourigan et al. (2005) and their recommendations for Ft error correction? Zonation is admittedly a pernicious issue, and so there might not be a great answer to this question without resorting to timeintensive in situ approaches, but the authors do need to elaborate more on the error discrepancies here.
 How do the results here compare with the Zr stoichiometric approach of Guenthner et al. (2016)? A comparison of Figure 4a in Guenthner et al. (2016) and Figure 7a seems to suggest that there might be good firstorder agreement between the 3D approach and the stoichiometric approach. Have these zircon grains already been dissolved? A useful followup would be a direct comparison among the 3D, 2D, and stoichiometric approach. This is likely outside the scope of the current study, but some additional discussion along these lines is warranted in the current text.
Willy Guenthner
UIUC
Citation: https://doi.org/10.5194/egusphere20233046RC3 
AC2: 'Reply on RC3', Spencer Zeigler, 21 Mar 2024
We thank Willy for his helpful review that will improve our manuscript! We address each of his points and suggestions below, with our replies in bold
 I am wondering how the Ft error would be different if a different set of 2D geometry equations were used. Both Hourigan et al. (2005, https://doi.org/10.1016/j.gca.2005.01.024) and Reiners et al. (2005, American Journal of Science v. 305, p. 259311) derive a set of Ft equations that take into the account the specific dimensions of the two pyramidal terminations in a given zircon grain. Specifically, see equations 13 in the Reiners et al. (2005) article. The Ketcham et al. (2011) equations do take the pyramid heights into account, but only as a uniform approximation, whereas the Hourigan et al. equations, further derived by Reiners et al., are grain specific. My question then is, is the magnitude of the errors that result from the 2D and 3D comparison of volume and Ft in figure 7 somewhat mitigated by using equations that incorporate metrics for the terminations? The authors seem to suggest as much at line 390. I would encourage the authors to examine this by measuring tip heights directly from their collected images. This is significant in so far as the authors are proposing a general correction that could be applied to previously published datasets, and I know from experience that all zircon (UTh)/He data sets generated at the University of Arizona (of which there are a bunch in the published literature at this point) use the Reiners et al. (2005) correction and not the Ketcham et al. (2011).
Thank you for this excellent point. We will add clarifying language around our decision to use the Ketcham (2011) equations over alternative approaches. We will also emphasize that the use of the Reiners et al. (2005) or Hourigan et al. (2005) geometry equations do not preclude the application of our corrections and uncertainties to previously published data. The mean length and width can be derived from measurements of the trunk and tip height and can be incorporated into the Ketcham et al. (2011) approach. We will add language to emphasize this fact.
We agree that it would be interesting to see how these different 2D methods impact the corrections and we would be happy to discuss sharing our grain images if you would like to collaborate on a technical note!
 There is little mention in the current version of the manuscript concerning U and Th zonation and its influence on the Ft correction. The authors have defined the scope of the current work to focus on corrections to potential systematic error introduced by relying on a 2D geometric approximation only, and this is fine and appropriate. A full consideration of this influence plus the zonation effect would likely be a separate study. However, again, given that the authors propose a generaluse error assignment for all zircon grains with only 2D measurements, my concern is that this correction could still give false confidence in what the actual, true Ft error correction should be. For example, common scenarios of U and Th zonation in zircon can lead to Ft correction errors of ~30 % (Hourigan et al., 2005), which is far greater than the errors discussed here. How do the authors consider their findings in comparison to those of Hourigan et al. (2005) and their recommendations for Ft error correction? Zonation is admittedly a pernicious issue, and so there might not be a great answer to this question without resorting to timeintensive in situ approaches, but the authors do need to elaborate more on the error discrepancies here.
We acknowledge that zonation can have a large influence on the magnitude of corrections and uncertainties. We stated at multiple places in the original paper that our corrections do not account for zonation, but to combat the real issue of “false confidence” we will add language to emphasize this more strongly in the introduction.
We will also explain in the introduction that our strategy in this study and some of our other work has been to compartmentalize and characterize different sources of uncertainty. This study is aimed at characterizing the geometric uncertainties associated with ZHe dates. Additional work could characterize the uncertainty arising from zonation, and then that uncertainty could additionally be propagated into the ZHe data. We see this paper as part of an ongoing effort in the thermochronology community to carefully characterize the different uncertainty components in (UTh)/He dates.
How do the results here compare with the Zr stoichiometric approach of Guenthner et al. (2016)? A comparison of Figure 4a in Guenthner et al. (2016) and Figure 7a seems to suggest that there might be good firstorder agreement between the 3D approach and the stoichiometric approach. Have these zircon grains already been dissolved? A useful followup would be a direct comparison among the 3D, 2D, and stoichiometric approach. This is likely outside the scope of the current study, but some additional discussion along these lines is warranted in the current text.
These grains have not been dissolved. This is a good idea and we also have previously discussed such a follow up study as part of setting up the stoichiometric method in our lab. Our lab has explored the stoichiometric approach several times since 2012 but have not felt comfortable implementing it without a way to independently “ground truth” the results. We agree that these zircon grains provide the opportunity to carry out a rigorous comparative study. We will also add mention of how the masses and volumes determined in this study compare with the results of Guenthner et al. (2016).
Citation: https://doi.org/10.5194/egusphere20233046AC2 
AC4: 'Reply on RC3', Spencer Zeigler, 05 Apr 2024
We appreciate the excellent suggestion by the AE to include the zircon photomicrographs in our data repository so that anyone can use the data to develop geometric corrections and uncertainties for any approach, including for the Reiners et al. (2005) and Hourigan et al. (2005) methods. We simply had not thought of this. We have now added the photomicrographs to the repository and updated our data availability statement accordingly.
Citation: https://doi.org/10.5194/egusphere20233046AC4
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