We are  grateful to Dr. Ketcham for his prompt, thorough, and thoughtful review that will improve our manuscript. We address each of his points and suggestions below, with our responses in bold. Figures and tables are included inline and as a higher resolution PDF. 

This is a nice study aimed at creating an easily useable means of getting more reliable numbers for various important parameters for (U-Th)/He thermochronology (volume, FT, equivalent radius, eU) using only traditional optical measurements, rather than going to the trouble of more precise but expensive and/or time-intensive methods.  This is certainly within the remit of this journal, and I highly recommend that it be published after addressing the mostly minor concerns below.

Linear relationships between quantities based on 2D measurements and “true” values obtained in 3D are used as conversion factors, and the scatter about those lines is used to characterize the uncertainty.  In theory, lab groups can continue doing exactly what they are doing today, and use these conversions to get better data and deal with uncertainties more quantitatively. 

Accordingly, it’s worth asking what other labs might consider barriers to adoption, whether methodological or psychological.  Although the latter can’t always be fixed, the main concern that comes to mind is that other labs could worry that these conversions may not be appropriate for how they collect their data.  Probably the best antidote is providing more and better data.  In particular, some aspects of how measurements are conducted should be better described, particularly for ellipsoidal grains as discussed below. It would also be good to compare the 2D data to the corresponding 2D-equivalent data extracted from Blob3D (e.g., length corresponding to BoxA, maximum width to BoxB) to verify that there are no errors where there should not be.  Some labs may also already be doing 3 measurements (i.e. to include thickness, or w1), and since the authors here also did 3 measurements, I think (based on lines 276-277), and it may be the lack of a third measurement for round grains that gives them a worse result, why not report them?  They can also be compared to the 3D BoxC measurement, which will perhaps document that the third measurement is indeed less reliable.

Thanks for these great suggestions.

We’ll add comparisons of the Blob3D dimension data to our “2D” dimensions to the tables, figures, and text discussion. Below is a copy of the updated Table 3 with the dimension comparison data in the same style as in Cooperdock (2019) Table 1. We will include scatter plots of the 2D length vs. Box A, 2D maximum width vs. Box B, and 2D minimum width vs. Box C (Reply-Fig1). 

Table 3:

As shown in the Reply-Fig. 1c scatterplots, you are correct that the third dimension (Box C) is less reliable than the length and maximum width. 

During data analysis for this paper, we had thoroughly explored the use of both widths for the corrections and uncertainties, but decided against it for the reasons discussed below. Thanks for pointing out that the rationale for this decision should be explained in the paper. 

We will revise the paper to include corrections and uncertainties for measurements that use all three dimensions (i.e., a length, a maximum width, and a minimum width) for those labs that would like to continue measuring all 3 dimensions (see Reply-Table 1 and Reply-Figure 2 below). The magnitude of both the correction and the uncertainties are larger for hexagonal grains when using all 3 dimensions (Reply-Table 1). For ellipsoid grains, the magnitude of the correction is slightly smaller, but the uncertainties are larger or the same when using all 3 dimensions.  Measuring the maximum width is much more consistent and “true” than measurements of the minimum width (Reply-Fig1c). Due to the ease and reliability of the measurements of the maximum width and because the corrections and uncertainties do not suffer from this simplifying assumption we will continue recommending using the maximum width approach. However, we will include further discussion and additions to Figure 4 in the manuscript to make it clearer how we measured the second width and will include the corrections and uncertainties that use all three dimensions in the Appendix.

Reply-Table 1:

A particular concern is how this method works for ellipsoidal grains. The residuals for hexagonal crystals are fairly evenly scattered as a function of size, but the residuals for ellipsoids are clearly structured, with 2D underestimating volume, FT, and RFT for smaller (less-wide) grains and over-estimating for larger ones. This is partly traceable to the residual lines being forced to pass through the origin, and probably reflects a transition in the characteristics of the error.  It’s hard to gauge exactly because it’s not 100% clear how the microscope measurements are done, and in particular what assumption is made for the third dimension. For example, if the third radius is assumed to be equal to the second, maybe this is a more reasonable assumption for small grains than large ones; perhaps a large flat grain is more likely to be accepted for analysis than a small flat one, as the larger dimensions of the latter are already at the edge of useability. (If this is the case, maybe a different estimate of the third radius would give a better result). Anyway, comparing the 3D-measured third radius to whatever the authors are using might help isolate error components for ellipsoidal grains (e.g. flatness vs. angularity), and point to a way for reducing them.

Thank you for the ideas on how to identify the source of error for ellipsoid grains. The structure in the residuals that you note still exist despite the use of the third dimension (see Reply-Fig. 2). This point deserves more investigation in the future, and we will mention it in the discussion

Interestingly, as shown in Reply-Fig. 1c, the minimum width vs. Box C plots do show that our method of measuring the third dimension cause sa systematic overestimation of that dimension for ellipsoid grains. This overestimation probably has to do with how exactly the second width is measured, so we will include extra description and additions to Figure 4 to make this clearer. 

It would also be worth looking into and discussing briefly how the approach in this paper meshes with the recently published work by He and Reiners in this journal on FT estimates for broken grains. 

Agreed. We will add some discussion about this. 

[Figure 1] This figure has several components that are difficult to understand.  What is being (schematically) measured, and how is that applied to the ideal model?  For the hexagonal case, on the left there is the appearance of using a bipyramidal model on a grain without pyramidal terminations, but a component of error for that is not shown (wouldn’t it underestimate volume if L is modeled as point-to-point rather than face-to-face?), and on the right, the “error” component consists of a bad interfacial angle (but that’s not how crystal faces work) and a mismeasured w2 (unless you’re assuming w2 is assumed rather than measured?).  For the ellipsoid, the L measurement does not appear to correspond to the true long axis; if one rotates the L and w1 measurements 45 degrees counter-clockwise the ellipsoid would fit better. Was this intentional?  It seems to confuse the issue of where one should measure very irregular to ellipsoidal grains.  Lastly, the text “top-down view” is confusing; maybe “along c axis view”?

We appreciate your detailed comments concerning this figure. This figure was intended to be a schematic representation of the issue at hand—microscopy measurements do a poor job accurately representing the true volume and/or surface area of a grain, but it is clear that we did not accomplish this goal. We will remove the pyramidal terminations from the ‘idealized geometry’ on the hexagonal case and rethink how to represent the ellipsoid grains. We will focus our efforts on how to represent the conceptual issue while remaining accurate to grain geometries and corresponding 2D measurements.   

[line 146-7] It’s more common to reference commercial software by company name, and perhaps version number; e.g., Dragonfly (Object Research Systems, v2022.2).  But maybe this journal has a different convention?

Thank you for the formatting suggestion, we will use it as we are unaware of any specific convention from this journal. 

[line 197-214; Figure 4] It’s awkward to utilize and discuss the maximum width before you have defined it, and how it’s measured.  Maybe refer back to Fig 1 to define it (w1) and forward to section 4.2 for how it’s measured?

Excellent suggestion, we will be sure to define the maximum width before we use it. 

[line 274-275] For angular ellipsoid grains, what is measured as the long axis?  For example, for the center grains in cell C1 of Fig 3b, is the long axis the corner-to-corner distance, or perpendicular to what appears to be a width?  How about for the left-column crystals in cell C2?  Might different conventions for measuring such crystals lead to different 2D-to-3D conversion factors?

We will clarify how the measurements were made in the paper. Generally, a “width” is identified first, which would theoretically be parallel to any flatly broken surface, since apatite grains tend to break perpendicular to the c-axis. The long axis is then identified as the axis perpendicular to what appears to be a width. Of course, as you point out, identifying a width can be extremely difficult (as shown by those left column grains in the manuscript’s Figure 3b, cell C2), so we can expect some variability in the 2D-to-3D conversion factors to arise from this issue. We tried to capture this variability in our dataset, which is why grains like this were not removed as long as the three workers who each measured these grains all had methods of measuring these grains that seemed legitimate and sensical. 

[line 294-304] What did you use for the third dimension for ellipsoidal grains?  Did you use the 3rd dimension under the microscope, or did you assume that third radius was equal to the second?

We measured a 3rd dimension for all ellipsoid grains under the microscope and will include this data in the raw data sheet available through OSF and in the summary tables (shown in the updated Table 3). For the 2D calculations presented in the main text, we assumed that the third radius was equal to the second radius (i.e., the “maximum width”) for the reasons discussed above. We will make this clearer in the main text. 

[line 321 (and Appendix B)] Is there a reason such a low X-ray energy was selected (40 kV)?  Using non-filtered, low-kV X-rays may have worsened the artifacts.  Also, in the Appendix table, are Height and Width really in µm?  Those dimensions look more like pixels.  Additionally, the X, Y and Z positions are not innately interesting or informative (they are where the stage was positioned for the scan), and could be safely omitted.

Low X-Ray energy in combination with very small source-sample-detector distances was determined to provide the highest resolution data at the lowest cost. Thank you for noting the units, those will be fixed and the unnecessary rows removed. 

[line 349-351] Sorry about the wire; maybe next time try aluminum.  Although the text mentions extensive culling of bad data due to artifacts, are there still uncertainties in the CT measurements?

We discussed this possibility with the CT technicians at the MIMIC Facility at CU Boulder who helped us run our samples. They told us that for preventative maintenance to pass, they need to achieve < 0.5% difference between the actual and measured grid size. Over time, this can drift but generally stays at < 1% difference. We then assumed a ± 1% uncertainty in our CT measurements and performed simulations in Blob3D by varying the voxel size similar to those done in Cooperdock et al. (2019). We found that any uncertainties present in the CT data translate to negligible differences in the relevant values output by Blob3D and are vanishingly small compared to the uncertainties in the 2D measurements. 

[line 365] Add “grains” to end of sentence.

We will add this.

[line 403-407] It would be good to also report how well the 2D measurements correspond to the caliper dimensions reported in Blob3D (e.g. Cooperdock et al. 2019, Table 1).

Excellent suggestion, these values are now included in our updated Table 3 attached above.

[line 693] Replace “, however,” with “, but”.  Otherwise, it’s a run-on sentence.

We will correct this. 

We appreciate Dr. Glotzbach’s time spent writing this prompt, constructive, and thorough review that will help us improve our paper. We have replied to each of his suggestions in bold below. Figures and tables are included inline and as a higher resolution PDF. 

Dear Authors,

Overall, I found the manuscript well-written, and scientifically interesting and the data is of high quality. I still have some comments and suggestions that I would like to see addressed by the authors:

• I do not get why small grains (<50 μm) are initially considered and later on the results not included. Either include them in the interpretation or (my favorite) do not include them in the manuscript since as you said such grains are commonly not used for apatite (U-Th)/He dating.

We initially included grains < 50 µm for our analytical work to evaluate if 2D measurements deviated from 3D measurements significantly more at small grain sizes, thus further justifying not analyzing grains that small. We found that they are excessively scattered and therefore we do not include these grains in the regressions to avoid biasing the results just to accommodate grains we don’t suggest analyzing. We will explain this more fully in the text and will consider whether/how to include these data in the figures and tables.  

• The manuscript provides a huge amount of CT data at a very high resolution, and I like to encourage the authors to do further analysis and explore the reasons for their overestimation and statistics of grain geometries.

As per the review left by Dr. Ketcham, we will include further analysis of the grain dimensions in 2D vs. 3D (see the updated Table 3 and Reply-Figure 1 attached below). Changes to the manuscript’s Figure 1 will focus on showing the reasons for overestimation more precisely and we will include some discussion about the reasons for overestimation in the text. 

Table 3:

• I do miss a discussion about the reasons this study found an overestimation in volume, FT, and radius. The authors did only consider the maximum width and since grains are usually not symmetric perpendicular to the c-axis, their finding is not a surprise. They should have noticed this since they have very high-resolution CT data, which they could use to e.g. make some statistics from the extracted 3D volumetric data (comparing W1 and W2 of hexagonal grains and W1 and L of ellipsoid grains).

Thanks for this suggestion. As also noted in the response to review 1, we will include a more detailed explanation of why we decided to use the “maximum width only” 2D measurements and how this decision impacts the corrections and uncertainties. Additionally, we will include statistics and plots comparing our 2D measured grain dimensions to the 3D measured grain dimensions that are output by Blob3D which can be found attached to this reply in the updated Table 3 and Reply-Figure 1 above. 

• Anyway, a simple additional measurement of the minimum width could correct the data and therefore no correction is required. In my study, I measured the minimum and maximum width and therefore could not find a systematic overestimation. In case you have measured the minimum width (at least you stated this in your manuscript) please provide all geometric estimates based on the minimum and combined minimum and maximum (volume, FT, and sphere-equivalent radius) measurements and a comparison with the CT data.

We thank you for noting this clear gap in our work. You will find the resulting corrections and uncertainties calculated using all three dimensions (L, W1, W2) attached to this reply in Reply-Table 1 and Reply-Fig. 2. Using all three dimensions does not negate the need for a correction, it simply changes the direction and magnitude. When we calculate the 2D volume, FT, and RFT using all three dimensions for hexagonal grains, we see that 2D measurements underestimate the 3D parameters. This results in a larger correction and larger uncertainties. However, for ellipsoid grains, using all three dimensions results in a smaller magnitude overestimation, while the uncertainties are larger or stay the same. We will include these results in the manuscript and include a more detailed description of why we favor using the maximum width only.  

Reply-Table 1:

• The authors stated, that the provided corrections might be simply transferable to other labs/users. I doubt that this is that easy and only possible in case the protocol is similar. Since the authors have not at least provided information on the protocols of other labs, this is just a guess. I personally do not like that you suggest a protocol in which only the maximum width of grains is measured and afterward the overestimation is corrected. This does introduce scatter to the data. Instead, I would suggest measuring at least both the minimum and maximum width, which should remove the overestimation. Those that want to be even more exact can measure according to the 3D-He approach or even use CT scanning.

As noted above, we will include more details on our measurement procedure and add the data and discussion regarding the use of both widths to the text. Thanks for pointing out the need for additional information here. 

• It would be consequent and useful to show the consequence of your applied corrections for the cooling history. I would therefore suggest that you model cooling histories from the presented data before and after the corrections are done.

The magnitude of the effect of our corrections and uncertainties on thermal history modeling depends strongly on how the uncertainties are input into the thermal modeling program and the cooling history experienced by the sample. There is a lot of variability in how modeling is done across the community, so we would prefer to leave this potentially complicated exercise for future users of the method. We will be exploring this in the future as we routinely incorporate this method in our own data reduction and thermal history modeling procedures. 

I hope you find my comments and suggestions helpful.

Yes, thank you.

Technical corrections:

Line 52: Please make it more clear why you preferentially overestimate the grain size. My guess is that the grain will lay down with the c-b axis parallel to a horizontal. This can be easily corrected if you would use low-adhesive tape and rotate around the c-axis the measure also the a-axis.

We will add text to clarify this point. Additionally, we will update Figure 4 and the text to explain how we measured the second width. 

Anyway, explain in Fig. 1, how you get to the red ‘overestimated area’.

We will rework Figure 1 based on your and Dr. Ketcham’s reviews. 

Line 131: I would say that according to present knowledge radiation damage does have a large effect in case of slow cooling or long stay in the PRZ.

We will add this. 

Line 175: It is not clear at this point why it is important to analyze apatites from different lithologies and ages? Please clarify.

We chose a wide range of lithologies and ages to ensure we were selecting apatites with grain characteristics that are representative of all the types of apatites dated regularly with (U-Th)/He thermochronology. Our lab’s research tends to focus on older basement samples, and we wanted to include igneous apatite from young igneous systems as well as detrital apatite to ensure that we weren’t inadvertently biasing the outcomes of this work.  We will clarify this point during revisions. 

Line 223: Maybe better say ‘code’ instead of ‘single value’.

Will change.

Line 254-255: I do see the benefit of having such a classification scheme, but it is not only useful for newcomers. Just say that this simple approach might be useful to easily report the overall morphological quality of grains in studies reporting apatite (U-Th)/He data.

Good suggestion. We will add this language, but do prefer to also retain mention of the particular value to newcomers because learning to pick apatite is difficult, partially because of the wide range of morphologies apatite can exhibit, which the GEM can help with. 

Line 267: That is a very important point, the reported corrections are only applicable under these conditions. Therefore, I am not sure if your method is that ‘simple and practical and even applicable retroactively. Please make this clear in the abstract and elsewhere.

We will clarify. However, to our knowledge, we use the same approach that most labs do for determining grain length and width measurements. 

Line 277: I agree that this is difficult on a glass slide only, but is quite simple with low adhesive double-sided tape. The extra work on doing this is at a maximum 1-2 minutes, nothing really difficult, and neglectable compared to the time needed to search and pick suitable grains. I also do not see why you are only using ‘maximum width’, which consequently results in an overestimation of volume, FT and radius.

We will clarify our decision to use the maximum width only as discussed above. We will also discuss and illustrate the difficulty of measuring the second width well (updated Table 3, Reply-Figure 1c). 

Line 351: I would suggest reporting a few of the reconstructed apatites.

We don’t feel comfortable reporting these data that are unreliable due to acquisition with a flawed analytical procedure. 

Line 361: This procedure is not clear to me, you have selected grains <50 μm in width and analyzed them and finally not considering them. Does not make sense to me. It would make sense to say from the start that you have not included grains <50 μm.

We will more clearly explain why we initially included grains <50 µm as noted above, and will consider including these data in some form. 

Line 364: Change to ‘typically’.

We will reword.

Line 449: Please say what statistical value is that e.g. correlation coefficients?

We will add this during revisions. You are correct that these values are correlation coefficients calculated using Pearson’s r. 

Line 489: The reason why this study found an overestimation is not that more grains have been analyzed, but the reported measurements are based on the maximum width and assuming an idealized grain geometry. You state in the method section that you also did minimum width measurements. In case you have the data, I would like to see the resulting measurements for those too, or at its best to combine both maximum and minimum measurements.

We will reword the sentence to avoid implying that we found an overestimation due to the number of grains measured. As noted above, we also will add the data, figure, and discussion regarding the use of one or both widths.  

Line 532-533: This is because I did the calculation based on the minimum and maximum width of grains or accurate measurements of the a, b and c axis.

Thank you for this important point. We will clarify that you measured all three dimensions and used these in your calculations when comparing our results to these outcomes. 

Figures

Fig. 1: Please explain the occurrence of the overestimated area. Is this based on the assumption that W1 is measured, but why in the ellipsoid example do you fit an asymmetric cross section (taking into account that W1 and L are different)? Please clarify.

Thank you for your suggestions. Wewill rework Figure 1 based on your and Dr. Ketcham’s reviews. 

Fig. 4: Could you use a slightly different color for those grains in morphological categories 1 or 2.

We are unsure which figure you are referring to since Figure 4 is a black and white photomicrograph, but would be happy to modify the color scheme on the figure you meant.