the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: A software framework for calculating compositionally dependent in situ 14C production rates
- 1Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA
- 2Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
- 1Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA
- 2Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
Abstract. Over the last 30 years, in situ cosmogenic nuclides (CNs) have revolutionized surficial process and Quaternary geologic studies. Commonly measured CNs extracted from the common mineral quartz have long half-lives (e.g., 10Be, 26Al), and have been applied over timescales from a few hundred years to millions of years. However, their long half-lives also render them largely insensitive to complex histories of burial and exposure less than ca. 100 ky. On the other hand, in situ cosmogenic 14C (in situ 14C) is also produced in quartz, yet its 5.7 ky half-life renders it very sensitive to complex exposure histories during the last ~25 ka – a particularly unique and powerful tool when analyzed in concert with long-lived nuclides. In situ 14C measurements are currently limited to relatively coarse-grained (typically sand-sized or larger, crushed/sieved to sand) quartz-bearing rock types, but while such rocks are common, they are not ubiquitous. The ability to extract and interpret in situ 14C from quartz-poor and fine-grained rocks would thus open its unique applications to a broader array of landscape elements and environments.
As a first step toward this goal, a robust means of interpreting in situ 14C concentrations derived from rocks and minerals spanning wider compositional and textural ranges will be crucial. We have thus developed a MATLAB®-based software framework to quantify spallogenic production of in situ 14C from a broad range of silicate rock and mineral compositions, including rocks too fine-grained to achieve pure quartz separates. As expected from prior work, production from oxygen dominates the overall in situ 14C signal, accounting for >90 % of production for common silicate minerals and six different rock types at sea-level and high latitudes (SLHL). This work confirms that Si, Al, and Mg are important targets, but also predicts greater production from Na than from those targets. The compositionally dependent production rates for rock and mineral compositions investigated here are typically lower than that of quartz, although that predicted for albite is comparable to quartz, reflecting the significance of production from Na. Predicted production rates drop as compositions become more mafic (particularly Fe-rich). This framework should thus be a useful tool in efforts to broaden the utility of in situ 14C to quartz-poor and fine-grained rock types, but future improvements in measured and modelled excitation functions would be beneficial.
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Journal article(s) based on this preprint
Alexandria J. Koester and Nathaniel A. Lifton
Interactive discussion
Status: closed
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RC1: 'Comment on gchron-2022-16', Reto Trappitsch, 21 Jul 2022
In the manuscript: "A software framework for calculating compositionally dependent in situ 14C production rates", Koester and Lifton present new results for calculating cosmogenic 14C production rates for various minerals other than quartz. These calculations are based on previous models and represent an extension that allows experimentalists to calculate exposure histories for quartz-poor samples.
These new production rates significantly broaden the applicability of exposure age dating via the cosmogenic 14C to a variety of minerals other than quartz. The results present a major contribution to the field of geochronology and are therefore ideally suited for publication in this journal. I highly recommend publication of this manuscript, however, would like to propose several clarifications / edits.
Major Comments:
===============You present production rates based on various minerals and give the composition of these minerals. Would it be easier / simpler to present elementary production rates and have the user ultimately calculate the overall production rate in a given mineral based on their specific composition? This could allow a user to easier work with the results from this manuscript. Please feel free to completely ignore this idea, I am not very familiar with the general approach in the field of terrestrial cosmogenic nuclides.
Section 3.1, second paragraph: In Reedy (2013), excitation functions for the production of 14C from elementary O and Si are presented and not from 16O and 28Si. Generally, cross-sections are measured using materials with natural isotopic abundances. This makes more sense, since these elements also occur in geological samples of interest in their normal isotopic composition.
For excitation functions from JENDL/HE-2007: Did you take the values for pure isotopic compositions as stated in line 128? I don't expect that your samples contain, e.g., isotopically pure 48Ti. Therefore, a Ti(n,X)14C excitation function where all isotopes are included in their terrestrial composition should be used for the calculations.Uncertainty determination for JENDL/HE-2007 excitation functions, last paragraph in Section 4.2. You estimate the overall uncertainties for the purely calculated excitation functions at 10-15%. The estimate is based on comparing the JENDL/HE-2007 (calculated, generally GNASH) with TENDL (calculated, TALYS). This comparison is not exactly fair. A better comparison would be to compare calculated excitation functions with measured ones, as, e.g., Broeders et al. (https://doi.org/10.14494/JNRS2000.7.N1), however, you obviously cannot do this for the reactions you are interested in. A better estimate to use for the uncertainty of calculated production rates is given in Reedy (2013), section 3.1, third-last paragraph: "[...] most formulae and codes give cross-sections for an individual nuclide that typically differ from measured ones by factors of ~2 (Ammon et al., 2009)". Your uncertainty estimate seems therefore far too optimistic.
Minor Comments:
===============Section 3.1, first paragraph: This paragraph contains quite a lot of information that is not understandable without reading Lifton et al. (2014) first. You are already describing what goes into the model in a very good way in Section 2.1. For this paragraph, it would be good if you could explain all abbreviations (LSDn, PARMA, SHA.DIF.14k - if this is an abbreviation). Furthermore, could you provide some detail on what the gridded R_C and dipolar R_CD models of Lifton et al. (2016) are?
Figure 1: For the measured curves, it might be good to present the measurements as symbols, in order to easier distinguish between interpolated and measured values.
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AC1: 'Reply on RC1', Alexandria Koester, 10 Oct 2022
We thank Dr. Reto Trappitsch for their helpful feedback to our manuscript. We respond to each comment in detail below:
- Major comments:
- You present production rates based on various minerals and give the composition of these minerals. Would it be easier / simpler to present elementary production rates and have the user ultimately calculate the overall production rate in a given mineral based on their specific composition? This could allow a user to easier work with the results from this manuscript. Please feel free to completely ignore this idea, I am not very familiar with the general approach in the field of terrestrial cosmogenic nuclides
We appreciate the reviewer’s comments, but the calculator already does what is suggested. It takes major elemental oxide data and calculates a theoretical production rate based on the sample composition. The production rate is then normalized to the calibrated production rate in quartz. Future work would include a geologic calibration for each mineral if possible. In response to the other reviewer, we have also derived an equivalent elemental production rate formula – this will be presented in the revised manuscript.
- Section 3.1, second paragraph: In Reedy (2013), excitation functions for the production of 14C from elementary O and Si are presented and not from 16O and 28Si. Generally, cross-sections are measured using materials with natural isotopic abundances. This makes more sense, since these elements also occur in geological samples of interest in their normal isotopic composition.
We thank the reviewer for noting the inconsistency in our manuscript. We have changed the wording in our description of Reedy’s measurements and updated the figures that show the measured excitation functions, noting that they are on natural isotopic abundances. We have also updated the text to reflect that most of the neutron excitation functions that Reedy presents are in fact not measured directly (with a few exceptions), but rather are derived from the measured proton excitation functions (line 130).
- For excitation functions from JENDL/HE-2007: Did you take the values for pure isotopic compositions as stated in line 128? I don't expect that your samples contain, e.g., isotopically pure 48Ti. Therefore, a Ti(n,X)14C excitation function where all isotopes are included in their terrestrial composition should be used for the calculations.
The reviewer is correct - we are assuming essentially pure isotopic compositions for the modelled excitation functions. For each of the modelled excitation functions, we used the most abundant isotope for each element. Of the elements we are considering here for the modelled excitation functions, only three of the isotopes do not have natural abundances of essentially 100%. These are 39K (93% elemental abundance), 40Ca (97% elemental abundance), and 48Ti (73% elemental abundance). While we agree that it would be more accurate to consider production from the natural abundances of each isotope for these elements, we note that the proportion of spallation production of in situ 14C from each is only a small fraction of total production for the ranges of compositions we consider. For instance, the percentage of total production predicted from 39K, as considered here, ranges from 0.1 to <0.01%, that from 40Ca ranges from 0.2 to 0.01%, and the percentage of total production from 48Ti is uniformly <0.001% in all cases considered (Table 3). Thus, we argue that any errors in our total predicted compositionally dependent production rates introduced by considering only the isotopes above, instead of the natural isotopic abundances for these elements, would likely be insignificant relative to other uncertainties in our calculations that we note. We have updated the text to clarify this argument in the manuscript. Also see our response below to the next comment.
- Uncertainty determination for JENDL/HE-2007 excitation functions, last paragraph in Section 4.2. You estimate the overall uncertainties for the purely calculated excitation functions at 10-15%. The estimate is based on comparing the JENDL/HE-2007 (calculated, generally GNASH) with TENDL (calculated, TALYS). This comparison is not exactly fair. A better comparison would be to compare calculated excitation functions with measured ones, as, e.g., Broeders et al. (https://doi.org/10.14494/JNRS2000.7.N1), however, you obviously cannot do this for the reactions you are interested in. A better estimate to use for the uncertainty of calculated production rates is given in Reedy (2013), section 3.1, third-last paragraph: "[...] most formulae and codes give cross-sections for an individual nuclide that typically differ from measured ones by factors of ~2 (Ammon et al., 2009)". Your uncertainty estimate seems therefore far too optimistic.
We agree that our uncertainty estimates for the modelled excitation functions could be more conservative. However, apart from 23Na, all the modelled reaction excitation functions have only minor impact on the overall production rates we predict (see above response as well). The percentages of total production of in situ 14C from 55Mn, 40Ca, 39K and 31P range from <0.001 to 0.2 for the compositions considered (Table 3). Even if reaction cross sections are off by a factor of 2, as suggested above from Reedy (2013), the impact to overall production is small. For instance, if we doubled the percentage of 14Cproduction from Ca for Wollastonite, it would only increase to 0.4 %. Thus, as noted above, we argue that the overall additional uncertainty in our results that might be introduced by using more conservative estimates of potential errors in the modelled cross-sections would insignificant relative to other uncertainties in the calculations. Of course, as we note, particularly for 23Na, this also points to the need for more measured excitation functions for in situ 14C production – both from protons and the neutron excitation functions derived from those measurements. We note in our conclusion that measured excitation functions (or those derived from measurements at natural abundances, such as for neutrons in most cases, per Reedy) would greatly improve our predictions, and have modified the text to reflect the additional points above.
- Minor comments:
- Section 3.1, first paragraph: This paragraph contains quite a lot of information that is not understandable without reading Lifton et al. (2014) first. You are already describing what goes into the model in a very good way in Section 2.1. For this paragraph, it would be good if you could explain all abbreviations (LSDn, PARMA, SHA.DIF.14k - if this is an abbreviation). Furthermore, could you provide some detail on what the gridded R_C and dipolar R_CD models of Lifton et al. (2016) are?
We acknowledge that we skimmed over the details of Lifton et al. (2014) but argue that interested readers can go to the original publication for full details of the nuclide-specific LSDn scaling methodology. We expect that interested readers will be familiar with the term “LSDn” because it is a common scaling method (along with St and Lm, as seen in the online UW v3 online calculator that we reference in text). We have also included some minor edits in line 115 for clarification.
- Figure 1: For the measured curves, it might be good to present the measurements as symbols, in order to easier distinguish between interpolated and measured values.
We appreciate the comment to clarify the figure and have added symbols to make it easier to distinguish measured values (or those inferred from measurements, such as most of the neutron data) from interpolated values.
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AC1: 'Reply on RC1', Alexandria Koester, 10 Oct 2022
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RC2: 'Comment on gchron-2022-16', Irene Schimmelpfennig, 22 Aug 2022
This manuscript reports theoretic production rates of in situ cosmogenic 14C in mineral and rock phases of various compositions, estimated from a specifically developed software framework.
Given the potential need for knowledge of 14C production rates in minerals and rocks other than quartz in future surface exposure dating studies, this manuscript is well suited for publication in Geochronology.
It is very well and clearly written. I suggest a few minor clarifications that should be addressed.
Lines 55-56: It could be good to clarify that the extraction procedures from mineral/rock phases other than quartz also still needs to be developed before these materials can be envisioned for geologic applications.
Lines 80-81: This sentence is unclear: does “well-constrained” refer to the exposure history? Natural variability of what? I don’t understand the point of the sentence.
Lines 81-82: The focus on quartz is also due to the fact that extraction procedures for other minerals or lithologies have not yet been developed or validated.
Line 149: Were elevation differences between individual samples at each site insignificant? Or were the concentrations corrected for them?
Lines 153-154: What is the calibrated value generated by the UWv3 calculator?
Lines 159-165: This should be simplified by saying that you calculate a correction factor P_Qcal/P_Qref , which gives 0.854 and which you multiply by the P_CDpred of all other tested mineral and rock phases. However, how reliable is this correction for other compositions, which are associated with other excitation functions than quartz?
Lines 237-238: Would it be possible to list the elemental 14C production rates, for direct comparison with those given in the Masarik (2002) abstract? This is also what is commonly done for the highly composition dependent 36Cl production.
Related to this, I suggest you should clarify whether or not the software also calculated production rates for compositions that differ from those considered here theoretically.
Caption of Table 1: Shouldn’t this be “Oxide compositions… and accordingly calculated number densities”? (It should be clarified what the numbers are.)
Irene Schimmelpfennig
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AC2: 'Reply on RC2', Alexandria Koester, 11 Oct 2022
We thank Dr. Irene Schimmelpfennig for her helpful comments to improve the manuscript. We have responded to each comment in detail below
- Lines 55-56: It could be good to clarify that the extraction procedures from mineral/rock phases other than quartz also still needs to be developed before these materials can be envisioned for geologic applications.
We thank the review for their comment. We have clarified this point in the manuscript at the end of our introduction (line 63-64)
Lines 80-81: This sentence is unclear: does “well-constrained” refer to the exposure history? Natural variability of what? I don’t understand the point of the sentence.
Yes, “well-constrained” does refer to the exposure history. We have edited the sentence for clarity.
- Lines 81-82: The focus on quartz is also due to the fact that extraction procedures for other minerals or lithologies have not yet been developed or validated.
We note that the first extraction techniques for in situ 14C utilized whole rock samples (e.g., Jull et al., 1992; 1994) in the introduction and were ultimately abandoned in favor of the simpler quartz systematics. (lines 55-56).
- Line 149: Were elevation differences between individual samples at each site insignificant? Or were the concentrations corrected for them?
In this 14C CRONUS-Earth global calibration from the references cited, there are samples at secular equilibrium along elevation transects that span a broad altitudinal range at a particular latitude. Those samples are incorporated into the estimate of the SLHL production rate. In addition, there are the primary CRONUS-Earth calibration sites with multiple samples that span limited altitudinal ranges. Sample locations (latitude, longitude, and altitude) are of course considered in deriving the SLHL production rate estimates, as those are required input for the scaling model. This dataset will be included in the supplement.
- Lines 153-154: What is the calibrated value generated by the UWv3 calculator?
The output value generated by the UWv3 calculator is 0.868, using dipolar RC parameterization from that calculator’s implementation. This value is the fitting parameter that is multiplied by the reference production rate for 14C, 15.8 atoms/g, which is that derived from the integral of the flux and excitation functions for 14C production from neutron and proton spallation in quartz, at SLHL (P_Qref). This yields a value of 13.7 at/g/y, which is the same value (well within 1 sigma uncertainty) that we derive using a dipolar RC parameterization similar to that in the UWv3 calculator in the manuscript (see line 154) and already mentioned in text (line 156).
- Lines 159-165: This should be simplified by saying that you calculate a correction factor P_Qcal/P_Qref , which gives 0.854 and which you multiply by the P_CDpred of all other tested mineral and rock phases. However, how reliable is this correction for other compositions, which are associated with other excitation functions than quartz?
We prefer to keep the equation grouped as presented because the P_CDpred and the P_Qref are both theoretical - we then multiply that by the geologic calibration of quartz. Algebraically it doesn’t matter of course, it’s just seems more logical to us in that order. Therefore, we prefer to keep the theoretical components together and separate from the geologic component.
The correction is as reliable as possible given our current knowledge of the scaling of fluxes, reaction cross sections, and geologic calibrations. We have attempted to quantify the uncertainties on this in general in the text already. As more excitation functions are measured for the reactions of interest here, and mineral specific geologic production rate calibrations are conducted, our confidence in these corrections will undoubtedly improve.
- Lines 237-238: Would it be possible to list the elemental 14C production rates, for direct comparison with those given in the Masarik (2002) abstract? This is also what is commonly done for the highly composition dependent 36Cl production.
We thank the reviewer for the suggestion and have derived a list of production from each element within the text (shown as atoms g-element-1 yr-1) at a SLHL location, and added discussion in the text of this. We have also provided a table below, which is now Table 6 in the manuscript.
Element
PRSLHL (atoms g-element-1 yr-1)
O
29.01
Si
0.84
Mg
2.19
Al
1.67
Fe
0.10
Na
15.59
K
0.08
Ca
0.06
Ti
0.05
Mn
0.03
P
0.22
- Related to this, I suggest you should clarify whether or not the software also calculated production rates for compositions that differ from those considered here theoretically.
The software framework can take in any XRF elemental analysis for any rock or mineral type. The user can input any elemental oxide percent from any location and calculate a theoretical production rate. We tried to compare predictions for as broad a compositional range as possible. We have added a sentence to line 143 for clarity.
Caption of Table 1: Shouldn’t this be “Oxide compositions… and accordingly calculated number densities”? (It should be clarified what the numbers are.)
The table lists the percentage of oxide compositions for each mineral and rock. These percentages are used to calculate the number densities as in equation 2 (line 139). We have edited the caption for clarity.
While we were at a conference, Dr. Schimmelpfennig suggested in person to include a figure of the production from minerals and rocks from a presentation about this work, so we are including that in the revised manuscript per her request.
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AC2: 'Reply on RC2', Alexandria Koester, 11 Oct 2022
Peer review completion
Post-review adjustments
Interactive discussion
Status: closed
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RC1: 'Comment on gchron-2022-16', Reto Trappitsch, 21 Jul 2022
In the manuscript: "A software framework for calculating compositionally dependent in situ 14C production rates", Koester and Lifton present new results for calculating cosmogenic 14C production rates for various minerals other than quartz. These calculations are based on previous models and represent an extension that allows experimentalists to calculate exposure histories for quartz-poor samples.
These new production rates significantly broaden the applicability of exposure age dating via the cosmogenic 14C to a variety of minerals other than quartz. The results present a major contribution to the field of geochronology and are therefore ideally suited for publication in this journal. I highly recommend publication of this manuscript, however, would like to propose several clarifications / edits.
Major Comments:
===============You present production rates based on various minerals and give the composition of these minerals. Would it be easier / simpler to present elementary production rates and have the user ultimately calculate the overall production rate in a given mineral based on their specific composition? This could allow a user to easier work with the results from this manuscript. Please feel free to completely ignore this idea, I am not very familiar with the general approach in the field of terrestrial cosmogenic nuclides.
Section 3.1, second paragraph: In Reedy (2013), excitation functions for the production of 14C from elementary O and Si are presented and not from 16O and 28Si. Generally, cross-sections are measured using materials with natural isotopic abundances. This makes more sense, since these elements also occur in geological samples of interest in their normal isotopic composition.
For excitation functions from JENDL/HE-2007: Did you take the values for pure isotopic compositions as stated in line 128? I don't expect that your samples contain, e.g., isotopically pure 48Ti. Therefore, a Ti(n,X)14C excitation function where all isotopes are included in their terrestrial composition should be used for the calculations.Uncertainty determination for JENDL/HE-2007 excitation functions, last paragraph in Section 4.2. You estimate the overall uncertainties for the purely calculated excitation functions at 10-15%. The estimate is based on comparing the JENDL/HE-2007 (calculated, generally GNASH) with TENDL (calculated, TALYS). This comparison is not exactly fair. A better comparison would be to compare calculated excitation functions with measured ones, as, e.g., Broeders et al. (https://doi.org/10.14494/JNRS2000.7.N1), however, you obviously cannot do this for the reactions you are interested in. A better estimate to use for the uncertainty of calculated production rates is given in Reedy (2013), section 3.1, third-last paragraph: "[...] most formulae and codes give cross-sections for an individual nuclide that typically differ from measured ones by factors of ~2 (Ammon et al., 2009)". Your uncertainty estimate seems therefore far too optimistic.
Minor Comments:
===============Section 3.1, first paragraph: This paragraph contains quite a lot of information that is not understandable without reading Lifton et al. (2014) first. You are already describing what goes into the model in a very good way in Section 2.1. For this paragraph, it would be good if you could explain all abbreviations (LSDn, PARMA, SHA.DIF.14k - if this is an abbreviation). Furthermore, could you provide some detail on what the gridded R_C and dipolar R_CD models of Lifton et al. (2016) are?
Figure 1: For the measured curves, it might be good to present the measurements as symbols, in order to easier distinguish between interpolated and measured values.
-
AC1: 'Reply on RC1', Alexandria Koester, 10 Oct 2022
We thank Dr. Reto Trappitsch for their helpful feedback to our manuscript. We respond to each comment in detail below:
- Major comments:
- You present production rates based on various minerals and give the composition of these minerals. Would it be easier / simpler to present elementary production rates and have the user ultimately calculate the overall production rate in a given mineral based on their specific composition? This could allow a user to easier work with the results from this manuscript. Please feel free to completely ignore this idea, I am not very familiar with the general approach in the field of terrestrial cosmogenic nuclides
We appreciate the reviewer’s comments, but the calculator already does what is suggested. It takes major elemental oxide data and calculates a theoretical production rate based on the sample composition. The production rate is then normalized to the calibrated production rate in quartz. Future work would include a geologic calibration for each mineral if possible. In response to the other reviewer, we have also derived an equivalent elemental production rate formula – this will be presented in the revised manuscript.
- Section 3.1, second paragraph: In Reedy (2013), excitation functions for the production of 14C from elementary O and Si are presented and not from 16O and 28Si. Generally, cross-sections are measured using materials with natural isotopic abundances. This makes more sense, since these elements also occur in geological samples of interest in their normal isotopic composition.
We thank the reviewer for noting the inconsistency in our manuscript. We have changed the wording in our description of Reedy’s measurements and updated the figures that show the measured excitation functions, noting that they are on natural isotopic abundances. We have also updated the text to reflect that most of the neutron excitation functions that Reedy presents are in fact not measured directly (with a few exceptions), but rather are derived from the measured proton excitation functions (line 130).
- For excitation functions from JENDL/HE-2007: Did you take the values for pure isotopic compositions as stated in line 128? I don't expect that your samples contain, e.g., isotopically pure 48Ti. Therefore, a Ti(n,X)14C excitation function where all isotopes are included in their terrestrial composition should be used for the calculations.
The reviewer is correct - we are assuming essentially pure isotopic compositions for the modelled excitation functions. For each of the modelled excitation functions, we used the most abundant isotope for each element. Of the elements we are considering here for the modelled excitation functions, only three of the isotopes do not have natural abundances of essentially 100%. These are 39K (93% elemental abundance), 40Ca (97% elemental abundance), and 48Ti (73% elemental abundance). While we agree that it would be more accurate to consider production from the natural abundances of each isotope for these elements, we note that the proportion of spallation production of in situ 14C from each is only a small fraction of total production for the ranges of compositions we consider. For instance, the percentage of total production predicted from 39K, as considered here, ranges from 0.1 to <0.01%, that from 40Ca ranges from 0.2 to 0.01%, and the percentage of total production from 48Ti is uniformly <0.001% in all cases considered (Table 3). Thus, we argue that any errors in our total predicted compositionally dependent production rates introduced by considering only the isotopes above, instead of the natural isotopic abundances for these elements, would likely be insignificant relative to other uncertainties in our calculations that we note. We have updated the text to clarify this argument in the manuscript. Also see our response below to the next comment.
- Uncertainty determination for JENDL/HE-2007 excitation functions, last paragraph in Section 4.2. You estimate the overall uncertainties for the purely calculated excitation functions at 10-15%. The estimate is based on comparing the JENDL/HE-2007 (calculated, generally GNASH) with TENDL (calculated, TALYS). This comparison is not exactly fair. A better comparison would be to compare calculated excitation functions with measured ones, as, e.g., Broeders et al. (https://doi.org/10.14494/JNRS2000.7.N1), however, you obviously cannot do this for the reactions you are interested in. A better estimate to use for the uncertainty of calculated production rates is given in Reedy (2013), section 3.1, third-last paragraph: "[...] most formulae and codes give cross-sections for an individual nuclide that typically differ from measured ones by factors of ~2 (Ammon et al., 2009)". Your uncertainty estimate seems therefore far too optimistic.
We agree that our uncertainty estimates for the modelled excitation functions could be more conservative. However, apart from 23Na, all the modelled reaction excitation functions have only minor impact on the overall production rates we predict (see above response as well). The percentages of total production of in situ 14C from 55Mn, 40Ca, 39K and 31P range from <0.001 to 0.2 for the compositions considered (Table 3). Even if reaction cross sections are off by a factor of 2, as suggested above from Reedy (2013), the impact to overall production is small. For instance, if we doubled the percentage of 14Cproduction from Ca for Wollastonite, it would only increase to 0.4 %. Thus, as noted above, we argue that the overall additional uncertainty in our results that might be introduced by using more conservative estimates of potential errors in the modelled cross-sections would insignificant relative to other uncertainties in the calculations. Of course, as we note, particularly for 23Na, this also points to the need for more measured excitation functions for in situ 14C production – both from protons and the neutron excitation functions derived from those measurements. We note in our conclusion that measured excitation functions (or those derived from measurements at natural abundances, such as for neutrons in most cases, per Reedy) would greatly improve our predictions, and have modified the text to reflect the additional points above.
- Minor comments:
- Section 3.1, first paragraph: This paragraph contains quite a lot of information that is not understandable without reading Lifton et al. (2014) first. You are already describing what goes into the model in a very good way in Section 2.1. For this paragraph, it would be good if you could explain all abbreviations (LSDn, PARMA, SHA.DIF.14k - if this is an abbreviation). Furthermore, could you provide some detail on what the gridded R_C and dipolar R_CD models of Lifton et al. (2016) are?
We acknowledge that we skimmed over the details of Lifton et al. (2014) but argue that interested readers can go to the original publication for full details of the nuclide-specific LSDn scaling methodology. We expect that interested readers will be familiar with the term “LSDn” because it is a common scaling method (along with St and Lm, as seen in the online UW v3 online calculator that we reference in text). We have also included some minor edits in line 115 for clarification.
- Figure 1: For the measured curves, it might be good to present the measurements as symbols, in order to easier distinguish between interpolated and measured values.
We appreciate the comment to clarify the figure and have added symbols to make it easier to distinguish measured values (or those inferred from measurements, such as most of the neutron data) from interpolated values.
-
AC1: 'Reply on RC1', Alexandria Koester, 10 Oct 2022
-
RC2: 'Comment on gchron-2022-16', Irene Schimmelpfennig, 22 Aug 2022
This manuscript reports theoretic production rates of in situ cosmogenic 14C in mineral and rock phases of various compositions, estimated from a specifically developed software framework.
Given the potential need for knowledge of 14C production rates in minerals and rocks other than quartz in future surface exposure dating studies, this manuscript is well suited for publication in Geochronology.
It is very well and clearly written. I suggest a few minor clarifications that should be addressed.
Lines 55-56: It could be good to clarify that the extraction procedures from mineral/rock phases other than quartz also still needs to be developed before these materials can be envisioned for geologic applications.
Lines 80-81: This sentence is unclear: does “well-constrained” refer to the exposure history? Natural variability of what? I don’t understand the point of the sentence.
Lines 81-82: The focus on quartz is also due to the fact that extraction procedures for other minerals or lithologies have not yet been developed or validated.
Line 149: Were elevation differences between individual samples at each site insignificant? Or were the concentrations corrected for them?
Lines 153-154: What is the calibrated value generated by the UWv3 calculator?
Lines 159-165: This should be simplified by saying that you calculate a correction factor P_Qcal/P_Qref , which gives 0.854 and which you multiply by the P_CDpred of all other tested mineral and rock phases. However, how reliable is this correction for other compositions, which are associated with other excitation functions than quartz?
Lines 237-238: Would it be possible to list the elemental 14C production rates, for direct comparison with those given in the Masarik (2002) abstract? This is also what is commonly done for the highly composition dependent 36Cl production.
Related to this, I suggest you should clarify whether or not the software also calculated production rates for compositions that differ from those considered here theoretically.
Caption of Table 1: Shouldn’t this be “Oxide compositions… and accordingly calculated number densities”? (It should be clarified what the numbers are.)
Irene Schimmelpfennig
-
AC2: 'Reply on RC2', Alexandria Koester, 11 Oct 2022
We thank Dr. Irene Schimmelpfennig for her helpful comments to improve the manuscript. We have responded to each comment in detail below
- Lines 55-56: It could be good to clarify that the extraction procedures from mineral/rock phases other than quartz also still needs to be developed before these materials can be envisioned for geologic applications.
We thank the review for their comment. We have clarified this point in the manuscript at the end of our introduction (line 63-64)
Lines 80-81: This sentence is unclear: does “well-constrained” refer to the exposure history? Natural variability of what? I don’t understand the point of the sentence.
Yes, “well-constrained” does refer to the exposure history. We have edited the sentence for clarity.
- Lines 81-82: The focus on quartz is also due to the fact that extraction procedures for other minerals or lithologies have not yet been developed or validated.
We note that the first extraction techniques for in situ 14C utilized whole rock samples (e.g., Jull et al., 1992; 1994) in the introduction and were ultimately abandoned in favor of the simpler quartz systematics. (lines 55-56).
- Line 149: Were elevation differences between individual samples at each site insignificant? Or were the concentrations corrected for them?
In this 14C CRONUS-Earth global calibration from the references cited, there are samples at secular equilibrium along elevation transects that span a broad altitudinal range at a particular latitude. Those samples are incorporated into the estimate of the SLHL production rate. In addition, there are the primary CRONUS-Earth calibration sites with multiple samples that span limited altitudinal ranges. Sample locations (latitude, longitude, and altitude) are of course considered in deriving the SLHL production rate estimates, as those are required input for the scaling model. This dataset will be included in the supplement.
- Lines 153-154: What is the calibrated value generated by the UWv3 calculator?
The output value generated by the UWv3 calculator is 0.868, using dipolar RC parameterization from that calculator’s implementation. This value is the fitting parameter that is multiplied by the reference production rate for 14C, 15.8 atoms/g, which is that derived from the integral of the flux and excitation functions for 14C production from neutron and proton spallation in quartz, at SLHL (P_Qref). This yields a value of 13.7 at/g/y, which is the same value (well within 1 sigma uncertainty) that we derive using a dipolar RC parameterization similar to that in the UWv3 calculator in the manuscript (see line 154) and already mentioned in text (line 156).
- Lines 159-165: This should be simplified by saying that you calculate a correction factor P_Qcal/P_Qref , which gives 0.854 and which you multiply by the P_CDpred of all other tested mineral and rock phases. However, how reliable is this correction for other compositions, which are associated with other excitation functions than quartz?
We prefer to keep the equation grouped as presented because the P_CDpred and the P_Qref are both theoretical - we then multiply that by the geologic calibration of quartz. Algebraically it doesn’t matter of course, it’s just seems more logical to us in that order. Therefore, we prefer to keep the theoretical components together and separate from the geologic component.
The correction is as reliable as possible given our current knowledge of the scaling of fluxes, reaction cross sections, and geologic calibrations. We have attempted to quantify the uncertainties on this in general in the text already. As more excitation functions are measured for the reactions of interest here, and mineral specific geologic production rate calibrations are conducted, our confidence in these corrections will undoubtedly improve.
- Lines 237-238: Would it be possible to list the elemental 14C production rates, for direct comparison with those given in the Masarik (2002) abstract? This is also what is commonly done for the highly composition dependent 36Cl production.
We thank the reviewer for the suggestion and have derived a list of production from each element within the text (shown as atoms g-element-1 yr-1) at a SLHL location, and added discussion in the text of this. We have also provided a table below, which is now Table 6 in the manuscript.
Element
PRSLHL (atoms g-element-1 yr-1)
O
29.01
Si
0.84
Mg
2.19
Al
1.67
Fe
0.10
Na
15.59
K
0.08
Ca
0.06
Ti
0.05
Mn
0.03
P
0.22
- Related to this, I suggest you should clarify whether or not the software also calculated production rates for compositions that differ from those considered here theoretically.
The software framework can take in any XRF elemental analysis for any rock or mineral type. The user can input any elemental oxide percent from any location and calculate a theoretical production rate. We tried to compare predictions for as broad a compositional range as possible. We have added a sentence to line 143 for clarity.
Caption of Table 1: Shouldn’t this be “Oxide compositions… and accordingly calculated number densities”? (It should be clarified what the numbers are.)
The table lists the percentage of oxide compositions for each mineral and rock. These percentages are used to calculate the number densities as in equation 2 (line 139). We have edited the caption for clarity.
While we were at a conference, Dr. Schimmelpfennig suggested in person to include a figure of the production from minerals and rocks from a presentation about this work, so we are including that in the revised manuscript per her request.
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AC2: 'Reply on RC2', Alexandria Koester, 11 Oct 2022
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Alexandria J. Koester and Nathaniel A. Lifton
Alexandria J. Koester and Nathaniel A. Lifton
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