the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Nov 2025
OSLThermo and ESRThermo: Libraries of codes for trapped-charge thermochronometry
Abstract. Over the past fifteen years, trapped-charge (T-C) thermochronometry has been established as an ultra-low temperature (<80 °C) thermochronometric system. Its novelty is its ability to resolve rock cooling within the final few km of Earth's surface, as well as rock-surface temperature changes since the Last Glacial Maximum to the present day. Deriving temperature histories from the luminescence signals of feldspar minerals, or the electron spin resonance signals of quartz minerals, requires the modelling of both signal accumulation and signal loss in response to mineral exposure to ionizing radiation and temperature, as well as athermal signal losses for feldspar minerals. Two open-source libraries have been developed in MATLAB that allow different numerical models to be used for this purpose; the first is applicable to the infra-red stimulated luminescence (IRSL) of feldspar minerals (OSLThermo) and the second to the electron spin resonance (ESR) signal of quartz minerals (ESRThermo). These libraries have been made available in GITHUB and this contribution describes their broad structure, the T-C models that have been implemented and their practical use.
Codes are available for download on GitHub: https://github.com/GeorginaKing/OSLThermo for luminescence thermochronometry & https://github.com/GeorginaKing/ESRThermo for ESR thermochronometry.
Competing interests: One of the co-author is part of GChron editorial board.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-5474', Jintang Qin, 17 Dec 2025
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AC1: 'Reply on RC1', Chloé Bouscary, 06 Feb 2026
RC1: The potential of trapped-charge systems, e.g., luminescence and ESR, to serve as wide spectrum and highly adaptive thermometer, has been realized by some experimental studies. However, these kind of attempts are far more less than those were expected at the emergence of this promising and unique technique. One barrier leading to this underperformance is the lack of an automatic or semi-automatic program to bridging the experimental data to the thermal information registered. This technique note, as well as the two programs posted, is a timely contribution to the T-C community and the users from a broader field, which I believe will intrigue iterative optimizations to make it be more powerful and robust. The note is well written and easy to follow by readers. I tentatively ran both two programs on my laptop with Matlab 2023b, and they work well in general. Therefore, I'd like to recommend a quick publication of this note and the related programs for more extended application, tests and optimizations, subjecting to minor revisions suggested as follows:
> Answer: We thank the reviewer for this review, and for having tested the MATLAB codes. The comments done will help improve the quality and the clarity of the manuscript, particularly through the addition of the workflow figure that was suggested.
1) I may suggest the authors emphasize the multi-thermometer feature of the T-C system in the introduction, e.g., Qin et al. (2015) Radiation Measurement; King et al. (2016) Quaternary Geochronology, since it is one of the most distinct pros of the T-C system. It is easy to measure in practice and the multi-thermometer strategy would reduce a lot the uncertainty and illness of the inversion problem. Indeed, both two programs take this benefits.
> Answer: We will expand the introduction to emphasise the use, advantages, and utility of the MET technique, particularly in its application as a thermochronometer.
2) The script names and outputs are listed in Table 1, which helps on understanding what we do step by step. To have a pilot view of the whole work flow, I may suggest the authors include a figure to show the logic and data flows of the programs to make readers follow easily, as that done for most of the programs and software.
> Answer: This is an excellent suggestion, thank you. We will add a new schematic figure illustrating the overall workflow, showing how data are input and output from each stage of the MATLAB codes.
3) For section 2.4, I think it is indeed the rate equations for the T-C system under different kinetics rather than anything related to data inversion, which are suggested to move to previous sections. Instead, for the "Data inversion" section here, a general description of the sampling methods, acceptance and convergence criteria as well as framework of uncertainty quantification, is encouraged to be included here.
> Answer: Based on this comment and the other reviewer’s comment, we will rename this section “Rate equations” and present the different rate equations for each combination of trapping and detrapping.
We think that adding a new section that discusses data quality criteria is beyond the scope of the present paper. This is a complex topic that we are currently addressing within a working group for a separate study. Depending on their objectives and their data, users may accept data that we would reject for our own applications. The acceptance criteria already implemented in the codes are discussed in section 5.5 of the manuscript, where we present the Stage 3a_Inversion of the MATLAB code.
4) I ran the ESRThermo demo program on my laptop with Matlab 2023b. The program went well; however, the color plot of Fig. 2 and Fig. 3 does not show as that expected. Please have a check.
> Answer: These codes were design and tested using MATLAB 2024b, we will add a note to the manuscript to clarify that. Some features may not be available in other older versions of MATLAB. We will attempt to modify the codes to ensure consistent behaviour across versions, some differences in colour rendering may remain.
5) Closure temperature is the key parameter for evaluating the sensitivity of T-C system to surface process; meanwhile, it is also crucial for referring the T-C system to other thermo-chronometers. Therefore, if the closure temperature could be evaluated/calculated and shown, it would be of great benefits to colleagues from both the T-C community and broader communities.
> Answer: We do not think that adding closure temperature is a good idea. Contrary to other thermochronometers, trapped-charge thermochronometry has a closure temperature that varies depending on sample, signal measured, exhumation rates, and other internal (mineral specific) and external (e.g., environmental dose rate) parameters. Including closure temperature calculations in these codes could be useful and beneficial for experienced trapped-charge users, but may be misleading and confusing for those new to the method.
6) Line 21, suggest change ‘final’ to ‘uppermost’; line 313, suggest change ‘fit to the natural measured data’ to ‘fitting to the natural data’.
> Answer: We will make the suggested corrections: L.21 will be changed to “uppermost few kilometres”, and fit replaced by “fitting”.
Citation: https://doi.org/10.5194/egusphere-2025-5474-AC1
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AC1: 'Reply on RC1', Chloé Bouscary, 06 Feb 2026
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RC2: 'Comment on egusphere-2025-5474', Nathan Brown, 07 Jan 2026
This contribution by Bouscary and colleagues presents two libraries of MATLAB codes which can be used to translate IRSL or ESR experimental results into plausible cooling or exhumation histories. Several kinetic models for signal accumulation and depletion are included, and the general framework could readily be expanded to include other models. It is a valuable and transparent resource for the trapped charge thermochronology community. Below I suggest some edits, most of which are simple points of clarification.
Line edits:
l.50, 53, and elsewhere: This may seem pedantic, but especially for luminescence measurements, I recommend against stating that we measure trapped-charge concentrations. We measure luminescence intensity, which ought to be proportional to the concentration of charge carriers that radiatively recombine during a given experiment. But that number may be only indirectly related to the concentration of trapped charges which accumulate during geologic history. For example, if the number of traps or centers evolves during an experiment. I recommend rephrasing to be something like: we measure the natural luminescence intensity in response to the geologic history as well as the intensity in response to laboratory doses at room temperature.
l.57: Please specify here that the apparent N value may depend on the underlying dose rate.
l.60: Recommended rephrase: "decay of the luminescence or ESR signals in response to storage at elevated temperatures."
l.80, 82: Please differentiate between these as the attempt-to-escape and attempt-to-tunnel frequency factors, and please cite Huntley (2006) for the assumed value of 3e15 s^-1. Note also that 10^15 has an incorrect negative sign in the exponent.
l.89: While I don't think the authors need to dwell on this point, I do think it is worth adding a statement here that states explicitly that at present there is no consensus among the community on which kinetic models perform best.
l.104: Suggested addition: "correcting the dose response data"
l.106: On first reading, I think I misinterpreted this point to be about how the user constrains saturation using the laboratory dose response curve and the natural signal intensity. But I think the authors are instead making the point that many natural samples should be considered to be in field saturation, and that this precludes applying trapped charge thermochronology in many geologic contexts. Perhaps the authors could differentiate between these ideas briefly here.
l.111: Suggested addition: "after effective fading time"
l.113: Perhaps replace 1.8 with z: "where z is the rate of change of trap lifetime (assumed to be 1.8; Huntley, 2006; Jain et al., 2012; 2015)" While ordinarily 1.8 seems to be a good choice, experiments can give a range of values (ex. 1-5 in Jain et al., 2015).
l.143: For Eq. 6, the exponent should be located between the two right parentheses.
l.147: Eq. 7 is presented in a strange way. The fractional saturation is not approximately the equivalent dose value, it is proportional to it. If the fractional saturation were 0.15 (dimensionless) and the equivalent dose were 500 Gy, these two numbers are not similar and one has a unit. It would also make sense to add a pre-exponential multiplier to this expression also, for parallelism with the other expressions and for dimensional consistency.
l.169: Might note that if beta is fixed at 1, equation 1 is undefined.
l.186: I think it would be valuable to include the differential forms of the luminescence models as well, for completeness in this section. Equations 8, 10, and 11 suffice for isothermal or fading experiments, but for inversions, the differential forms are used, so they should ideally be listed here also. And because these choices of growth and decay functions are 'modular' in nature (ex. one could choose either SAR or GOK for growth and GOK or GAUSS for decay, either for an OSL sample or an ESR sample), I would suggest presenting each loss and gain differential equation individually, rather than the current framing of Eqs. 13 and 14, which present only two permutations of these choices.
l.188: Somewhat related to the previous comment, this statement seems prone to misinterpretation. If users were to fit an isothermal decay experiment using the BTS model, they would derive some E_t value. That E_t value would be inappropriate in Equation 1, as written. In other words, it would be less ambiguous if the authors provided some generalized form of the equation: change in [n-tilde] through time equals accumulation term minus loss term(s), where accumulation and loss terms can take several forms. Otherwise, some readers might assume Eq. 1 (as written) is always the form to be used when inverting for thermal history. It should be clear that whichever model components are selected to determine kinetic parameters from experimental datasets must be the same expressions and parameters used when performing the thermal history inversion.
l.192: How is the distribution of activation energies defined for the case of ESR thermal loss modeling?
l.196: Here, as with Eq. 7, I recommend rewriting the equation in terms of proportionality not approximation.
l.214: I recommend simply defining 'effective fading time' for the reader here. The Aitken book is a sensible reference to give, but many readers may not have easy access to this book. It would also be helpful to give a simple description of what effective fading time means: some fading happens during irradiation, so to accurately quantify the effective time that a sample has been fading, one must add a bit more time between when the laboratory dosing period ended and when the IRSL stimulation began. That extra time is the dose duration normalized by Euler's number, e ~ 2.718.
l.217: Optional suggestion to add a statement like this: "Note that Analyst t* values are reported in units of hrs and the Excel input sheet used here requires units of ks." The authors already state these units, but this would be an easy mistake to make.
l.315: Does M need to be summed for all IRSL signals considered? Also, the nomenclature of [sigma][n-tilde]_nat could be misunderstood to mean the product of [sigma] and [n-tilde]_nat. The authors might consider putting [n-tilde]_nat as a compound subscript of [sigma]
l.331: Could the authors please expand on how this user-prescribed time-temperature history would be input? For example, would the user still need to run the Stage3a_Inversion code? An example line of code to define an arbitrary history would be useful.
l.351: Should this read "time-depth histories" rather than "time-temperature" histories?
Citation: https://doi.org/10.5194/egusphere-2025-5474-RC2 -
AC2: 'Reply on RC2', Chloé Bouscary, 06 Feb 2026
RC2: This contribution by Bouscary and colleagues presents two libraries of MATLAB codes which can be used to translate IRSL or ESR experimental results into plausible cooling or exhumation histories. Several kinetic models for signal accumulation and depletion are included, and the general framework could readily be expanded to include other models. It is a valuable and transparent resource for the trapped charge thermochronology community. Below I suggest some edits, most of which are simple points of clarification.
> Answer: We thank the reviewer for their careful reading of the manuscript and their review. The comments will improve the clarity and precision of the manuscript, particularly with respect to terminology, and equations.
Line edits:
L.50, 53, and elsewhere: This may seem pedantic, but especially for luminescence measurements, I recommend against stating that we measure trapped-charge concentrations. We measure luminescence intensity, which ought to be proportional to the concentration of charge carriers that radiatively recombine during a given experiment. But that number may be only indirectly related to the concentration of trapped charges which accumulate during geologic history. For example, if the number of traps or centers evolves during an experiment. I recommend rephrasing to be something like: we measure the natural luminescence intensity in response to the geologic history as well as the intensity in response to laboratory doses at room temperature.
> Answer: We acknowledge that the relationship between measured signal intensity and trapped-charge population may vary between natural and laboratory conditions, however this assumption is made to enable the use of trapped-charge data in thermochronometric studies. While we recognise the importance of clarifying this specificity and will explicitly note it in the introduction, we will retain the term “trapped-charge” throughout the remainder of the manuscript as it remains a widely accepted term for describing luminescence and ESR thermochronometry.
L.57: Please specify here that the apparent N value may depend on the underlying dose rate.
> Answer: We disagree. Whilst the apparent N in a fading system will depend on the dose rate and the rate of athermal detrapping, we correct for this (following Kars et al., 2008; Huntley, 2006) to provide N. n/N is however affected by the dose rate.
L.60: Recommended rephrase: "decay of the luminescence or ESR signals in response to storage at elevated temperatures."
> Answer: Done, this will now read:
“The second experiment (Fig. 1C and Fig. 1F) measures the thermal decay of the luminescence or ESR signals in response to storage at elevated temperature.”
L.80, 82: Please differentiate between these as the attempt-to-escape and attempt-to-tunnel frequency factors, and please cite Huntley (2006) for the assumed value of 3e15 s^-1. Note also that 10^15 has an incorrect negative sign in the exponent.
> Answer: Done, this will now read:
“The second term describes thermal loss at a given temperature, T (K), where s (s-1) is the attempt-to-escape frequency factor, Ea (eV) is the activation energy of the electron trap, kb (eV·K-1) is the Boltzmann constant, and β the order of kinetics 1. The final term describes athermal loss where s˜(3 x 1015 s-1; Huntley, 2006) is an attempt-to-tunnel frequency factor, ρ' is a dimensionless description of the density of recombination centres and r' is a dimensionless distance between traps and recombination centres (Huntley, 2006).”
Thank you for spotting the incorrect negative sign in the exponent of s˜.
L.89: While I don't think the authors need to dwell on this point, I do think it is worth adding a statement here that states explicitly that at present there is no consensus among the community on which kinetic models perform best.
> Answer: Thank you for this suggestion. We will add a few sentences stating that: “At present, there is no consensus within the community regarding which kinetic models perform best, or how to evaluate best performance. Therefore, the choice of models is left the user. Also, note that only the most commonly used models are currently implemented, and that the OSLThermo and ESRThermo libraries will evolve as new kinematic models are developed and incorporated in the future.”
L.104: Suggested addition: "correcting the dose response data"
> Answer: Not sure to add this, as we also use the fading data to correct the isothermal decay experiments.
L.106: On first reading, I think I misinterpreted this point to be about how the user constrains saturation using the laboratory dose response curve and the natural signal intensity. But I think the authors are instead making the point that many natural samples should be considered to be in field saturation, and that this precludes applying trapped charge thermochronology in many geologic contexts. Perhaps the authors could differentiate between these ideas briefly here.
> Answer: Thanks for highlighting this ambiguity. We will revise this section of the text to explicitly distinguish between (1) constraining saturation in the laboratory, and (2) the more fundamental limitation that many natural samples may already be in field saturation, which precludes the application of trapped-charge thermochronometry to certain geological settings.
L.111: Suggested addition: "after effective fading time"
> Answer: This will be added as suggested.
“The rate of anomalous fading induced signal loss after effective fading time can be calculated from:
n(t*) = n(0) . φ (t*) (2)
where n(0) is the initial trapped-charge concentration at time 0, n(t*) is the signal remaining after effective fading time t* (s) […]”
L.113: Perhaps replace 1.8 with z: "where z is the rate of change of trap lifetime (assumed to be 1.8; Huntley, 2006; Jain et al., 2012; 2015)" While ordinarily 1.8 seems to be a good choice, experiments can give a range of values (ex. 1-5 in Jain et al., 2015).
> Answer: We will adopt this notation, thanks.
" φ (t*) = exp(-ρ' ln(z s˜ t*)^3) (3)
where z is the rate of change of trap lifetime (assumed to be 1.8, from Huntley, 2006; note that other experimental values can be observed, e.g., Jain et al., 2015) […]”
L.143: For Eq. 6, the exponent should be located between the two right parentheses.
> Answer: Thanks for spotting this error, we will correct the equation.
L.147: Eq. 7 is presented in a strange way. The fractional saturation is not approximately the equivalent dose value, it is proportional to it. If the fractional saturation were 0.15 (dimensionless) and the equivalent dose were 500 Gy, these two numbers are not similar and one has a unit. It would also make sense to add a pre-exponential multiplier to this expression also, for parallelism with the other expressions and for dimensional consistency.
> Answer: We agree that Eq. 7 should be express in terms of proportionality. And we will add a pre-exponential multiplier to be consistent with the other SAR model formulations.
L.169: Might note that if beta is fixed at 1, equation 1 is undefined.
> Answer: We will do that.
L.186: I think it would be valuable to include the differential forms of the luminescence models as well, for completeness in this section. Equations 8, 10, and 11 suffice for isothermal or fading experiments, but for inversions, the differential forms are used, so they should ideally be listed here also. And because these choices of growth and decay functions are 'modular' in nature (ex. one could choose either SAR or GOK for growth and GOK or GAUSS for decay, either for an OSL sample or an ESR sample), I would suggest presenting each loss and gain differential equation individually, rather than the current framing of Eqs. 13 and 14, which present only two permutations of these choices.
> Answer: The differential forms of the growth and decay models used in the inversions will be more explicitly listed. Based on this comment and another from a reviewer, we will modify section 2.4 to be titled “Rate equations” and present the different rate equations for each combination of trapping and detrapping.
L.188: Somewhat related to the previous comment, this statement seems prone to misinterpretation. If users were to fit an isothermal decay experiment using the BTS model, they would derive some E_t value. That E_t value would be inappropriate in Equation 1, as written. In other words, it would be less ambiguous if the authors provided some generalized form of the equation: change in [n-tilde] through time equals accumulation term minus loss term(s), where accumulation and loss terms can take several forms. Otherwise, some readers might assume Eq. 1 (as written) is always the form to be used when inverting for thermal history. It should be clear that whichever model components are selected to determine kinetic parameters from experimental datasets must be the same expressions and parameters used when performing the thermal history inversion.
> Answer: Initially, we believed presenting the equation terms separately was a good idea, but now realise it might be better to present the rate equations for each combination of trapping and detrapping (as suggested in the previous comment). This revised manuscript and equations will better reflect the structure of the inversion procedure and enhance clarity for users wishing to implement or modify specific kinetic parameters.
L.192: How is the distribution of activation energies defined for the case of ESR thermal loss modeling?
> Answer: In the case of ESR thermal loss, the activation energies are defined in the same way as for thermal loss in IRSL. The code assumes that many traps/defects exist, each with a slightly different activation energy (Ea), ranging from 0 and 9 eV. These energies follow a Gaussian distribution. The observed ESR thermal loss is then the sum of contributions from all these traps.
L.196: Here, as with Eq. 7, I recommend rewriting the equation in terms of proportionality not approximation.
> Answer: We will revise the equation as suggested.
L.214: I recommend simply defining 'effective fading time' for the reader here. The Aitken book is a sensible reference to give, but many readers may not have easy access to this book. It would also be helpful to give a simple description of what effective fading time means: some fading happens during irradiation, so to accurately quantify the effective time that a sample has been fading, one must add a bit more time between when the laboratory dosing period ended and when the IRSL stimulation began. That extra time is the dose duration normalized by Euler's number, e ~ 2.718.
> Answer: We will include a concise definition of “effective fading time (t*)” directly in the text, including a brief explanation of how it is calculated, rather than relying solely on the reference to Aitken (1985).
L.217: Optional suggestion to add a statement like this: "Note that Analyst t* values are reported in units of hrs and the Excel input sheet used here requires units of ks." The authors already state these units, but this would be an easy mistake to make.
> Answer: We will add the suggested note warning users of this difference in units.
L.315: Does M need to be summed for all IRSL signals considered? Also, the nomenclature of [sigma][n-tilde]_nat could be misunderstood to mean the product of [sigma] and [n-tilde]_nat. The authors might consider putting [n-tilde]_nat as a compound subscript of [sigma]
> Answer: Right now, in the MATLAB code, M is averaged over all the IRSL or ESR signals considered. However, this can be modified by the users, for example to calculate M for individual signals only. In this case, different cooling histories could be obtained for each of the considered signals. We chose to average the misfit across all the considered signals as they are expected to record the same cooling history, and using multiple thermochronometric signals for the same sample improves the fit of modelled thermal histories and reduced uncertainty. We will add a note on this averaging in the manuscript.
We also will update the notation to to avoid confusion with a product.
L.331: Could the authors please expand on how this user-prescribed time-temperature history would be input? For example, would the user still need to run the Stage3a_Inversion code? An example line of code to define an arbitrary history would be useful.
> Answer: We can expend this part of the manuscript to present how the time-temperature histories are computed, which will be the lines of the code that must be modified to input user-prescribed time-temperatures histories.
Any change to input parameters must be made in the Stages a (2a, 3a, 4a), as the Stages b (2b, 3b, 4b) scripts are solely used for plotting.
We also plan to add a workflow figure presenting all the input and output parameters at each stage of the MATLAB code, which should help users understand the code structure, and how it can be modified.
L.351: Should this read "time-depth histories" rather than "time-temperature" histories?
> Answer: Thanks for spotting this error, we will change "time-temperature histories” to "time-depth histories".
Citation: https://doi.org/10.5194/egusphere-2025-5474-AC2
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AC2: 'Reply on RC2', Chloé Bouscary, 06 Feb 2026
Model code and software
OSLThermo library Chloé Bouscary and Georgina E. King https://github.com/GeorginaKing/OSLThermo
ESRThermo library Chloé Bouscary and Georgina E. King https://github.com/GeorginaKing/ESRThermo
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- 1
The potential of trapped-charge systems, e.g., luminescence and ESR, to serve as wide spectrum and highly adaptive thermometer, has been realized by some experimental studies. However, these kind of attempts are far more less than those were expected at the emergence of this promising and unique technique. One barrier leading to this underperformance is the lack of an automatic or semi-automatic program to bridging the experimental data to the thermal information registered. This technique note, as well as the two programs posted, is a timely contribution to the T-C community and the users from a broader field, which I believe will intrigue iterative optimizations to make it be more powerful and robust. The note is well written and easy to follow by readers. I tentatively ran both two programs on my laptop with Matlab 2023b, and they work well in general. Therefore, I'd like to recommend a quick publication of this note and the related programs for more extended application, tests and optimizations, subjecting to minor revisions suggested as follows:
1) I may suggest the authors emphasize the multi-thermometer feature of the T-C system in the introduction, e.g., Qin et al. (2015) Radiation Measurement; King et al. (2016) Quaternary Geochronology, since it is one of the most distinct pros of the T-C system. It is easy to measure in practice and the multi-thermometer strategy would reduce a lot the uncertainty and illness of the inversion problem. Indeed, both two programs take this benefits.
2) The script names and outputs are listed in Table 1, which helps on understanding what we do step by step. To have a pilot view of the whole work flow, I may suggest the authors include a figure to show the logic and data flows of the programs to make readers follow easily, as that done for most of the programs and software.
3) For section 2.4, I think it is indeed the rate equations for the T-C system under different kinetics rather than anything related to data inversion, which are suggested to move to previous sections. Instead, for the "Data inversion" section here, a general description of the sampling methods, acceptance and convergence criteria as well as framework of uncertainty quantification, is encouraged to be included here.
4) I ran the ESRThermo demo program on my laptop with Matlab 2023b. The program went well; however, the color plot of Fig. 2 and Fig. 3 does not show as that expected. Please have a check.
5) Closure temperature is the key parameter for evaluating the sensitivity of T-C system to surface process; meanwhile, it is also crucial for referring the T-C system to other thermo-chronometers. Therefore, if the closure temperature could be evaluated/calculated and shown, it would be of great benefits to colleagues from both the T-C community and broader communities.
6) line 21, suggest change ‘final’ to ‘uppermost’; line 313, suggest change ‘fit to the natural measured data’ to ‘fitting to the natural data’.