the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Aug 2026
Improving the estimation of high natural luminescence doses using OTOR solutions for SAR-derived data
Abstract. In luminescence dating, dose-response curve fitting is critical to obtain dose estimates that are equivalent to the natural dose. For high natural doses several fitting functions are in use, but dose underestimation remains a common result. To address this, we analyse two functions directly derived from the one trap one recombination centre (OTOR) model alongside the single-saturating exponential function (SSE), typically used for data generated by a single-aliquot regenerative dose protocol (SAR) and, we test fit parameters using a set of natural samples.
Combining theory with empirical evidence we show, in agreement with earlier studies, that OTOR and SSE functions are the same in terms of their parameterisations, with OTOR allowing for one extra degree of freedom represented by the parameter R=An/Am. By allowing R to vary, OTOR produces dose-response curves with high statistical significance. SSE produces dose-response curves that show “early” bending towards a dose plateau because, as theory reveals, it assumes that An/Am is fixed at unity. Empirically however, R values are ~0.26 (quartz) and ~0.40 (K-rich feldspars) confirming the observed sublinear response to increasing doses, which is stronger with quartz than with feldspars. For both dosimeters extracted from our natural samples, the OTOR-derived characteristic saturation dose is 30–50 % higher than the D0 value obtained from the SSE function. We provide full explanation why the D0 parameter is always underestimated for quartz and feldspars. Overall, the OTOR solutions are beneficial, not least due to the physical meaning of the fit parameters derived from the simplest possible model.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Geochronology.
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-2026-4397', Anonymous Referee #1, 04 Sep 2026
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AC1: 'Reply on RC1', Barbara Mauz, 19 Oct 2026
The referee is clearly in favour of the OTOR model and its solutions developed by Pagonis and Lawless. We are glad that we met the referee’s idea about the use of physical models to describe experimental DRCs.
Citation: https://doi.org/10.5194/egusphere-2026-4397-AC1
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AC1: 'Reply on RC1', Barbara Mauz, 19 Oct 2026
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RC2: 'Comment on egusphere-2026-4397', Anonymous Referee #2, 06 Sep 2026
The manuscript “Improving the estimation of high natural luminescence doses using OTOR solutions for SAR-derived data” is a natural continuation of the work of Lawless and Timar-Gabor (2024). The earlier paper introduced the OTORX approach, while this paper goes further by testing how OTOR/OTORX can be used to estimate high natural doses in luminescence dating.
A strong point of the paper is that it combines a simple theoretical model with experimental data. The authors show why the commonly used single-saturating exponential (SSE) may underestimate high doses and how OTOR can provide a better description of the dose-response curve. The results for both quartz and feldspar support this argument.
The comparison with the double-saturating exponential (DSE) is also useful. DSE can fit these data well and can give results similar to OTOR. However, OTOR has the advantage that its parameters have a physical meaning, rather than simply describing the curve as the sum of two exponential components.
Of course, OTOR/OTORX is a simple model and cannot fully describe the physical processes involved in quartz luminescence that are certainly much more complex. The authors also recognise this limitation. Still, I find the approach mathematically elegant. Its simplicity is, in fact, one of its strengths.
Overall, I find the paper interesting, useful and clearly presented. I see no major problem that would prevent its acceptance for publication.
Citation: https://doi.org/10.5194/egusphere-2026-4397-RC2 -
AC2: 'Reply on RC2', Barbara Mauz, 19 Oct 2026
We thank the referee for their positive comment. In fact, we wanted to advance the work provided by Pagonis et al. and by Lawless and Timar-Gabor in such a way that the theory is broadly accessible and that the experimental data demonstrate potential and limit of the fit functions. The R 'Luminescence' software is updated and allows the user to adopt the approach.
Citation: https://doi.org/10.5194/egusphere-2026-4397-AC2
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AC2: 'Reply on RC2', Barbara Mauz, 19 Oct 2026
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RC3: 'Comment on egusphere-2026-4397', Anonymous Referee #3, 02 Oct 2026
This manuscript addresses a highly relevant problem in luminescence dating—the underestimation of equivalent doses when SAR dose-response curves are fitted with the conventional SSE—and it provides a clear, physically based comparison between SSE and OTOR/OTORX solutions. The theoretical demonstration that SSE is a special case of OTOR with R = 1, together with the empirical estimates of R (~0.26 for quartz and ~0.40 for feldspar) and the finding that D63 exceeds D0 by 30–50%, is interesting and potentially useful for high-dose dating. The paper is generally well structured and the conclusions are supported by a substantial dataset. I recommend publication after Minor Revision. My comments and suggestions are provided below for your reference.
(1) Would it be possible to provide a clearer distinction between “long DRCs” and “short DRCs,” for example, based on the maximum laboratory dose and the saturation dose?
(2) The statement that “Data displayed in Table A1 clearly show agreement of De values obtained from OTOR and DSE fits” holds for most samples. However, for samples such as CST_inf63-90 and CST_inf4-11, there are significant differences in De between the two functions. Would it be possible to further explore under what conditions the two functions yield inconsistent results and which one is more reasonable?
(3) Table 2 gives fitted chi-square ratios of SSE to OTOR. It is unclear whether the ratio is calculated as the ratio of the reduced chi-square of SSE to that of OTOR. Since the two functions contain different numbers of parameters, it would be more reasonable to use the ratio calculated from the reduced chi-squares.
(4) Page 2, line 69, redundant opening parentheses.
(5) Inconsistent symbols: Equation (2) uses D63%, whereas Table 2 uses D63.
(6) For the 4–11 µm quartz sample in Figure 7, the OTOR and OTORX functions fail to fit the high-dose data points. Would DSE yield a more precise fit in this situation?
(7) Page 15, lines 359–360: “The data generated in this study suggest ca 10–30% underestimation of De in the dose range 100–1000 Gy (Fig. 8) when using the SSE to construct the DRC.” The intended meaning of “underestimation” here is unclear. Does it mean that the natural dose is underestimated by 10–30% when applying a SSE, or that the De obtained from the SSE fit is 10–30% smaller than that obtained from the OTOR fit? Please clarify the reference value relative to which the underestimation is defined.
Citation: https://doi.org/10.5194/egusphere-2026-4397-RC3 -
AC3: 'Reply on RC3', Barbara Mauz, 19 Oct 2026
We thank the referee for their positive comments and reply as follows:
(1) We agree, a clearer definition of 'long' and 'short' DRC is beneficial. At line 232 we will include a qualitative and quantitative description: a long DRC is one that includes enough data points at high dose that the saturation intensity can be clearly determined. When looking at figure 3a, the DRC should include multiple dose points at D/D63 > 10 to accurately establish the saturation intensity.
(2) The differences are most likely the result of (a) different fit algorithms used by Timar-Gabor et al. (2012) and by us, (b) different aliquot data used to perform the fit algorithms and, (c) the generally (too) small number of aliquot data used to calculate the De. We will point this out in the header of Table A1 – thank you for the advice. The DSE function was not explicitly subject of our study (see reasoning in the introduction including key literature). The negligible difference for sample MV104-11suggests that more aliquot data and, of course, a relatively small De (i.e. interpolation well below saturation) improve the accuracy of the De.
(3) We agree. We have used the reduced chi-square value. We will make this clear in the header of Table 2.
(4) Thanks.
(5) Thanks – we will standardise the symbols.
(6) The two fits displayed in the supplement show negligible difference for the high-dose data points. The DSE function seems to describe the curvature of the DRC poorer than the OTOR function.
(7) Thanks for spotting the ambiguous use of the term ‘underestimation’. In fact, the 2nd formulation applies because the true palaeodose of the samples is unknown. We will rephrase the text in page 15 accordingly.
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AC3: 'Reply on RC3', Barbara Mauz, 19 Oct 2026
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Review of the manuscript equsphere-2026-4397
In this manuscript, the authors report on <<Improving the estimation of high natural luminescence doses using OTOR solutions for SAR-derived data>>. I found this manuscript to be of crucial importance. I fully agree with the authors on the value of exploring exact OTOR solutions and their application to the description of dose–response curves (DRCs) in optically stimulated luminescence (OSL) and stimulated luminescence phenomena more generally. The study demonstrates the benefits of applying physical models to describe experimental DRCs in applications such as dating. I strongly recommend the manuscript for publication.