the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Feb 2026
Past the first date: Resolving successive lead-loss episodes in zircon
Abstract. Zircon uranium–lead (U–Pb) geochronology is a cornerstone of Earth science for resolving the timing of deep-time processes, yet the U–Pb system in zircon does not always behave as a closed chronometer. Selective loss of radiogenic Pb can shift isotopic ages and generate discordant analyses that record later alteration, fluid-rock interaction, or heating. Many zircon datasets preserve evidence for more than one Pb-loss episode, yet many Pb-loss modelling approaches return a single "best" loss time. Here, we extend the concordant-discordant comparison (CDC) framework to recover multi-episode Pb-loss histories by using concordant analyses as a reference age distribution and scoring candidate Pb-loss times by how well reconstructed discordant ages reproduce that reference.
The updated workflow can partition discordant analyses into internally coherent sub-arrays, retain reproducible local optima across Monte Carlo realisations rather than collapsing each realisation to a single optimum, and summarise statistically supported candidates as an ensemble catalogue with empirical 95 % uncertainty intervals and support values that quantify run-to-run stability.
Synthetic benchmarks spanning single-stage and two-stage discordance geometries across three scatter tiers show that CDC achieves lower overall median absolute error and higher event-wise coverage than a discordia-likelihood discordance-dating (DD) approach. CDC performs best for single-stage benchmarks and for mixtures in which episodes remain well separated, whereas DD variants are more accurate and attain higher coverage in higher-scatter two-stage cases where likelihood surfaces are broad and competing modes occur. By reporting reproducible local optima rather than a single optimum, the CDC ensemble catalogue enables explicit recovery of multi-episode Pb-loss histories from discordant zircon U–Pb populations. Future work will focus on strongly overlapping multi-episode scenarios that remain difficult to deconvolve when candidate Pb-loss ages are tested one at a time.
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RC1: 'Comment on egusphere-2026-280', Donald Davis, 19 Feb 2026
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AC1: 'Reply on RC1', Lucy Mathieson, 31 Mar 2026
This manuscript presents a statistical approach, which the authors call concordant–discordant comparison (CDC), for processing discordant U–Pb data to derive estimates for discrete ages of partial resetting. Several efforts to derive useful geologic information from discordant data sets have previously been published by the authors and others. This presents an approach for treating data sets that involve multiple secondary ages. It seems like an impressive application of statistical theory that could lead to useful information if the hypotheses on which it is based were correct.
We thank Dr. Davis for this careful review and for engaging with the central assumptions of the manuscript. We agree that the usefulness of CDC depends on the geological circumstances under which it is applied. Accordingly, we will clarify the method’s assumptions and limitations more explicitly and frame recovered ages as candidate Pb-loss ages that require independent geological support. We will provide additional examples demonstrating the geological use of the tool.
In my opinion, however, at least one assumption is generally not correct in the case of zircon, as explained below.
The problem of zircon U–Pb discordance from what should be a robust mineral was a puzzle to early geochronologists. We now know that the chemical and mechanical stability of zircon (ZrSiO4) derives from its structure and not its chemical composition, as in the case of baddeleyite (ZrO2). The zircon structure is subject to degradation due to alpha recoil events following decay of U and its alpha-emitting daughter radionuclides. A high alpha dosage in an old or very high-U zircon gradually destroys the crystal structure leaving a disordered or metamict state. This significantly expands the volume of the crystal which, in the case of a non-uniform U distribution, introduces internal stress that cracks the crystal. This by itself does not affect the U–Pb budget. I have obtained concordant data from many uniformly highly damaged zircon crystals after abrading off the surfaces. However, any water that encounters metamict domains results in alteration and loss of most or all radiogenic Pb accumulated up to that time. Fluid can enter the crystal along cracks produced by metamictization but alteration is commonly incomplete, which suggests that the source of fluid is often the small amount of magmatic water left over from magma crystallization. Most analyses are done on an assemblage of altered and unaltered domains within the same grain, and data often scatter about a discordia line between the crystallization age and a younger age of alteration. The age of Pb loss may be controlled by the time at which a given crystal domain achieves sufficient radiation damage to allow alteration, which should be variable since zircon is commonly zoned in U. In such a case one should see an array of discordant data fanning out from an older age on concordia representing crystallization and bounded by a lower intercept age of zero, which would be a horizontal line on the inverse concordia plots used by the authors. In cases where older inherited zircon has been reheated in a younger magma or subjected to a prolonged high-temperature metamorphic event, the data may form a discrete array where lower and upper intercept ages represent real geologic events but variable low-temperature Pb loss will be superimposed if later alteration has not been completely removed.
We thank Dr. Davis for this detailed mechanistic discussion of zircon discordance. We agree that much zircon U–Pb discordance can reflect progressive radiation-damage-assisted fluid access, incomplete alteration, and mixing of altered and unaltered domains within a single analytical volume. In such cases, discordance need not preserve a small set of discrete recoverable Pb-loss ages and may instead produce fan-like or otherwise diffuse arrays.
To address this concern, we will add a benchmark case in which discordant analyses fan toward 0 Ma without converging on a common lower intercept. In that geometry, no discrete interior Pb-loss age would be reported under the reporting criteria. We will also make explicit that flat, monotonic, or boundary-dominated responses are treated conservatively as unresolved rather than as evidence for a discrete event. In addition, we will clarify that progressive damage-threshold behaviour and later low-temperature Pb-loss superimposed on earlier reheating or inherited histories are genuine limitations of the method.
The authors first hypothesis is the assumption that alteration-related discordance in zircon represents disturbance caused by an interesting (regional) geologic event, which in some cases may be true. The second hypothesis is that such data reflect a series of Pb loss lines having a single upper concordia intercept age and a discrete number of lower intercept ages, with the data being otherwise scattered only by measurement errors.
We thank Dr. Davis for identifying this point, which required clarification. We agree that CDC relies on a simplified geometric approximation. For each trial lower-intercept age, discordant analyses are back-projected to concordia and the resulting reconstructed upper-intercept age distribution is compared with the empirical age distribution of the concordant subset. The assumption is therefore a chord-based Pb-loss model used to assess candidate disturbance ages.
However, the method does not fit each discordant analysis to one of a small number of discrete discordia lines, nor does it require a single upper-intercept age for the whole dataset. Instead, the concordant analyses provide an empirical reference distribution that may itself be mixed, and the comparison is performed at the level of the full age distributions. Candidate Pb-loss ages are inferred from recurring maxima on the CDC surface across Monte Carlo realisations rather than from a final assignment of individual analyses to explicit fitted chords.
In a revised manuscript, we will clarify these assumptions more explicitly, including the chord-based approximation, the need for appropriate common-Pb correction or filtering, and the dependence on a defensible concordant reference population. We will also remove the discordant clustering step from the workflow and frame recovered peaks as candidate Pb-loss ages whose geological significance must be assessed using petrographic, textural, and regional context.
They seem to successfully test the method by generating a random synthetic data set according to the above constraints and extracting the ages of disturbance. It seems to me that a major problem with natural samples comes from the fact that in most cases one does not sample discrete Pb-loss domains, even with in-situ methods. The scale of most sampling probably includes multiple domains that may have lost Pb at different times. This should effectively destroy information on discrete lower intercept ages if it were present to begin with. The authors could challenge this view if they could apply their method to a natural data set where results (ages of disturbance) are clear and correlate with already known events. They have attempted this in a few previous publications using a previous version of the CDC approach, but it is not clear at least to me that resetting events were clearly resolved and if the present procedure would work any better.
We agree that analytical mixing of disturbed and undisturbed zircon domains is a major challenge for any attempt to recover geological information from discordant data, and in some datasets it may destroy recoverable lower-intercept structure. A revised manuscript will therefore not assume that each discordant analysis samples a single discrete Pb-loss domain, or imply that every natural zircon dataset should yield recoverable discrete disturbance ages.
However, we maintain that in-situ datasets can preserve geologically useful information in the discordant component and that this can be accessed. Especially in texturally targeted analyses, some zircon populations may retain enough discordant structure for candidate Pb-loss ages to be recovered at the population level, even where individual analyses are not pure single-stage reset domains. To address this concern, we will replace the earlier illustrative Gawler Craton example with a case study from the South West Terrane and western Youanmi region of the Yilgarn Craton, Western Australia, comprising 27 samples (743 spot analyses) in total. Sample 224351 yields a reproducibly bimodal ensemble surface with peaks at 786 Ma (support 96%) and 927 Ma (support 97%). These align with distinct peaks in a regional Pb-loss distribution compiled from the other 26 samples and broadly overlap independently compiled magmatic crystallisation, metamorphic, and cooling ages from the western Yilgarn margin. Under the legacy single-optimum workflow, this sample would have returned a single age of 916 Ma with a 95% interval of 776–1007 Ma, spanning both peaks. We present this as an example in which the updated workflow yields geologically plausible candidate Pb-loss ages in a natural dataset, not as proof that all discordant zircon populations preserve isolated single-stage reset histories. We include a preview of this proposed case study as a supplement pdf to this response because Dr. Davis specifically asked whether the updated workflow could be demonstrated on a natural dataset with independently known events.
I admire the work involved in developing this approach and am sorry to be so critical of its potential usefulness for zircon data, but any statistical analysis is only as good as the assumptions on which it is based. I hope that the authors can show my opinions to be wrong.
We entirely agree with Dr. Davis that any statistical analysis is only as good as the assumptions on which it rests, and we sincerely appreciate the critical comments which will greatly improve our contribution. In response, a revised manuscript will be intentionally narrower and more conservative. We will state the assumptions and failure modes of CDC more explicitly, emphasise conditions under which the method should abstain, and restrict geological interpretation to statistically supported candidate Pb-loss ages that are evaluated against independent context.
One additional minor point is to not use the word “deconvolve” (lines 18 and 76). Convolution is a specific mathematical procedure that is not relevant in this application.
We agree and we will remove the word “deconvolve” throughout and replace it with wording that is more appropriate in this context, for example “separate”.
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AC1: 'Reply on RC1', Lucy Mathieson, 31 Mar 2026
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RC2: 'Comment on egusphere-2026-280', Anonymous Referee #2, 26 Feb 2026
The presence of discordance and Pb loss is an unavoidable aspect of many U–Pb datasets. In igneous and metamorphic contexts, Pb loss generates discordia lines in U–Pb isotope space, whose upper and lower intercepts constrain both the protolith age and the timing of Pb loss.
In detrital settings, where the goal of U–Pb geochronology is to obtain age spectra, the traditional strategy for dealing with discordance has been to reject discordant analyses based on a chosen criterion and to retain only concordant data. This approach can be frustrating when most analysed grains are discordant. Moreover, excluding discordant analyses may bias the chronological record, potentially obscuring source regions that predominantly yield discordant zircons.
It is therefore unsurprising that geochronologists have sought alternative approaches. Reimink et al. (2016) proposed a numerical algorithm that fits lines through clusters of discordant U–Pb data and identifies the lower and upper intercepts of the lines passing through the largest number of analyses.
The authors of the present manuscript have published several papers on this topic (Mathieson et al., 2025a, 2025b), modifying the approach of Reimink et al. (2016) by first considering the distribution of the concordant subpopulation and using its modes to constrain the upper intercepts before searching for lower intercepts. They refer to this as the "Concordant Discordant Comparison" (CDC) approach.
Pb loss is linked to radiation damage, as clearly explained by Don Davis in his review of the manuscript. This process can produce fanning arrays of discordant zircons (Case 3 of 7 in the manuscript). Reimink et al. (2025) dated a quartzite by fitting the lower intercept of such a fanning array of discordant zircons that were reset by a metamorphic event approximately 25 Ma ago.
Andersen et al. (2019, 2022) demonstrated that tectonically driven metamorphism is not required to induce Pb loss. Even surface weathering can cause a metamict zircon to lose its Pb, leading to the well-known phenomenon of apparent "modern Pb loss". Andersen et al. (2019, 2022)'s examples likewise resemble fanning arrays of discordant data with a single lower intercept and multiple upper intercepts.
In their new manuscript, Mathieson and Kirkland propose a generalisation of the CDC method to accommodate multiple episodes of Pb loss. These are summarised in Figures 1 and 2 as seven "Cases". Case 1 corresponds to a simple discordia line, solvable by York regression. Case 3 represents the fanning arrays previously discussed by Reimink et al. (2025) and Andersen et al. (2019, 2022).
Cases 2, 4, 5, 6, and 7 are new and involve various combinations of upper and lower intercepts. I have several concerns regarding these scenarios and the algorithm used to resolve them:
1. Although the five new scenarios are straightforward to simulate numerically, they are problematic from a geological perspective. It is difficult to envisage a Pb-loss event that completely resets one zircon population but leaves another unaffected. The authors suggest that such discrete arrays could correspond to zircon cores and rims. However, I have not encountered such clear separation between two populations in real datasets.
2. The manuscript presents only one real-world example (inset in Figure 8), which is not particularly convincing. There is no demonstration that the two arrays are statistically robust. Furthermore, roughly one third of the discordant analyses fall on neither array. If this is the strongest available example, then fitting multiple arrays is a straw man problem.
3. In the title of Mathieson et al. (2025b), the authors celebrate their algorithm's ability to turn "trash into treasure". This is acceptable only if there is a reliable way to distinguish trash from treasure. I am concerned that such a mechanism is lacking in the new algorithm. Broad application of this method risks introducing spurious interpretations into the literature. I do not question the quality of the Gawler Craton data shown in Figure 8; I assume the isotopic ratios are accurately plotted on the concordia diagram. However, in this case, the discordant analyses appear to contain little or no chronometric information. It would be risky to claim otherwise.
4. The description of the algorithm indicates that the fitting procedure requires the user to define a modelling window for the upper intercepts to guide estimation of the lower intercepts. Zircons are classified as "concordant" or "discordant" based on an arbitrary concordance threshold. Discordant grains are then deemed "valid" or "invalid" depending on whether a line connecting them to a proposed lower intercept falls inside or outside the modelling window. These binary classifications impose an artificial dichotomy on what is inherently continuous data. In reality, concordance and validity exist along a spectrum. The authors have developed a highly sophisticated algorithm, but sophistication alone does not guarantee correctness.
Unfortunately, I do not think that this contribution is ready for publication.
References:
Andersen T, Elburg MA, Magwaza BN. Sources of bias in detrital zircon geochronology: Discordance, concealed lead loss and common lead correction. Earth-Science Reviews. 197:102899, 2019.
Andersen T, Elburg MA. Open-system behaviour of detrital zircon during weathering: an example from the Palaeoproterozoic Pretoria Group, South Africa. Geological Magazine.159(4):561-76, 2022.
Mathieson, L. M., Kirkland, C., Bodorkos, S., and Daggitt, M.: From discordance to discovery: extracting fluid–rock interac-
tion timescales through zircon U–Pb analyses in the Arunta region, Central Australia, Journal of the Geological Society, 182,
https://doi.org/10.1144/jgs2024-111, 2025a.Mathieson, L. M., Kirkland, C., and Daggitt, M.: Turning trash into treasure: Extracting meaning from discordant data via a dedicated875
application, Geochemistry, Geophysics, Geosystems, 26, https://doi.org/10.1029/2024GC012066, 2025bReimink, J. R., Davies, J. H., Waldron, J. W., and Rojas, X.: Dealing with discordance: a novel approach for analysing U–Pb detrital zircon
datasets, Journal of the Geological Society, 173, 577–585, https://doi.org/10.1144/jgs2015-114, 2016.Reimink, J. R., Beckman, R., Schoonover, E., Lloyd, M., Garber, J., Davies, J. H. F. L., Cerminaro, A., Perrot, M. G., and Smye, A.:
Discordance dating: A new approach for dating alteration events, Geochronology, 7, 369–385, https://doi.org/10.5194/gchron-7-369-2025,
2025.Citation: https://doi.org/10.5194/egusphere-2026-280-RC2 -
AC2: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
The presence of discordance and Pb loss is an unavoidable aspect of many U–Pb datasets. In igneous and metamorphic contexts, Pb loss generates discordia lines in U–Pb isotope space, whose upper and lower intercepts constrain both the protolith age and the timing of Pb loss.
In detrital settings, where the goal of U–Pb geochronology is to obtain age spectra, the traditional strategy for dealing with discordance has been to reject discordant analyses based on a chosen criterion and to retain only concordant data. This approach can be frustrating when most analysed grains are discordant. Moreover, excluding discordant analyses may bias the chronological record, potentially obscuring source regions that predominantly yield discordant zircons.
It is therefore unsurprising that geochronologists have sought alternative approaches. Reimink et al. (2016) proposed a numerical algorithm that fits lines through clusters of discordant U–Pb data and identifies the lower and upper intercepts of the lines passing through the largest number of analyses.
The authors of the present manuscript have published several papers on this topic (Mathieson et al., 2025a, 2025b), modifying the approach of Reimink et al. (2016) by first considering the distribution of the concordant subpopulation and using its modes to constrain the upper intercepts before searching for lower intercepts. They refer to this as the "Concordant Discordant Comparison" (CDC) approach.
We thank the reviewer for this summary. We think it is very important to clarify one point regarding method lineage. The concordant–discordant comparison (CDC) approach was not developed as a modification of Reimink et al. (2016). CDC has its own development history, initially preceeding Reimink et al. (2016). Beginning with Morris et al. (2015) and subsequently expanded in Kirkland et al. (2017, 2020) and in our later work (Mathieson et al., 2025a,b). The CDC and Reimink et al. (2016) approaches are related in motivation only (namely, to recover useful age information from discordant datasets) but they are entirely methodologically distinct.
In CDC, the concordant population is used as an empirical reference for the expected upper-intercept age structure. For each candidate Pb-loss age, discordant analyses are back-projected to reconstructed upper-intercept ages, and those reconstructed ages are then compared probabilistically with the observed concordant population. Reimink et al. (2016) instead evaluate combinations of upper and lower intercepts directly in concordia space and identify those solutions that best fit the discordant data. Thus, Reimink et al. (2016) method is a geometric approach, whereas the CDC is a Monte Carlo implementation of a Bayesian approach. The present manuscript therefore does not modify the Reimink et al. method but instead extends the CDC workflow from a single-optimum summary to an ensemble-based multi-peak procedure. We consider this a significant useful advance.
In their new manuscript, Mathieson and Kirkland propose a generalisation of the CDC method to accommodate multiple episodes of Pb loss. These are summarised in Figures 1 and 2 as seven "Cases". Case 1 corresponds to a simple discordia line, solvable by York regression. Case 3 represents the fanning arrays previously discussed by Reimink et al. (2025) and Andersen et al. (2019, 2022).
Cases 2, 4, 5, 6, and 7 are new and involve various combinations of upper and lower intercepts. I have several concerns regarding these scenarios and the algorithm used to resolve them:
- Although the five new scenarios are straightforward to simulate numerically, they are problematic from a geological perspective. It is difficult to envisage a Pb-loss event that completely resets one zircon population but leaves another unaffected. The authors suggest that such discrete arrays could correspond to zircon cores and rims. However, I have not encountered such clear separation between two populations in real datasets.
We agree that the original framing invited too strong a geological reading of some of the synthetic scenarios. We will therefore present these cases as benchmark geometries used to test recoverability and failure modes, rather than as claims about the prevalence of any particular natural discordance geometry.
We also clarify that the present study is not a formal “generalisation” of CDC, but an extension from a single-optimum summary to an ensemble-based procedure that preserves supported local optima across Monte Carlo realisations. Cases 2 and 4 will be described as dataset-level mixtures of single-stage discordance arrays, not as claims that one event selectively resets one population while leaving another untouched. Case 2 is retained because it directly demonstrates a limitation of the legacy workflow: two imposed Pb-loss episodes collapse to a single broad young solution under a single-optimum K–S search, whereas the ensemble procedure preserves both supported modes. The more strongly overprinted multistage cases are presented as limiting benchmarks, and it is important to us that the manuscript is transparent where other methods, such as Reimink et al. (2016, 2025), may perform better. An eighth case will be added to demonstrate that the workflow abstains when the discordant geometry does not support a discrete interior Pb-loss age. We hope this revised framing makes clear that the synthetic suite is intended to test recoverability and failure modes, not to imply that all benchmark geometries are common in natural zircon datasets.
- The manuscript presents only one real-world example (inset in Figure 8), which is not particularly convincing. There is no demonstration that the two arrays are statistically robust. Furthermore, roughly one third of the discordant analyses fall on neither array. If this is the strongest available example, then fitting multiple arrays is a straw man problem.
We thank the reviewer for this comment. We will strengthen the demonstration of the geological utility of the tool and will also remove the clustering/array-assignment step from the workflow. We will provide a fuller case study from the South West Terrane and western Youanmi region of the Yilgarn Craton, Western Australia comprising 27 samples (743 spot analyses). Multimodality will be demonstrated directly from the ensemble goodness curve and Monte Carlo support statistics rather than from visual separation of points into inferred arrays. We include a preview of this proposed case study as a supplement pdf to this response. The upper panel shows that sample 224351 yields a reproducibly bimodal ensemble surface with peaks at 786 Ma (support 96%) and 927 Ma (support 97%). These correspond closely to distinct peaks in the regional Pb-loss distribution compiled from the other 26 samples and broadly overlap regional geological events and independently compiled magmatic, metamorphic, and cooling ages from the Yilgarn Craton (lower panel). For comparison, the legacy single-optimum “optimal age” summary for this sample is 916 Ma with a 95% interval of 776–1007 Ma, effectively spanning the two peaks on the goodness curve rather than resolving them.
We do not think the mixed-age benchmark is a straw-man problem. Even without clustering, Case 2 demonstrates a genuine limitation of the legacy workflow, in which a single-optimum K–S search collapses a dataset with two imposed Pb-loss ages to a broad, effectively non-unique young solution and misses the older episode entirely. The ensemble procedure was introduced to preserve and report such multimodality rather than forcing a single optimum. Similar mixed and overprinted geometries were explored in Kirkland et al. (2020), which documented both the successes and the limitations of CDC in such settings.
- In the title of Mathieson et al. (2025b), the authors celebrate their algorithm's ability to turn "trash into treasure". This is acceptable only if there is a reliable way to distinguish trash from treasure. I am concerned that such a mechanism is lacking in the new algorithm. Broad application of this method risks introducing spurious interpretations into the literature. I do not question the quality of the Gawler Craton data shown in Figure 8; I assume the isotopic ratios are accurately plotted on the concordia diagram. However, in this case, the discordant analyses appear to contain little or no chronometric information. It would be risky to claim otherwise.
We agree with the reviewer that any method seeking chronometric information from discordant data must distinguish stable structure from weak or potentially spurious signal, and that the original submission did not make this limitation explicit enough. Hence, we will state a series of safeguards more clearly (we absolutely agree this is important to prevent misuse of the tool). Specifically, at the run level, candidate peaks must satisfy prominence, separation, and width criteria, and a Monte Carlo realisation may contribute no peaks at all if the penalised surface is effectively flat. At the ensemble level, retained peaks must be prominent on the median goodness surface and reproducibly supported across Monte Carlo realisations, with support reported for each retained peak. A new fan-to-zero benchmark can show this behaviour directly. The discordant geometry drives the curve to the young boundary and no interior peak is retained. A defensible peak requires the curve to rise and fall, so that the maximum can be identified; a curve that simply increases toward the grid edge does not meet this requirement regardless of how high it rises. Flat, monotonic, or boundary-dominated ensemble curves are therefore not interpreted as discrete CDC ages but are treated conservatively as unresolved or as recent-boundary responses, reported with a one-sided upper bound on the timing of disturbance. The earlier Gawler Craton example will also be replaced with a Yilgarn Craton case study that reports only ensemble-catalogue results and evaluates candidate Pb-loss ages against independently compiled regional geochronology.
- The description of the algorithm indicates that the fitting procedure requires the user to define a modelling window for the upper intercepts to guide estimation of the lower intercepts. Zircons are classified as "concordant" or "discordant" based on an arbitrary concordance threshold. Discordant grains are then deemed "valid" or "invalid" depending on whether a line connecting them to a proposed lower intercept falls inside or outside the modelling window. These binary classifications impose an artificial dichotomy on what is inherently continuous data. In reality, concordance and validity exist along a spectrum. The authors have developed a highly sophisticated algorithm, but sophistication alone does not guarantee correctness.
Our original description could have been clearer in distinguishing the concordance prefilter from the candidate-age-specific validity check as the reviewer’s comment here does not actually reflect the calculation approach. We clarify the text following this comment to make our method more apparent.
The modelling window in our implementation is the search interval for candidate Pb-loss ages (lower intercepts), not an upper-intercept fitting window. For each candidate age, each discordant analysis is back-projected to concordia to obtain a reconstructed upper-intercept age. Whether that back-projection is valid depends on the candidate age being tested; the same analysis may yield a valid reconstruction at one candidate age and not at another (where a valid age is one that falls between 0 and 4.5 Ga). This will be stated explicitly in the revised Methods: “Validity is therefore evaluated separately for each candidate age rather than being a permanent label attached to that analysis”.
Invalid reconstructions are not discarded, as they still provide information in a probabilistic sense. Their effect enters continuously through the invalid-reconstruction fraction ƒinvalid(ti), which is combined with the K–S mismatch in the penalised goodness function Spen(ti). Candidate ages are therefore ranked by a continuous score reflecting both distributional similarity and the proportion of analyses admitting geologically permissible back-projection, rather than being accepted or rejected by a second fixed binary threshold.
Geochronologists for decades have been applying U-Pb concordance as a means of filtering open from closed system processes. We also agree that the concordance definition is an operational choice and will now state more clearly that CDC is most appropriate where a defensible concordant subset exists and is likely to represent the relevant upper-intercept age structure. Flat, monotonic, or boundary-dominated surfaces are treated as poorly resolved rather than as discrete geological events.
Unfortunately, I do not think that this contribution is ready for publication.
We thank the reviewer for the candid assessment. In response, we will revise the manuscript to reframe the synthetic cases as recoverability benchmarks rather than claims of geological prevalence, remove the clustering step, add a fan-to-zero abstention benchmark, replace the earlier natural example with a Yilgarn Craton case study, and state the reporting criteria, assumptions, and failure modes of CDC very explicitly. We believe these revisions directly address the reviewer’s concerns.
References:
Andersen T, Elburg MA, Magwaza BN. Sources of bias in detrital zircon geochronology: Discordance, concealed lead loss and common lead correction. Earth-Science Reviews. 197:102899, 2019.
Kirkland, C. L., Johnson, T. E., Kinny, P. D., Kapitany, T.: Modelling U–Pb discordance in the Acasta Gneiss: Implications for fluid-rock interaction in Earth’s oldest dated crust, Gondwana Research, 77, https://doi.org/10.1016/j.gr.2019.07.017, 2020.
Mathieson, L. M., Kirkland, C., and Daggitt, M.: Turning trash into treasure: Extracting meaning from discordant data via a dedicated application, Geochemistry, Geophysics, Geosystems, 26, https://doi.org/10.1029/2024GC012066, 2025b
Reimink, J. R., Davies, J. H., Waldron, J. W., and Rojas, X.: Dealing with discordance: a novel approach for analysing U–Pb detrital zircon datasets, Journal of the Geological Society, 173, 577–585, https://doi.org/10.1144/jgs2015-114, 2016.
Reimink, J. R., Beckman, R., Schoonover, E., Lloyd, M., Garber, J., Davies, J. H. F. L., Cerminaro, A., Perrot, M. G., and Smye, A.: Discordance dating: A new approach for dating alteration events, Geochronology, 7, 369–385, https://doi.org/10.5194/gchron-7-369-2025,
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AC3: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
Publisher’s note: this comment is a copy of AC2 and its content was therefore removed on 2 April 2026.
Citation: https://doi.org/10.5194/egusphere-2026-280-AC3
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AC2: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
Status: closed
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RC1: 'Comment on egusphere-2026-280', Donald Davis, 19 Feb 2026
This manuscript presents a statistical approach, which the authors call concordant–discordant comparison (CDC), for processing discordant U-Pb data to derive estimates for discrete ages of partial resetting. Several efforts to derive useful geologic information from discordant data sets have previously been published by the authors and others. This presents an approach for treating data sets that involve multiple secondary ages. It seems like an impressive application of statistical theory that could lead to useful information if the hypotheses on which it is based were correct. In my opinion, however, at least one assumption is generally not correct in the case of zircon, as explained below.
The problem of zircon U-Pb discordance from what should be a robust mineral was a puzzle to early geochronologists. We now know that the chemical and mechanical stability of zircon (ZrSiO4) derives from its structure and not its chemical composition, as in the case of baddeleyite (ZrO2). The zircon structure is subject to degradation due to alpha recoil events following decay of U and its alpha-emitting daughter radionuclides. A high alpha dosage in an old or very high-U zircon gradually destroys the crystal structure leaving a disordered or metamict state. This significantly expands the volume of the crystal which, in the case of a non-uniform U distribution, introduces internal stress that cracks the crystal. This by itself does not affect the U-Pb budget. I have obtained concordant data from many uniformly highly damaged zircon crystals after abrading off the surfaces. However, any water that encounters metamict domains results in alteration and loss of most or all radiogenic Pb accumulated up to that time. Fluid can enter the crystal along cracks produced by metamictization but alteration is commonly incomplete, which suggests that the source of fluid is often the small amount of magmatic water left over from magma crystallization. Most analyses are done on an assemblage of altered and unaltered domains within the same grain, and data often scatter about a discordia line between the crystallization age and a younger age of alteration. The age of Pb loss may be controlled by the time at which a given crystal domain achieves sufficient radiation damage to allow alteration, which should be variable since zircon is commonly zoned in U. In such a case one should see an array of discordant data fanning out from an older age on concordia representing crystallization and bounded by a lower intercept age of zero, which would be a horizontal line on the inverse concordia plots used by the authors. In cases where older inherited zircon has been reheated in a younger magma or subjected to a prolonged high-temperature metamorphic event, the data may form a discrete array where lower and upper intercept ages represent real geologic events but variable low-temperature Pb loss will be superimposed if later alteration has not been completely removed.
The authors first hypothesis is the assumption that alteration-related discordance in zircon represents disturbance caused by an interesting (regional) geologic event, which in some cases may be true. The second hypothesis is that such data reflect a series of Pb loss lines having a single upper concordia intercept age and a discrete number of lower intercept ages, with the data being otherwise scattered only by measurement errors. They seem to successfully test the method by generating a random synthetic data set according to the above constraints and extracting the ages of disturbance. It seems to me that a major problem with natural samples comes from the fact that in most cases one does not sample discrete Pb-loss domains, even with in-situ methods. The scale of most sampling probably includes multiple domains that may have lost Pb at different times. This should effectively destroy information on discrete lower intercept ages if it were present to begin with. The authors could challenge this view if they could apply their method to a natural data set where results (ages of disturbance) are clear and correlate with already known events. They have attempted this in a few previous publications using a previous version of the CDC approach, but it is not clear at least to me that resetting events were clearly resolved and if the present procedure would work any better.
I admire the work involved in developing this approach and am sorry to be so critical of its potential usefulness for zircon data, but any statistical analysis is only as good as the assumptions on which it is based. I hope that the authors can show my opinions to be wrong.
One additional minor point is to not use the word ‘deconvolve’ (lines 18 and 76). Convolution is a specific mathematical procedure that is not relevant in this application.
Don Davis
Citation: https://doi.org/10.5194/egusphere-2026-280-RC1 -
AC1: 'Reply on RC1', Lucy Mathieson, 31 Mar 2026
This manuscript presents a statistical approach, which the authors call concordant–discordant comparison (CDC), for processing discordant U–Pb data to derive estimates for discrete ages of partial resetting. Several efforts to derive useful geologic information from discordant data sets have previously been published by the authors and others. This presents an approach for treating data sets that involve multiple secondary ages. It seems like an impressive application of statistical theory that could lead to useful information if the hypotheses on which it is based were correct.
We thank Dr. Davis for this careful review and for engaging with the central assumptions of the manuscript. We agree that the usefulness of CDC depends on the geological circumstances under which it is applied. Accordingly, we will clarify the method’s assumptions and limitations more explicitly and frame recovered ages as candidate Pb-loss ages that require independent geological support. We will provide additional examples demonstrating the geological use of the tool.
In my opinion, however, at least one assumption is generally not correct in the case of zircon, as explained below.
The problem of zircon U–Pb discordance from what should be a robust mineral was a puzzle to early geochronologists. We now know that the chemical and mechanical stability of zircon (ZrSiO4) derives from its structure and not its chemical composition, as in the case of baddeleyite (ZrO2). The zircon structure is subject to degradation due to alpha recoil events following decay of U and its alpha-emitting daughter radionuclides. A high alpha dosage in an old or very high-U zircon gradually destroys the crystal structure leaving a disordered or metamict state. This significantly expands the volume of the crystal which, in the case of a non-uniform U distribution, introduces internal stress that cracks the crystal. This by itself does not affect the U–Pb budget. I have obtained concordant data from many uniformly highly damaged zircon crystals after abrading off the surfaces. However, any water that encounters metamict domains results in alteration and loss of most or all radiogenic Pb accumulated up to that time. Fluid can enter the crystal along cracks produced by metamictization but alteration is commonly incomplete, which suggests that the source of fluid is often the small amount of magmatic water left over from magma crystallization. Most analyses are done on an assemblage of altered and unaltered domains within the same grain, and data often scatter about a discordia line between the crystallization age and a younger age of alteration. The age of Pb loss may be controlled by the time at which a given crystal domain achieves sufficient radiation damage to allow alteration, which should be variable since zircon is commonly zoned in U. In such a case one should see an array of discordant data fanning out from an older age on concordia representing crystallization and bounded by a lower intercept age of zero, which would be a horizontal line on the inverse concordia plots used by the authors. In cases where older inherited zircon has been reheated in a younger magma or subjected to a prolonged high-temperature metamorphic event, the data may form a discrete array where lower and upper intercept ages represent real geologic events but variable low-temperature Pb loss will be superimposed if later alteration has not been completely removed.
We thank Dr. Davis for this detailed mechanistic discussion of zircon discordance. We agree that much zircon U–Pb discordance can reflect progressive radiation-damage-assisted fluid access, incomplete alteration, and mixing of altered and unaltered domains within a single analytical volume. In such cases, discordance need not preserve a small set of discrete recoverable Pb-loss ages and may instead produce fan-like or otherwise diffuse arrays.
To address this concern, we will add a benchmark case in which discordant analyses fan toward 0 Ma without converging on a common lower intercept. In that geometry, no discrete interior Pb-loss age would be reported under the reporting criteria. We will also make explicit that flat, monotonic, or boundary-dominated responses are treated conservatively as unresolved rather than as evidence for a discrete event. In addition, we will clarify that progressive damage-threshold behaviour and later low-temperature Pb-loss superimposed on earlier reheating or inherited histories are genuine limitations of the method.
The authors first hypothesis is the assumption that alteration-related discordance in zircon represents disturbance caused by an interesting (regional) geologic event, which in some cases may be true. The second hypothesis is that such data reflect a series of Pb loss lines having a single upper concordia intercept age and a discrete number of lower intercept ages, with the data being otherwise scattered only by measurement errors.
We thank Dr. Davis for identifying this point, which required clarification. We agree that CDC relies on a simplified geometric approximation. For each trial lower-intercept age, discordant analyses are back-projected to concordia and the resulting reconstructed upper-intercept age distribution is compared with the empirical age distribution of the concordant subset. The assumption is therefore a chord-based Pb-loss model used to assess candidate disturbance ages.
However, the method does not fit each discordant analysis to one of a small number of discrete discordia lines, nor does it require a single upper-intercept age for the whole dataset. Instead, the concordant analyses provide an empirical reference distribution that may itself be mixed, and the comparison is performed at the level of the full age distributions. Candidate Pb-loss ages are inferred from recurring maxima on the CDC surface across Monte Carlo realisations rather than from a final assignment of individual analyses to explicit fitted chords.
In a revised manuscript, we will clarify these assumptions more explicitly, including the chord-based approximation, the need for appropriate common-Pb correction or filtering, and the dependence on a defensible concordant reference population. We will also remove the discordant clustering step from the workflow and frame recovered peaks as candidate Pb-loss ages whose geological significance must be assessed using petrographic, textural, and regional context.
They seem to successfully test the method by generating a random synthetic data set according to the above constraints and extracting the ages of disturbance. It seems to me that a major problem with natural samples comes from the fact that in most cases one does not sample discrete Pb-loss domains, even with in-situ methods. The scale of most sampling probably includes multiple domains that may have lost Pb at different times. This should effectively destroy information on discrete lower intercept ages if it were present to begin with. The authors could challenge this view if they could apply their method to a natural data set where results (ages of disturbance) are clear and correlate with already known events. They have attempted this in a few previous publications using a previous version of the CDC approach, but it is not clear at least to me that resetting events were clearly resolved and if the present procedure would work any better.
We agree that analytical mixing of disturbed and undisturbed zircon domains is a major challenge for any attempt to recover geological information from discordant data, and in some datasets it may destroy recoverable lower-intercept structure. A revised manuscript will therefore not assume that each discordant analysis samples a single discrete Pb-loss domain, or imply that every natural zircon dataset should yield recoverable discrete disturbance ages.
However, we maintain that in-situ datasets can preserve geologically useful information in the discordant component and that this can be accessed. Especially in texturally targeted analyses, some zircon populations may retain enough discordant structure for candidate Pb-loss ages to be recovered at the population level, even where individual analyses are not pure single-stage reset domains. To address this concern, we will replace the earlier illustrative Gawler Craton example with a case study from the South West Terrane and western Youanmi region of the Yilgarn Craton, Western Australia, comprising 27 samples (743 spot analyses) in total. Sample 224351 yields a reproducibly bimodal ensemble surface with peaks at 786 Ma (support 96%) and 927 Ma (support 97%). These align with distinct peaks in a regional Pb-loss distribution compiled from the other 26 samples and broadly overlap independently compiled magmatic crystallisation, metamorphic, and cooling ages from the western Yilgarn margin. Under the legacy single-optimum workflow, this sample would have returned a single age of 916 Ma with a 95% interval of 776–1007 Ma, spanning both peaks. We present this as an example in which the updated workflow yields geologically plausible candidate Pb-loss ages in a natural dataset, not as proof that all discordant zircon populations preserve isolated single-stage reset histories. We include a preview of this proposed case study as a supplement pdf to this response because Dr. Davis specifically asked whether the updated workflow could be demonstrated on a natural dataset with independently known events.
I admire the work involved in developing this approach and am sorry to be so critical of its potential usefulness for zircon data, but any statistical analysis is only as good as the assumptions on which it is based. I hope that the authors can show my opinions to be wrong.
We entirely agree with Dr. Davis that any statistical analysis is only as good as the assumptions on which it rests, and we sincerely appreciate the critical comments which will greatly improve our contribution. In response, a revised manuscript will be intentionally narrower and more conservative. We will state the assumptions and failure modes of CDC more explicitly, emphasise conditions under which the method should abstain, and restrict geological interpretation to statistically supported candidate Pb-loss ages that are evaluated against independent context.
One additional minor point is to not use the word “deconvolve” (lines 18 and 76). Convolution is a specific mathematical procedure that is not relevant in this application.
We agree and we will remove the word “deconvolve” throughout and replace it with wording that is more appropriate in this context, for example “separate”.
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AC1: 'Reply on RC1', Lucy Mathieson, 31 Mar 2026
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RC2: 'Comment on egusphere-2026-280', Anonymous Referee #2, 26 Feb 2026
The presence of discordance and Pb loss is an unavoidable aspect of many U–Pb datasets. In igneous and metamorphic contexts, Pb loss generates discordia lines in U–Pb isotope space, whose upper and lower intercepts constrain both the protolith age and the timing of Pb loss.
In detrital settings, where the goal of U–Pb geochronology is to obtain age spectra, the traditional strategy for dealing with discordance has been to reject discordant analyses based on a chosen criterion and to retain only concordant data. This approach can be frustrating when most analysed grains are discordant. Moreover, excluding discordant analyses may bias the chronological record, potentially obscuring source regions that predominantly yield discordant zircons.
It is therefore unsurprising that geochronologists have sought alternative approaches. Reimink et al. (2016) proposed a numerical algorithm that fits lines through clusters of discordant U–Pb data and identifies the lower and upper intercepts of the lines passing through the largest number of analyses.
The authors of the present manuscript have published several papers on this topic (Mathieson et al., 2025a, 2025b), modifying the approach of Reimink et al. (2016) by first considering the distribution of the concordant subpopulation and using its modes to constrain the upper intercepts before searching for lower intercepts. They refer to this as the "Concordant Discordant Comparison" (CDC) approach.
Pb loss is linked to radiation damage, as clearly explained by Don Davis in his review of the manuscript. This process can produce fanning arrays of discordant zircons (Case 3 of 7 in the manuscript). Reimink et al. (2025) dated a quartzite by fitting the lower intercept of such a fanning array of discordant zircons that were reset by a metamorphic event approximately 25 Ma ago.
Andersen et al. (2019, 2022) demonstrated that tectonically driven metamorphism is not required to induce Pb loss. Even surface weathering can cause a metamict zircon to lose its Pb, leading to the well-known phenomenon of apparent "modern Pb loss". Andersen et al. (2019, 2022)'s examples likewise resemble fanning arrays of discordant data with a single lower intercept and multiple upper intercepts.
In their new manuscript, Mathieson and Kirkland propose a generalisation of the CDC method to accommodate multiple episodes of Pb loss. These are summarised in Figures 1 and 2 as seven "Cases". Case 1 corresponds to a simple discordia line, solvable by York regression. Case 3 represents the fanning arrays previously discussed by Reimink et al. (2025) and Andersen et al. (2019, 2022).
Cases 2, 4, 5, 6, and 7 are new and involve various combinations of upper and lower intercepts. I have several concerns regarding these scenarios and the algorithm used to resolve them:
1. Although the five new scenarios are straightforward to simulate numerically, they are problematic from a geological perspective. It is difficult to envisage a Pb-loss event that completely resets one zircon population but leaves another unaffected. The authors suggest that such discrete arrays could correspond to zircon cores and rims. However, I have not encountered such clear separation between two populations in real datasets.
2. The manuscript presents only one real-world example (inset in Figure 8), which is not particularly convincing. There is no demonstration that the two arrays are statistically robust. Furthermore, roughly one third of the discordant analyses fall on neither array. If this is the strongest available example, then fitting multiple arrays is a straw man problem.
3. In the title of Mathieson et al. (2025b), the authors celebrate their algorithm's ability to turn "trash into treasure". This is acceptable only if there is a reliable way to distinguish trash from treasure. I am concerned that such a mechanism is lacking in the new algorithm. Broad application of this method risks introducing spurious interpretations into the literature. I do not question the quality of the Gawler Craton data shown in Figure 8; I assume the isotopic ratios are accurately plotted on the concordia diagram. However, in this case, the discordant analyses appear to contain little or no chronometric information. It would be risky to claim otherwise.
4. The description of the algorithm indicates that the fitting procedure requires the user to define a modelling window for the upper intercepts to guide estimation of the lower intercepts. Zircons are classified as "concordant" or "discordant" based on an arbitrary concordance threshold. Discordant grains are then deemed "valid" or "invalid" depending on whether a line connecting them to a proposed lower intercept falls inside or outside the modelling window. These binary classifications impose an artificial dichotomy on what is inherently continuous data. In reality, concordance and validity exist along a spectrum. The authors have developed a highly sophisticated algorithm, but sophistication alone does not guarantee correctness.
Unfortunately, I do not think that this contribution is ready for publication.
References:
Andersen T, Elburg MA, Magwaza BN. Sources of bias in detrital zircon geochronology: Discordance, concealed lead loss and common lead correction. Earth-Science Reviews. 197:102899, 2019.
Andersen T, Elburg MA. Open-system behaviour of detrital zircon during weathering: an example from the Palaeoproterozoic Pretoria Group, South Africa. Geological Magazine.159(4):561-76, 2022.
Mathieson, L. M., Kirkland, C., Bodorkos, S., and Daggitt, M.: From discordance to discovery: extracting fluid–rock interac-
tion timescales through zircon U–Pb analyses in the Arunta region, Central Australia, Journal of the Geological Society, 182,
https://doi.org/10.1144/jgs2024-111, 2025a.Mathieson, L. M., Kirkland, C., and Daggitt, M.: Turning trash into treasure: Extracting meaning from discordant data via a dedicated875
application, Geochemistry, Geophysics, Geosystems, 26, https://doi.org/10.1029/2024GC012066, 2025bReimink, J. R., Davies, J. H., Waldron, J. W., and Rojas, X.: Dealing with discordance: a novel approach for analysing U–Pb detrital zircon
datasets, Journal of the Geological Society, 173, 577–585, https://doi.org/10.1144/jgs2015-114, 2016.Reimink, J. R., Beckman, R., Schoonover, E., Lloyd, M., Garber, J., Davies, J. H. F. L., Cerminaro, A., Perrot, M. G., and Smye, A.:
Discordance dating: A new approach for dating alteration events, Geochronology, 7, 369–385, https://doi.org/10.5194/gchron-7-369-2025,
2025.Citation: https://doi.org/10.5194/egusphere-2026-280-RC2 -
AC2: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
The presence of discordance and Pb loss is an unavoidable aspect of many U–Pb datasets. In igneous and metamorphic contexts, Pb loss generates discordia lines in U–Pb isotope space, whose upper and lower intercepts constrain both the protolith age and the timing of Pb loss.
In detrital settings, where the goal of U–Pb geochronology is to obtain age spectra, the traditional strategy for dealing with discordance has been to reject discordant analyses based on a chosen criterion and to retain only concordant data. This approach can be frustrating when most analysed grains are discordant. Moreover, excluding discordant analyses may bias the chronological record, potentially obscuring source regions that predominantly yield discordant zircons.
It is therefore unsurprising that geochronologists have sought alternative approaches. Reimink et al. (2016) proposed a numerical algorithm that fits lines through clusters of discordant U–Pb data and identifies the lower and upper intercepts of the lines passing through the largest number of analyses.
The authors of the present manuscript have published several papers on this topic (Mathieson et al., 2025a, 2025b), modifying the approach of Reimink et al. (2016) by first considering the distribution of the concordant subpopulation and using its modes to constrain the upper intercepts before searching for lower intercepts. They refer to this as the "Concordant Discordant Comparison" (CDC) approach.
We thank the reviewer for this summary. We think it is very important to clarify one point regarding method lineage. The concordant–discordant comparison (CDC) approach was not developed as a modification of Reimink et al. (2016). CDC has its own development history, initially preceeding Reimink et al. (2016). Beginning with Morris et al. (2015) and subsequently expanded in Kirkland et al. (2017, 2020) and in our later work (Mathieson et al., 2025a,b). The CDC and Reimink et al. (2016) approaches are related in motivation only (namely, to recover useful age information from discordant datasets) but they are entirely methodologically distinct.
In CDC, the concordant population is used as an empirical reference for the expected upper-intercept age structure. For each candidate Pb-loss age, discordant analyses are back-projected to reconstructed upper-intercept ages, and those reconstructed ages are then compared probabilistically with the observed concordant population. Reimink et al. (2016) instead evaluate combinations of upper and lower intercepts directly in concordia space and identify those solutions that best fit the discordant data. Thus, Reimink et al. (2016) method is a geometric approach, whereas the CDC is a Monte Carlo implementation of a Bayesian approach. The present manuscript therefore does not modify the Reimink et al. method but instead extends the CDC workflow from a single-optimum summary to an ensemble-based multi-peak procedure. We consider this a significant useful advance.
In their new manuscript, Mathieson and Kirkland propose a generalisation of the CDC method to accommodate multiple episodes of Pb loss. These are summarised in Figures 1 and 2 as seven "Cases". Case 1 corresponds to a simple discordia line, solvable by York regression. Case 3 represents the fanning arrays previously discussed by Reimink et al. (2025) and Andersen et al. (2019, 2022).
Cases 2, 4, 5, 6, and 7 are new and involve various combinations of upper and lower intercepts. I have several concerns regarding these scenarios and the algorithm used to resolve them:
- Although the five new scenarios are straightforward to simulate numerically, they are problematic from a geological perspective. It is difficult to envisage a Pb-loss event that completely resets one zircon population but leaves another unaffected. The authors suggest that such discrete arrays could correspond to zircon cores and rims. However, I have not encountered such clear separation between two populations in real datasets.
We agree that the original framing invited too strong a geological reading of some of the synthetic scenarios. We will therefore present these cases as benchmark geometries used to test recoverability and failure modes, rather than as claims about the prevalence of any particular natural discordance geometry.
We also clarify that the present study is not a formal “generalisation” of CDC, but an extension from a single-optimum summary to an ensemble-based procedure that preserves supported local optima across Monte Carlo realisations. Cases 2 and 4 will be described as dataset-level mixtures of single-stage discordance arrays, not as claims that one event selectively resets one population while leaving another untouched. Case 2 is retained because it directly demonstrates a limitation of the legacy workflow: two imposed Pb-loss episodes collapse to a single broad young solution under a single-optimum K–S search, whereas the ensemble procedure preserves both supported modes. The more strongly overprinted multistage cases are presented as limiting benchmarks, and it is important to us that the manuscript is transparent where other methods, such as Reimink et al. (2016, 2025), may perform better. An eighth case will be added to demonstrate that the workflow abstains when the discordant geometry does not support a discrete interior Pb-loss age. We hope this revised framing makes clear that the synthetic suite is intended to test recoverability and failure modes, not to imply that all benchmark geometries are common in natural zircon datasets.
- The manuscript presents only one real-world example (inset in Figure 8), which is not particularly convincing. There is no demonstration that the two arrays are statistically robust. Furthermore, roughly one third of the discordant analyses fall on neither array. If this is the strongest available example, then fitting multiple arrays is a straw man problem.
We thank the reviewer for this comment. We will strengthen the demonstration of the geological utility of the tool and will also remove the clustering/array-assignment step from the workflow. We will provide a fuller case study from the South West Terrane and western Youanmi region of the Yilgarn Craton, Western Australia comprising 27 samples (743 spot analyses). Multimodality will be demonstrated directly from the ensemble goodness curve and Monte Carlo support statistics rather than from visual separation of points into inferred arrays. We include a preview of this proposed case study as a supplement pdf to this response. The upper panel shows that sample 224351 yields a reproducibly bimodal ensemble surface with peaks at 786 Ma (support 96%) and 927 Ma (support 97%). These correspond closely to distinct peaks in the regional Pb-loss distribution compiled from the other 26 samples and broadly overlap regional geological events and independently compiled magmatic, metamorphic, and cooling ages from the Yilgarn Craton (lower panel). For comparison, the legacy single-optimum “optimal age” summary for this sample is 916 Ma with a 95% interval of 776–1007 Ma, effectively spanning the two peaks on the goodness curve rather than resolving them.
We do not think the mixed-age benchmark is a straw-man problem. Even without clustering, Case 2 demonstrates a genuine limitation of the legacy workflow, in which a single-optimum K–S search collapses a dataset with two imposed Pb-loss ages to a broad, effectively non-unique young solution and misses the older episode entirely. The ensemble procedure was introduced to preserve and report such multimodality rather than forcing a single optimum. Similar mixed and overprinted geometries were explored in Kirkland et al. (2020), which documented both the successes and the limitations of CDC in such settings.
- In the title of Mathieson et al. (2025b), the authors celebrate their algorithm's ability to turn "trash into treasure". This is acceptable only if there is a reliable way to distinguish trash from treasure. I am concerned that such a mechanism is lacking in the new algorithm. Broad application of this method risks introducing spurious interpretations into the literature. I do not question the quality of the Gawler Craton data shown in Figure 8; I assume the isotopic ratios are accurately plotted on the concordia diagram. However, in this case, the discordant analyses appear to contain little or no chronometric information. It would be risky to claim otherwise.
We agree with the reviewer that any method seeking chronometric information from discordant data must distinguish stable structure from weak or potentially spurious signal, and that the original submission did not make this limitation explicit enough. Hence, we will state a series of safeguards more clearly (we absolutely agree this is important to prevent misuse of the tool). Specifically, at the run level, candidate peaks must satisfy prominence, separation, and width criteria, and a Monte Carlo realisation may contribute no peaks at all if the penalised surface is effectively flat. At the ensemble level, retained peaks must be prominent on the median goodness surface and reproducibly supported across Monte Carlo realisations, with support reported for each retained peak. A new fan-to-zero benchmark can show this behaviour directly. The discordant geometry drives the curve to the young boundary and no interior peak is retained. A defensible peak requires the curve to rise and fall, so that the maximum can be identified; a curve that simply increases toward the grid edge does not meet this requirement regardless of how high it rises. Flat, monotonic, or boundary-dominated ensemble curves are therefore not interpreted as discrete CDC ages but are treated conservatively as unresolved or as recent-boundary responses, reported with a one-sided upper bound on the timing of disturbance. The earlier Gawler Craton example will also be replaced with a Yilgarn Craton case study that reports only ensemble-catalogue results and evaluates candidate Pb-loss ages against independently compiled regional geochronology.
- The description of the algorithm indicates that the fitting procedure requires the user to define a modelling window for the upper intercepts to guide estimation of the lower intercepts. Zircons are classified as "concordant" or "discordant" based on an arbitrary concordance threshold. Discordant grains are then deemed "valid" or "invalid" depending on whether a line connecting them to a proposed lower intercept falls inside or outside the modelling window. These binary classifications impose an artificial dichotomy on what is inherently continuous data. In reality, concordance and validity exist along a spectrum. The authors have developed a highly sophisticated algorithm, but sophistication alone does not guarantee correctness.
Our original description could have been clearer in distinguishing the concordance prefilter from the candidate-age-specific validity check as the reviewer’s comment here does not actually reflect the calculation approach. We clarify the text following this comment to make our method more apparent.
The modelling window in our implementation is the search interval for candidate Pb-loss ages (lower intercepts), not an upper-intercept fitting window. For each candidate age, each discordant analysis is back-projected to concordia to obtain a reconstructed upper-intercept age. Whether that back-projection is valid depends on the candidate age being tested; the same analysis may yield a valid reconstruction at one candidate age and not at another (where a valid age is one that falls between 0 and 4.5 Ga). This will be stated explicitly in the revised Methods: “Validity is therefore evaluated separately for each candidate age rather than being a permanent label attached to that analysis”.
Invalid reconstructions are not discarded, as they still provide information in a probabilistic sense. Their effect enters continuously through the invalid-reconstruction fraction ƒinvalid(ti), which is combined with the K–S mismatch in the penalised goodness function Spen(ti). Candidate ages are therefore ranked by a continuous score reflecting both distributional similarity and the proportion of analyses admitting geologically permissible back-projection, rather than being accepted or rejected by a second fixed binary threshold.
Geochronologists for decades have been applying U-Pb concordance as a means of filtering open from closed system processes. We also agree that the concordance definition is an operational choice and will now state more clearly that CDC is most appropriate where a defensible concordant subset exists and is likely to represent the relevant upper-intercept age structure. Flat, monotonic, or boundary-dominated surfaces are treated as poorly resolved rather than as discrete geological events.
Unfortunately, I do not think that this contribution is ready for publication.
We thank the reviewer for the candid assessment. In response, we will revise the manuscript to reframe the synthetic cases as recoverability benchmarks rather than claims of geological prevalence, remove the clustering step, add a fan-to-zero abstention benchmark, replace the earlier natural example with a Yilgarn Craton case study, and state the reporting criteria, assumptions, and failure modes of CDC very explicitly. We believe these revisions directly address the reviewer’s concerns.
References:
Andersen T, Elburg MA, Magwaza BN. Sources of bias in detrital zircon geochronology: Discordance, concealed lead loss and common lead correction. Earth-Science Reviews. 197:102899, 2019.
Kirkland, C. L., Johnson, T. E., Kinny, P. D., Kapitany, T.: Modelling U–Pb discordance in the Acasta Gneiss: Implications for fluid-rock interaction in Earth’s oldest dated crust, Gondwana Research, 77, https://doi.org/10.1016/j.gr.2019.07.017, 2020.
Mathieson, L. M., Kirkland, C., and Daggitt, M.: Turning trash into treasure: Extracting meaning from discordant data via a dedicated application, Geochemistry, Geophysics, Geosystems, 26, https://doi.org/10.1029/2024GC012066, 2025b
Reimink, J. R., Davies, J. H., Waldron, J. W., and Rojas, X.: Dealing with discordance: a novel approach for analysing U–Pb detrital zircon datasets, Journal of the Geological Society, 173, 577–585, https://doi.org/10.1144/jgs2015-114, 2016.
Reimink, J. R., Beckman, R., Schoonover, E., Lloyd, M., Garber, J., Davies, J. H. F. L., Cerminaro, A., Perrot, M. G., and Smye, A.: Discordance dating: A new approach for dating alteration events, Geochronology, 7, 369–385, https://doi.org/10.5194/gchron-7-369-2025,
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AC3: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
Publisher’s note: this comment is a copy of AC2 and its content was therefore removed on 2 April 2026.
Citation: https://doi.org/10.5194/egusphere-2026-280-AC3
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AC2: 'Reply on RC2', Lucy Mathieson, 31 Mar 2026
Data sets
LeadLoss reproducibility data for “Past the first date: Resolving successive Pb-loss episodes in zircon” (Zenodo release paper-2025-peak-picking-v1.2.1) Lucy M. Mathieson and Christopher L. Kirkland https://doi.org/10.5281/zenodo.18217446
Model code and software
LeadLoss: Pb-loss peak picking tools and manuscript reproduction workflow (paper-2025-peak-picking-v1.2.1) Lucy M. Mathieson and Christopher L. Kirkland https://doi.org/10.5281/zenodo.18217446
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This manuscript presents a statistical approach, which the authors call concordant–discordant comparison (CDC), for processing discordant U-Pb data to derive estimates for discrete ages of partial resetting. Several efforts to derive useful geologic information from discordant data sets have previously been published by the authors and others. This presents an approach for treating data sets that involve multiple secondary ages. It seems like an impressive application of statistical theory that could lead to useful information if the hypotheses on which it is based were correct. In my opinion, however, at least one assumption is generally not correct in the case of zircon, as explained below.
The problem of zircon U-Pb discordance from what should be a robust mineral was a puzzle to early geochronologists. We now know that the chemical and mechanical stability of zircon (ZrSiO4) derives from its structure and not its chemical composition, as in the case of baddeleyite (ZrO2). The zircon structure is subject to degradation due to alpha recoil events following decay of U and its alpha-emitting daughter radionuclides. A high alpha dosage in an old or very high-U zircon gradually destroys the crystal structure leaving a disordered or metamict state. This significantly expands the volume of the crystal which, in the case of a non-uniform U distribution, introduces internal stress that cracks the crystal. This by itself does not affect the U-Pb budget. I have obtained concordant data from many uniformly highly damaged zircon crystals after abrading off the surfaces. However, any water that encounters metamict domains results in alteration and loss of most or all radiogenic Pb accumulated up to that time. Fluid can enter the crystal along cracks produced by metamictization but alteration is commonly incomplete, which suggests that the source of fluid is often the small amount of magmatic water left over from magma crystallization. Most analyses are done on an assemblage of altered and unaltered domains within the same grain, and data often scatter about a discordia line between the crystallization age and a younger age of alteration. The age of Pb loss may be controlled by the time at which a given crystal domain achieves sufficient radiation damage to allow alteration, which should be variable since zircon is commonly zoned in U. In such a case one should see an array of discordant data fanning out from an older age on concordia representing crystallization and bounded by a lower intercept age of zero, which would be a horizontal line on the inverse concordia plots used by the authors. In cases where older inherited zircon has been reheated in a younger magma or subjected to a prolonged high-temperature metamorphic event, the data may form a discrete array where lower and upper intercept ages represent real geologic events but variable low-temperature Pb loss will be superimposed if later alteration has not been completely removed.
The authors first hypothesis is the assumption that alteration-related discordance in zircon represents disturbance caused by an interesting (regional) geologic event, which in some cases may be true. The second hypothesis is that such data reflect a series of Pb loss lines having a single upper concordia intercept age and a discrete number of lower intercept ages, with the data being otherwise scattered only by measurement errors. They seem to successfully test the method by generating a random synthetic data set according to the above constraints and extracting the ages of disturbance. It seems to me that a major problem with natural samples comes from the fact that in most cases one does not sample discrete Pb-loss domains, even with in-situ methods. The scale of most sampling probably includes multiple domains that may have lost Pb at different times. This should effectively destroy information on discrete lower intercept ages if it were present to begin with. The authors could challenge this view if they could apply their method to a natural data set where results (ages of disturbance) are clear and correlate with already known events. They have attempted this in a few previous publications using a previous version of the CDC approach, but it is not clear at least to me that resetting events were clearly resolved and if the present procedure would work any better.
I admire the work involved in developing this approach and am sorry to be so critical of its potential usefulness for zircon data, but any statistical analysis is only as good as the assumptions on which it is based. I hope that the authors can show my opinions to be wrong.
One additional minor point is to not use the word ‘deconvolve’ (lines 18 and 76). Convolution is a specific mathematical procedure that is not relevant in this application.
Don Davis