the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 May 2026
Technical Note: Remarks on Assessing Complexity in Thermal History Models
Abstract. Modelling low-temperature thermochronology data to understand geological history relating to near-surface thermal perturbations caused by processes like faulting, erosion, intrusion, or hydrothermal circulation, has become relatively routine. However, it is clear that not all modelling efforts include rigorous testing of various modelling decisions. This happens in part because of a lack of understanding about each of the different model parameters and how modifications to those parameters may control different model outputs or predictions. In an effort to reduce ambiguity around how model complexity is dealt with in the modelling program QTQt, we delve into the details behind the algorithm that accepts and/or rejects models with greater complexity (i.e., many time-temperature points within a thermal history), and explore example thermal histories to show the effect of choosing the accept or reject more complex models that do not improve the data fit. Generally, where the data control the model outputs and the data fit is good the model outputs and age predictions are indistinguishable. When the choice is made to accept more complex models, users must be aware that this choice adds more complexity in the areas of the model space that are not controlled by the data and effectively smooths the expected thermal history. Because of this effect, caution should be used when interpreting the expected thermal history from a run that accepts more complex models. To verify if the choice to accept or reject more complex models plays an important part in model interpretation, we suggest this decision is always tested by running the same model rejecting the complex models and comparing the model outputs.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2328', Peter van der Beek, 22 Jun 2026
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RC2: 'Comment on egusphere-2026-2328', Marissa Tremblay, 29 Jun 2026
Review of “Technical Note: Remarks on Assessing Complexity in Thermal History Models” by Alyssa Abbey and Kerry Gallagher
This manuscript describes changes to the thermal history modelling software QTQt – specifically, changes to the algorithm that QTQt uses to propose new temperature-time (T-t) paths, and the option that was added when this algorithm was changed to accept or reject more complex models that do not improve the model’s ability to predict the observed data. The manuscript also presents several modelling examples wherein synthetic data (ages, track lengths) are generated with a forward model T-t path and then used as the input data for inverse models which either accept or reject more complex T-t paths that do not improve the model predictions of the data.
First, I agree that this manuscript is appropriate as a technical note in terms of manuscript type. I am also generally supportive of manuscripts like this one that aim to provide greater context and understanding for the modelling frameworks we use to interpret thermochronology data. I agree with Peter van der Beek’s review that the writing could be tightened up and have provide some additional line comments below in this regard. I also have a few overarching questions/concerns:
- Why was the ‘accept more complex models’ option added when the proposal algorithm for new T-t paths was changed? From reading the manuscript, it seems like the authors think there are limited (or perhaps no) scenarios where this option should be selected.
- In the example thermal histories, why model only AFT or AHe synthetic data separately? This choice is never justified, but presumably synthetic ages can be generated for both systems, at least for the first two prescribed T-t histories in the manuscript, and then used to evaluate the inverse models with accept vs. reject complex T-t paths. I suggest this because, in real thermochronology applications, it’s generally not recommended (and to my knowledge avoided by most) to have a single sample with just AHe dates like in the second T-t example, unless there is a very large spread in eU that would result in very different thermal sensitivities.
- In a similar vein to point #2, I encourage the authors to consider whether their points could be better illustrated by using real thermochronology data, in addition to synthetic data alone. Are there real datasets that you can highlight, either from your own work or the literature, where you can demonstrate that over-interpretation might occur from accepting more complex paths that do not improve the model fit to the data? I thought these kinds of examples were very effective in the Abbey et al. (2023) paper.
Line comments:
Lines 9-11: This sentence is challenging to read. Suggested revision: Low-temperature thermochronology can provide record near surface thermal perturbations caused by processes like faulting, erosion, intrusion, or hydrothermal circulation. Modelling low-temperature thermochronology data to understand the timing and duration of these geologic processes has become relatively routine.
Line 16: Change ‘the accept’ to ‘to accept’.
Lines 22-24: Clarify here: ‘To verify if the choice to accept or reject complex models plays an important part in model interpretation, we suggest this decision is always tested by running the same model using the same data and input parameters but rejecting the complex models, and comparing the model outputs.’ To my mind, rejecting the more complex T-t paths means the model is inherently not the same.
Line 40: Suggest revising to say “a user specifies a single set of model parameters”.
Lines 70-71: I assume that this statement about what many researchers do may be informed by the authors’ personal experiences (e.g., running pre-conference modelling workshops and corresponding with authors via email). However, it seems like a statement like this should somehow be backed up, either with examples from the literature or by explaining how the authors arrived at this assessment.
Lines 80-92: I recommend reorganizing this paragraph to first describe how the original QTQt proposed and made decisions about accepting new T-t paths, and then explaining how the newer versions of QTQt proposes and makes decisions about accepting new T-t paths. Right now the two versions are discussed somewhat in parallel and it is a bit challenging to follow. I also think the authors should emphasize that if the ‘reject more complex models’ option is selected in newer versions of QTQt, more complex models, i.e., T-t paths with more change points, will be allowed but only if they improve the data fit (if I understand correctly). Currently this point is a bit unclear in this paragraph as written.
Line 147: ‘The timing is not as accurate’ - Be more specific and say the maximum heating occurs later.
Lines 154-158: These statements are pretty vague – can you provide a more explicit example?
Figure 1. This figure is a lot to digest with so many sub-figures. One way to make this easier for the reader to understand would be to combine the top panel in Figure 1A with Figure 2, as they are both showing information about number of T-t points. Then the maximum posterior and maximum likelihood T-t paths could be a separate figure, and the data predictions (current panel B) could be a third figure. In addition, for the top figure in panel A, at first I did not recognize that the scale was different for the left- and right-hand axes. I recommend making the scales the same so that the reader can see that the yellow/green likelihood chain overall has many more T-t points than the teal or magenta chains. For panel B, I recommend adding a line or point to show what the ‘true’ synthetic age is. I also suggest including the model results for the track length distribution compared to the ‘true’ synthetic track length distribution, since the models are also attempting to fit these data. The conclusions about model complexity should still hold for the track length data.
Line 197: RDAAM needs to be defined.
Line 199: Since the AHe paths are not actually the same as those in Wolf et al. (1998), it would be much simpler for the reader to just refer to the paths the authors choose for their AHe model as paths 1 and 2 and not try to link them back to comparable/similar paths in earlier publications.
Figure 3. This figure needs the different panels to be lettered, and the figure caption needs to refer to this lettering. This will make it much easier to understand which panels in the figure are being described by different sentences in the caption.
Lines 232-233: “skews even more to capture the dearth of possible pre-40 Ma temperature changes” I am not sure what you mean by this, please clarify.
Lines 265-267: The fact that neither the complex nor simple models predicts the synthetic T-t history is really interesting. I recommend expanding the discussion here a bit because this says something about the resolution when using a single chronometer like the AHe system, regardless of the modeling choices that are made. (This may also be a good reason to consider including models that predict ages for more than one chronometer, as mentioned above).
Lines 269-270: The algorithm details are not actually described here but earlier (lines 80-92).
Lines 279-282: I think a more descriptive summary/synthesis of what was learned from the modelling examples is needed here. The rest of this paragraph is more focused on recommendations and should probably be a separate paragraph from such a synthesis/summary of the new model results presented.
Citation: https://doi.org/10.5194/egusphere-2026-2328-RC2
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This manuscript provides some very useful guidance for users of the popular QTQt inverse thermal history modelling code for thermochronometric data, and therefore fits well into the Special Issue of Geochronology to which it was submitted. The authors focus on a (relatively little known?) choice option in the more recent versions of QTQt, to accept or reject more complex thermal histories (i.e., histories characterised by more T,t points) that fit the data similarly to simpler models. In my understanding, earlier versions of QTQt rejected such models by default. However, I actually found the comparison between the different “optimal” models (i.e., the maximum likelihood, maximum posterior and expected models) the most interesting aspect of this contribution. I felt like I learnt something on that aspect from this manuscript (in particular why the expected models so often appear to suggest reheating), whereas the differences between the inversion runs that accept or reject more complex paths are rather subtle and the manuscript does not end up providing very detailed guidance on whether or not (or when) to accept more complex models in inversions. I am wondering whether the authors would consider putting more emphasis on the comparison between the different optimal models, at the expense of the comparison between models allowing more or less complexity. I believe this would also serve the community very well, as I have the impression many users of QTQt are often at a loss which of these options to present and use, and I have been wondering myself about the apparent reheating shown by so many QTQt inversion outcomes. I realise some of this material was covered in the Abbey and Gallagher (2023) paper, of which this technical note can nearly be considered a “spinoff”, but since that was a quite long and involved treatment of many different aspects of QTQt modelling, the message concerning the different representative thermal history paths may not have come through as clearly. I am thus leaving this suggestion here for the authors’ consideration.
I have a few general comments on the manuscript and a series of more minor editorial issues. Overall, the writing could be tightened up a bit, as the current manuscript can be a bit confusing in places due to imprecise and sometimes somewhat colloquial expressions. I am providing the editorial comments as edits on an attached pdf file of the manuscript and focus here on the more general comments only.
First, although I realise this is a technical note that is supposed to be short, I do think that some concepts could do with a very short (1-line) explanation or at least a reference to where readers can find more information about them. For instance, the “likelihood” of a model is used throughout but not defined. Also, what is meant by the maximum-likelihood, maximum posterior, and expected models should be made clear somewhere. In line 148, it is stated that the maximum posterior model is “possibly the preferred individual best model in Bayesian approaches”, but without justification for this statement. Again, most of this is already in the literature, but it really helps the reader to have a short explanation the first time these terms are used.
It is argued in several places in the manuscript that, in more complex models, time-temperature points will only be added in the parts of the model space that are unconstrained by the data (e.g., lines 76-77; 273-274). This is not intuitive for me and could therefore do with some justification / explanation. I would agree that model complexity is increased in those parts of the model space that are unconstrained by the data (and this is nicely shown in Figs. 1, 3, and 4), but could very well imagine that additional t,T points are added throughout the model space, but do not influence the complexity of the models where these are well constrained by the data (in other words, in those parts of the model space one could add additional t,T points as long as they align with the well-constrained thermal history).
After reading the manuscript, the one question that lingers is the actual usefulness of the expected model in defining the thermal history. Even for the relatively simple input thermal histories shown in Figs. 1 and 2, it does not capture the thermal histories particularly well, and one wonders whether some other weighting scheme for this model might produce “better” results? As it is, it appears quite heavily influenced by (the probably fairly large number of) models that do not fit the data particulary well. In most cases, the parts of the model space characterised by high relative probability appear to capture the input thermal history significantly better. This ties in to a long-standing discussion within the community about the significance of relative probability and whether/how we should use that as a criterion to select predicted thermal histories. I provide some more details in comments on the pdf.
Overall, however, this is a nice contribution that will be useful to the community. I will let the authors decide in how much they want to take up the above points and would only insist on the points that are meant to increase the readability of the manuscript.