| 22 May 2026
Technical note: Guidance on setting up Pecube inversions with the neighbourhood algorithm
Abstract. Pecube is a three‑dimensional thermal‑kinematic model that enables the prediction of thermochronometry data and the investigation of past tectonic and topographic change, using both forward and inverse modelling approaches. However, the problems addressed by Pecube inversions are typically non‑linear and high‑dimensional, such that multiple models can often reproduce the data equally well. Pecube inversions, which involve the evaluation of large numbers of forward models against observations, are performed using the neighbourhood algorithm (NA), enabling guided exploration of the parameter space. Despite more than a decade of applications, practical guidance on how to configure NA–Pecube inversions remains limited. Furthermore, the recent development of a user‑friendly interface for Pecube is expected to broaden its user base and further increase the need for clear guidelines on NA configuration. This contribution aims to provide intuition and general guidance for performing NA–Pecube inversions through a conceptual approach. Although the proposed guidelines remain intentionally broad and do not guarantee optimal performance for user‑specific problems, they are intended to support informed decision‑making and to provide a practical starting point for NA–Pecube inversions. Users are encouraged to explore and adapt NA tuning parameters to their specific modelling objectives and problem settings.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Geochronology.
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“Technical note: Guidance on setting up Pecube inversions with the neighbourhood algorithm” by Bernard et al is an interesting exploration of how best to use the neighbourhood algorithm. I would recommend minor revisions.
The paper does an excellent job at providing the background to different inversion methods but this background is perhaps aimed at a specialised audience. Whereas people that will benefit from this paper are likely people who want to use the NA and Pecube and may nt need to know about other methods. If the aim of this paper is to highlight how the NA differs from other methods, then a bit more information is required to introduce these methods. For example, on line 45 the concept of a parameter space is introduced without describing what it is. I am not sure that many people need to know the names of steepest descent, conjugate gradient or Gauss–Newton methods. It is also not clear why these references are chosen. Surely the original references should be used, or maybe examples where these have been used in geomorph or geochron studies. Perhaps the idea of a 2D misfit landscape could be introduced more gently as most people are more used to thinking about a 2D surface than a high dimensional space. This could be tied to Figure 1 and contours of parameter space could help reinforce the idea of a landscape with slopes and curvatures.
A section on how the NA has been used in other aspects of geomorphology should be included. It has been used in Fox and Shuster (EPSL, 2014) and in Han et al., (Nature Geoscience, 2024). The results presented here are important and useful for these papers too.
It would be really nice to actually invert the true data to understand how well the model works without any error introduced to the data. At the moment, it is not clear if the inversion is not working because of the noise added to the data or the choice of NA parameters. In particular, the “True” 1D marginals of the posterior density function do not provide the correct values used to predict the data. The relief parameter is relatively flat between 0.2 and 0.7 and the tu parameter has a clear, well defined peak at the wrong location (~15 Ma). The heat production and basal temperature models do not converge to the correct value at all. Is this because of the noise introduced or because the NA is not finding the correct solution?
It would be useful to combine the heat production and basal temperature, with a background average exhumation rate to get an estimate of the near surface geothermal gradient. The data are clearly resolving a geothermal gradient, but because the geothermal gradient is a function of heat production, basal heat flux and exhumation rate, heat production and basal temp can not be independently resolved. The inversions all do a bad job at predicting the correct values of these parameters, but perhaps they do a good job at predicting the correct near surface average present day geothermal gradient. This would simply be an additional plot that could be created from the sampled combinations of parameters, assuming a steady state model, and plotted as a function of misfit. It would be nice to see if this combined parameter is well resolved and would explain why you can’t resolve the other parameters. You can also extract the resolution matrices and correlation matrices from the ensemble of forward models. This would also help explain the resolution of the parameters. It would enable you to say that model and data can not resolve the parameters and eliminate the possibility that the NA is not working correctly.
The recommendation should be that people need to do a resolution test. The parameter spaces are all so different and the data sets are all so different, completely different combinations of NA parameters might be required to provide an optimal solution. Ultimately, however, the computational effort required to more fully sample parameter space and rely less on optimization is small compared to the effort of climbing mountains to collect vertical profiles, crushing and separating rocks, picking apatite grains, ….Perhaps the recommendation should be that people should oversample to be on the safe side.
Some of the topic sentences at the start of paragraphs are not very clear. For example “How about Nm?”, is not an effective introduction to a paragraph. It also relies too heavily on the previous text. A better topic sentence could be “How does the value of Nm control the …..”
This topic sentence does not make sense “Lastly, rather than focusing on the number of iterations, the total number of models performed is a more relevant measure when considering the effect of dimensionality.”. I think simplifying the text would help here.
Sincerely,
Matthew Fox
Line comments:
47: “local curvature of the misfit landscape” Are you sure that these algorithms use the curvature of the misfit landscape and not the slope?
66: Add Fox et al., (G-cubed), 2014 where the NA was used and correlations in parameter space were assessed.
277: What does a random noise mean in this instance? Are the ages changed by 10 %? It seems strange to add on 10% error to the data but then estimate the uncertainty to be only 5%. I suppose this is likely what lots of datasets look like, but with much larger errors.
280: It is not appropriate to refer a true distribution. This is never actually shown, instead you show the results of the sampling stage of the NA and 1d marginals through PPD. This is not a “true” distribution as it is simply inferred with more models, than the other distributions. This should be called something else, maybe target would be best. Especially because the stars are referred to as showing the true parameter values. In fact, after the noise and uncertainty has been added, the target misfit distribution might have minimums that are very far from the actual values used to generate the data. Because of this, the inversions with different NA parameters should be compared with the minimum values of the target distribution not the true values. Please rename the true distributions to something else throughout the manuscript.