Publisher’s note: a supplement was added to this comment on 28 February 2025.

This manuscript develops and applies a Bayesian calibration of XRF with instrumental data, in order to then hindcast Holocene temperature time-series for two varved lakes. 

Inferring fossil climate from calibrating XRF to recent temperature by necessity assumes that the relationship has been stationary over time, and that any other factors which didn't occur as much further back in time, e.g. soil erosion or nutrient pollution, do not affect the temperature reconstructions (or even more importantly, the calibration period). However, humans have messed up many records over the past centuries/millennium, possibly affecting the varved record as well (note that especially Diss Mere is located in a severely human-influenced region). How can these factors be disentangled? This is mentioned in the discussion, but it would be useful to expand more on this problem in the Introduction.

Why did you decide to only use non-biological proxy data? Perhaps this has to do with additional complexities of interacting/competing ecosystem components, but it would be good to spell this out (e.g., in section 2.1).

Null counts (inferred absences, x_i=0) are frequent in most types of proxy datasets, e.g. pollen diagrams. Would this be a problem for your approach if used in other studies, given the clr transformation? Could the approach be amended to account for null counts (even if just by adding a small constant to all values)?

line 161-2, it is unfortunate that age uncertainty is not considered in this modelling approach. This is problematic, even for this varved lake (note that the varves of Diss Mere don't reliably extend to present-day, causing even more chronological uncertainties). Could age uncertainty not be included as a module of the Bayesian analysis? Lots of work has gone into developing Bayesian age-models, so you could build on existing methods (e.g., https://gchron.copernicus.org/articles/4/409/2022/).  

Lines 163-5, See also Blaauw et al. 2010 who produced random-walk 'fake' proxy datasets, some of them steered by (again fake, random-walk) environmental forcers [https://doi.org/10.1177/095968360935518]

Why did you use a polynomial regression model (equation 4)? Would other models such as a smooth spline have worked?

Vague normal/uniform distributions were used as priors. Did you explore how different/stronger priors would affect the results?

Figs. 1/2: I agree with the other reviewer that it is very hard to visually spot much of a correlation between temperature (black dots) and the variables (or between true and reconstructed temperature in Fig. 2 - my eyes would tell me that there's essentially no correlation). This is especially because temperature shows very little variability, ranging only from -2 to 2 degC, with the far majority centered around 0 (so, reconstructed temperature anomalies >1 degC would be based on very few calibration data). But perhaps I am misunderstanding these graphs. Could the individual leave-some-out sets be shown with different colours in Fig. 2?

Can you show the structure of the MCMC run's 'energy'? How many parameters were involved? Line 384, how do you mean 4 chains were used - were the results joined afterward? Was any thinning necessary?

Figure 4 - the temperature reconstruction of Nautajarvi seems close to what is generally assumed for Holocene temperature time-series, with a HTM followed by a late-Holocene cooling. However this is not visible for Diss Mere. This is reported in the Discussion. A devil's advocate might say that the authors were lucky with Nautajarvi's reconstruction as it follows known Holocene patterns, but weren't as lucky with Diss Mere. Did you try multiple runs with different settings/priors, and were the results robust?

 

The manuscript will need a thorough grammar/punctuation check because at times it is difficult to follow. I am suggesting a few specific changes here:

line 41 - has heightened the need

line 53 - please define your timescale at first use - is the present AD 2024, AD 2000, AD 1950?

line 71 - even though this is key...

line 273, periods

line 288, from 10 to 2 thousand years before 1950 CE (best to discuss time series forward in time)

line 289, ...; it thus has a...

line 302, increased detrital input...

line 320, break up or restructure this long sentence, e.g., by adding a comma after 'present'

line 356, values which the model picks from (?)

line 398, replace full stop with comma?

line 400, Out-of-sample evaluation?

It is great that the authors have produced an R package for the approach presented here. Unfortunately, I was unable to actually install and run the R package. JAGS has to be installed in order to run. Of the 23 additional packages that had to be installed on my systems (I tried this on both linux and mac), it was 'rjags' that caused issues. This seems to be caused by the version of JAGS (4.3.2) not coming with 'modules-4', or owing to linking problems. Would it be possible to swap to another MCMC sampler? For example, twalk (Christen and Fox 2010 Bayesian Analysis 5: 263-282) is available as an R package. Even though this twalk package uses pure R and will thus be slower than e.g. c++ versions, at least I expect it would be easier for users to install and run everything without too many issues. 

The manuscript develops a Bayesian calibration model of XRF data with the aim of providing hindcast climate reconstructions at a greater temporal resolution than is available from other proxy sources. It is noted that current proxy source climate reconstructions typically have a temporal resolution of 100-200 years. Though there has been progress in reducing the timescales to decadal using other proxies, this is via the usage of mathematical models with the associated challenge that it is not possible to separate patterns observed at this improved temporal resolution between climate variability and model artefacts. As such XRF is offered as providing a solution. Overall the authors do a good job of articulating why their proposed work is necessary.

In the following I will chiefly focus  the comments with the statistical modelling aspects/

Comments:

The authors frequently mention quantitative proxy values (say line 78) but are the proxy records they collect not quantitative data, in terms of intensities, as is much of the proxy data collected in terms of tree rings, battles, diatoms, pollen etc. It would be good to clarify this as qualitative proxy records are mentioned throughout but it is not clear to me what this refers to.

(Line 225 and Figure 1). From a modelling perspective there is no clear rationale made for why a quadratic relationship is appropriate, perhaps some form of smoother would work equally well without the tail assumptions of the polynomial model. In Figure 1 visualisations of the fits for each chemical is made however there is no clear relationship and the figures reflect a lot of noise., This may be due to only one climate proxy being presented (temperature?) whereas it is possibly the case that the proxy could depend on several - the authors should comment in this regard.

The authors mention that uncertainty quantification is a strong basis of their approach and note (Line 417) “Nevertheless, gaining an 80% coverage percentage is acceptable for this modelling approach.“. It appears that the constructed 95% HPD regions only contain 80% of observations. Why is the 80% acceptable, or a stronger argument needs to be made in this regard. Perhaps the reduction in uncertainty coverage is due to the log-ratio transformations of the XRF data and modelling inter-element relationships with a multivariate random effect which is acting as a poor equivalent to accounting for the compositional nature of the data? While the authors claim reasonable performance from an uncertainty quantification perspective, insufficient discussion is made of mean/median (unclear which) predictions in Figure 2. I note that authors later calculate the correlation between Diss Mere and the LMR but provide no similar calculation here ?  Figure 2 seems to suggest that the R^2 in this case would be very poor, is this why it is not presented?

A weakness (in my opinion) of the results presented in the two case studies later on stems from an insufficient evaluation of predictions of the mean temperature for the calibration dataset at Diss Mere - predictive performance in terms of the uncertainty may be 80% coverage, but it is not clear that the center of the prediction intervals are accurate - this perhaps explains the commentary on the performance of Diss Mere later on. Was an analysis of the calibration approach carried out at the Finnish site? If so, does it explain why the predictive performance is potentially better there than Diss Mere? Alternatively, do the weaknesses in predictive performance in Figure 2 also manifest at the Finnish site? Similarly annual mean temperature is used - is precipitation potentially useful to incorporate here or is predictive performance poor when it is incorporated as observed at Diss Mere? Additional evaluations in this regard could be included in the Supplementary materials.

In terms of model assessment, the sensitivity of results to specified priors is not provided - the priors as presented are very vague but could some information be incorporated to make these more informative? Since the XRF is rescaled using a centred log ratio - is it plausible that intercept values of +-200 are possible, which is what is suggested by the vague prior. Similar arguments apply to the priors for the other components - are some of the values suggested by the prior impossible?

The manuscript also requires substantial editing as there are a number of grammatical errors, typos and excessive use of language which makes the manuscript difficult to follow at times. For eg, SCUBIDO is spelt incorrectly twice and some of the text used either side of equations causes confusion. I have noted several of these below.

Typos/suggestions/clarifcations

Line 31: “downcore”? This caused confusion, perhaps “down the core” would be better

Line 111 - Sweeney changes to 2017 from 2018?

Line 159: “n” in formula is not in mathscript, though it is in Line 157

Line 193-195: “Where” - sentence needs to be reformatted as it continues previous lines and reads poorly. There are several instances of lines continuing through outlined formulae which are difficult to read/ correct.

Line 204: “casual” relationship? Is this supposed to be “causal”?

Line 215: Line starts with “with” and consequently reads strangely 

Line 224: Mathematics of mean vector are confusing as the subscript commas and commas between variables are difficult to distinguish

Line 309 -  “found  a qualitative link” - what is a qualitative link?

Line 329 - “Sweeney et al (2017)” - this appears to vary between 2017 and 2018 in the manuscript?

Line 334 - “and thus the model did not find a good enough relationship. Annual mean temperature on the other hand worked well, which support the temperature signal recorded in the qualitative XRF-CS data during the Holocene “ - what is meant by a “good enough relationship? Why was the temperature signal and XRF-CS relationship deemed good enough?

Line 337: “Another point to highlight at this stage is that we run the Bayesian model using a   multivariate dataset made of the elements measured by the XRF scanner, which differentiates SCUBIDO from other recent reconstructions based on varved sediments “ - How does it differ?

Line 339: “We therefore rely on the Hadley  Central England Temperature (HadCET, Met Office) data” - is this proximate to the site?” As such, does it capture temperature change att he site reasonably?

Line 350: “𝑋𝑅𝐹𝑚was resampled to annual means “ - How was it sampled or adapted? Was the XRF data not at annual level in any case?

Line 356: replace “in” with “from”?

Line 366” “fitted using within” line unclear.

Line 445: “is cooler than except” typo

Figure 5 legend “The LGMR and Temp12k presented at a 200-year.” Typo

Line 546: “The most important choice was to use of “ 

Line  551: “ SCUBDIO “ 

Line 580: “ “And finally, “ and is unnecessary?

Line 584: “ “the SUBIDO approach “ - typo

Line 600: : “of which Paul Lincoln if funded by “