Response to Reviewer 1 Comments (RC1):

We thank Reviewer 1 for their insightful comments and suggestions. A detailed response is provided below:

Review of Raberg et al.,

General comments

The manuscript of Raberg and colleagues reports the investigation of the impact of different environmental parameters on the distribution of branched GDGTs (brGDGTs) in a globally distributed set of lake sediment samples. Following this analysis, the authors propose new calibrations for the use of brGDGTs as paleo-proxies. Branched GDGTs are lipid biomarkers that are ubiquitous in continental settings and are increasingly used in paleo-studies to reconstruct past air temperatures (and sometimes pH) from lacustrine archives. However, the organisms producing brGDGTs are still unknown so the relationships between their distribution in a sample and environmental parameters (temperature, pH ...) remain empirical. In this context, Raberg and colleagues provides a very comprehensive analysis of the relationships between the lipid distribution and a wide range of environmental parameters. Furthermore, they extend the latitudinal coverage of the worldwide sample set typically used to establish brGDGT calibrations to high latitude lakes. This study is thus of great interest for the community. The manuscript is clear and well written although it would benefit from reducing some parts (see below). I thus consider the manuscript to be suited for publication in Biogeosciences after minor revisions. The authors will find below a list of specific scientific comments and a list of technical ones.

Specific comments

-The approach of dividing the compounds into subsets to isolate each structural variation is interesting and valuable as it enabled the authors to reveal some physiological links between the lipid structures and the environmental parameters. I would suggest the authors to more specifically explain the rationale for their groupings in the introduction (l. 111-112). It would also be interesting to further discuss the relationships revealed by their approach in light with the literature on other biomarkers, such as isoprenoid GDGTs or alkenones. Are the observed lipid structure adaptations coherent with the homeoviscous membrane adaptation theory?

We thank the reviewer for these suggestions. We will briefly outline our rationale behind the brGDGT groupings in the introduction, leaving the main discussion for Section 3. We will discuss connections to homeoviscous membrane adaptation theory for isoGDGTs and alkenones as a potential explanation for brGDGT structural distributions. A more involved discussion is beyond the scope of this work, but readers are directed to the Weijers et al. (2007) reference for a more detailed treatment of this subject.

-Moreover, I strongly recommend the authors to better emphasize why the calibrations they set up are better than the previously established ones, especially the one, still under review but available as preprint, proposed by Martinez-Sosa and colleagues. I am, up to now, not convinced that the authors temperature calibration would perform better than others. Eventually, the paleo-community needs to know which calibration is the best suited for their archive(s). The authors should thus clearly and specifically state in their introduction and in the discussion part, the benefits for the paleo-community of using the calibrations they defined in the present manuscript over the others previously published calibrations.

We thank the reviewer for this concern. We agree that “better” and “best” are ambiguous terms for evaluating our results that should be avoided. It is more accurate to say that our calibrations have some advantages in comparison to previous ones. In terms of R², the structural set calibrations perform comparably well to those derived using the standard approach (slightly worse for temperature and pH, slightly better for conductivity). The main advantage of using the structural set calibrations is that they can perform this well using a smaller number of compounds chosen to isolate variations in a single structural variable. In theory, this selective approach could provide some protection against the unwanted influences of other environmental parameters on different compounds (e.g. L618-621). Furthermore, subset-specific calibrations using only the most abundant compounds make it easier to apply brGDGT proxies to organic-lean samples, where only some (major) compounds are typically present above detection limit. However, we fully recognize the need to test these calibrations in paleoclimate archives, ideally with independent proxies for comparison. Such tests will be the subject of future work from our group, and we hope from the broader paleoclimate community as well. We have included the Full set temperature calibration (Eqn. 11) for such comparisons, but will emphasize this point in the text.   

-The proposed calibration with the conductivity of the lake water column is novel and of high potential for paleo-studies. The authors note that, in their dataset, pH and conductivity covary but they never suggest an explanation for this covariation and treat them separately all along the manuscript. In fact, it is not surprising to observe links between pH and conductivity in a lake water column. This aspect should be further discussed in the manuscript.

We thank the reviewer for this suggestion. Indeed, it is not surprising to find that conductivity and pH covary in our dataset. Variations in the concentration of H₃O+ (or OH-) will affect conductivity both directly and indirectly through altering the solubility of various ions. Furthermore, both pH and conductivity can be controlled by shared factors such as rock dominance and precipitation chemistry (Wetzel, 2001). While it is therefore not surprising that these variables covary in our dataset, the exact nature of their connection is complex and varies from one site to the next. An in-depth analysis of these connections is beyond the scope of this study; however, an understanding of modern pH and conductivity controls on a given site would be crucial for interpreting a downcore reconstruction of these variables using our proposed calibrations. We will therefore discuss the connection between pH and conductivity in the revised manuscript, both in the context of our modern dataset and for consideration during future downcore applications.

Wetzel, R.G., 2001. Salinity of Inland Waters, in: Wetzel, R.G. (Ed.), Limnology. Academic Press, pp. 169–186.

-In line with the previous comments, parts three and four seemed often redundant and sometimes too descriptive. The manuscript will benefit from a reorganization/condensation of these two parts. This reorganization should put forward comparisons of the study results with previous literature.

We thank the reviewer for this feedback. We recognize that the separation of Section 3 (“Partitioning brGDGTs into structural sets for FA calculations”) from Section 4 (“Results and Discussion”) results in some redundancies; however, we choose not to merge/reorganize these sections because they serve distinct purposes. Section 3 aims to outline the new structural set methodology, while Section 4 applies the methodology to the lake sediment dataset. We will, however, work to condense and/or eliminate any redundancies in these sections where we are able.

Comparisons of our results with previous literature are generally deferred to Section 4.4.4 (“Recommended Calibrations”), which aims to gather all applicable calibration results for clarity and convenience. 

-In the introduction, the authors should briefly describe the four temperature indices they used and the differences between them (l. 114).

We thank the reviewer for this suggestion. We will add a brief description of the four temperature indices and their differences in the introduction, leaving a more detailed discussion for Section 2.4.

-Also, the authors should mention in the introduction the previous studies that evidenced the multiple sources of brGDGTs in lake sediments: from the lake catchment but also from in situ production in the water column or in the sediment. This aspect will have implications to define the environmental parameters the producers are effectively experiencing and could warrant further discussion in their discussion part notably in l. 592 (can the depth habitat of the producer have a role?) and in l. 601-614 (could the export mechanism also play a role here?).

We thank the reviewer for this suggestion and agree that a discussion of the various sources of brGDGTs to lake sediments would be valuable to include. We will do so in the revised manuscript.

-In the material and methods part, I wonder if the paragraph 2.3 really belongs there. Maybe the authors could put it in the supplementary material instead. Also, some details on their statistical procedure are missing. It would be important to know if their variables were all normally distributed or if the authors transformed and centered them before defining the linear models, for example.

Paragraph 2.3 (Comparison of ASE and BD extraction methods) outlines a methodological result that is auxiliary to the main points of the paper, but we believe will be of interest to the brGDGT community. We opted to put it in the main text for this reason (and because it is within the space constraints of the manuscript), but have no qualms moving it to the Supplement and will leave the final decision to the discretion of the editor.

The dataset was constructed from our own data and the published studies available to us and were therefore not normally distributed. Logarithmic transformations for some variables (e.g. conductivity) resulted in a much more even spread of the data. BrGDGT data were normalized through fractional abundance calculations. No other transformations were performed.

Technical comments

1. 54: move “indices” before “methylation”
2. 63-64: “e.g.” should be added before the reference cited
3. 67: “of the dependencies of brGDGTs on...”
4. 114: no S at “temperature”
5. 377: provide reference for the existing correlation.

Figure 7: replace r2 by R2 in the caption. In the legend p-value should be italicized and with a small p.

1. 428: R2 is relevant only to evaluate the quality of a regression model. To discuss the correlation between two variables it is more appropriate to mention the correlation coefficient (r) and its p-value.
2. 459: explain what DC stands for l. 593: same remark for HP5

We thank the reviewer for these technical comments. All will be addressed in the revised manuscript.

Response to Reviewer 2 Comments (RC2):

We thank Reviewer 2 for their insightful comments and suggestions. A detailed response is provided below:

Raberg et al. investigate the relative abundance of branched GDGTs in a number of high- latitude lakes, and compare those distributions to previously published datasets from the tropics and mid-latitude sites. Through this work, they empirically derive global calibrations of the brGDGT distributions to temperature, salinity, and pH for use in paleoclimate reconstruction. The authors provide a comprehensive analysis of the existing and new data and develop a number of new indices to quantify the distributions of brGDGT abundances, some of which improve our understanding of how the lipid structures vary in response to environmental conditions. Overall, the authors have done a very good job and the new methods will be of wide interest to organic geochemists and the paleoclimate community. I recommend publication with minor but important revisions that I hope will improve the manuscript.

General notes:

1) The authors propose new ways to quantify brGDGT abundances through the use of ‘sets’ of brGDGTs with similar structures. This is a novel approach, although ultimately the authors seem to fall back on our existing understanding of how the different structures relate. Whatever the case, the authors should explain how and why they grouped the different sets. In addition, the authors examine a lot of different sets and report all of them, even though only some appear to be useful. The different ratios become a bit overwhelming by the end of the manuscript, and even though the authors should be commended for being comprehensive I’d suggest trying to limit the discussion to only the sets that ultimately proved useful.

We thank the reviewer for this comment. The structural sets were formed solely to isolate each structural variable in turn. The approach was motivated by observations showing the relationship of methylation number with temperature and cyclization number with pH, but we decided to build a framework to systematically examine all structural variations in turn. We will clarify this in the text.

We understand that due to this systematic approach, we generate a large number of structural sets and associated nomenclature. However, a major goal of this publication is to outline the new structural set framework in full. While the Meth and Cyc-Isom sets appear to be the most important for this dataset, for example, subsequent research may find other sets to be more relevant. At this early stage of method development, we therefore opted to show and discuss the complete structural set framework.

2) The authors suggest that the ‘best’ temperature calibration is based on a set of methylated brGDGTs (the “meth” set, maybe not the ideal name) to the average temperature of the months above freezing. It would be worth some more thinking and text about what “best” means. Ultimately, these calibrations will require extensive ‘field testing’ in different lacustrine environments to determine what works and what doesn’t (just because a calibration ‘works’ with surface sediment does not mean it will produce meaningful downcore reconstructions). And what makes one calibration ‘best? Although the calculations of fractional abundances within brGDGT “sets” are a new approach and are discussed at length in the paper, ultimately the best temperature regression (as measured by RMSE) uses the traditional method with all 15 brGDGTs to calculate the abundances. Lastly, although the ‘months above freezing’ is meaningful in regions with strong temperature seasonality it is not a particularly meaningful concept in low-latitude areas where there is no monthly variation; thus, the calibration target might not be ‘best’ in these regions. It would be worth it to consider these issues more in the conclusions.

For the first portion of this comment, we refer the editor to Reviewer 1’s similar comment and our reply, which is reproduced below:

“We thank the reviewer for this concern. We agree that “better” and “best” are ambiguous terms for evaluating our results that should be avoided. It is more accurate to say that our calibrations have some advantages in comparison to previous ones. In terms of R², the structural set calibrations perform comparably well to those derived using the standard approach (slightly worse for temperature and pH, slightly better for conductivity). The main advantage of using the structural set calibrations is that they can perform this well using a smaller number of compounds chosen to isolate variations in a single structural variable. In theory, this selective approach could provide some protection against the unwanted influences of other environmental parameters on different compounds (e.g. L618-621). Furthermore, subset-specific calibrations using only the most abundant compounds make it easier to apply brGDGT proxies to organic-lean samples, where only some (major) compounds are typically present above detection limit. However, we fully recognize the need to test these calibrations in paleoclimate archives, ideally with independent proxies for comparison. Such tests will be the subject of future work from our group, and we hope from the broader paleoclimate community as well. We have included the Full set temperature calibration (Eqn. 11) for this reason, but will emphasize this point in the text.”

We agree that Months Above Freezing is only meaningful for cold sites, especially those with strong seasonality. At lower latitudes, where MAF is identical to MAT, the distinction is meaningless. In such cases, regional calibrations using lakes that do not go below freezing may indeed be more desirable. However, we note that our high-latitude sites from the Canadian Arctic overlap with high-altitude sites from East Africa in almost every MAF plot (e.g. Fig 7). This result suggests that using MAF instead of MAT allows data from high-latitude regions to be leveraged for calibrations that are relevant in the tropics. As noted in the text, temperatures reconstructed using the MAF calibrations might be interpretable as MAT in warm or low latitude regions. We therefore suggest using the MAF calibrations in paleoclimate applications and equating the resulting MAF temperatures with MATs where appropriate.

3) The Fit to MAF is interesting in that most sediment trap studies suggest brGDGT fluxes peak during events. Admittedly, “most” means only 2-3 studies, and it is not clear to me that those results can be reconciled with good fit to MAF. Does the improved fit to MAF imply that seasonal production and fluxes of brGDGTs are indeed biased toward summer, and if so, what are we missing from sediment trap studies? If calibrations are done to ‘shoulder season’ temperatures, are the calibrations worse? The authors briefly discuss these issues, but it would be interesting to dig a bit deeper.

We thank the reviewer for this comment and agree that much remains to be reconciled between sediment trap studies and calibration efforts. With sediment trap (and sub-annually resolved water filtrate) studies showing brGDGT production to vary temporally and to be tied to numerous potential influence, it is somewhat remarkable that the pool of brGDGTs in a lake surface sediment relates to an average air temperature at all. We, too, noted that MAF is probably roughly equal to shoulder-season temperature in most cases. Unfortunately, it proved difficult to standardize a “shoulder-season” across this varied dataset. We tried calibrating against the first and last positive-degree months, or the first and last two, but our monthly temperature resolution proved to be too coarse. Additionally, if shoulder-season temperatures are relevant, it is likely due to overturning events and/or seasonal nutrient fluxes occurring at these times, which will vary widely between lakes. We thus abandoned these efforts. However, we will expand our discussion to include this subject in the text.

4) I have some concerns about the section starting on line 580 that develops calibrations for dissolved oxygen. Although this is inconclusive, I question whether we the environmental data is good enough to meaningfully address this. Is DOmean the average of the entire water column? And over what seasons? Calculating this variable is a fraught exercise without access to each lakes’ actual DO profiles, many of which do not appear to exist.

We agree with the reviewer’s concerns, and echo them in the discussion at the end of the section. Given the increasing evidence of a dissolved oxygen influence, we believe the section on DO will be of interest to readers and will highlight the need for better DO data. However, given that the results are inconclusive, we will discuss the possibility of moving the technical aspects of this discussion to the Supplement with the editor.

5) Several of the indices and calibrations utilize fractional abundances of the bicyclized penta- and/or hexamethylated compounds that are often not abundant in sufficient quantities to be accurately measured in many of the published datasets. It is not clear how (a) the authors treated those sites in their calibrations, (b) what their limits of detection are for the different compounds in their new sites and how those were determined, and (c) what they suggest to do at sites where these compounds (chiefly IIc, IIc’, IIIb, IIIb’, IIIc, IIIc’) are below detection levels. This could create problems for some of the sets that isolate these structural groups.

We thank the reviewer for this important concern and note that it is relevant to both traditional calibrations and those constructed using the new structural sets. For applications involving samples with compounds below the detection limit, we believe that our new method actually provides a unique advantage by allowing for the construction of calibrations that rely solely on high-abundance compounds (e.g. Ia, Ib, Ic, IIa, IIa’, IIIa, IIIa’; Eqns. S1, S4, and S7).

We treated compounds below the detection limit as having an absolute abundance of zero. This assumption led some sites to have compounds with FA = 0 and/or FA = 1. All of these FAs are plotted as such (e.g. Fig. 7c) and tend to be associated with noisier trends (presumably due in part to the lower abundances). Removing these sites from the dataset would have removed valuable points from the stronger trends (e.g. Fig. 7a), upon which our calibrations primarily rely. For subset-specific calibrations (e.g. Eqns. S1-S9), we did not face this issue and removed samples with any FA = 1.

We will add the above discussion, along with a description of our own detection limit, to the Methods section. We will also stress the potential applications for low-abundance samples in the Discussion.

6) Line 432. The text below highlights a challenge in working with these data – the environmental variables themselves are strongly correlated. This makes it difficult to conclusively support some of the statements in this paragraph – “temperature may therefore play a secondary role”... for instance. This assumes that temperature actually does play a role, rather than that temperature is correlated to pH and conductivity, and therefore is (spuriously) correlated to the brGDGTs. It might be worth considering application of multivariate statistical methods that take into account collinearity among the predictors, such as redundancy analysis, to address this issue.

We agree with the reviewer – correlations between environmental variables pose an inherent challenge to this type of work. We will add a correlation table for the environmental variables in the Supplement and expand our discussion in this section and elsewhere in the text. We further agree that redundancy analysis and other multivariate statistical methods would be a valuable extension of this work and will be the subject of a future publication.

Minor things:

Line 59. Why “however”? The shifts in community composition can track shifts in environmental conditions.

We use “however” to indicate that changes in community composition could affect brGDGT distributions independently of a physiological response.

Line 74. As stated above, note that, at many sites, the highly cyclized brGDGTs are often below detection levels, such that equation 2 is reduced to the fractional abundances of only the most abundant compounds.

We will include a discussion of this point either here or later in the text.

Line 138-139. How many sites had water chemistry data?

We will include this information.

Line 220. Did the logarithmic scaling result in a normal distribution of these environmental variables?

Logarithmic scaling greatly improved the normality of these variables, resulting in a much more even spread of the data, but they were not normally distributed in the end (did not pass a Shapiro-Wilks normality test). We will include this information.

Line 301. Here and elsewhere throughout the text, it would be best to provide p values for the correlations you report.

Due to the large number of R² values discussed in the text, we found that including accompanying p-values made the text overwhelming and more difficult to follow. As the vast majority of p-values were < 0.01, we opted to only report p-values ≥ 0.01. This explanation is included in the Methods.

Line 398. There is some thinking that a substitution closer to the head group would be more influential on membrane fluidity (structural disruption closer to the surface of the compound). Your results suggest this is a minor effect.

We thank the reviewer for this interesting comment. We would appreciate if the reviewer could provide some references to us so we could explore this topic in our dataset.

Line 427. This does not suggest they have similar influences on brGDGTs. Rather, it suggests that conductivity and temperature covary in the environment.

We thank the reviewer for pointing this out. We agree and will change this text. 

Line 433. Could you cite a table or similar for this statement?

We will add a reference to the supplemental figures containing the relevant statistical values.

Line 471. Similarly, how did you assess that ring number is “primarily” correlated with pH rather than conductivity? Based on an r2 difference of 0.04?

We agree that an R² difference of 0.04 is small. However, this (or a comparable) difference was apparent across almost all 15 compounds (Fig. 9 vs. Fig. S20). 

Line 499. Regressions of the temperature variables onto what? Which brGDGT formulations?

We will change the sentence beginning on L499 to read: “For each structural set and subset defined in Section 3, we performed regressions of brGDGT FAs against five temperature variables to generate multiple global-scale calibrations.”

Line 505. A challenge here is that MAT = MAF in the low latitudes. The main reason for the MAF formulation is to account for the additional complexity introduced by a global calibration that includes high latitude systems. It would be worthwhile to reemphasize this here.

We will reemphasize this nuance in the text.

Line 540. This would make some sense, since MAT = MAF in the sites included in the Russell et al. (2018) calibrations.

Agreed.

Line 541. “On a regional scale”... It would be worthwhile to mention the relatively unique (highly alkaline) nature of these lakes.

We thank the reviewer for noting this and will include it in the text.

Figure 10. It is a bit difficult to figure out what is being plotted in these figures, in particular panel a. It would be most helpful if the equations are introduced alongside this figure. Related to this, it appears from the text that a very simple formulation, MBT’5Me, performs nearly as well as more mathematically complicated (e.g. equation 10) versions. Is this correct? Lastly, although a high r2 is great, the RMSE is in some ways more important to climate reconstruction. It might be good to include a plot showing the RMSE, similar to figure 10A.

We thank the reviewer for these suggestions. We will explore the option of introducing the equations alongside the figures.

It is true that MBT’_5Me performs nearly as well as Eq. 10. This is perhaps not surprising, as the Meth FAs in Eq. 10 were inspired by the same underlying principle as the MBT’_5Me index – that methylation number varies in response to temperature. We do not suggest abandoning the MBT’_5Me index, but we present the Meth structural set as a more targeted approach at isolating the underlying connection between methylation number and temperature.

We thank the reviewer for pointing out that a plot similar to Fig. 10A comparing the fits using RMSE rather than R² will be of interest to the paleoclimate community. We will explore options for including such a plot, either as part of the main text figures (Fig. 10 and 11) or in the Supplement. 

Line 674. This is correct in a way, but the use of structural sets does not ultimately improve calibration performance. Correct?

We will clarify that the structural sets “improve compound-specific correlations with environmental parameters...” in line 674. It is true that they perform comparably well to traditional methods in terms of R². However, we believe the fact that the structural sets can perform this well while isolating only the relevant structural changes is an “improvement”. This point is currently ambiguous in the text, however. We thank the reviewer for pointing this out and will revise accordingly.

Line 692, could add a clause of “particularly in high-latitude environments”.

We will incorporate this helpful suggestion.

The paper refers to papers by Sosa et al. (2020, 2020a) that are not in the references. Please provide the correct citations.

The references are under Martínez-Sosa et al., rather than Sosa et al. However, we found references to both “Martínez-Sosa et al. (2020)” and “Martínez-Sosa et al. (2020b)” in the text, though we only intended to cite one publication by this author (the preprint, as submitted to Geochimica et Cosmochimica Acta). We will correct this.

Response to Editor Comments 1 (EC1):

We thank the Editor for his additional insightful comments and suggestions. A detailed response is provided below:

Additional comments from Associate Editor:

Thank you for submitting this very interesting manuscript to Biogeosciences. I think the reviewers have some good suggestions and raise interesting questions, some of which I also have, so won’t repeat them here in detail.

Further, I wonder if you could provide more details about in situ production of brGDGTs in the lakes vs what is the imprint of brGDGT supply from the lake catchments. The origin of the brGDGTs will determine which parameters can be reconstructed, such as pH in soils vs in the water column, temperatures of different water depths, etc? I also think a more detailed discussion about the reasons for the apparent covariance between conductivity and pH in your dataset would be useful.

We thank the editor for these comments and suggestions. We agree that the relative abundance of in situ lacustrine vs. catchment-derived brGDGTs has important implications for calibration studies and downcore applications. Much research has been invested to tease apart the sources of brGDGTs to lake sediments as a result. Unfortunately, even basic studies of the sources of brGDGTs to the lake surface sediment are missing for the vast majority of the lakes in our study, limiting our ability to address these issues here. This unavoidable source uncertainty likely enters our study as scatter in the data – a lake with significant soil input might be shifted from its “pure lacustrine” position. We will include a discussion of this topic in the text. We will also discuss the covariance between conductivity and pH, as outlined in our response to Reviewer 1’s comment.

I also wonder if there should be more information about global vs regional/location calibrations for the reader that is less familiar with the topic and to explain why you rather extend the global calibration instead of developing another regional calibration that better capture the strong seasonality.

We thank the editor for this suggestion and agree that it will be a valuable point to discuss in the text. We initially set out to construct regional calibrations for our Canadian and Icelandic datasets. However, we found that brGDGTs were not able to adequately resolve temperature differences within the small MAF range (6.6°C, or 3.2°C without the warm and cold end-members) of these datasets. This is an important result as it indicates that other environmental and/or site-specific effects complicate the link between lake sediment brGDGT distributions and air temperature. We will discuss this in the text.