Authors’ response to RC1 (Ferrier):

We thank Dr. Ferrier for a very supportive review of the paper. The review has one general comment and a number of minor technical comments, which we address separately below. 

The general comment is that “The main text didn’t have quite as much detail as I would have liked about a few things, including equations and parameter values for the diffusive loss of these isotopes, as well as more detail about the model for the production, decay, mixing, and diffusive loss of these isotopes.” The review then suggested transferring a variety of technical material from the description of the model in the supplement into the main text.

In writing the paper, of course, we intentionally minimized the amount of technical material relating to the model in the main text, both to make the paper suitable as a ‘short communication,’ and also to focus on the main idea of the paper, which is that the observed near-surface depletion in cosmogenic noble gases is a signature of wildfire heating. The model is mainly intended as a demonstration of concept: it shows that our interpretation of the data is physically possible. It is not intended to be uniquely invertible for a specific wildfire heating scenario. In fact, as we explain in the text, several important parameters in the model (e.g., the specific diffusion kinetics and the inherited/background ²¹Ne concentration) have not been measured, and without those measurements it is really not possible to use the model for anything more than a proof of concept. Although it is an interesting model (and we appreciate the reviewer’s recognizing this), in truth it is a very simple model that only explains a few aspects of the data. Although it basically simulates the broad features of the data set, we are not at all sure that this is the optimal model framework for interpreting this type of data in the future. For these reasons, we do not think it is helpful or desirable to focus the bulk of the paper closely on the model details, so we included only a general description of the model in the main text and put the technical details in the supplement. 

Thus, as our aim is to keep the paper short, simple, and focused on the main point that cosmogenic noble gas concentrations in soil quartz contain information about wildfire history, we do not propose to move significant amounts of the model description from the supplement into the main text. However, we will add the technical information requested by this reviewer (mainly, the equations and parameters for calculating diffusion kinetics) to the supplement. 

With regard to the specific technical comments,

“Page 3, line 22: I like the description of the characteristic time scales of these isotopes in the latter half of this paragraph, but I'd like to see a little more detail about how these were calculated.  I suggest adding a few sentences that describe the sensitivity of diffusive loss to temperature and grain size, including a few equations that show this (e.g., Equations 2-3 in Tremblay et al., 2014).  Then, I suggest listing values for the parameters in that equation relevant for ²¹Ne and ³He (e.g., those used in the supplementary Matlab code) in a table in the main text or in the supplement.  That would be helpful because it would enable readers to calculate the time scales of diffusive loss for these isotopes for themselves without going back to the studies cited at the end of this paragraph to look up the relevant equations and parameter values.  This would also set up the last four sentences of this paragraph nicely.”

As noted above, we will add the details of the diffusion kinetics calculations to the supplement. However, in the section that the reviewer refers to on page 3, we intentionally tried to include the minimum amount of information necessary for the reader to understand what is going on – our goal is to avoid diluting the main points of the paper by repeating material that is already very thoroughly covered in existing publications on noble gas diffusion. We interpret the reviewers’ comment to indicate that even if we did not include everything that might be relevant here, we did get above the ‘minimum amount’ threshold. Regardless, we can revisit this section and try to improve it a bit. 

“Page 4, line 10: Are there any other possible explanations besides heating by wildfire?  The statement here that surface heating is "the most likely explanation" seems to suggest that there are other possible explanations that the authors rejected.  Is that the case?  If so, what are those alternative explanations, and why are they less likely?”

Actually, we can’t think of any other believable explanations. The difference between the ¹⁰Be and ²¹Ne depth profiles requires heating to a reasonably high temperature, because in the absence of heating they have similar production mechanisms and behavior. This wording is really just to hedge in case we are missing something obvious. Now that two reviewers have also failed to find any other obvious explanations, we will clarify this in the text. 

“Page 6, first paragraph: The model simulation summarized here strikes me as useful and appropriate for exploring the effects of wildfire on CRN concentrations.  My only suggestion is to move most of the model description from the Supplement to the main text.  My first impression while reading through the main text was that I wanted more detail about how the simulations were done and how the values were calculated.  These are things the Supplement does well, so I suggest moving much of that text from the Supplement to the main text.”

As we discuss above, we decided to keep most of the technical details of the model in the supplement to maintain the focus of the paper on the main idea – cosmogenic noble gas concentrations contain information about wildfire history – and not on a model simulation which, as we describe, is highly simplified anyway and is not intended or expected to explain all possible aspects of the data. 

“Supplement, Section 1, paragraph 2: To help readers verify quantitative statements like these (“no more than 6% of ³He present would be expected to be lost during sonic treatment”), please list the adopted parameter values for diffusive loss for ³He in quartz and the equations used for this calculation.  This is similar to my suggestion above to add a table of parameter values used to calculated diffusive loss.”

As noted above, we will add the specific parameter values in the supplement instead of just referring to the Shuster paper. However, as regards equations for calculating diffusive loss, these equations have been described in great detail in standard reference works (e.g., Fechtig and Kalbitzer), and precisely reproducing them would require a fairly extensive discussion of the assumptions and approximations needed to derive them. Thus, we think it is clearer, more concise, and overall more helpful to refer to those references than to reproduce them. 

“Supplement, Section 4, paragraph 2: Is the “sigma k” here a typo?  It looks like the standard deviation is the product of an undefined variable sigma and the value of k itself.  For clarity, I suggest making the "k" here a subscript on the “sigma”.  This will help other readers avoid the same kind of confusion I experienced for a few minutes here.”

Yes, the k is intended to be subscripted. We will fix this.  

“Supplement, Section 4, paragraph 2: Typo.  Near the end of the second-to-last line of this paragraph, the “-1” in “Z_i,j-1” should be subscripted, as it is elsewhere in this paragraph.”

Corrected.  

“Supplement, page 3, last paragraph: Is the adopted grain diameter of 0.43 mm appropriate for the soil at the study site?  Diffusive loss is sensitive to grain size, so it'd be useful to state how close this value is to the typical grain diameter for quartz here.”

Yes, the quartz we analyzed was taken from the 0.25-0.5 mm grain size fraction (section 1 of the supplement), so in fact it is a pretty good approximation. It’s one of the least speculative parameters in the model.  

To summarize, we propose to make the following corrections in response to this review:

1. Add parameter values and other technical details for computing diffusion kinetics to the supplement.
2. Clarify the ‘other possible explanations’ section of the main text (p. 4).
3. Correct technical errors with the mathematical notation in the supplement.

As this comment has been converted to RC1, we respond to it in RC1. 

Authors’ response to RC2 (Sarikaya):

We thank Dr. Sarikaya for a helpful and supportive review of the paper. We address all of the review comments below. Only a subset of the review comments require changes to the paper, and we summarize our proposed changes at the end of this response. 

“They assume zero erosion for the surface for 425 ka! Would this be possible? There should be some justification for that. If you assume (or estimate soil erosion), what did your production profile (and results) look like?”

We agree that zero erosion is probably rare in real life. In this example, however, the field and remote sensing observations (see the LaHusen, 2020 reference and Struble and Roering, 2021 as cited below) indicate that the evolution of the landslide surface after emplacement has been characterized by a decrease in surface roughness, which would imply locally variable erosion and deposition across the surface. At present, the site has near zero curvature, implying near zero net erosion. Thus, it is possible that the site has experienced local net erosion, net deposition, or neither, and a zero erosion assumption is most likely closer to the truth for this site than for more typical geomorphic settings. For the model simulation, we assumed zero erosion because (i) our aim in the paper is to present the simplest possible model that quantitatively explains the observed near-surface depletion in cosmogenic noble gases; (ii) field observations, as noted above, indicate minimal erosion; (iii) we have no independent constraints on the erosion and/or deposition rate; and (iv) the purpose of the model is to explore the effects of wildfire heating and not to estimate the age of the surface. The text is clear that the age estimate that assumes zero erosion may be inaccurate. With regard to the heating/mixing simulation, adding soil erosion would simply require a small increase in the mixing rate to match the ¹⁰Be data and a small increase in wildfire heating time or temperature to match the ²¹Ne data; there would be no change to the overall conclusions of the paper. 

“They mentioned a similar approach on bedrock surfaces (Page 2, Line 4-5). In my opinion, it could be more reasonable to apply this method on a forested bedrock surface. What about taking samples on a nearby bedrock surface instead of this soil profile? Alternatively, could the authors explain why they chose this soil profile to apply this method?”

One general reason is that bedrock surfaces are simply not common in heavily forested areas: extensive forest cover requires well-developed soils. Likewise, landscapes with extensive bedrock outcrop are expected to support very different forest types and therefore have a very different fire regime. Thus, wildfire history information derived from soil-mantled and bedrock-dominated landscapes would not be interchangeable. For this study specifically, the practical reason is that bedrock in the Oregon Coast Ranges is weakly consolidated and highly weatherable, the landscape is almost completely soil-mantled, and there are no bedrock outcrops near the site. 

In addition, as we describe in the text, because of the ability of soils to support vertical mixing, the type of information on fire heating history that one would derive from soil and bedrock depth profiles are fundamentally different. Vertical mixing in soils permits a much longer history of heating events to be recorded. 

Finally, with regard to why we chose this soil profile, we didn’t choose this soil profile specifically to investigate wildfire depletion of cosmogenic noble gases. The site was already the subject of studies of soil carbon storage because geomorphic observations indicated that the site was likely much more stable than soils on surrounding hillslopes and therefore was likely to have a relatively long soil residence time. Originally the cosmogenic-nuclide measurements were intended just as an attempt to get an estimate of the deposit age. Perhaps we should have expected to observe cosmogenic noble gas depletion due to wildfire heating, but we didn’t – we were initially surprised by the ²¹Ne and ³He data before we figured out what was happening. 

“They used an average soil density for the mixed layer (1.7 g/cm3, derived from field measurements). Did they measure the bulk density of soil in every single sample, or did they use a single bucket of soil to represent the whole profile? There should be some difference in both approaches.”

The density was obtained from the weight of soil samples collected in an auger bucket of known dimensions. We will add this information to the supplement. 

“They omitted muon production; this might have some effect, especially for the deeper samples.”

This is correct. We discussed this in section 4 of the supplement. 

“P1L10. Typo “Earth?s”

Corrected. 

“Fig1a. A location indicator with a cross is already provided; however, this alone is insufficient for proper georeferencing. Please include at least one additional location indicator within the map. Additionally, I recommend removing the straight arrow line; the dashed-line arrows accurately indicate the mass movement directions for the landslide, while the straight arrow may be misleading. Or, just remove the arrow-head. Moreover, it would be beneficial to delineate the landslide source area for the readers' clarity.”

The latitude and longitude of the site are stated at the beginning of section 2 of the main text, so georeferencing of Fig. 1 is not necessary for locating the site. The main purpose of the upper left panel of Figure 1 is simply to show the overall topographic context. Regardless, we will consider these suggestions for Figure 1. 

“Fig1c. Not all samples in this picture have been processed. Specifically, 13 samples are missing from the analysis. Furthermore, there are 16 Ne-21 and He-3 samples, while only 14 Be-10 samples were measured. Please mention this somewhere in the text, or may be in the caption.”

This is correct. The matching of cosmogenic-nuclide measurements to samples is given in Table S1 in the supplement. We can edit the caption of this figure to indicate that all samples shown in the figure were not analyzed for all nuclides. 

“P3L5-9. The authors briefly explained why they chose an ancient landslide surface for sampling, and justifyed the stability of the surface. This may seem counterintuitive, considering that landslide deposits are typically perceived as less stable. Is there a specific cosmogenic point of view guiding this choice?”

As we discuss above and as is also discussed in the LaHusen and Struble/Roering references, geomorphic observations indicate that the broad, flat, and undissected deposition area of the landslide is, in fact, more stable than surrounding hillslopes. The original selection of the site, as we mention above, was because the apparent stability of the site implied a relatively long soil residence time. 

“P2-Section 2. More information is needed for the sample site. Snow cover and duration? Topographic shielding correction?”

This site does not experience significant snow cover. The topographic shielding correction is negligible and we can add this information to the supplement. 

“P3L16. What would be the vertical error in cm due to the auger sampling procedures? The samples were taken in 10 cm intervals. A couple of words due to the sampling uncertainties would be good.”

The vertical position of the auger head can be accurately measured during field sampling, so the uncertainty in this measurement is not significant. It is more likely that a vertical uncertainty would be caused by small amounts of mixing or overlap between adjacent auger samples, but it is not clear how to quantify this. We will add a sentence discussing this to the supplement. 

“P3L32. Mean “local” production rate?”

Yes, this value is the mean production rate in the mixed layer at this location. 

“Fig2-3. On the x-axis of the graphs, I suggest to write “10^6 atoms” instead of “Matoms”. “

This is a matter of journal style and we will let the copy editors make this decision.  

“Why He-3 has brackets in Fig2, but other don’t have?”

An error. We will fix this. 

“Fig3. The red lines indicate the onset time of fire-regime. i.e. the fires started after that time. What about if the fire regime stopped some time before the red lines and started again. Some sort of inheritance due to the fire-regime?”

As we discussed in the text, diffusion models are inherently nonunique, so there exist many different scenarios that can explain a particular end state. Thus, it is certainly possible to propose more complicated multistage histories that yield the same final state as a simple two-stage history. The purpose of the model simulation here, as we discussed in the response to the other review, is to construct the simplest possible model that explains the observations and illustrates the main points of our data interpretation. 

Regardless, the effect of having fire occur early and late, but not in the middle, of the model run would mostly (although not always) be to decrease the concentration gradient (because the gradient developed during the first period would be reduced by mixing before the beginning of the second period). Thus, periods of fire would not be precisely additive: two 50 ka periods of fire separated by 50 ka would not yield exactly the same result as 100 ka of continuous fire. Again, however, this is off topic with regard to the main points of the paper.

“P6L4. Is random walk distance only in vertical? i.e. one-direction solution. Please indicate?”

Yes, the model is 1-dimensional so the particle can only go up or down. We will clarify this in the text. 

P6L16. partway or “pathway”?

It would be more specific if we said “...part of the way through the simulation.” We will clarify this in the text. 

To summarize, proposed corrections in response to this review are as follows:

1. Add information about density measurements and topographic shielding to the supplement.
2. Clarify dimensionality of model in main text.
3. Clarify vague or confusing sections of the text highlighted by the reviewer.
4. Correct minor errors and omissions.

References cited:

Struble, W.T., Roering, J.J., 2021. Hilltop curvature as a proxy for erosion rate: wavelets enable rapid computation and reveal systematic underestimation. Earth Surf. Dynam. 9, 1279–1300. https://doi.org/10.5194/esurf-9-1279-2021