the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Oct 2025
Muon paleotopometry
Abstract. Recent advances in measuring muon fluxes at great depths for neutrino experiments, along with improvements in in-situ terrestrial cosmogenic nuclide (TCN) measurements, have enhanced our understanding of muogenic nuclide production rates at decametre and hectometre depths. These developments allow us to explore muogenic TCN as a tool for estimating long-term (>10⁵ years) erosion rates. There are theoretical advantages of utilizing muogenic TCN for long-term landscape evolution analysis (µ-paleotopometry). We summarize recent advances in knowledge of deep muon flux used in the interpretation of neutrino interactions at kilometre depths. We discuss strategies being considered for the µ-paleotopometry method to address otherwise intractable landscape evolution questions. We demonstrate an achievable resolution of calculated erosion rates with TCN measurements in quartz at rock depths of 37.8 x 103 to 67.5 x 103 g cm-2 (~ 140 and 250 m). In settings where assumptions of constant erosion rate are suitable, the uncertainty is controlled by nuclide concentration measurement error and the effective time (duration over which the isotope concentration reflects the erosion history) is limited by radio-decay. Other environmental complexities, such as variable glacier cover, unknown complexity in initial topography, or mineral composition of rock may restrict the addressable questions and limit precision. Where a time-varying erosion rate is sought, deeper-time variances have inferior representation.
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Status: open (until 03 Dec 2025)
- RC1: 'Comment on egusphere-2025-4370', Anonymous Referee #1, 30 Oct 2025 reply
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RC2: 'Comment on egusphere-2025-4370', Anonymous Referee #2, 18 Nov 2025
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Muon paleotopometry
Gosse et al.
Gosse et al. present a very well written, thorough, and easy to follow framework for utilizing deep muon production of Terrestrial Cosmogenic Nuclides on the decameter and hectometer scale for determining various timescale erosion rates. Scientifically, the methods developed and utilized appear to follow best practices, and significant efforts were made to minimize contamination and ensure accurate analytical results. Several proof of concept and sensitivity analyses were highlighted that provide examples and help with future steps for other authors. A detailed analytical study was performed and presented, with preliminary analyses from ongoing studies highlighted. Underlying assumptions and limitations/strengths of the deep muon paleotopometry method were compared with other methods, and how the deep muon method fills a methodological gap not well resolved with current methods. Overall, this study is an excellent contribution to furthering the utility of TCNs beyond a simple chronometer and highlights the utility of muon produced TCNs. Below are minor comments to further improve this manuscript.
The Introduction and Background are very detailed and well written, and sets the reader up well with the theory and background for utilizing muons and assumptions in the method. References to other types of basin wide and TCN based point erosion rate studies, though, are minimal throughout the paper. The reader would benefit from having references to other studies throughout the paper to compare the utility of the presented research. Many of the references cited are also from a selection of the current authors or a few methodological papers from very well-known papers in the cosmo community. There are other work in watershed erosion rates (numerous work by D. Granger i.e. (Granger et al., 2001, 1997; Odom and Granger, 2022)) and recent shallow cosmogenic depth profile modelling i.e. (Balter-Kennedy et al., 2021; Graham et al., 2023; Hawkins et al., 2025) amongst other examples.
Lines 31-33: Consider including references.
Figure 2: The X-axis caption includes (km.w.e.). It is not defined up to this point, and only much later in the paper text (Line 256). Please include the definition in the caption.
Table 1. The following calculated values for the 50 m depth should be re-evaluated. It appears, based on a linear relation, that the Depth (km.w.e) at 50 m should be [0.1325] instead of [0.0325] reported in the table. The two following values in the row of [35] and [37.3] also appear to be potentially low, based on the other values in the last two columns, but difficult to tell with the non-linear relationship.
Line 277: Citation Margreth et al, 2015 is not included in the References.
Line 467-468, Supp F1. The main text indicates the SUFCO-001 duplicate was chemically processed and AMS analysis with the January 2018 batch, however the Supplemental Figure 1 caption indicates 1d was AMS analyzed during the November 2019 batch as part of the 4 bold samples. One of these should either be corrected or additional clarification provided.
Lines 483-484: This sentence does not appear to fit well in this paragraph and the preceding sentences. It would be better suited in the following paragraph that refers to Figure 11.
Figure 12: Missing context information, including North, scale, legend, etc. Country boundaries would be a useful indicator for context.
Line 634: “product rate” likely should be ‘production rate’.
Supplemental Table S1: for sample 3517, the mass reported for the 150-250 split is higher than the <150 fraction. Is this a typo (should it be 136?), are the values flipped, or was more material added?
Examples of additional References:
Balter-Kennedy, A., Young, N.E., Briner, J.P., Graham, B.L., Schaefer, J.M., 2021. Centennial- and Orbital-Scale Erosion Beneath the Greenland Ice Sheet Near Jakobshavn Isbræ. J. Geophys. Res. Earth Surf. 126, e2021JF006429. https://doi.org/10.1029/2021JF006429
Graham, B.L., Briner, J.P., Young, N.E., Balter-Kennedy, A., Koppes, M., Schaefer, J.M., Poinar, K., Thomas, E.K., 2023. In situ 10Be modeling and terrain analysis constrain subglacial quarrying and abrasion rates at Sermeq Kujalleq (Jakobshavn Isbræ), Greenland. The Cryosphere 17, 4535–4547. https://doi.org/10.5194/tc-17-4535-2023
Granger, D.E., Fabel, D., Palmer, A.N., 2001. Pliocene−Pleistocene incision of the Green River, Kentucky, determined from radioactive decay of cosmogenic 26Al and 10Be in Mammoth Cave sediments. GSA Bull. 113, 825–836. https://doi.org/10.1130/0016-7606(2001)113%253C0825:PPIOTG%253E2.0.CO;2
Granger, D.E., Kirchner, J.W., Finkel, R.C., 1997. Quaternary downcutting rate of the New River, Virginia, measured from differential decay of cosmogenic 26Al and 10Be in cave-deposited alluvium. Geology 25, 107–110. https://doi.org/10.1130/0091-7613(1997)025%253C0107:QDROTN%253E2.3.CO;2
Hawkins, A.C., Goehring, B.M., Menounos, B., 2025. Terrestrial cosmogenic nuclide bedrock depth profiles used to infer changes in Holocene glacier cover, Vintage Peak, southern Coast Mountains, British Columbia. Geochronology 7, 157–172. https://doi.org/10.5194/gchron-7-157-2025
Odom, W.E., Granger, D.E., 2022. The Pliocene-to-Present Course of the Tennessee River. J. Geol. 130, 325–333. https://doi.org/10.1086/719951
Citation: https://doi.org/10.5194/egusphere-2025-4370-RC2
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- 1
Gosse et al. present a robust theoretical framework and accompanying calculations for using samples from deca- to hectometer depths to quantify erosion rates through time using cosmogenic nuclides. They further demonstrate the applicability of this approach through two well-chosen case studies. The theoretical development is sound, and the authors provide a thorough and thoughtful discussion of the underlying assumptions and methodological considerations. The presented data show that this method can in principle be employed to assess erosion at temporal and spatial scales that are not well resolved by conventional cosmogenic nuclide or thermochronologic techniques. Overall, this study represents an excellent contribution to the field and GChron. Below, I provide minor comments aimed at further improving the manuscript.
Figure 5: I found the definition of the “%” unit in panel A confusing. Is % effect defined as the percent reduction of TCN concentration compared to the no-overburden case? If so, how is a reduction of more than 100% possible for the lake scenario? It also took me some time to piece together the scenarios in panel B from the text and caption. Consider clarifying this directly in the figure—perhaps by adding schematic labels or text annotations (e.g., “10% exposure time,” “50% exposure time”). I eventually understood it, but the presentation was not intuitive.
Table 1. Abbreviation Eμ wasn’t defined (I assume energy muon?).
L271-280: This is true for bedrock samples. In practice, most studies use catchment-average erosion rates, which filter a lot of the stochastic signals (Schide et al., 2022). Would be good to clarify the bedrock vs. alluvial sample distinction.
L302: I had difficulty visualizing the formation of an anticline above a sample without vertical movement of the sample itself. This would require a detachment horizon between the sample and the surface and would place the sample at depths too great for measurable TCN production. It may be clearer to instead refer to scenarios involving increased overburden due to sediment deposition.
L360: Please clarify why multiple closely spaced samples improve resolution. Is the improvement due to statistical averaging, better spatial sampling, or another factor?
Figure 7: Wouldn’t it make more sense to plot the Al/10Be ratio with depth to illustrate the advantage of multiple nuclides?
Figure 9A: Please add the surface projection of the mine shaft and sample locations to the map. As currently presented, it is unclear which surface features influence which samples. Also, consider plotting elevation on top of the hillshade—this would allow readers to compare incision depths of topographic features with sample depths.
In addition, since Figure 4 includes theoretical radii of production cones, it would be valuable to plot these on the map as well. This would help illustrate which topographic features significantly affect the samples and which can be neglected. A visualization of the production cones—analogous to the theoretical case—would nicely demonstrate the degree to which nearby topography matters. While the authors argue for including all topography within ~50 km, the majority of production should still originate from the simplified 75 degree cone calculated in Section 5.4, correct?
Section 5.2. I understand the intent to keep calculations simple to illustrate first-order applicability. However, I was surprised that a simplified 3D erosion model was not attempted. For instance, assuming a flat initial surface and intersecting the 75° 3D cones of the samples with modern topography could provide valuable insight with minimal additional complexity.
Figure 12 is missing vertical and horizontal axis for the profiles and coordinates, scale bar, north arrow, legend, etc. for the map.
L534: There are several cosmogenic nuclide catchment-average and low-temperature thermochronology rates published for the area. I suggest putting this number into context of existing data.
Figure 13: Please show the surface trace of the production cone on the map. The map currently lacks a legend, and the coordinate labels are too small to read.
Section 5.5.:
Schide, K., Gallen, S. F., & Lupker, M. (2022). Modeling the systematics of cosmogenic nuclide signals in fluvial sediments following extreme events. Earth Surface Processes and Landforms. https://doi.org/10.1002/ESP.5381