Petrenko et al. explore the potential of 14CO measurements in ice cores as a means to investigate the stability of the galactic cosmic ray (gcr) flux outside the heliosphere (the local interstellar spectrum, LIS). The rationale behind the approach is, that 14CO production in firn/ice below ~70 m is dominated by fast muons which are produced by gcr of very high energy (>100 GeV). Such high energy gcr are nearly unaffected by the helio- and geomagnetic fields. Thus, changes in 14CO production by fast muons can inform about changes in the flux of gcr outside the heliosphere, which is of importance for all studies using cosmogenic radionuclides (e.g., solar activity reconstructions) as the constancy of the LIS is an underlying assumption to all of them.

The paper first reviews previous data and modelling results previously obtained from Greenland and Antarctic ice cores that allowed narrowing down the uncertainty of some of the required parameters for understanding 14CO-concentrations in ice. This lead up to the formulation of the method conceptualized here and to the identification of site characteristics required for testing it.

Using the site of EPICA Dome C as an example, the authors employ a firn model and an ice-only model to demonstrate the expected importance of the different 14CO production mechanisms over depth and the effect of prescribed changes in the cosmic ray flux on 14CO concentrations in the ice.

Lastly, the authors test, under which scenario a change in the LIS could be detected from measurements. Owing to the large temporal averaging of the big samples and the large penetration depth of fast muons, these results indicate that short term changes in the LIS are unlikely to be detected using this method (or at least the changes have to be so big that they would also become obvious from simpler methods). But the method may be able to detect a linear increase of 4% of the GCR flux over the Holocene.

This paper is building upon the work of the same group of authors and it is another great addition to the portfolio of scientific questions that may be asked through gas-specific 14C-analyses in ice. The possibility to test the stability of the LIS over time is intriguing and the paper is well written and scientifically excellent.

Hence, I only have some minor comments that I will outline below.

Minor Comments:

14CO can only provide constraints on the stability of the LIS above 100 GeV (the energy required for deep production by fast muons). The production of 10Be on the other hand is mainly caused by primary protons below 10 GeV (because there are so much more). With respect to the possibility to use 14CO as a constraint for the assumption of a constant LIS in 10Be-based solar activity reconstructions: Over which energy range can changes in the LIS be assumed to be proportional?

L19: “GCR flux”: I would replace this with the term “local interstellar spectrum (LIS)” as this is clearly defined to be outside the heliosphere and thus outside the influence of helio- or geomagnetic modulation. Please also check this for the remainder of the manuscript, as I think in most instances, it is the LIS you’re referring to and not e.g., the GCR-flux into the atmosphere.

L27-28: “linear change/step increase”: define for which duration

L37: “14C abundance”: Replace with 14C/12C

L45: “solar GCR flux modulation”: Consider changing to “solar modulation of the GCR flux”, as I was for a second thinking you’re referring to solar cosmic rays.

L52: “suggest”: replace with “assume” – I don’t think the mentioned studies provide any results to suggest this

L143: The 14C half-life has been revised (https://doi.org/10.1016/j.nuclphysa.2003.11.001)

L275-280 (& figure 4): where does the increase in 14CO from shallow processes (dashed blue) come from? Is this only an increase in closed porosity?

Figure 4: I suggest to add a panel to illustrate the applied production changes. These are now only mentioned in the text, described by age, while the 14CO is plotted on depth. It would be nice to get a visual overview over all of it.

L402: “the assumption of GCR flux constancy”: add “during the Holocene” (and change to LIS)

The manuscript by Petrenko et al. presents a programmatic paper presenting and quantifying a novel approach to measuring 14CO in ice as a proxy of the long-term flux of high-energy (>100 GeV) cosmic rays. It is shown that this method is feasible and can indeed be used to study the GCR consistency on the time scale of thousands of years. The authors describe the physics behind the approach very well and provide a quantitative assessment of the method's sensitivity to demonstrate that it is sufficient for the task. The authors also correctly specify the related challenges.

I found this work very important expectedly becoming a reference paper for the new method.

I am happy to recommend this manuscript for potential acceptance subject to a minor revision related to some clarifications in the methodological description as specified below.

• A reader would benefit from a brief general description of how 14CO is measured in ice.
• Line 24: “insensitive” -- > “almost insensitive”.
• Line 33: after “solar irradiance” a reference to Wu et al. (2018b, doi: 10.1051/0004-6361/201832956) can be added.
• Line 35: please add a reference to a review by Usoskin (2023, doi: 10.1007/s41116-023-00036-z) focused on the cosmogenic method for solar activity reconstructions.
• Line 44: In addition to meteoritic studies, cosmogenic isotopes in lunar rocks can provide an estimate of the very long-term (mega-years) flux of cosmic rays (see, e.g., Poluianov et al., 2018, doi: 10.1051/0004-6361/201833561 and references therein). This method is free of geomagnetic shielding and uncertainties related to the orbit and erosion, but of course, is strongly affected by solar modulation. This can be briefly mentioned here in addition to the meteoritic data.
• Line 57: the statement about the isotropy of the GCR flux at the level of 1 permil needs clarification and a reference. The flux of GCR (in the GeV energy range) near Earth has a level of anisotropy of about 1% due to the orbital motion and diffusion+convection of particles by solar wind. Probably, the authors’ statement is related to higher energies. A reference is needed.
• Line 113: “Hmiel et al. (2023)” -- > “Hmiel et al., 2023)”.
• Line 118: for what conditions (geomagnetic and solar) is the P_{n, SLHL}^Qtz(0) defined?
• Line 119: should the units be molecules (viz. 14CO) or atoms (viz. 14C)? Referring to to the text above, it should be atoms. Please check.
• Description after Eqs 2 and 3 are quoted from Hmiel et al. (2023) but this is not optimal since some important information is missing there as probably provided elsewhere in the cited paper. The authors are advised to describe the formulas, especially Eq.3, in full detail. In particular, it is not described how \beta(h) is obtained.
• Line 140: since the ablation exposes ancient ice to neutrons, the additional production of 14C by neutrons needs to be considered and possibly corrected for. From the subsequent narrative, I understand that this effect is neglected, but this is not clear.
• Line 203+, also 270: while parameters R1 and L1 are described, it is unclear how they are used. Please provide a formula for that.
• Figure 4a: The Y-axis can be plotted logarithmically (optional).
• Lines 350-351: please remove quotation marks.
• The unnumbered equation in line 354 is unclear. I am ignorant of this but it doesn’t look like the probability (e.g., can it be greater than unity if Delta a is small?). Please explain this formula and/or give a reference.
• Line 376: please check that the term “frequentist probability” is correctly used here.
• Lines 382-384 repeat what is said in lines ~330.
• Line 388: was the step-like increase at 3.5 ka or 3 ka as stated in line 331?
• Line 405: lunar rocks can be also mentioned here.
• Line 411: measurements of d15N were not discussed in the text and appear out of the blue here. It needs to be removed or introduced somewhere.