We thank the referee for his important comments. We refer here to the three major ones.

The detailed comments will be treated in order in the revised manuscript.

1. In section 5.2 it is argued that the difference in the long-to-short lived isotope ratios between cores ADE-2 compared to ADE-17 and ADE-1 must be related to a difference in the release of ²²⁶Ra. This is not consistent with the fact that it is the short-lived isotope activities that change between these cores; ²²⁶Ra is similar in all 3 cores, while the short-lived isotopes change by 1-2 orders of magnitude. Therefore, the explanation must be related to something that changes the release of the short-lived isotopes from the sediment grains. It is shown that ²²⁸Th and ²²⁷Ac (the parents of the short-lived isotopes) have higher activities on grain surfaces compared to bulk sediments, thus wouldn’t a simpler explanation be that in the higher salinity core (ADE-2), more of these isotopes are released into the porewaters before decaying? The authors argue that this cannot be the case because Ra-226 is not increased in ADE-2 porewaters (with the idea being that all Ra isotopes should increase with higher salinity), but they have shown that more of the ²²⁶Ra parent (Th-230) is locked inside sediment grains compared to the short-lived isotopes parents, so I would expect that there would be a larger source of surface-available short-lived isotopes. In other words, there are more short-lived isotopes available at the grain surface compared to ²²⁶Ra that are ready to be released into porewaters when the salinity increases. Another possible explanation could involve recoil, which would be propelling the short-lived isotopes into the pore space more often than ²²⁶Ra because of their shorter half-lives.

• We completely agree. Actually, this is what we basically wrote. The parent radionuclides, ²²8Th and ²²⁷Ac, which are concentrated on grain surfaces, allow ²²³Ra and ²²⁴Ra to get in pore space (no chance for such short-lived to get out of the grain, e.g., Lines 415-417), and with the higher salinity in ADE-2 and possibly some liquid water, more is left in the pore space of the more saline core. The problem indeed is that this does not happen with the ²²⁶Ra, which has to make its way mainly form inside the grains (diffusion), which takes time, in particular considering the low T. About the recoil. The ²³⁰Th/²²⁷Ac ratios are not concentration ratios, but rather activity ratios. Accordingly, there is much more recoils of the ²²⁶Ra compared with the ²²³Ra, in particular when bulk is considered. We will further elaborate and highlight this in the revised text.

2. I do not agree with the argument that cold temperatures would reduce adsorption but not diffusion (which is invoked to explain how ²²⁶Ra could be released from the inside of sediment grains after long time periods). I agree that a slow diffusion process could become significant over time, but if atoms are moving via diffusion what would stop them from coming into contact with grain surfaces and becoming adsorbed? Both are processes related to the movement of atoms and should therefore be affected by temperature the same way. The authors point out that higher salinities in the ground ice will further reduce adsorption, but wouldn’t this also reduce diffusion because radium is a cation? The comparison between measured ²²⁶Ra in porewaters and estimated ²²⁶Ra in the CEC fraction (Figure 11) also shows that most ²²⁶Ra must be adsorbed onto mineral surfaces.

• We never wrote that diffusion is not lower in low T. It is clearly noted in the paper that it should be very low (e.g., Lines and 448-450 and simulation in figure 14), and will be further highlighted in the revised version. However, experimental data is not available, therefore apparent quantitative approach is not possible. What we suggested was that the ²²⁶Ra diffusion out of the grain mainly goes either through the mineral lattice (solid) or through frozen nanopores. The discussion of adsorption was just to cover for the case that some of the nanopores (inside the grains) are not completely frozen. Accordingly, the discussion and simulations (next comment) were for an end-member case, where diffusion goes through solely liquid water. Liquid water is evidently sometimes found in permafrost pore space (e.g., Keating et al. 2018; Gilbert et al. 2019; Weinstein et al. 2019), therefore the suggeted adsorption in this case. However, this is much less likely within the permafrost grains, where water:rock ratios is much lower and heat loss should be much more effective (see discussion of porosity effect on freezing in Rotem et al. 2023). Nevertheless, even if liquid exists, this is only one pathway (and please see more in the reply to Q. 3), while diffusion out of the grains could still go through the more frozen nanopores or mineral lattice, where adsorption is not relevant. This will be further explained in the revised.

3. In section 5.2.2 the authors do a simulation to estimate how much ²²⁶Ra could be released from within sediment grains. Assuming an R of 10 in the equation on line 460 is on low end of what might reasonably be expected; I have more often seen R= 10^3 used for saline water (e.g. Diego-Feliu et al., 2021; Kumar et al., 2020), and because R decreases with increased salinity and the salinities in this study are generally lower than that of seawater, it would be more reasonable to assume a higher R. Also, R is linearly related to K_d, which will increase at lower temperatures (Rama & Moore, 1996), thus R in permafrost will be higher than R in temperate groundwater systems. It is noted on line 466 that a higher R would reduce effective diffusion. Would the diffusive hypothesis still hold if R is on the order of 10^3?

• Thanks for allowing us to elaborate on this. First, again, this is about the end-member case, whereas diffusion out of the grain is probably mainly through solid, so adsorption should have a small effect, relevant for some liquidized nano-pores, if exist. Specifically about the adsorption. We first note that we did not present a quantitative approach, which is due to the absence of low-T data. Also, we do not think that R in saline water is 10^3. Actually, Diego-Feliu et al. (2021) mention that the characteristic R in saline water is 10^1 (paper’s conclusions; and in Kumar et al. 2020, there is a wide Kd range of several orders of magnitudes). This is particularly so in our case, considering the anoxic condions and the low pH in the permafrost soils. Nevertheless, if we chose to use R=1000, as suggested, then the diffusion coefficients should be higher (i.e., 10^-22 instead of 10^-24) or, alternatively, that the effective diffusion would cover shorter distances. While <<1 micorn distances are getting close to recoil distances, diffusion would still facilitate ²²⁶Ra input to porespace. We note that as shown in the paper, there is a lot of ²³⁰Th in the grains, so even if effective diffusion is <1micron, it could still add a significant amount of ²²⁶Ra to the pore space, assuming enough time has been allowed (as happened in the two cores other than ADE-2). And again, this whole discussion is just about diffusion in liquidized nanopores.

We thank Referee #2 for his review and comments.

Our responds are in Bold

Before responding to comments, we wish to highlight two points:

• The environment discussed in this manuscript is not the common for Ra isotope studies. While Ra isotope research usually deals with the aquatic setup, the permafrost is predominantly frozen, where the rules of the game are very different. Moreover, while other permafrost isotopic works dealt mainly with large ice bodies (e.g. Kipp et al. 2024), the work with granular pore space ground ice is much more challenging, and most parameters are unfortunately unknown.
• Although a basic equation for the radium buildup is presented, we did not use it to calculate residence times. We just showed similarities between parent and daughter nuclide ratios, and inferred about possible contribution from inside the grains. The mentioned 2 ka age is based on OSL ages (of the syngenetic PF) from other works.

We respond below to the referee’s three main comments, as well as to some of the more fundamental specific comments.

C1. Terminology and conceptual definition of radionuclide pools: Several key radionuclide concepts are not used or defined with sufficient precision. This makes parts of the interpretation difficult to follow and, in some cases, conceptually ambiguous. The manuscript should clearly distinguish between activity and concentration, bulk sediment activity, alpha-recoil-accessible activity, exchangeable or surface-associated activity, and dissolved activity in porewater or ground ice. This is especially important for the use of the “CEC fraction”. CEC is a sediment property, but the manuscript appears to use “CEC activity” as a proxy for exchangeable or surface-associated Th/Ac activity. The authors should define exactly what this fraction represents, how it was isolated analytically, and why it is the relevant pool to compare with dissolved Ra activities or activity ratios. In addition, terms such as “secular equilibrium” and “steady state” are used several times in a way that appears inconsistent with their strict radionuclide meaning. The authors should clarify whether they refer to radioactive parent–daughter secular equilibrium, steady-state transport conditions, or an apparent balance between production, transport, adsorption/desorption, and decay. Finally, the term “diffusion” also lacks a clear conceptual framework. In some parts of the manuscript, it could be interpreted as diffusion through liquid-filled nanopores or pore films, whereas in other places the authors seem to imply solid-state diffusion from inside mineral grains. These processes are physically different and should be clearly distinguished. Without these clarifications, comparisons between bulk activity, “CEC activity”, dissolved Ra activity, and inferred equilibrium ratios are difficult to evaluate.

(1) We understand about the ambiguity. For Ra isotopes, we always use activities and activity ratios. 'concentration' is mentioned in certain cases in order to address readers who may not be familiar with the term 'activity.' In the revised ms, we will go through the text and make changes, whenever not clear,

(2) Regarding the CEC. In the methods chapter, we described what we did, which is leaching the sediment, using a common protocol with ammonium acetate, and measuring the parent thorium and actinium isotopes (the way done with the bulk sediment). We agree that referring to it as “CEC activities” is confusing, and we’ll make sure to correct in the revised

(3) We thank the referee for the opportunity to elaborate about 'steady state' and 'secular equilibrium'. When 'secular equilibrium' is mentioned, it refers to equilibrium with the parent isotope in the system (i.e. similar activities), and by secular equilibrium ratios we mean assumed parent isotope activity ratios (e.g.  21.7 for 238U/235U and 226Ra/223Ra). We will go again through the text and change wherever it is not within these terms. The term 'steady state' is used twice (Lines 394 and 532) in order to describe the condition of constant activities or ratios, which may depend on other factors except for the secular equilibrium ones (e.g. the 224/228 ratios, which are commonly higher than 1). We will try to imrove the text in the revised

1. By “Diffusion” we do mean: ‘the spontaneous net movement of atoms, ions, or molecules from an area of higher concentration (e.g. inside the grains) to an area of lower concentration’. It’s true that in the environment we discuss, the diffusion can be through solid mineral lattice, ice or liquid water (both in nano-pores), or a combination of all the three. This is widely discussed in the paper (e.g. section 5.2.2). We wrote that there could be a whole spectrum, from solid-state to liquid-filled nano-pores (e.g. Line 447 on). We further discuss it in the reply to C3. We will try to make it clearer in the revised manuscript.

 C2. Limitations of the Ra isotope model and AR interpretation: The modelling framework used to interpret the Ra isotope data is not sufficiently developed to support some of the residence-time interpretations. Eq. (1) is introduced as a single-radionuclide mass-balance formulation, but the manuscript uses it to interpret activity ratios involving several Ra isotopes from different decay chains. The assumptions and limitations of this extrapolation should be made explicit.

In particular, the model appears to assume homogeneous conditions, constant source terms, constant retardation/partitioning, no changes in water chemistry, and no mixing between fluids with different histories or salinities. These assumptions are critical in this study, because the proposed interpretation depends on comparing isotope ratios among cores that differ strongly in salinity, chemistry, and inferred residence time. The authors should also explain why modelling the ²²⁶Ra/²²³Ra ratio provides additional information beyond modelling ²²⁶Ra ingrowth alone at the timescales considered. As currently presented, the model is useful as a conceptual illustration, but it does not yet provide a sufficiently robust quantitative basis for the inferred residence times.

- Thanks for the comment. We first wish to highlight that, in practice, there is no attempt to use the equation in a quantitative way, and (unfortunately) no ages were determined based on it. It is used only in order to describe the buildup of Ra isotope activities. Second, we do explain that in terms of isotope ratios and the relevant times (>>years), 223 (and 224) may be considered uniform (steady state activities, Lines 394-5), therefore it is only the long-lived 226 that matters (Lines 396-7).

We agree with the reviewer that things could (always) be much more complicated. But again, we treat our observations in a very robust way. Specifically, we mentioned that ratios in ADE-2 (the more saline) seem close to equilibrium with parent activity ratios in the CEC fraction (surface-bound) while in ADE-17 they are much higher, closer to parent activity ratios in bulk sediment. We note that, as highlighted widely in the paper, ground ice chemistry (ion ratios) in the more saline ADE-2 is quite similar to seawater, which calls for the dominance of binary mixing between seawater and a fresh end-member, while WRI is more significant in ADE-17  (e.g. Lines 335-340 and Figure 4a; section 5.3).

“why modelling the ²²⁶Ra/²²³Ra ratio provides additional information beyond modelling ²²⁶Ra ingrowth alone at the timescales considered”?

Modelling of 226 alone requires control on too many parameters, e.g. recoil efficiency, adsorption/desorption, as well as the main unknown, which is how much of the recoiled (and desorbed) radium was actually sampled, considering the limitations on ground ice extraction (e.g. Lines 154-6). This is at least partly solved, using isotope ratios. We highlighted the above by showing that major part of the radium is not sampled (e.g. Lines 372-5), which could only partly be explained by adsorption, considering the frozen condition of most samples.

In summary, we did use the equation to show how radium isotopes and ratios build-up to secular eq. with parents, but our conclusions are not based on this. Rather, it is the robust observation of low ratios in one core, which are similar to parent ratios on grain surfaces, while much higher ratios in the other (closer to bulk sediment). This drove us to the conclusion about diffusion from inside the grains (no quantitative constraints).

Last, the mentioned 2000 years is not coming from equation-based calculations, but rather from observations about the syngenetic sediments, where ages were defined mainly by OSL (Lines 424-5; Gilbert et al. 2018).

C3. Insufficient evidence for diffusion from inside mineral grains: A central interpretation of the manuscript is that elevated long-to-short-lived Ra isotope ratios reflect ²²⁶Ra diffusion from inside mineral grains over long timescales. However, the evidence for this mechanism is not sufficiently demonstrated. The manuscript should define what is meant by “diffusion from inside grains”: solid-state diffusion through the mineral lattice, diffusion through nanopores or microfractures, or release from alpha-recoil zones. These processes have very different physical meanings and expected rates, especially under low-temperature or frozen conditions. The authors should also justify why diffusion is required to explain the data, rather than alternative processes such as alpha recoil from mineral surfaces or exchange/desorption, differences in sediment texture or surface area, or heterogeneous parent-nuclide distributions. At present, the conclusion that ²²⁶Ra diffusion from inside grains controls the observed activity ratios is plausible as a hypothesis, but it is not yet sufficiently supported by the presented data or model.

- We agree that we cannot provide a quantitative modelling support for the diffusion, but we do believe that this is the most plausible explanation for our observations. First, we do not believe that there should be a major difference in sediments texture and chemistry within 30m. If this has been the case, nobody could use representative core compositions. Nevertheless, we show large differences between parent isotope ratios on grain surfaces and the bulk, as well as between Ra isotopes in the different cores. We, accordingly, believe that the most reasonable explanation is that in one core Ra isotopes are controlled by what released from surface, and in others it is joined by radium (only 226) that comes from deeper in the grains (e.g. Lines 469-470). This should probably be elaborated on in the revised.

As discussed above (C1.4), diffusion could be through mineral lattice or nano-pores (ice or liquid), which is discussed in length in the paper (Section 5.2.2). About the recoil from mineral surfaces. This could be a source, however, this should not be different from surface-bound, unless diffusion is involved, and apparently should not produce differences between the long and short-lived.  The only way is by import from inside the grains, where ratios are apparently much higher than 238/235 eq. ratios, and this should go by diffusion, this way or another. We will discuss the recoil from surface more in depth in the revised.

Specific comments

Line 275: “Activities of ²²⁶Ra, ²²⁸Ra, and ²²⁴Ra in ground ice are quite similar, varying between <1 to 60 dpm L⁻¹ … while ²²³Ra is an order of magnitude lower…”.  The reliability of the low ²²³Ra activities should be better documented. Most ²²³Ra activities, especially in ADE-17, are below or around 0.5 dpm L⁻¹. Considering that the recovered ground-ice volumes ranged from only a few mL to approximately 1 L, the total ²²³Ra activity loaded onto the Mn-fibers may have been very low. As a conservative example, a sample with 0.5 dpm L⁻¹ and1 L of recovered water would contain ~0.5 dpm of ²²³Ra. Assuming a RaDeCC detection efficiencyof ~50%, this would correspond to ~0.25 cpm at the time of extraction. However, ²²³Ra was measured after approximately 10 days, which is close to one ²²³Ra half-life. Therefore, the expected detector count rate would decrease by approximately a factor of two, to ~0.125 cpm, before considering background, adsorption losses, and other corrections. At such low count rates, obtaining counting uncertainties below ~10% would require on the order of at least 100 net counts, equivalent to counting times of ~800–1000 min or longer. Such long RaDeCC counting times may be problematic because instrumental limitations, including He leakage, can affect measurement stability and reliability.

• Unfortunately, it seems that the referee missed the quoted uncertainties on ²²³Ra, which were “up to >30%” (Lines 164-5). In the revised, we will clearly mention the range of uncertainty. We also wish to note several things: 1. our samples were never a few ml (“42-1391 ml”, Line 140); 2. when low, we did measure ²²³Ra overnight, and indeed, whenever there was a He leak we repeated the measurements, sometimes up to 5 or more runs. And no, long runs did not affect measurement stability.

In addition, ²²⁴Ra activities are generally about one order of magnitude higher than ²²³Ra activities. A simple decay calculation indicates that, after 10 days, ²²⁴Ra activities would still remain substantially higher than ²²³Ra activities, because the initial ²²⁴Ra/²²³Ra activity ratio is large. For example, if ²²⁴Ra is initially ~10 times higher than ²²³Ra, after 10 days the remaining ²²⁴Ra/²²³Ra ratio would still be approximately 3, considering the different half-lives of ²²⁴Ra and ²²³Ra. Therefore, ²²⁴Ra–²²³Ra cross-talk may be an important additional source of uncertainty…

• Considering the mentioned large uncertainty, the cross-talk after 10 or more days is within the error range. Please also note that even if errors are up to 50%, it will not change the general picture of difference between the 226/223 ratios in ADE-17 and ADE-2, which are much larger (average of 51 and 9, respectively).

Line 300: “²²⁸Th activities in the CEC are similar to those in the bulk”. This result requires further explanation and methodological validation.… Therefore, it is difficult to understand how the ²²⁸Th activity in the “CEC fraction” can be comparable to the bulk ²²⁸Th activity, especially when ²³²Th and ²³⁰Th are two to three orders of magnitude lower in the same fraction. Such a pattern would require a clear mechanism for strong ²²⁸Th enrichment on exchangeable /surface sites, or an external supply of radionuclides followed by adsorption, which is not straightforward in this setting “

• We are very grateful to the referee for this comment. Seems like we had a mistake in the ²²⁸Th activities of three of the samples (quoted activities were for the whole sample instead of per gram). After correction, 228 activities in the CEC fraction are on the average about twice those of ²³²Th (0.18 and 0.08 dpm/g, respectively). This seems o.k., considering the fact that ²³²Th is almost solely part of the mineral lattice, while ²²⁸Th is produced by the decay of ²²⁸Ra, which on top of production by the little ²³²Th that exists in the CEC fraction, is also produced by (1) recoil during the decay of ²³²Th next (10’s nm) to grain surface, (2) little (if any) diffusion from inside the grains (should be within years, considering ²²⁸Ra half-life of 5.75 years). In the revised version, we will definitely add a short discussion of the sources of ²²⁸

Line 390: “The concentration of a certain Ra isotope in groundwater at time t is described by Equation (1), assuming negligible dissolution and diffusion…”. The assumptions behind Eq. (1) should be stated more completely. This formulation is an analytical solution of a radionuclide mass-balance model in groundwater and involves additional assumptions beyond negligible dissolution and diffusion. In particular, it assumes a simplified homogeneous system, steady production terms, constant adsorption/retardation conditions, and no temporal or spatial changes in water chemistry or aquifer properties. This is importanthere because the manuscript interprets activity ratios involving several Ra isotopes from different decay chains and relates them to different parent radionuclides. Treating each isotope with a single-radionuclide formulation, without explicitly accounting for coupled parent–daughter ingrowth, sequential decay, mixing, or changes in retardation, may limit the reliability of the model-based interpretation. The authors should clarify these assumptions and discuss how they affect the interpretation of Ra activity ratios.

• In a locked space like the permafrost pore space, a homogenous system, steady production and (if at all) constant retardation are not less (probably more) likely than in the common aquifer. Why should there be a change in retardation or mixing in standing water (if liquid). Moreover, all of these affect similarly all isotopes, so it is not clear why not using the same formulation, in particular that with the times involved, the short-lived is not supposed to change, so it’s all about one isotope – ²²⁶ We do talk about mixing, and this is the event of saline water introduction, discussed in this paper.
• Actually, we should indeed discuss the possibility of a continuous water introduction process, which will be done in the revised.

Line 395: “K is a unitless adsorption coefficient.” I believe K should be described as a distribution coefficient, as it represents how much of the radionuclide is adsorbed versus dissolved.

• We prefer the dimension-less K, following Krishnaswami et al. 1982, which is directly related to the retardation factor (R=K+1). We used it in a lot of other papers (e.g. Lazar et al. 2008; Kiro et al. 2012,2013; Weinstein et al. 2019,2021; Rotem et al. 2024)

Line 400: “(²²⁶Ra/²²³Ra)AR will reach CEC ²³⁰Th/²²⁷Ac activity ratios (secular equilibrium)…”. If the authors are using the advective transport model in Eq. (1), this should not be described as “secular equilibrium”, which refers specifically to radioactive parent–daughter systems where the parent half-life is much longer than the daughter half-life. It is also not the same as steady state, which is already an assumption of the model. Here, the authors appear to refer to convergence between dissolved Ra activity ratios and parent-nuclide activity ratios in the defined CEC fraction, which is a different concept and should be named more carefully.

• We agree that we need to re-phrase. Will consider and do in the revised version.

In addition, the expected convergence between dissolved Ra ARs and CEC parent ARs should be justified. If porewater Ra receives contributions not only from surface-associated/CEC parent nuclides but also from alpha recoil from the mineral lattice, then the dissolved Ra isotope ratios would not necessarily be expected to converge to the CEC parent ratios. This additional Ra source should be explicitly considered.

• We do not expect it to converge to the CEC ratios. It has ratios similar to the Th ratios in the CEC fraction. What we meant was that assuming the Ra isotope ratios in ground ice are in equilibrium just with the CEC, than… But ADE-17 shows that there is an additional contribution etc. We agree that this part should be differently written in the revised.

Line 405: “For instance, if K = 10, as is the case for seawater salinities…”. The assumed value of K = 10 for seawater appears to be at the lower end of reported Ra distribution coefficients for saline conditions. The authors may want to compare it with published Kd ranges, for example those compiled by Kumar et al. (2020) and Diego-Feliu (2022), and discuss how sensitive the model results are to this assumption. See also the attached figure.

• First, Diego-Feliu et al. (2021) mentions that the characteristic R in saline water is 10^1 (paper’s conclusions; and in Kumar et al. 2020, there is a wide Kd range of several orders of mag). Also, the attached figure 1.5 (from Diego-Feliu’s thesis) shows that the median of saline water Kd’s is about 2-3. Using a porosity of 0.3 and dry density of 2.5, K=12-18, which is not very different than our 10. Also, the low oxygen and low pH should result in lower K. But mainly, as mentioned above, our conclusions are not based on the adsorption values. Nevertheless, and following the comment, in the revised we will relate also to higher K’s.