Jafarov et al. conduct a modeling study using ATS to assess the impact of freeze-thaw and freeze-up on lateral flow in high- and low-centered polygons. This study integrates a new modeling capability into ATS that enables tracking of non-reactive tracer movement due to advective transport.  This study incorporates two transects (i.e., domains) representing high- and low-centered polygons and two freeze thaw scenarios – one scenario with seasonally dynamic freeze-thaw and one scenario with the active season only (i.e., excluding freeze-thaw and freeze-up) to assess lateral tracer movement over two years. This study confirmed field studies by Wales et al. (2020) that suggests that freeze-up has a large impact on tracer transport. Simulations show significant lateral transport within two thaw seasons and this transport was greater in scenarios with freeze-thaw. Results also showed that the impact of freeze-thaw was greater in low-centered polygons, as evidence by the increased difference in tracer transport between freeze-thaw enabled and disabled scenarios for low-centered polygons compared to high-centered polygons.

Overall, this is an interesting and important study and will be of interest to the readership of The Cryosphere. This study not only contributes important advances in cryohydrogeological modeling, but also provides important insights into lateral flow in ice-wedge polygons and potential carbon transport. The modeling setup and analyses are sound, and the results are clearly conveyed.

I have a few general and line specific comments articulated below:

General comments:

• The discussion section needs to be expanded and developed to include more explanation and context to the points addressed. In select sections such as 4.3, the discussion reads more like a results section than a discussion of the findings, leaving the reader with questions such as: Why does freeze-up impact tracer transport? Why is it greater in some scenarios than others? What are the drivers and processes at play? Why does most of the tracer flux for low-centered polygons occur during the freeze-up period in low permeability scenarios? The results are interesting and important, but the manuscript lacks depth beyond results reporting. Addressing these questions in addition to other similar questions will greatly improve the manuscript and the impact of the paper.
  • Similarly, the drivers of transport were not discussed in the manuscript. There is no text discussing hydraulic gradients and little with respect to thermal gradients. This is important when discussing lateral flow with time. How do the hydraulic gradients change with time? Between scenarios? How about the thermal gradients? I strongly addressing these questions, or thoroughly discussing drivers of flow in the text. Adding in even a few well-crafted and well-placed sentences discussing the processes influencing the results will significantly improve the manuscript and its impact.
• While a tracer is one way to track lateral flow of a non-reactive solute, DOC is reactive. Given the focus on and links to carbon transport made in the manuscript, I suggest adding text that addresses how DOC transport differs from tracer transport. Perhaps it is obvious, however, it is important to mention that DOC is (1) reactive, (2) can be entrapped in ice, and (3) impacted by local conditions. Please also add text as to how this may impact the results of this study.
• Please check the manuscript for typos. There are several instanced throughout the manuscript, some of which have been identified below.

Specific comments:

Line 26-27: Rephrase. Perhaps add ‘on’ after ‘controls’.

Line 28: I suggest adding examples of transport conditions.

Line 45-55: This section is repetitive and seems to jump between sentences. I suggest reordering the text to incorporate the hypothesis in the first paragraph then what was done in the second to avoid repeating findings of Wales et al. (2020).

Line 51: add ‘but’ after the comma.

Line 61: Add an ‘s’ to simulation.

Line 64: Add an ‘s’ to implication.

Line 83: Please clarify the Q^c term and how it is determined.

Equation 4: Define ε.

116: Please add a reference for the domain specifications.

Line 199. Please add ‘is’ after ‘and’.

Line 130. For clarity, this sentence could be rephased to ‘no-flow energy boundary conditions on the sides of the domain.’

Line 131: Please more thoroughly explain the 4 cm. Why at 4 cm? Is this a point or a line segment, and if so, from where to 4 cm? Would the seepage location impact the results?

Line 132: I believe ‘drainage’ should be ‘drain’.

Line 137: I suggest adding ‘started’ after ‘season’.

Line 142: Remove the second ‘in’.

Line 145-150: Were diurnal temperature changes included?

Line 257: This sentence needs more detail. Impacts of what? “may be responsible…” for what? More text in this sentence will add clarity and make the point (and this section) clearer.

Figure 1: Please include units in the axis titles. Also, I suggest reassigning letters to the plots to match the rest of the figures (i.e., a,b,c,d rather than a,c,b,d). Additionally, it may help to find a way to indicate a dynamics permafrost boundary in b and d. The depiction as is was initially confusing.

The paper discusses the effect of freeze/thaw cycles on lateral transport of conservative solutes in polygonal tundra, and links this transport to soil carbon cycling. A new transport capability is incorporated into ATS, an existing hydrothermal model. By comparison to field data, the modelled cases indicate that lateral transport may be an important feature of dissolved carbon.

The paper is well structured, easy to follow and the modelling mostly appears scientifically sound and well performed.

Below, I first provide some more general comments, followed by minor or editorial comments.

Major comments:

1. While the introduction nicely explains why lateral transport of carbon is important to understand and quantify, it remains somewhat unclear if the lateral transport in a single polygon is critical. That is, the paper could somewhat elaborate on what happens with dissolved carbon once it reaches the edge (trough) of a single polygon. If it is released immediately similarly to the carbon which is transported vertically, maybe the effect is minor. Also, it would be helpful if the authors could provide some more detail on in what form carbon is transported, and what its ultimate form is when released. Maybe by outlining the relevant reactions this would become clearer.
2. In order to mimic the tracer experiment, the tracer source is placed on the surface of the polygon. I wonder if not a more realistic source, in order to ultimately understand DOC transport, would have been to distribute the source vertically within the active layer.
3. The paper clearly demonstrates how the freeze/thaw cycle promotes lateral transport relative to the freeze/thaw disabled case. But is not this enhanced transport mainly a fact of assigning a zero permeability in the active layer for the freeze/thaw disabled case such that solute becomes immobilized for large parts of the year? That is, how does vertical transport compare between the two cases; is that also enhanced for the freeze/thaw enabled case?
4. Concerning the governing equations (1)-(2) and equation (3), I note the following:
   1. C_l should be mass fraction (rather than mass as stated)?
   2. The units of the LHS of eq (1) and (2) are not the same (seem to differ by a length unit)
   3. In eq (3), should not the RHS be divided by porosity in order to obtain the liquid velocity?
5. Did Wales et al. (2020) observe the same pattern (differences) between the two consecutive years as in the numerical simulations? If not, please elaborate on the possible deviation.
6. As a complement to Figures 3-6, I think it would be helpful to plot cumulative mass discharge as a function of time at the polygonal boundary (i.e., at 10 m distance from center). This would aid in understanding the temporal evolution.

Minor comments:

1. Line 27: insert ‘what’ before ‘controls’.
2. Line 119: Should be ‘equals’.
3. Lines 137-138: Clarify when the tracer is applied; i.e., is it 20 days after the end of the first thaw season?
4. Lines 145-146: Is the impermeable layer constant in space?
5. Line 153: Specify if the suggested time period of several days to weeks is site-specific or a general statement.
6. Line 211: How much is porosity reduced in this variant?
7. Line 219: How much is permeability reduced in this variant?
8. Lines 235-238: Did the modelling include unsaturated flow?
9. Line 313: Superscript missing in 0°C.