General Comments

 Hamm and Frampton employ a hydrology-thermal model to analyze the role of slope on active layer thicknesses for idealized Svalbard hillslopes. The authors suggest that subsurface temperatures are warmer on the uphill side of hillslopes and as a result, these regions have deeper active layers. While the work presented is likely of interest to the hydrologic and cryospheric communities, there are several specific problems involving the downslope model boundary conditions, lack of model calibration, upscaling of findings, and disclosure of modeling assumptions/limitations that need to be addressed before this manuscript should be considered for publication. I have included additional information that details specific major areas for improvement below.

1. As stated on L135-136, the “downhill end of the transect represents the valley bottom and allows for water accumulation and potential ponding on the surface”. According to Figure 2, this downhill boundary is a no-flow and no-heat flux boundary but there is little justification for this no-flow condition. It looks like in Figure 1c that these hills ultimately flow into a river so are instead, flow boundaries. It may make more sense to represent these as flux or constant pressure boundaries. As no-flow boundaries, I worry that they are artificially blocking heat transport and accumulating water, which is why the rightmost column in Figure 4 does not make sense with the rest of the modeled cross-section. If these no-flow boundaries are not affecting the model outputs, it would be helpful to see a comparison of model outputs with and without the no-flow downstream boundary in the supplements. If this downslope no-flow boundary does change results, please revisit much of the results text, including your third conclusion.
2. The presented models are referred to as idealized but are based on field data from Adventdalen, Svalbard which makes me wonder why a calibration was not performed? I think that uncalibrated models can be useful thought experiments, and I understand that calibrating and validating a model can be taxing. However, I question the validity of using conclusions from a model that is not calibrated to existing field measurements, especially using a model that is in the middle ground between an uncalibrated generalized model and a model that is calibrated. At a minimum, the authors need to suggest how the model results may compare to field observations of similar sites.
3. It is unclear how relevant these findings are to permafrost landscapes throughout the Arctic. How often are there hillslopes of a constant slope without valleys and lateral (cross hillslope) water flow? Even more basic, what percent of the Arctic is sloped terrain? Any additional information that could be provided to aid in the upscaling of these results outside of Svalbard would be beneficial.
4. The assumptions of the study, especially the modeling assumptions, should be specifically stated in a separate section. For instance, this simulation doesn’t include an organic layer, but organic layers exist in many permafrost landscapes and have very different thermal properties from mineral soil (this goes back to if these results can be upscaled or not). Is it reasonable to model hillslopes in only two-dimension? I think it can be but the reason for doing so needs to be stated and supported with other peer-reviewed papers.
5. The main text needs to be revised for clarity. The figures are attractive and easy to see, which is appreciated, but many of the figures need additional annotations or subfigures to help with comprehension. It is also unusual to have the results and discussion sections combined. I would highly recommend separating these sections so you can have a more thorough discussion section where you interpret your results and compare them to other peer-reviewed studies. As is, this combined section is quite long and hard to digest. I have pointed out some specific examples below where the text and figures need to be revised for clarity.

Specific Comments

L6, How representative are these hillslopes of Arctic landscapes as a whole?

L15, Since this study only considers one slope versus a ‘hilly’ landscape, I would hesitate to draw this conclusion about hilly terrain.

L29, Rather, permafrost degradation has been found to increase groundwater discharge into surface waters, not decrease the seasonal variability.

L41, How much topography is ‘more topography’? Is there are slope cutoff? Be specific.

Section 2.1, What are typical active layer depths at the study site?

L107, How far is this from the weather station in km?

L118, What is the hillslope length?

Figure 2, It would be helpful to show node locations.

L136, What is the depth of the mineral soil?

Table 1, Thermal conductivity values are low for a mineral soil, I would expect closer to 2.7 W/mK.

L140, What makes the no flow lateral (right and left) boundaries? Are they a watershed divide? Seems unlikely given the flat lateral topography.

Figure 3, I’m confused about what these plots are showing. It would help with clarity to first plot the temperature time series for the steep, medium, and flat simulations for both uphill and downhill and then plot these differenced values. Would also be helpful to annotate this figure, for example, you could write ‘uphill warmer’ above the x-axis in (a).

L192, What about the large November peak at 0.75 m in Figure 3a?

Figure 4, Label color bar with units. Which is the uphill side? Horizontal distance=0 m? Label this on the figure. Why is the far-right column in each subfigure so different than the other columns? It looks like a potential modeling error due to the no-flow boundary conditions that do not physically make sense. This difference was pointed out in section 3.2 but is concerning. Also, are the two dotted lines in the October subfigures showing the presence of a horizontal talik?

L279-280, This is likely due to the no-flow boundary on the downslope side, and is not realistic if there was a river or otherwise at this boundary.

L284-286, What about the role of specific heat, where specific heat is higher for saturated soil than unsaturated soil? This may explain your results on L390-391.

L326, Vertical diffusion of what? Heat diffusion? Be explicit even though you go on to reference heat.

L430-440, Why are these processes more relevant for a high-Arctic hillslope setting if they are for sites with no topography?

Technical Comments

L2, What is ‘its’? Permafrost?

L4, Delete ‘want to’.

L6, Indicate that these are the ‘steep’ and ‘medium’ cases.

L50-54, These sentences seem out of place and are too short to form a paragraph. Add more studies, incorporate them into the previous paragraph, or remove them.

L55, What is the length of the hillslopes? I imagine hillslope length will alter results.

L55, Add ‘two-dimensional’.

L54-73, Condense into one paragraph, move study site details to study site section.

L68-69, Delete, repetitive.

L71, To ‘what’ extent.

L71, I think replacing ‘inclination’ with ‘slope’ would make this easier to understand as it uses the more common term.

L72, Typo, ‘to’.

L89 and L93, Citation typo.

L112, This is the mean snow and rain for 2013-2019, correct? It’s unclear as written.

L118-119, Change to ‘slope’.

L149, What does ‘field values’ mean here?

L162, Typo ‘initialization’.

L186, Delete ‘significant’ are these trends statically significant?

L187-188, Highlight these times (thaw and freeze up) in Figure 3 with shading or otherwise.

Table 2 and 3, Can move to supplementary material.

L199-203, Redundant, can be removed.

L205-206, I don’t think you can draw this conclusion from the presented data, save this for the discussion.

L207, What do you mean by ‘inversion of temperature differences’? Please reword.

L207, Again, I don’t think this necessarily indicates this conclusion, remove.

Figure 5, Delete panel (b), panel (a) is clearer and shows a very similar result.

L279, I’m not sure what lateral gravitational water flow means exactly since water flows vertically due to gravitational attraction.

Throughout, Refer to as ‘heat’ diffusion.

L337, This is an important point to make.

Section 3.7, Add a more descriptive header.

L435-436, Also see McKenzie and Voss, 2013.

McKenzie, J. M., & Voss, C. I. (2013). Permafrost thaw in a nested groundwater‐flow system. Hydrogeology Journal, 21(1), 299–316. https://doi.org/10.1007/s10040‐012‐0942‐3

This paper uses idealized thermal hydrology models to investigate the influence of sloped topography on active layer thermal dynamics.  Essentially a sensitivity study is performed with varying sloped domains.  The sloped model domains caused subsurface water flow, drainage from uphill and increased saturation on the bottom of the slope.   These are very complex processes and it is very difficult to untangle everything that is going on.  To the authors credit they provide a thorough explanation of many of the possible mechanisms controlling the thermal state of the domain, which is inherently complex.  Untangling these processes to understand thermal hydrology on sloped domains is important and of interest to the readers of Cryosphere.  Unfortunately, as complex as the processes discussed in this paper are, the message becomes lost and confusing due to the complexity of the problem. Be that as it may, this means that the authors must work hard to simplify the message as much as possible and work to focus the manuscript so that the reader can understand what mechanisms are important.  I therefore recommend substantial revisions to focus the text on the main processes driving the thermal state of the simulated domains.   This is not to say that the work is not good.  In fact, I am impressed by the modeling and all the analysis done.  However, I strongly encourage the authors to edit and trim for the sake of clarifying the message of the paper.   

• Based on what I read, the main message is because of variable saturation, hillslopes experience different thermal regimes with warmer upslope areas and cooler down slope areas. The paper seems to focus on how increased moisture in the down slope area causes increased evaporative cooling.  However, the overall thermal state of the domain is slightly warmer.   I’m left wondering why are sloped simulations overall warmer?  Only at the end of the manuscript when the authors do an additional sensitivity study by adding more precipitation do we see a general cooling effect of the entire domain.  This then suggests that it is a water balance mechanism caused by slope, i.e the system tips the evapotranspiration into an energy limited system rather than water limited and as more water is added.  And that area of the domain with more evaporative cooling outweighs the domain that is water limited.  However, the water balance verses degree slope, which appears to control the overall thermal state of the entire domain is not discussed.   

• Similarly – and at a much smaller scale, Abolt et al., (2020) found (using the same ATS model) that rims in polygonal ground warm more in the summer due to drier conditions and associated weakened evaporative cooling, which then provides energy laterally to the cooler saturated troughs in the summer (see section 5.2 of Abolt et al., 2020). However, what determines if a saturated area is cooler or not also depends on the mass of water present.  If enough water is present, especially on the surface, then a Talik will begin to form, as demonstrated in a 1D column by Atchley et al., (2016-section 4.2) and by Abolt et al., (2020) for wide troughs. This is because the timing of phase change during freeze up when snow is building can cause wet areas to stay warm throughout the winter, especially as the amount of water increases because it then requires a lot more energy loss to cross the freeze curtain.   The difference with the study presented here is: 1) vary little surface inundation occurs due the surface runoff boundary condition and the assumed energy equilibrium at the downhill domain boundary condition. This assumption may not capture the thermal influence of the saturated condition beyond the boundary of the domain.  And 2) very little snow accumulation occurs, which would otherwise insulate the more saturated areas during freeze up.  Given that the simulations with added precipitation showed an overall decrease in ALT, this work might suggest that increased evaporative cooling affect may outweigh the increased energy loss necessary to cross the freeze curtain.  However, given the larger thermal hydrology work in literature, it would be beneficial discuss these tradeoffs as well as discuss how influential an appreciable snowpack may change the results. i.e there could be a combined warming in the dry areas (little evaporative cooling) and persistent warm winter conditions in wet areas from insulative snowpacks.

Abolt, C.J., Young, M.H., Atchley, A.L., Harp, D.R. and Coon, E.T., 2020. Feedbacks between surface deformation and permafrost degradation in ice wedge polygons, Arctic Coastal Plain, Alaska. Journal of Geophysical Research: Earth Surface, 125(3), p.e2019JF005349.

Atchley, A.L., Coon, E.T., Painter, S.L., Harp, D.R. and Wilson, C.J., 2016. Influences and interactions of inundation, peat, and snow on active layer thickness. Geophysical Research Letters, 43(10), pp.5116-5123.

Minor comments:

L58-59:  In this case the benefit of numerical modeling probably has less to do with the remoteness of the study area, and more to do with a characterized sensitivity study as well as being able to dissect the energy fluxes across the full domain, something that would take tons of sensors to do in the field. 

L72: Change ‘Tho’ to ‘To’

L89:  (Painter, 2011) is outside of either sentence, I think it goes with the previous one. 

L118: Omit one of the ‘a steep case’.

L147-148: Why would you want to maintain a constant (same) snow accumulation across the hillslope domain, and is that realistic?  This is likely to have a strong effect of simulations results.

L153-161: Note that these CV locations are right at the domain boundary, and therefore subject to any edge effects of the model domain.  The assumptions and implications of being on these domain boundaries needs to be discussed in more detail.­­ This might be especially problematic with the downhill CV, given that the no flow (energy) boundary condition assumes equilibrium with a larger body of water or saturated area.   

L207-208:  This sentence needs to be more specific.  What do you mean by inversion of temperature differences?  Differences between uphill and downhill observations? Or differences between sloped and flat?  Also, what are the different processes responsible here?

Figure 3 needs more explanation in the caption.  Hard to interpret it at a glance.

L215: “The upper three panels in each figure…”. I assume you are talking about Figure 4 here, but it is not clear.  I suggest phrasing this as, “The upper three plots in each panel…” as ‘figure’ refers to figure 1 through 9 in the paper, ‘panel can refer to a and b, and plot is the sub plot of each panel. 

Figure 7:  I like this figure, or at least what it is attempting to convey.  However, I think it could be improved, or perhaps simplified.  Is the story in the time series of the flux?  Is it necessary to show the whole time series?  If not, I would suggest just showing the cumulative flux, or maybe the difference of the fluxes between the cases.  That may help with the scale issue. Additionally, the location of the representative volumes in relation to the fluxes going in and out is confusing, i.e, the lateral energy flux going in the downhill volume (positioned right in the domain) is found left in the figure.  This means the reader (me) has to mentally flip the image.   

Figure 8:  These are pretty small fluxes.  Is this figure necessary?  I think this paper as a whole makes a decent argument that groundwater dynamics are important in determining the thermal state of the hillslope, even if advective fluxes only play a small role.  In other words, the influence of groundwater dynamics happens in other processes.  I would suggest focusing as much as possible on those processes rather than advection. 

L462:  “as compared to the flat case (0.75cm).” is confusing.  Does the flat case change in the simulations?  I thought the flat case provided a reference datum and therefore should be 0.

Figure 9:  “The sign convention adopted is positive values represent heat entering the CV and negative values

leaving the CV.”  This would mean that I should see the evaporative cooling affect?  Correct?  Heat and mass leaving the downslope CV during summer?

Section 3.6:  This section tests the effect of overall precipitation and demonstrates the overall effect of increased evaporative cooling – at least I think that is the purpose.  However, as written it seems to play only a minor role in the manuscript (the text devoted to this seems like an after thought), and there is no figure associated with this text that actually illustrates the point other than those in the supplementary information. It would be better to have a figure in this text.  

L424-L432:  This paragraph provides a good summery of what was found.  It seems like it would fit better in the conclusion section. 

L458-46:  “This downhill cooling effect is up to about 1.2 C for steep (22_) and 0.6 C for medium (11_) inclinations across a lateral distance of 50m representative for valleys in Adventdalen, Svalbard.”  Seems to me that the bigger story here is not the increased downhill cooling caused by the evaporative flux, but the increased uphill warming presumably caused by the lack of an evaporative flux because overall the entire domain is warmer than the flat case.

The conclusion section is not very impactful.  The paragraph in L424-432 seems to be a much better conclusion paragraph.    Also, after reading the paper several times, I am confused as to why the entire sloped domains are over all warmer than flat domains?  The focus appears to be more on the evaporative cooling effect, yet the domains are overall warmer unless precipitation is increased.