Robel et al. present a simplified model of a subglacial salt wedge and apply a simple parameterization of associated subglacial melting in ice sheet models to estimate the effects of this process on sea-level projections. They offer a valuable extension of the work recently presented by Wilson et al. (2020) from intrusion in subglacial channels to intrusion in a subglacial water film. Overall, I found the manuscript clearly written, with some additional suggestions for improving clarity provided below. The primary concern I’d like to see the authors address, elaborated below, pertains to the feasibility of the simulated melt rates.

Major comments:

When you discuss the conditions for maintaining stratification between layers, showing that the Reynolds number indicates a laminar regime would be helpful. (Roughly around L240)

A table of some of the cases you discuss in Sections 3.1 and 3.2, i.e., the parameter combinations and distance estimates, would be a useful reference.

It seems that you consider the bed slope but not the ice slope in Equations 3,4. However, I think you also make the assumption that ice base slope is the same as bed slope such that the subglacial film thickness is constant. I think that’s fine since you treat the velocity of the upper layer as a free parameter, but I’d like to see Equations 3,4 presented in as general a form as possible.

Can you provide an argument that such intrusion-induced melt rates can exist in a steady state? Given such thin films, I would think it’s possible that heat exchange (in this laminar regime) from the open ocean upstream through the subglacial layer might be too slow to maintain these melt rates. 

L540: This line reads like a recommendation. However, with such a wide range of intrusion distances and the strong sensitivity to the bed type, this recommendation seems too general to be useful to ice sheet modelers. Can you settle instead on something like, “uncertainty in intrusion-induced melt should be incorporated into uncertainty of sea-level rise projections using ice sheet models” or “sensitivity of sea-level rise projections to intrusion-induced melt should be tested in ice sheet models.” Or something even more specific like “given large uncertainties, we recommend applying melt to partially-grounded cells”

Minor comments:

L7. Since you haven’t yet discussed what you mean by “hard bed” I recommend instead calling it an impermeable bed.

L11. “10-50% higher or 100% higher” This is a strange way of expressing it without indicating what makes the difference between the two cases.

L12: “whether the conditions are met for extensive seawater intrusion” or “whether extensive seawater intrusion occurs”

L50: “distance” >> “extent”

L89: “the bulk porosity of the sheet” Wouldn’t it be better to define \phi_1 and \phi_2 for each layer in Equations 3,4 so that the equations are more general? And similarly for c_d to acknowledge that the ice and bed could have different roughnesses?

L91: This is the final term in Equation 3 but not Equation 4

L106: “vertical interface” To me, this is unclear and would be better stated just as the horizontal extent of the saline layer.

L107: “without considering their compositional differences” Are you referring to the inclusion of the buoyancy (reduced gravity) term? Or the representation as a two-layer system? 

L113: “after H_2 is eliminated” This would make more sense if h=H_1/H had already been introduced.

L116: I think it would be helpful to describe what \gamma represents qualitatively (i.e., porosity).

L118: “Fr = Fr_0 h^{-2/3}” should be explained

Figure 1. I think it would be helpful to include a second panel that is the schematic of the soft bed case.

Figure 2. Define h in the caption.

L191: “single hydraulic potential” implies that Equation 12 will contain the hydraulic potential rather than U_in.

L195: Can you direct readers to where in the literature \alpha is defined?

L222: “which” is ambiguous between g’ and the density difference.

L246: I think you mean “it is still possible to maintain two layers in water sheets 10cm thick”?

L250: Provide a reference for maximum packing density.

L252: “That could be supported in such a thin water sheet” by virtue of what? Do you mean supporting two layers within the film? How did you determine the c_d value of 0.01? If it is just the upper bound in the literature, then it would be clearer to delete the clause I reference here. 

L265-272: This paragraph seems to be a distraction. As far as I can tell, the key point is that the layer in the ice sheet interior is on the order of mm and thus too thin for the 2-layer model to apply. That could be stated in the previous paragraph with the Engelhardt and Kamb (1997) reference.

L294: delete “equation”

Figure 3: It is hard to view inset box in panels a,c. It might be worth stating in the caption that the blue region is above the critical slope.

Figure 3 and 4: I wonder if you might find a better colormap for these plots. It’s pretty hard to see the difference between values just above and below 10m. Another option would be a contour at 100m since that is the lowest value you implement in the ice sheet model.

L341: Add units to K

L346: “perhaps in under” >> “perhaps under”

Figure 6: Add a legend to panel b for the two points located at x=0

L478: The local bed type isn’t easy to accomplish in a model if we still don’t have a continent-wide map of hard/soft bed.

L491: “act to prevent strong curvature” This isn’t clear offhand. Can you provide a reference?

L531: “rights” >> “right”

L533: “under the right circumstances” repetitive with previous sentence

This study tackles a very critical concept in the world of ice sheet-ocean interactions which to date has not received a great deal of attention. Using simplified mathematical descriptions of the near-terminus subglacial environment, it builds on previous work to describe intrusions of warm salty water into the subglacial water layer under marine ice sheets, and establishes that there could potentially be warm water underlying subglacial environments kilometers from the grounding line. It then considers, through a simple parameterisation, how the presence of this water, if able to effect high melt rates compared that that observed in ice-shelf cavities, might impact marine ice sheet stability. In most respects the study is comprehensive, well thought out and well explained, and feel it deserves publication. I have two main comments for the authors and editor to consider, followed by a number of minor ones.

Main Comments:

1) While the hard-bed treatment of the subglacial layer is very detailed and well explained, and one can clearly see how physical considerations lead to mathematical results, I feel the soft-bed case just presents results without intuition. I appreciate that soft-bed transport is probably not the mode by which subglacial transport occurs, given the volumes involved -- but it would be nice to understand, if only qualitatively, where 12-14 come from without needing to read the Strack paper referenced.

2) The parameterisation for under-ice melt in (17) and illustrated in Fig 5 (and was actually also used by Parizek et al 2013 -- and in fact was required by that study to show instability of Thwaites) is acknowledged to be just a parameterisation with little oceanographic basis -- but I still feel it is a bit of a cop-out to say that we don't have the understanding to rigorously model melt so we will just use an approach that is linear in space, as an exploratory tool. This method still leads to extremely high melt rates under grounded ice, which is known (from sources cited in the manuscript) to have a much larger impact of grounded ice than melt of similar magnitudes under ice shelves. I am certainly not an expert in boundary-layer oceanography but I know that the melt rates suggested by e.g. the equations of Holland and Jenkins 1999 under ice shelves exposed to CDW require quite developed boundary layers and high levels of turbulent mixing, and Im unsure if such mixing rates  and layer thicknesses are allowed by the theory. The examples cited (Kimura and Begeman) invoke double diffusion -- but I believe that in both of these works, the under-ice ocean conditions below the ice would lead to much higher melt rates than observed considering under-shelf plume type flow. I bring this up not because I understand the physics of flow in these subglacial environments -- but simply because the analogues cited to justify these high melt rates actually show very very low melt rates under such stratification envisioned in this study, and it is difficult to imagine what could make them higher. It would be quite a lot to ask the authors to come up with a better parameterisation, or to redo their experiments.  But i feel, and if the editor agrees, that the use of such a parameterisation should be far more heavily caveated than it is, and in more places in the text than just its introduction.

Minor comments:

Line 92: this is not the final term in eq 4

line 92 Rominger reference: it would still be nice to see intuition for the functional form of this term

Derivation of (5), and expressoin for Fr: I think some clarity is needed. do you not require eqs 1 and 2 as well (or at least eq 1)? How is H2 cancelled, is it via H2 = H-H1? The nondimensionalisatoin seems to imply H is a constant, rather than a varying field.. if this is the case, i can't find where it is made clear.

line 138 hard-->difficult

line 146: what is W

Figure 2: labels (a) through (d) not shown. what are the parameters in eq 5 for these solutions other than the ones shown in the legend?

paragraph at line 218: awkward. shouldn't the solutions to eq 5 be *exactly* this length scale, as you are implicitly defining the length scale through this equation?

line 246: *stratification within* water sheets?

line 274: what does "exponentiated" mean in this context? does L become an exponent somewhere?

line 287 2nd "of till" redundant

Holland, D. M., & Jenkins, A. (1999). Modeling thermodynamic ice–ocean interactions at the base of an ice shelf. Journal of Physical Oceanography, 29(8), 1787-1800.

Parizek, B. R., et al. (2013), Dynamic (in)stability of Thwaites Glacier, West Antarctica, J. Geophys. Res. Earth Surf., 118, 638– 655, doi:10.1002/jgrf.20044.