Please see attached document.

Review of “Local forcing mechanisms challenge parameterization of ocean thermal forcing for Greenland tidewater glaciers” by Hager et al.

Hager et al. present ocean model simulations with MITgcm for an idealized domain and use those to test the accuracy of melt parameterisations for Greenland fjords as they are used in large-scale projections. This is a relevant work as ocean-driven retreat of glaciers is one of the important processes driving Greenland mass loss and of interest for publication in TC. I suggest some modifications to the analysis and presentation as detailed below to improve the accuracy and understanding of the work.

General comments:

•  Structure: the structure of the manuscript could be improved as at the moment it is not clearly going towards one aim, which makes it hard to read. Information is spread into several places, e.g., the ISMIP melt parameterisations are introduced in the introduction, the new ones in parts in the Methods 2.2, in the discussion in Section 4.2. You could make the thermal forcing parameterizations your central point and move it earlier. In addition, you should introduce all thermal forcing parameterizations explicitly, i.e., giving their equations, in the methods in Section 2.2. Then you can validate them against the model simulations in the results and discuss their caveats and benefits in the Discussion. Ideally, you can end with a recommendation.
• Experimental design / results: At the moment you are comparing apples and oranges for the different parameterizations: the AMmelt/ISMIP6melt and AMretreat/ISMIP6retreat parameterizations are evaluated by comparing theta_gl, while the AMberg, AMconst and AMfit parameterization are evaluated with the profile. This makes it hard to actually see how much AMberg improves over AMmelt (there is a lot about the importance of the iceberg melt in the document, but the actual effect on melt rates remains unclear, as it influences mainly the upper layers). I suggest that you compare all parameterizations with respect to all three quantities theta_gl, theta_z, theta_A as well as the corresponding melt rates through equation (2), and also compare all to the measurements (Fig 5). Best would be to summarize results for all parameterizations in one table / figure. Otherwise, it is not clear how you rank the importance of processes (section 4.1).
• Generalization of results: in your ocean model runs you use one background forcing and one idealized geometry – how much do your results depend on this? You should at least discuss this caveat.

Specific comments:

Abstract:

• Line 13: What the 2.9°C refer to is unclear, maybe rather give the maximum modification that the TD experiences.
• Line 15-17: It’s unclear if your parameterisation includes bathymetry?

Introduction:

• line 31: Morlighem et al., 2019 is no projection, Jourdain et al., 2020, introduces parameterisations for Antarctica, so neither citation really fits to your sentence
• line 31: Seroussi et al. is for Antarctica, the citation does not fit here.
• line 40: Smith et al., 2020 presents satellite observations of thickness changes, it does not link them to the ocean forcing, the citation does not seem to fit here.
• Equation (1) here glacier front changes are directly linked to frontal melt changes, however, this misses out changes in ice dynamics: a glacier terminus could stay in the same position for higher melting when the ice discharge increases at the same time (at least for a while). This seems to be missing some physics?
• Explicitly state somewhere that you do not evaluate melt parameterizations, just the thermal forcing aspect. And state clearly, that the ISMIP parameterisations underlies a thermal forcing parameterisation, that the resulting melt is relevant, however, this is still open and here always done using the equation (2, except for the retreat parameterisation in ISMIP6).
• My understanding is that equation (2) is mainly used to put the importance of thermal driving differences in the context to melt rates and not suggested as a valid melt parameterisation? If this is correct, state it. 

Methods:

• line 121: Where was the background velocity implemented?
• What about sea ice in MITgcm?
• line 155: do you want a new paragraph for the sentence “We compare..”
• line 157: Does “modeled area-mean” mean that it is averaged over the entire depth? And above, is the TD at the grounding line the one from the lowest cell?
• Table 1: Define better exactly how the thermal forcing is calculated (e.g., which grid cells are used, just the closest to the calving front or are they averaged? How is this handled with different resolutions?).
• in general, I miss more motivation for your methods, e.g., why do you want to quantify sill-driven mixing? Why do you use three thermal forcing metrics (and not just one)? 
• furthermore, I miss a motivation and explanation for the newly introduced melt parameterisations in the method.

Results:

• Line 210: Not sure where exactly you find the grounding line average salinity in the Figure? Is is simply the deepest value (at -800m)?
• line 215: “..when iceberg keels extend… or subglacial discharge … below sill depth” – from the figure 2, this seems to be true for sill depth of -250 and -100m. How can you draw the logical conclusion that this is linked to the keel depth and vertical extend of the plume from this figure?
• line 219-221: this is hard to see from Figure 2. At least in panel (e) it looks like there might be blue triangles left and right of black triangles (and the lines intersect above of -200m).
• line 224: again, this refers to the middle and right columns, or how can this be seen more precisely in the figure?
• line 237: the third EOF “depicts temperature variability coincident with the terminal depth of subglacial plumes” – I am not sure this is is very clear, e.g., the lower terminal plume depth around -400 m does not coincide with a change in the temperature profile? Why does this EOF not represent the reflux?
• line 243-247: where are the absolute numbers? Can you add a table containing them? 
• line 248 – 250: this is simply because of the latent heat required to melt the icebergs, or?
• Figure 2: Are the profiles from the center of the calving front or are they averaged over the calving face? I would mention earlier on that the columns are for the different sill depth, e.g., add this as titles to the columns. The figure is quite dense, you could help the reader by indicating what features they should look at in the figure. E.g. for the sentence in lines 212-214 “However, water properties…” you could add in the end “.. for S100 runs (compare the blue and black triangles indicating the depth-averaged thermal driving in the ocean simulations across the three lower panels). Same for lines 216, explain how the reader can see that “iceberg keels extend beyond sill depth” and “subglacial plumes reach neutral buoyancy”. Same for the next sentence. It looks like some triangles are missing, e.g., there are no black triangles in panel (f)?
• Figure 4b: What does this mean that there is higher reflux with higher freshwater input at depth?
• equation 12: what is the motivation for this “skill score” definition, is this something commonly used?

Discussion:

• I would move part of the discussion to the results, e.g., the definition of the new parameterisations for thermal driving, how this is translated into melt.
• Section 4.1: you are comparing unlike things here as you are using for 1. the average thermal driving as the relevant quantity, while in 2.-4. your relevant quantity is the variability in the thermal driving profile. If you want to list the processes “in order of importance”, I suggest that you think about what defines their importance (relevant quantity is resulting basal melt rate, temperature profile or the average temperature) and then compare them with respect to this quantity.
• lines 350 and following: is this caveat (“the dependence on specific depth when calculating thermal forcing”) not the same caveat as discussed in the paragraph above, i.e., that sills are highly relevant for thermal forcing in the fjords?
• give the equations for the parameterisations, e.g., how exactly follows the AMberg the Gade line (what ambient water masses do you assume to mix with, how much mixing occurs, see line 380)?
• line 386: “iceberg melting” instead of “submarine melting”?
• Figure 5: ISMIP6retreat label should be AMretreat, or (this is also mixed up in the text)? Please add the other thermal driving parameterisations as well, i.e.,. AMmelt, AMconst as well as dots for the ISMIP6 ones. How well do they perform?
• line 405: ISMIP6melt is not on the figure 5, AMretreat shows higher temperatures. The difference could also stem from other reasons than “temporally varying conditions”, i.e., horizontal variability in the sill and ice conditions...
• Figure 6: Difference between each theta and what? The far-field theta/boundary conditions? How are sub-shelf melt rates calculated with (2) when using a thermal driving profile? Non-iceberg runs are black? I think also the green markers show the thermal forcing parameterisations differences in thermal driving relative to the boundary conditions / ISMIP6retreat case? Don’t you model melt rates with MITgcm and IcePlume, why don’t you compare to those as well?
• line 417: how much is the 200m/yr in relative terms (i.e., how large are the melt rates overall)?
• line 420: within a given run, theta_z, theta_A and theta_gl calculated by the forcing parameterisations differed…(or how did you estimate the difference)?
• line 434: Could it be that the reflux is hard to get from the EOF because it is linked to the bathymetry and you removed that in your EOF analysis?
• line 484: “reduces error in thermal driving profiles compared to ismip6 estimates”..
• line 461: add “in shallow silled fjords in our idealised simuations”.
• Add that it remains an open question which theta to use, or how to translate the profile into melt rates.
• I miss a discussion of the next steps (develop and evaluate melt parameterizations) and caveats (idealized model domain, only one background forcing, comparing to one fjord,...).

Appendix:

• State what the abbreviation TEF stands for.
• line 489: what do you mean with volume conservation? In general, mass, energy and momentum are conserved, but volume might change with density (temperature, salinity, pressure) changes. Please explain.
• Equation A4: How do these follow from “mass and volume conservation”? Is it rather that you assume salinity on the glacier side is lower because of mixing with melt water?
• Figure C1: This is the algorithm for AMfit, right? The definition of effective depth could be repeated here, or you could point to the relevant location in the methods.
• Table C1: Please add theta_gl and theta_z here as well.