The manuscript, ‘Supraglacial lake drainage through gullies and fractures’ by Humbert et al. seeks to characterize the ice surface and englacial behavior associated with repeated supraglacial lake drainage on Nioghalvfjerdsbræ Glacier using a wide range of in situ, satellite and airborne observations.

Overall, I found the individual observations interesting – particularly the radargrams. However, I believe that there are several fundamental issues with the manuscript. My major concerns are detailed below followed by line comments.

1. The manuscript is missing a story. Many datasets are presented, but by the end, I am still unclear about the manuscript’s main conclusions. Those indicated in the final section of the paper aren’t well supported by the analysis presented.
2. Why not term these moulins? Particularly after they start receiving persistent meltwater and reactivate over time? I understand the argument that these structures aren’t cylindrical (at least at the surface) but drainage to the bed along cracks is certainly a moulin. The imagery presented here are very similar (at least in my mind) to figures in Hoffman et al. (2018), Chudley et al. (2019), and Doyle et al (2013). Yes, the englacial geometry is complex, but that is not unexpected (e.g. Covington et al. 2020). Plus, I’ll note that even Das et al. (2008) refer to established surface-to-bed flow as ‘moulin flow’. These features are moulins and calling them something else complicates the story, particularly when modeling the deformation of a circle at the surface.
3. The analysis of the englacial features is limited to the visual inspection of a series of radargrams. It would be preferable to more carefully analyze these unique data and explore how the results link to surface behavior of both the supraglacial lake and crevasses/cracks.
4. Not all the methods are described in the Methods section. The manuscript references GNSS derived ice velocities, inverse modeling, methods for displacement along a crack and subglacial modeling. In these cases, the methods are not clearly described. In other cases, where the method is described, there are missing references to the tools or software used.
5. There is an overall lack of referencing, particularly in the discussion. There has been a reasonable amount of recent work looking at the mechanisms, geometry and impact of moulins on the subglacial hydrologic system. I have included some of these references below, but there are a number of others.
6. The manuscript would benefit from a through proof reading, including grammar, punctuation and abbreviations.

L3 The first sentence is missing something.

L30 The literature indicates that additional meltwater can both act to accelerate AND slow basal sliding depending on the structure and evolution of the subglacial hydrologic system. It would be worth clarifying that here.

L38 How does lake overflow differ from feeding downstream lakes and streams?

L40 Consider revising this section. I think the general mechanism of lake drainage is reasonably understood – in compressional lake basins, there needs to be a precursor tensile event (e.g. Hoffman et al., 2018; Stevens et al., 2015; Christofferson et al., 2018). What causes the tensile event is still up in the air and can vary from place to place and because these events are difficult to observe (Poinar and Andrews, 2019) there are outstanding questions.

L45 “In Greenland, there are…”

L45 Gulley et al. (2009) provides a nice review of the mechanisms described in this paragraph and it would be beneficial to include some of the information included there.

L55 The primary difference isn’t just scale. The current understanding is that most of the englacial structure in Greenland is formed via hydrofracture. Other mechanisms like cut and closure struggle due to ice temperatures and overburden pressures.

L85 Include a table of the satellite, image names, dates collected and resolution. Table 1 is close but doesn’t have all the information to be reproducible.

L165 So, reading the CARRA documentation, it looks like skin temperature is “Average air temperature at the surface of each grid column.” Which is different than the temperature of the uppermost surface layer – which shouldn’t respond instantaneously to surface fluxes. Some clarity here would be beneficial.

L170 It would be beneficial to have a cross-sectional diagram as well as Figure 2 or clarity that the model is only for surface deformation. Also, this modeling framework is in direct contradiction to the argument in the introduction about not being circular, thus not being a moulin.

L213 Table 2 would be better as a figure! Further, how is the ‘begin filling’ and ‘filling complete’ dates determined? It seems that these would be difficult to determine and the ‘filling complete’ would just be the date that drainage started.

L255 Inferring that the drainage paths were shut should be in the discussion, not the results.

L241 This is the first mention of ice-based GNSS position measurements. These measurements and the processing to velocities should be described before this section. 10% variation seems small when looking for the addition of meltwater to the bed.  Also, the inference that there is meltwater at the bed should go in the discussion.

L255 This figure reference is out of order.

L268 (& L289). How are ice block widths measured? Using 10-m Sentinel-2 imagery would not permit widths less than 10 m.

L274 If the 2020 ‘gulley’ was still active, drainage did take place. Do you mean to indicate that no ‘rapid’ drainage took place?

L298 These sentences are interpretation best left for the discussion.

L317 What is meant by ‘shade’?  Shading?

L336 What inverse modeling? Such methods should be described in Materials and Methods. What velocity fields are used? This choice would drastically affect the derived stress fields.

L345 without more details about the inverse methods and associated choices, this statement is speculative.

L347 Is there other evidence that Figure 10 actually shows uplift? In this case, I would expect one edge to be sharper. What is the sun angle and orientation?

L419 The modeling results need further description and justification. Is this meant to be a vertical cylinder in the ice? horizontal? Why only run the model for 20 days when the time between lake drainages can be several years? The figure seems to show results at or near the surface because there would be substantial creep closure at depth, but it is unclear to me if the englacial conduit is modeled as water filled or air-filled.

L430-435. This paragraph is not well justified and the reference an undefined subglacial model needs further description. I think it is conceivable that the water table within the conduits is identifiable in Figure 12a-b, but additional, careful justification is needed. Subglacial models are notoriously poor at capturing observed subglacial pressures, particularly if they do not include point supraglacial inputs and there is no modeling to support that an englacial conduit could remain open in the absence of supraglacial water inputs. I will note that Figure 12c could indicate a water filled moulins, which can be quite complex (e.g. Covington et al., 2020).

L437-441 This paragraph is unclear. Consider rewriting.

L442-444 The reflections in Figure 12 would be due to the difference between ice and air or ice and water – it’s unclear how these reflectors can provide information about whether the moulins (or englacial conduits) have experienced any creep closure or thermally driven opening.

L446 This behavior is consistent with moulin behavior – moulin reoccupation is common and dictated by surface gradients and moulin advection. However, what evidence justifies the statement of reoccupation? Figure 12? Why?

L460 Or it could be that the moulins/gullies closed at depth between drainages and needed to fill in order to hydrofracture and reactivate.

L466 The skin temperatures display a clear seasonality from 1991 (Figure 15). What exactly is meant here?

L473 The statement that the englacial channel is due to increased surface temperatures is not justified here. Perhaps there is more frequent lake drainage due to higher meltwater production.

Figure 3. In panel b, what do the different orientation of the triangles mean? This isn’t described.

Figure 4. What is the color scale in panel a?

Figure 5. Having the panels and regions be the same letters is confusing.

Figure 7. No panel letters. The spatial resolution and orientation of panel c? is different. Why?

Figure 12. What are the F’s, T’s and W’s? They aren’t referenced in the caption or text.

Figures 12 and 13. Can the flight lines be added to a map?

References

Andrews, L. C., Poinar, K. and Trunz, C.: Controls on Greenland moulin geometry and evolution from the Moulin Shape model, The Cryosphere, 16(6), 2421–2448, doi:10.5194/tc-16-2421-2022, 2022.

Christoffersen, P., Bougamont, M., Hubbard, A., Doyle, S. H., Grigsby, S. and Pettersson, R.: Cascading lake drainage on the Greenland Ice Sheet triggered by tensile shock and fracture, Nature Communications, 9(1), 1064, doi:10.1038/s41467-018-03420-8, 2018.

Chudley, T. R., Christoffersen, P., Doyle, S. H., Bougamont, M., Schoonman, C. M., Hubbard, B. and James, M. R.: Supraglacial lake drainage at a fast-flowing Greenlandic outlet glacier, PNAS, 116(51), 25468–25477, doi:10.1073/pnas.1913685116, 2019.

Covington, M. D., Gulley, J. D., Trunz, C., Mejia, J. and Gadd, W.: Moulin Volumes Regulate Subglacial Water Pressure on the Greenland Ice Sheet, Geophysical Research Letters, 47(20), e2020GL088901, doi:https://doi.org/10.1029/2020GL088901, 2020.

Das, S. B., Joughin, I., Behn, M. D., Howat, I. M., King, M. A., Lizarralde, D. and Bhatia, M. P.: Fracture Propagation to the base of the Greenland Ice Sheet during supraglacial lake drainage, Science, 320(5877), 778–781, doi:10.1126/science.1153360, 2008.

Doyle, S. H., Hubbard, A. L., Dow, C. F., Jones, G. A., Fitzpatrick, A., Gusmeroli, A., Kulessa, B., Lindback, K., Pettersson, R. and Box, J. E.: Ice tectonic deformation during the rapid in situ drainage of a supraglacial lake on the Greenland Ice Sheet, The Cryosphere, 7(1), 129–140, 2013.

Gulley, J. D., Benn, D. I., Screaton, E. and Martin, J.: Mechanisms of englacial conduit formation and their implications for subglacial recharge, Quaternary Science Reviews, 28(19–20), 1984–1999, doi:10.1016/j.quascirev.2009.04.002, 2009.

Hoffman, M. J., Perego, M., Andrews, L. C., Price, S. F., Neumann, T. A., Johnson, J. V., Catania, G. and Lüthi, M. P.: Widespread Moulin Formation During Supraglacial Lake Drainages in Greenland, Geophysical Research Letters, doi:10.1002/2017GL075659, 2018.

Poinar, K. and Andrews, L. C.: Challenges in predicting Greenland supraglacial lake drainages at the regional scale, The Cryosphere, 15(3), 1455–1483, doi:10.5194/tc-15-1455-2021, 2021.

Stevens, L. A., Behn, M. D., McGuire, J. J., Das, S. B., Joughin, I., Herring, T., Shean, D. E. and King, M. A.: Greenland supraglacial lake drainages triggered by hydrologically induced basal slip, Nature, 522(7554), 73–76, doi:10.1038/nature14480, 2015.

Humbert et al. present a detailed study into the long-term drainage history at a previously unreported lake at N79 glacier in northeast Greenland. The study integrates a wide-ranging array of highly technical methods with a high degree of competence. The paper is dense and technical, and clearly the work that went towards it is commendable. The two most novel parts of the study, in my opinion, are: (i) the observation of a system than, within the satellite observational record, developed from no lake at all into a lake that displays repeated rapid drainage to the bed; and (ii) the first (as far as I am aware) radar observations of the annual fracture history caused by repeated lake drainage.

My comments on the paper largely align with that of Reviewer #1. I feel that my understanding of the paper was limited by some strange terminology choices and a dense and confusing structure, which has made me feel as though I might be missing the main thrust of the story. I hope that this can be fixed largely within the terminology and structure, rather than implying any deficiencies in the work itself.

General Comments

It is a key part of the study, but I am still unclear as to what the authors mean when they refer to ‘gullys’, beyond the general dictionary description of a water-incised channel. I initially read the paper following my interpretation of the dictionary definition, whereby the ‘gullies’ are the three drainage channels extending E-NE from the three ‘branches’ of the lake (e.g. Fig. 1a), and ‘drainage through gullies’ would refer to the lake overtopping and draining due to the incision of these channels (as described in Tedesco et al. 2011, doi:10.1088/1748-9326/8/3/034007). However, as I read the manuscript, it became increasingly clear that ‘gullies’ appeared to refer to point features that might be analogous to moulins. Most obviously this includes: Figure 3b (as triangles); L236 (“a hole… is the first feature we identify as a gully”); L254 (“a gully [can be] inferred due to ponding … which has a form consistent with a drainage pathway”); and Figure 7 (the ‘gully’ here seems explicitly to be the point depression). Gullies are also frequently referred to as ‘triangular’, although it is not clear in what context (plane? profile?). 

To me, if these point features are what the authors are referring to, I cannot see why they are not referred to as moulins. The authors take time to explicitly seem to reject this in paragraph beginning L75 as  ‘are neither formed by melting nor round in shape’. I have never encountered the necessity that a moulin must be formed by melting, nor strictly round (beyond the fact they can be generally modelled as point rather than linear inputs to the en/subglacial system). Post-drainage surface-to-bed (or, at least, surface-to-englacial-environment) connections are commonly called a moulin in the drainage literature. Looking at the drainage pathways visualised in the study (Fig 5a; 7; 8c, 8d), I cannot see how they are different from those referred to as ‘moulins’ in previous drainage studies, which also show rivers terminating into thermomechanically-maintained holes along the relict fracture (Das et al. 2008, Fig. 1 inset, doi:10.1126/science.1153360; Doyle et al. 2012, Fig. 4a, doi:10.5194/tc-7-129-2013; Chudley et al. 2019, Fig. 5e, doi:10.1073/pnas.1913685116). 

If I am right that the gullies are the point features, then - to me - these drainage events bear a close resemblance to previous events: (i) background fractures exist oriented according to the principal stress (L337); (ii) which, aided by transient flow acceleration (L454-455), the water can then exploit (or reactivate) via hydrofracture (as in Christoffersen et al. 2018, doi:10.1038/s41467-018-03420-8). The authors say that hydrofracture isn’t occurring at L78-79, although I can’t see any evidence to reject Occam’s razor, especially as no other mechanism is proposed for the ‘propagation’ referred to at L343-346); (iii) this fracture opening results in drainage to the bed (or, at least, englacial environment); (iv) full-depth fracture will close elastically along most of the length (L426-427); (v) apart from where rivers intersect the fractures (L334) and surface-to-bed connections (moulins) can be maintained through thermo-mechanical erosion of the vertical drainage pathway. If this is the case, then ‘gully refilling’ may be similar the relict moulin refilling previously noted by Chudley et al. (2019) in the literature (cf. Fig 11 of the manuscript with, e.g. Fig 5c insets in Chudley et al.), although they attribute this overtopping to the ‘top-down’ filling of a closed moulin rather than ‘bottom-up’ water rising from the bed in this paper. 

I do not think that similarity to previous studies is a bad thing: instead, the choice to choose different (and poorly explained) terminology for relatively ambiguous reasons is confusing when trying to place this study into the context of other work (at least, it is for me!). If I have been misled by my interpretation, then perhaps the authors might need to take more time to more carefully explain the new terminology, and how and why this lake drains differently from previous studies.

Specific Comments

[Abstract] Include ‘79˚N Glacier’ as alternative name within abstract if there is space?

[Introduction] I found it surprising how dense some of the introductory material is, covering quite technical aspects of flow dynamics, englacial hydrology, and fracture mechanics that are not touched upon again in the rest of the paper. Some work could be done to remove unnecessary content here. Perhaps this relates to Reviewer 1’s comments about a lack of clear story - a more cohesive set of key findings would in turn help to identify the necessary material for the introduction.

[L24-27] Is this level of detail necessary for the introduction? Could just say that AF is well-established to have occurred in this region (citing Khan, Humbert, Zeising).

[L27] ‘In this study’ - perhaps a misrepresentation of what this study is doing? It is perhaps not surprising to find how rising surface temperatures could lead to a meltwater lake.

[L29-35] Given the well-established lake literature (and how none of this really comes up in the rest of the paper?), this is a lot of words to say that lakes occur where surface melt collects in topographic depressions. 

[L75-78] I am quite confused as to why this text is located here, in between to other completely standard final-paragraph-of-the-introduction prose.

[L85-92] I do not think this section needs to be three separate sentence-long paragraphs. This applies elsewhere as well - the abrupt appearance of short interspersing pargraphs gives the impression the sentences/paragraphs have been cut-and-pasted together without much regards for coherent structure or flow.

[L94] Perhaps ‘single-polarization (hereafter single-pol)’ at the first instance.

[L103] Was there significant difference in the relative basins (barring vertical difference due to melt, presumably) between the three DEMs? This would be of interest as, if the three DEMs gave broadly similar results, it would mean that long-term lake volume studies could be produced from confidence using only one good DEM of the empty lake basin (from e.g. the ArcticDEM mosaic product)

[Section 2] Could this be further separated into 2.1 Satellite Methods, 2.2 Airborne Methods, and 2.3 Modelling for clarity, with current subsections as subsubsections?

[Table 1] could be moved to a/the supplement for brevity

[L211-217] could be methods?

[L223-4] Once again, is this really its own paragraph? I note at this point in the results there start to be single-spaced line breaks and double-spaced line breaks. This is again confusing - what are paragraphs and what aren’t? 

[P13] Could a timeseries plot be a useful way of visualising this narrative? Noting e.g. maximum extents per year, with drainages marked.

[L231] Here and elsewhere, satellite imagery used to build the narrative is not shown. Perhaps as supplementary material, before/after satellite images of the drainages could be visualised?

[L253-257]. This is the first point in the text that locations A and B are referenced, and after finishing the manuscript I am still unclear as to exactly why the specific locations are important or what is happening in them that is special. Is it where the ‘gullies’ (moulins?) are located? Are they the same ones being reactivated and advecting along? This needs to be much more clearly explained. Also, it is confusing to track them between figures - can they be marked on all of them?

[L258] ‘Gully A’ referenced here and, as far as I can tell, never again.

[L293]. and elsewhere - present tense rather than past tense.

[Section beginning L360] I agree with Reviewer 1 that the aerial data is remarkably lightly analysed considering - as I identify in my opening paragraph - it is truly spectacular and unique data with a wealth of opportunity within.

[Paragraph beginning L430] Other studies that discuss the elastic opening/closure of full-depth crack closure/opening suggest it must be dependent on continued flow of water to remain open, and closes rapidly after the main drainage event is complete (e.g. Doyle et al, Chudley et al, Stevens et al). However, here it is implied that, with just the hydraulic head alone, (i) full-depth cracks can remain open; and (ii) water does not freeze (cf. e.g. Hubbard et al 2021). My instinct here is that this is quite unrealistic without further evidence?

[L433 - 441], and potentially elsewhere: does ‘head’ refer to the hydraulic head?

[L456-457]- Post-drainage vertical displacement along the crack face was also reported by Doyle et al. (2013)

[L455-465] I agree that it is likely the 2005/06 event is likely the earliest event (within the satellite observational record), but surely the radargram data merely confirms that no drainage occurred from the date of the farthest-downstream-observation of the radargram through to 2012?

[Figure 3] maximum lake extent appears to be getting smaller through time? Is this significant?

[Figure 3b] do the triangles represent the current (advected) locations of the gulleys, or the contemporary drainage locations? Triangle directions aren’t explain within caption and require reference to main text.

[Fig 8a]  The shades of the principal (stress? strain?) crosses are very hard to differentiate easily. Perhaps colour-blind-friendly colour contrast would be better here? 

[Figure 14]  explicitly label the panels “3-4/7-8 weeks after drainage” as well as the interferogram dates for clarity?