This manuscript uses a combination of Cryosat-2 laser altimetry and DEMs from SAR and optical measurements to provide detailed measurements over four previously identified subglacial lakes in Greenland, and one prospective, but not previously identified lake.  It provides some details of a set of techniques for combining measurements from these sensors, and offers a longer time series of elevation changes for the lakes than previous studies did, with somewhat more temporal detail.  The use of Cryosat-2 data allows the authors to measure the depth of the lake under Flade Isblink immediately after its drainage, and finds a depth for the collapse feature that is significantly deeper than that measured in previous studies.  I had trouble identifying the scientific questions that the study answered.  Since four of the lakes had been identified in previous studies, the fact of their existence is not news, and the behavior documented in this study is not especially surprising.  The fifth, potential lake identified here is extremely small and is close to one of the previously known lakes, so I am not sure what significance I should attach to its existence.

The study may be interesting to researchers with a deep knowledge of, and interest in, the particular subglacial lakes studied here, but I am not sure how wide this audience is likely to be.  The authors suggest that measurements over subglacial lakes have the potential to inform our understanding of subglacial water flow, but I really didn’t see much development of this potential in this study. The abstract identifies the demonstration of techniques as  a goal of the study, but the technical discussion of the techniques is brief and the presentation of the measurements is not very detailed.  I would recommend reworking the study, either to focus on how each of the techniques performed at lake 4 (which had very large relief and elevation change) and at lakes 2 and 3 (which were small, and where the Cryosat-2 data didn’t work well), or to try to better understand the implications of the measurements for the subglacial hydrology of the ice sheet. 

Line 34:  Should note that this possibility was investigated in some detail by other studies (Stearns 2008, https://www.nature.com/articles/ngeo356)  (Smith et al, 2017 (cited in the  manuscript)  And (Zwally and others, 2002, https://www.science.org/doi/10.1126/science.1072708), and that  net dynamic changes after very large water inputs were negligible.

Line 88: “Classified” is not the right verb here.  “Asserted” might be better

Section 3-1:   Is there any way the selection of thresholds can be formalized?  The thresholds selected here seem ad hoc, and it would be useful to discuss how they were chosen.

Line 140: “highly dynamic” should be “rough”

Line 141: Is the incoherent component in the processing, or in the radar reflections?

Line 145: should be “assumed to be representative”

Line 145: “were deemed as errors”  should be “were assumed to be errors”

Line 146: “Across swath tracks close to the basin rim” should be “swath-processed data from tracks close to the basin rim”

Line 148: remove commas around “which is removed”

Line 183 “vertical alignment” should be “vertical offset”

Line 184: delete “found to be”

Line 197: “but we see” should be “and we see”

Line 201: “such as” -> “including”

Line 211: What is the basin shapefile?

Figure 1 (and all similar figures)

1. The map extent is too broad to give a useful context for the lake location.  Should instead show a context map with the regional topography and the locations of adjacent glaciers in some detail, with a reference map in a separate figure to indicate the locations of figures 1-7
2. Need to provide a color bar for panel c
3. The yellow lines in panel b are very hard to see
4. The range of contrast in the colors in panel b does not really allow the distinction between different CS2 dates.  Different symbols should be used to denote different dates.
5. The legend should explain the blue shaded bar

Line 224: Subtracting the median height does not make sense, as the offset subtracted is will depend on the height distribution of the rim.   It would be better to subtract a median height anomaly relative to some reference DEM.  Is this what the authors mean to say?

Line 226: “cubing the 2sigma”: What is this, and why does it give an error estimate?  This needs much more detail to explain and/or justify what is done here. 

Line 228: Need to specify which depths and volumes are used here, and need to connect these, using consistent terminology, with the depths derived from the DEMs and from CS2.  Are “the depths” referenced here the depths of the deepest point from CS2?

Line 231 / equation 1.   How does the derivation of R and V take the error bars into account?  More detail is needed.

Line 236: It would be useful to demonstrate how R~(t) varies in time based on the available DEM data.

Lines 225-236: The methodology here does not seem to capture the true uncertainty in depth (and volume) estimates based on the CS2 data.  When there is a large spatial variation in elevations in the DEM data, they are assessed a large error based on the slope and roughness within the relevant part of the lake, but CS2 data generally give a small number of elevation measurements at these times, and are assessed a smaller error.  Would it not make sense to apply roughness information from the DEMs to the CS2 data to assess their errors?

Line 246: add comma after “coverage”

Line 264: It would be useful to explore why CS2 did not provide data over lakes 2 and 3.  Were there no footprints that intersected the lake boundary?   Was the coherence too low?

Line 265: Please show the power image from TanDEM-X for early 2011.  It would be interesting to know if there are any reflectance features associated with the about-to-drain lake.

Line 279: “CS2 point data” :should this be “CS2 swath data”

Volume calculations: Except for Flade Isblink, these volumes are exceedingly small.  Compared to lake discharges in Antarctica, they are miniscule, and those Antarctic discharges had almost no effect on ice dynamics.  What is the justification for saying that the lakes studied here might be important for ice dynamics?

320: Should compare volume-change estimates against surface runoff estimates from (e.g.) RACMO.

358: “shortly” should be “briefly”

373: “off-nadir” should be “off nadir”

376-384: this repeats material found in the methods section.

378: delete “parameters”

387: is “highly active” all that can be determined here?  This doesn’t seem like a lot has been learned.

Section 6.6

To conclude that the activity of the new potential lake affected the drainage of lake 2, the authors would need to present evidence that it is unusual for water to reach the bed in volumes comparable to those discharged by the new lake.  Looking at the images in appendix B, it appears that there is abundant water on the surface of the glacier, and it seems likely that this water often drains through moulins.  Why, then, should we believe that the drainages of lakes 2 and 3 are anything but coincidental?  Even if they were not coincidental, what specifically does this tell us about the hydrology of the glacier bed that we could not have inferred already? 

Appendix A:  Why would the basal melt rates be important in this area?  Water fluxes from surface melt must dwarf these rates by orders of magnitude.  Please consider surface melt first.

Appendix B:

Figure B1:  Indicate the location of this lake relative to lake 2.  Also- what is being mapped here?  The difference between panels a and b seems to mostly be that in panel B the surface is covered with snow, while in panel A it is mostly bare ice.  The interpretation of the change in the collapse basin is not at all clear to me.

Figure B2: There is a lot of variability in surface conditions between these images.  The interpretation in the text is not at all convincing.

Data availability: I didn’t see a statement about data availability for the CS2 swath-mode data.

General Comments

This paper combines multiple satellite missions to improve the temporal resolution of ice surface elevation change measurements over 4 previously identified active subglacial lakes in Greenland to provide new constraints on lake volume and evolution. In addition, they find one potential new active lake that might be hydrologically connected to one of the known lakes (although see specific comments). The study is generally well written with some nice figures, and I found the combination of methods to improve the temporal resolution convincing. I did, however, find quite a few minor errors or places which needed further clarification (see specific comments below), and I agree with the other reviewer that the implications of their findings are currently not clear, and could do with expanding / reworking. For example, could you combine your improved monitoring of recharge rates with your basal melt modelling (expanded to all sites), to make this a more significant component to better explore the role of surface vs basal melt. How do your recharge rates/ drainage rates compare to elsewhere? Can you use your improved timings of drainage to better link to triggers?

Specific Comments

L4 – Antarctic Ice Sheet

L6 – I think it would be worth mentioning earlier in the abstract that active lakes are typically identified from ice-surface elevation changes to put this point into context.

L14 – It is odd to mention surface hydrology at the end as this is not discussed in the rest of the abstract.

L21 – not sure this reference is appropriate here as it focuses on predicting lake locations. Perhaps refer to the Livingstone et al. (2022) study instead.

L24 – “steeper ice surface slopes”

L27 – delete “further”. Your previous points were around different settings not detection.

L30 – the use of e.g. in this sentence does not work that well. Can you combine the first part of this sentence with the second part of the next to provide a more general mechanism for lake drainage?

L33 – I think Palmer look at vertical displacement, but don’t really mention horizontal displacement. It might be better to refer to some of the key velocity studies in Antarctica or Iceland here.

L35 – suggest – “Notably, the period of lake recharge following a drainage event provides…”

L49 – should this be InSAR not SARIn?

L56 – delete “source of” to avoid repetition of this word.

L59 -this makes it sound like there have just been 4 active lakes identified in Greenland. There are actually 7 – see Livingstone et al. (2019). Worth noting this and rephrasing to justify the four you have chosen. 

L66 – this makes it sound like Bowling et al. (2019) identified all these lakes. It would be better to cite the original papers for all these lakes.

L72 – Figure 2a is cited before Figure 1.

L83 – is this a subsidence event in 2004? Not clear.

L94 – suggest:  “… which could indicate some recharge of the subglacial lakes by surface water”.

L97 – Flade Isblink Ice Cap

L105 – clarify whether this was infill of the collapse surface basin or infill of the subglacial lake by surface water causing the ice surface to rise.

L107 – can you quantify the elevation change associated with this event?

Section 3 – it would be useful to provide details on the final resolution and vertical/ horizontal errors of the processed datasets.

L112 – SARIn has already been defined.

L124 – It would be helpful to quantify this change in density.

L128 – “… thresholds compared to those usually applied ….”

L134-138 – Maybe this is because I am a visual person, but a figure showing the raw to processed data points would be really helpful here in allowing the reader to judge the effectiveness of the approach.

L143 – not sure why you need the word “apparent”?

L145 – “assumed to be representative”

L146 – how close in time? This is rather vague and could do with rephrasing.

148 – would be useful to get a rough estimate – 1%, 10%, 90%? See my comment above, a figure showing the stages in the processing would be helpful here.

L160 – “data takes located”? Is there an error here, I didn’t follow this part of the sentence?

L181 – “the vertical bias.”

L192 – given you correct using local ice flow, it would be useful to know here whether this 100 m in 10 years equates to a local ice flow in this region of ~10 m/yr.

L198 – “One reason for this is that the…” I don’t really get the point around the size of the lake as surely it is the lake edge that you are tracking.

Section 4.2 – are these calculations still based on the local difference compared to the basin rim? If not, could these not be influenced by the different penetration depths etc? I don’t really follow the approach to calculating the deepest depths (why take a mean if looking for deepest point) or the use of standard deviation. Is this not just a measure of roughness of the floor of the basin? This needs clarifying.  

L226 – In other papers error is calculated by multiplying the internal error of the DEM by the lake area both before and after drainage and adding together in quadrature. What is the basis for your approach, especially as you state that 2 standard deviations is not a true measure of their accuracy?

L260 – does this actually show uplift? Could you run regression analysis over the two periods to calculate the recharge rates more accurately.

L276 – Flade Isblink Ice Cap

Section 5.1 – Some of the text in this section would I think be better incorporated into the figure captions e.g., “To maintain a visually clear plot not all data sets are shown in Figure 5b.” This would help the flow of this section while making the figures standalone.

L297 – Although this is the maximum volume measured, it is the minimum possible volume (given you might have missed the period of maximum collapse (i.e. it might have collapsed and then recharged between data points).

L310 – can you quantify this – re.  number of data points over X years?

L313-315 – There does seem to be some signal of the final collapse and then beginning of the recharge period though during the winter 2011/2012 period. To better test this it would be better to split these components and calculate the recharge for the upwards tick as a rate vs. the summer after.

L316 – How do you know it is bedrock? Suggest change to “bed”

L318 – Ok, but could this not be associated with a decrease in filling over time as the area increases (i.e. for a given melt input the rate will decreases because of the basin shape?). I think it is fairly common for recharge rates to slow over time.

L320 – “model estimates of basal melt rates” – ok, based on what data? Need a supporting reference and to quantify. I don’t quite see how this point fits with the idea of ice flow/ snowfall. What is the surface mass balance change?

L321 – Appendix not Append.

L322 – capitalise vatnajokull ice cap

L330 – A more positive spin would be to give the time span over which the drainage could have happened.

L331 – “drains”

L332 – “spring”

L334 – In which case, how do you know whether Lake 2 is actually a supraglacial lake that is filling and draining? It would be useful to confirm whether the 2011 data is associated with surface water or not.

L347 – please state the infilling rate from this calculation.

L352 – It would be useful to incorporate the results of Liang et al. (2022) into this discussion as they look at seasonal recharge (i.e. impact of warmer summers on recharge rate, with rates of up to 49 m/yr).

L357-358 – “which shortly affected the local horizontal ice velocity” – needs rephrasing.

L368 – “basins are flat”

L378 – You use SARIn elsewhere.

L386 – Ok, but others have shown this in their data, so should acknowledge this.

L387-388 – this needs clarifying? Where is this low pressure region?

Section 6.5 – this seems rather tagged on and is not explained in the methods, and very briefly here. I would suggest introducing earlier in the method section and showing in the results, or deleting.

L402 – There is also a new paper in TCD by Fan et al. (2022) with lots of new active subglacial lakes. Is this one of the lakes in their inventory? https://tc.copernicus.org/preprints/tc-2022-122/

Section 6.6 – given that this period coincided with a large melt event could these both be responding independently to large volumes of water accessing the bed in this region? More information is needed here to better test this hypothesis.

L422 – Greenland Ice Sheet.

L423 – “investigated elevation changes”

Figures/ Tables

Given that you correct based on the elevation outside of the collapse basins, I was surprised to see many of the plots with a y-axis of elevation rather than elevation anomaly (relative to the tie points). It would be useful to clarify whether you use similar time periods as cross-over points or how you are able to show these.  

Figure 1 – what is the blue shaded bar? (also in figures 2 and 3)

Figures 2 and 3 – what are the red bars? (also true for Figure 7)

Figure 6 – what is the grey-blue bar around the points? Need to clarify. Why do only (a) and (d) have red lines?