Large ice loss variability at Nioghalvfjerdsfjorden Glacier, Northeast-Greenland

Nioghalvfjerdsfjorden is a major outlet glacier in Northeast-Greenland. Although earlier studies showed that the floating part near the grounding line thinned by 30% between 1999 and 2014, the temporal ice loss evolution, its relation to external forcing and the implications for the grounded ice sheet remain largely unclear. By combining observations of surface features, ice thickness and bedrock data, we find that the ice shelf mass balance has been out of equilibrium since 2001, with large variations of the thinning rates on annual/multiannual time scales. Changes in ice flux and surface ablation are too small to produce this variability. An increased ocean heat flux is the most plausible cause of the observed thinning. For sustained environmental conditions, the ice shelf will lose large parts of its area within a few decades and ice modeling shows a significant, but locally restricted thinning upstream of the grounding line in response.

a region important for solid ice discharge from the ice sheet, and freshwater delivery to the Nordic Seas. Existing temporally-sparse remotely-sensed, and field data are supplemented by thickness estimates based on tracking the surface expression of a lateral grounding line. These innovative data reveal highly variable mean annual ice shelf thinning rates, which, due to their high magnitude, implicate increased ocean heat flux as the only plausible cause. If the greatest observed thinning rates were sustained, the ice shelf could lose 75 % of its thickness over a single decade, with significant implications for upstream ice flow and calving rates. This is an important and interesting paper that I believe will be of great interest to others in the community and the wider field. My comments are mostly fairly minor and concern grammar and wording, but there are quite a few of these issues that I believe need to be addressed.
Specific points (by Line number, L) L12: Given the next sentence, I wonder if it is worth expanding on how this observation was made. L13: Consider changing 'was' to 'has been'. L13: 'Lack in' should be 'Lack of'. L14: Consider changing '…no temporal evolution of this bulk ice loss has been presented so far…' to '…to date no temporal evolution of this bulk ice loss has been presented…'. L15-16: Consider changing '…ice thickness and bedrock data it is possible to describe…' to '…ice thickness and bedrock data, we describe…'. L18: Consider adding 'instead' between 'are' and 'governed'. L19-20: Consider changing 'The high values of up to 13 m ice thickness reduction within one year indicate…' to 'Observed thinning of up to 13 m/yr indicates…'. L23: 'of' should be 'in'. L24: 'at its centre' sounds a bit odd and I wonder if 'at mid-distance' might be better? L30:'early' should be 'already'. L30-38: How does this paragraph equate with the second sentence of the abstract? It would be worth checking that both parts are consistent. L35: Consider inserting 'has' before 'experienced'. L36: Missing a full-stop. L37: In some places it is 'the 79…' and in others just '79…'. I would pick one and be consistent (I prefer no 'the'). Also missing an apostrophe 'Glacier's'. L39: Consider changing 'Recent observations of' to 'Recently observed'. Otherwise the sentence suggests that it is the observations that will affect the stability, rather than the changes themselves. L43-44: These areas should be annotated on Figure 1 given that they are mentioned here. L44: Insert 'have' between 'measurements' and 'revealed' L45: Consider changing 'It's deepest' to 'The glacier's thickest'. L48: 'Represents a remarkable' L53-55: I wonder if it the best approach to present the final conclusions so early on. L53-54: Consider changing 'data on oceanic and atmospheric forcing' to 'oceanic and atmospheric forcing data'. L74: 'providing values for ice thickness'. Also, remove 'the' before 'water depth'. L78: Consider changing 'provides the ice thickness and the bedrock elevation underneath' to 'provides the underlying ice thickness and the bedrock elevation'. L86-87: The grey shading is not clear in the pdf reproduction of the figure. L88: Consider changing 'Those' to 'These'. L106-107: Consider changing 'Landsat archive have been selected for' to 'Landsat archive for'. L107: Consider changing 'periods' to 'separation' L115: Consider changing 'The oceanic' to 'Oceanic' L116: Consider changing 'have been' to 'were' L119: 'calving front towards' L120-121: Consider changing 'An ice-shelf plume model (20) estimates' to 'We employ an ice-shelf plume model (20) to estimate' L114: Consider changing 'So far' to 'To date' (otherwise could be misconstrued as meaning within this article only). L145-146: Consider changing 'The comparison of the ice thicknesses on the ice shelf from' to 'Comparison of ice shelf thicknesses from' L152: I would recommend being consistent with the phrasing and sign of the thickness changes. L157: 'with' should be 'as'. L167: 'high temporal resolution' is vague. It would be better to give an actual value, for example 'an approximately annual temporal resolution' L168: Consider replacing 'the ice ridge feature' with 'it'. L173: Make clear that it is the lower panel of Figure 3 that is referred to here. L189-191: It would be better to have consistent axes extent (i.e. figure panel extent) and font sizes for the two parts of this figure. L193: It would be good to annotate the first 3.2 km of the light blue line on Figure 4. L195: To be consistent you should also state the relevant vertical exaggeration value for the upper figure. L197: I realise it may seem obvious, but it would aid in quick interpretation of the figure to add 'N' and 'S' at the ends of the profile presented in Fig. 3. L214: Consider changing 'grounding line. This inhibits' to 'grounding line, which inhibits'. L220-221: Change the ',' in column 3 of the table to '.' to be consistent with the main text. L224: I don't think that 'will' is necessary here. L257: Space after 'until'. L281 (and elsewhere): 'Atlantic Water' L317: The modelled melt rate is comparable but quite a bit (~30 %) lower. Any ideas why? Did the plume consist only of melted ice shelf -i.e. was there any additional 'forced' convection based on the subsurface runoff of geothermal melt and basal frictional melt at the grounding line? The inclusion of realistic values for these may act to increase the model-derived melt rates. I don't think it is necessary to re-run the model, but I think it would be a good idea to at least mention some reasons to explain the relatively low modelled melt rates. L336: Consider replacing 'this' with 'our', otherwise the meaning is slightly ambiguous as you could also be referring to reference (1). L341: Change 'could show' to 'have shown'. L357: Consider changing 'We could demonstrate that the ice loss into the ocean water below' to 'We have demonstrated that basal ice melt by ocean water below' L363: 'for' should be 'in' L363-364: What about increased surface melt and/or increased basal melt? Maybe not from ice acceleration, but perhaps from temporal variations in geothermal heat flux and atmospheric temperatures? Surface melt was higher 2001-2005and 2009-2010). This might be worth a brief discussion. L366: 'towards the' is unnecessary. L371: Consider changing 'ends' to 'results'. L373: 'loses' could change to 'could lose'. L374: Not just the rate of entrainment (presumably related to the volume of subsurface glacier meltwater runoff at the grounding line?), but the water temperature too. Maybe: 'sustained high sub ice shelf oceanic heat flux' would be better than 'intensified warm water entrainment'? L375: Consider adding 'with' after 'However,'.
Reviewer #3 (Remarks to the Author): • Key results: This is an interesting paper about thickness changes on a major glacier in Greenland. The authors use a combination of in situ and remote sensing observations, combined with oceanographic measurements to conclude that ocean-driven basal melting has caused the long-term changes in ice thickness. The strength of this paper is the fact that the authors have a new result (quantification of thickness change) and some creative methodology (using the migration of a shear zone to derive long-term thickness changes).
• Validity: The main conclusion, that ice shelf thinning is due to basal melting from warming ocean temperatures, is essentially based on 4 CTD casts taken years/decades apart. There is an abundance of literature showing that fjord temperatures undergo large seasonal changes, so inferring anything from a few point measurements is tenuous. I recognize the modeling work that the authors did to combat the data scarcity, but am still skeptical.
• Originality and significance: The use of a shear margin to infer thickness change is original and the high rates of thinning on this ice shelf are definitely interesting and significant. However, as it is written now, I do not find this paper to be of "immediate interest" to non-glaciologists.
• Data & methodology: This work uses a lot of very disparate datasets (ground-based, remote sensing and modeling). While I find the writing and organization hard to follow, the authors do include all the relevant data descriptions.
• Appropriate use of statistics and treatment of uncertainties: Yes, the authors are careful about statistics.
• Conclusions: Overall, I found the conclusion that the ice shelf has thinned to be convincing and well documented. The inferences about atmospheric forcing from positive degree day estimates and a 20 year old plume model based on 4 CTD casts are not very convincing (or as well described).
• Clarity and context: This paper is possibly Nature-worthy if it was easier to follow and written more concisely. The first time I read the paper I thought the shear-zone analysis was going to be the major point of the paper. But, the main conclusion is the long-term thinning (which is an interesting result), and the shear zone is just one tool used to derive thickness change.
I've included some specific comments for the first few pages. However, most of these are editorial comments, so I did not continue to make the corrections for the latter part of the text. Throughout the text, the verb tenses are confusing, there are multiple typos and it doesn't seem to follow the Nature guidelines (for length, location of methodology, structure of abstract, or placement of figures).
Abstract: It is slightly confusing what the main question/problem is here. For example, "A considerable loss in ice thickness was observed" -is this your result or a previous observation? Per Nature guidelines, they like the summary paragraph to state the problem and then conclude with "Here we show…" 15: The transition from "Based on the migration of a surface feature" to "ice thickness and bedrock data" is awkward (and missing some verbs). 17: "for producing" -> to produce 18: This statement seems overly confident…your results definitely suggest this conclusion, but not definitively.
27: This sentence needs more detail -could contribute to 1.1 m of sea level rise (under what conditions? Over what time interval? Based on what?) 28: Add some more detail to this implication -how much does it contribute to freshwater flux? A significant amount? It's a pretty slow moving glacier that does not calve icebergs frequently. 30: early? 31: Need references for this statement 36. Missing a period 37: "strong increase in ice flux" -by how much? 38: Glacier's 39-42: This paragraph doesn't seem necessary, especially given the strict word limit 44: "extensive cavity beneath the ice shelf" -does this just mean that the shelf is floating, or that there is a big bed depression under the ice shelf? 48: represents "a" remarkable… 53: The transition to this last sentence is awkward Fig 1: Suggest changing the color of one of the "light blue" features and adding the location of the grounding line. 60: as "a" red dot 94: How were the ATM data smoothed? Why? 106: "was tracked" and "have been selected" ?
We carefully revised the manuscript and tracked the changes. All remarks of the reviewers are listen and commented below.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): Major concerns: (1) Overall, the paper is very well written and well organized. The main message of the study is that high values of up to 13 m ice thickness reduction within one year indicate that the ice shelf could lose up to 75% of its thickness within one decade for given environmental conditions. My main concern is that the paper focus on a small area of 79 glacier, and do not show why (supported by evidence) this is important for the mass balance of the northeast Greenland ice stream (NEGIS). To publish in nature communications, the study must deliver something more than just an improvement of the temporal evolution of bulk of ice loss on 79 glacier. The study could include ice flow modeling (see e.g. Choi et al, 2017) and show how the observations presented in this study could have an impact on the total mass budget of the drainage basin. A paper that simply improve the temporal evolution of the floating part of the 79 glacier is more suitable for a technical journal.
We would like to emphasize that this the first time that detailed thinning rates could be derived for quite a long period on a major outlet glaciers of NE Greenland. There is no other way to retrieve such a unique data set for the past, than by the observation of the Midgardsormen ice ridge. This has never been demonstrated before and the variability is surprisingly large. Therefore, we think that this is a major contribution to the discussion of the mass balance conditions in NE Greenland. However, we agree with the reviewer that a broader context will definitely strengthen the impact of the manuscript. For this purpose we conducted a numerical simulation of ice flow for this sector of the ice sheet. Due to time constraints and because this is not the focus of the manuscript, we kept the model setup simple, but robust with regards to the envisaged dynamic consequences. The model itself is now briefly described in the Supplementary Material, including the results of the simulation. In the manuscript itself we refer to this material in the methods section and discuss the results in the Results and Discussion, also in relation to the results of Choi et al. (2017). The outcome is that the floating part of the glacier very likely will disappear during the coming decades and that there is a considerable but confined influence on the ice flow of the adjacent ice sheet.
(2) Line 365 to 376 list potential consequences of breakup of the floating ice tongue in the fjord. Again, my concern is that none of these consequences are supported by any analyze presented in the paper. As far as I see it, this entire section is speculations, and should therefore be removed. I suggest the authors either delete the section or include ice flow modeling that potentially could support their statements. Modeling is important, for instance, the Peterman glacier in northwest Greenland lost a huge amount of the floating tongue in 2012, and however, it did not generate any notable ice loss upstream glacier. Similar, if you claim that breakup of the floating ice tongue will have consequences for the upstream area; this must somehow be demonstrated in the paper.
We now performed several model runs for investigating the actual ice shelf stability and the potential break-up consequences. The set-up of a fully-fledged ice shelf break-up model was not in the scope of our revision. However, we investigated the temporal thinning of the ice shelf. From these results it is very likely (a major part of the ice shelf reduces to ice thicknesses below 10 m within the simulated period of 100 years) that the ice shelf will disintegrate during the coming decades. We now support our description by the model results.
Minor comments I think the title is misleading, "causes" are not showed in any way in this paper. Also, by "Nioghalvfjerdsjorden Glacier", I imagine the entire glacier and especially the grounded portion of the glacier. However, this paper focus on the floating tongue, which if melted completely will not cause sea level rise (only melt of land based ice causes sea level rise).
We removed "causes" from the title. There is no defined upper boundary of Nioghalvfjerdsfjorden Glacier. The name is usually used for the floating tongue alone, as the name "fjord" indicates. Therefore we leave it as it is.
Line 12: "Nioghalvfjerdsfjorden is one of the largest outlet glaciers", in term of what ? drainage area? flux rate ? ice loss?
This refers to drainage area and ice flux. However, there is not enough space in the abstract to be more specific. We now describe it as a major outlet glacier.
Line 13. "A considerable loss in ice thickness was observed across the floating part of this glacier since 1999". Well, floating ice do not contribute to sea level rise. So why is this interesting?
We do not understand this question. Are only observations interesting, which influence the global sea level? If environmental conditions lead to a massive loss of the total ice volume, this is a serious consequence in itself. Even more so, because this ice shelf represents the drainage channel for a significant part of the ice sheet. The potential consequences are now presented in a more concise way in the discussion.
Line 27: "1.1 m global sea level rise". Out of context. This paper is not about sea level rise! We agree that this paper does not deal with sea level rise. However, it is important to put the work into the context that variations in the ice shelf will influence the dynamic conditions of the ice drainage in the region and thus the ice resources of this sector of the ice sheet. Therefore we prefer to keep the description about the significance of this region of the ice sheet.
Line 33: "The area of 79 North Glacier has remained remarkably stable since about 1906 (7) Summary This manuscript presents an improved time series of ice shelf thinning rates from NE Greenland in a region important for solid ice discharge from the ice sheet, and freshwater delivery to the Nordic Seas. Existing temporally-sparse remotely-sensed, and field data are supplemented by thickness estimates based on tracking the surface expression of a lateral grounding line. These innovative data reveal highly variable mean annual ice shelf thinning rates, which, due to their high magnitude, implicate increased ocean heat flux as the only plausible cause. If the greatest observed thinning rates were sustained, the ice shelf could lose 75 % of its thickness over a single decade, with significant implications for upstream ice flow and calving rates. This is an important and interesting paper that I believe will be of great interest to others in the community and the wider field. My comments are mostly fairly minor and concern grammar and wording, but there are quite a few of these issues that I believe need to be addressed.
Specific points (by Line number, L) L12: Given the next sentence, I wonder if it is worth expanding on how this observation was made.
We included: "by comparison of digital elevation models". However, we also had to shorten the abstract.

Text has changed
L13: 'Lack in' should be 'Lack of'.

Done
L14: Consider changing '…no temporal evolution of this bulk ice loss has been presented so far…' to '…to date no temporal evolution of this bulk ice loss has been presented…'.

Done
L15-16: Consider changing '…ice thickness and bedrock data it is possible to describe…' to '…ice thickness and bedrock data, we describe…'. The two parts do not contradict each other. In the abstract we state that due to a lack of observations it is not possible to quantify the temporal evolution of mass change of 79 North Glacier. In the paragraph of the Introduction we explain that the spatial extent of the glacier has been stable since the first observations. However, the disintegration of the frontal shelf of Corrected L37: In some places it is 'the 79…' and in others just '79…'. I would pick one and be consistent (I prefer no 'the'). Also missing an apostrophe 'Glacier's'.
We now use "79 North Glacier" throughout the manuscript.
L39: Consider changing 'Recent observations of' to 'Recently observed'. Otherwise the sentence suggests that it is the observations that will affect the stability, rather than the changes themselves. Here we refer to the cavity, not the glacier. Therefore "deepest" should be appropriate.

L48: 'Represents a remarkable'
Inserted L53-55: I wonder if it the best approach to present the final conclusions so early on.
We removed this sentence and now only mention the analysis of possible drivers.
L53-54: Consider changing 'data on oceanic and atmospheric forcing' to 'oceanic and atmospheric forcing data'.

Changed
L78: Consider changing 'provides the ice thickness and the bedrock elevation underneath' to 'provides the underlying ice thickness and the bedrock elevation'.
Because it is only the bedrock which is underlying the ice, we now wrote: "provides the ice thickness and the underlying bedrock elevation".
L86-87: The grey shading is not clear in the pdf reproduction of the figure.
We intensified the grey shading.  We tried to be consistent now and describe always the loss or loss rate as a positive value.
Corrected L167: 'high temporal resolution' is vague. It would be better to give an actual value, for example 'an approximately annual temporal resolution' Changed L168: Consider replacing 'the ice ridge feature' with 'it'. Figure 3 that is referred to here.

L173: Make clear that it is the lower panel of
Thank you for pointing at a given but wrong distance, which was left from an earlier version of the figure. We corrected this now. The distance is the same for the upper and the lower panel in Fig. 3. Done L197: I realise it may seem obvious, but it would aid in quick interpretation of the figure to add 'N' and 'S' at the ends of the profile presented in Fig. 3.
We now explained the light blue line with respect to Fig. 3. Therefore it is not necessary to include "N" and "S" in addition.

L214: Consider changing 'grounding line. This inhibits' to 'grounding line, which inhibits'.
Done L220-221: Change the ',' in column 3 of the table to '.' to be consistent with the main text.
Changed L224: I don't think that 'will' is necessary here.

L281 (and elsewhere): 'Atlantic Water'
Changed L317: The modelled melt rate is comparable but quite a bit (~30 %) lower. Any ideas why? Did the plume consist only of melted ice shelf -i.e. was there any additional 'forced' convection based on the subsurface runoff of geothermal melt and basal frictional melt at the grounding line? The inclusion of realistic values for these may act to increase the modelderived melt rates. I don't think it is necessary to re-run the model, but I think it would be a good idea to at least mention some reasons to explain the relatively low modelled melt rates.
In general modelled melt rates are comparable to observations but the computed ice thickness reduction based on the increase in modelled melt rates is 30% lower than suggested by the retreat of Midgardsormen ridge. The modelled average melt rates using, e.g., 1998 hydrographic conditions (8.7 1.1 m/yr) compare nicely to glacier mass budget calculations from that time (8 m/yr, Mayer et al (2000, GRL)). Furthermore maximum melt rates of 40-60 m/yr at 5-10 km downstream the grounding line are inferred from the model and comparable to melt rates published by Wilson et al. (2017). Thus, we believe that the model represents the ice-ocean interaction quite well. Using the model we estimated the ice thickness loss over time (i.e

., taking also into account the ice velocity) having in mind that the uncertainties are relatively large. The total thinning based on glacier observation is clearly at the upper bound of our ice loss estimate from the model. However, smaller contributions from surface melt and/or changes in the ice flux most likely also contributions to the overall ice loss.
You are right that we initialize the model by using typical values for the meltwater flux beneath ice streams (1*10 -3 m 2 /s). Subsurface runoff from geothermal flux melt and basal frictional melt is however expected to be negligible, while subglacial discharge originating from surface melt which drains to the bed of the ice sheet is likely to play an important role for an additional "forced" convection. However, the initial flux of subglacial runoff for glaciers around Greenland is not well constrained and most likely highly variable in space and time (e.g. Straneo et al., 2011). In general, subglacial runoff may accelerate ice shelf basal melting near the grounding line in summer (e.g. Motyka et al., 2003Motyka et al., , 2011Straneo and Heimbach, 2013). By freshening the meltwater plume and thus increasing the initial density contrast to ambient water, subglacial runoff enhances basal melting close to the grounding line. Higher ice-shelf basal melt rates are expected in warmer summers, which may cause large seasonal and interannual variability in basal melt rates. Further model experiments applied to 79N Glacier suggest that a change in the freshwater discharge by four orders of magnitude increases the melting by 50%, i.e., increasing the average basal melt rate by about 5 m/yr -1 .
While we agree with the reviewer that this issue merits discussion in the manuscript, we believe that thoroughly revising the above points would be slightly misleading. Instead, we added the following sentences to clarify the interpretation of the model results, also having in mind the comments of the reviewer on the temporal variability of the oceanic forcing. L336: Consider replacing 'this' with 'our', otherwise the meaning is slightly ambiguous as you could also be referring to reference (1).  Figure S1). This might be worth a brief discussion.
While geothermal heat flux is unlikely to account for large subglacial discharge, variability in surface melt may be relevant for the observed ice thickness variability not only due to surface mass loss but also due to changes in subglacial discharge. From Figure S1 we find increased surface melt in 2002-2005, 2008, and 2011-2014. This may be linked to the increased ice loss in 2002-2005 but cannot explain the strong ice loss observed in 2010.
Also in response to the comments of reviewer #3, we rewrote the discussion in the above lines, which now provides more detailed information on oceanic observations of a warming/shoaling of the Atlantic water layer and includes a discussion of the above aspects: "We investigated the potential causes for the observed ice loss, finding that neither a change in ice dynamics, nor a more negative surface mass balance are likely to explain the persistent thinning of the glacier. Instead, we demonstrated that observed variations in ocean temperature at the ice base would induce sufficient additional melting to cause the estimated mass loss of the ice shelf.
[…]While our analysis suggests that the ocean is likely the main driver of the observed changes at 79 North Glacier, the regional dynamics that control the heat transport into the ice shelf cavity and other contributors, such as subglacial discharge induced by surface melt or geothermal heat flux will need further attention to fully understand the observed thickness evolution." L366: 'towards the' is unnecessary.

Changed
L374: Not just the rate of entrainment (presumably related to the volume of subsurface glacier meltwater runoff at the grounding line?), but the water temperature too. Maybe: 'sustained high sub ice shelf oceanic heat flux' would be better than 'intensified warm water entrainment'? Formulation changed to: "in case of sustained high ocean heat flux into the ice shelf cavity." L375: Consider adding 'with' after 'However,'.

Done
Reviewer #3 (Remarks to the Author): • Key results: This is an interesting paper about thickness changes on a major glacier in Greenland. The authors use a combination of in situ and remote sensing observations, combined with oceanographic measurements to conclude that ocean-driven basal melting has caused the long-term changes in ice thickness. The strength of this paper is the fact that the authors have a new result (quantification of thickness change) and some creative methodology (using the migration of a shear zone to derive long-term thickness changes).
• Validity: The main conclusion, that ice shelf thinning is due to basal melting from warming ocean temperatures, is essentially based on 4 CTD casts taken years/decades apart. There is an abundance of literature showing that fjord temperatures undergo large seasonal changes, so inferring anything from a few point measurements is tenuous. I recognize the modeling work that the authors did to combat the data scarcity, but am still skeptical.
We fully agree with the reviewer that the few observations beneath the ice shelf cannot be used to infer a warming of ocean temperatures inside the cavity. This was never our intention and the statement that the observed ice shelf thinning is likely to be primarily driven by oceanic changes was not derived from the 4 CTD casts on their own. Instead, this main conclusion is essentially based on the combination of the findings that: 1

. Surface melt and changes in ice dynamics can most likely be ruled out to have caused the observed thickness changes (exclusion of other drivers). 2. Unlike the atmospheric and ice dynamical changes, the observed variations in ocean
temperature inside the cavity are indeed capable of inducing changes in basal melting that are large enough to cause the estimated mass loss of the ice shelf (plausibility of the mechanism). This inference is robust independent of whether the observed temperature changes are part of a seasonal cycle (all profiles are from August and September, suggesting limited influence of seasonal changes) or due to a successive warming signal (which is consistent with, but not proven by the data).

Recent literature shows that the Atlantic Water layer off the NE Greenland coast and
on the shelf has coherently been warming and shoaling over the period when the glacier thinning occurred, implying that some of that signal may also propagate further into ice shelf cavity (Consistency with large scale trends). In particular, we compared the few CTD casts taken in the sub-ice cavity with observations from the Northeast Greenland continental shelf (where we find a large number of hydrographic profiles taken between 1984 and recent years, Schaffer et al., 2017)  The discussion has been extended by adding more detailed information and references on oceanic observations of a warming/shoaling of the Atlantic water layer, as well as by adding a discussion of ocean heat fluxes into the cavity, and emphasizing lack of hydrographic observations from the 79 North Glacier cavity.
• Originality and significance: The use of a shear margin to infer thickness change is original and the high rates of thinning on this ice shelf are definitely interesting and significant. However, as it is written now, I do not find this paper to be of "immediate interest" to nonglaciologists. We tried to include all relevant data, which support the observations of the Midgardsormen migration. It is not a simple task to present all these different data in a concise form and still keep the manuscript short enough to be attractive to read. We tried to improve the writing in the Data section in order to allow easier reading.
• Appropriate use of statistics and treatment of uncertainties: Yes, the authors are careful about statistics.
• Conclusions: Overall, I found the conclusion that the ice shelf has thinned to be convincing and well documented. The inferences about atmospheric forcing from positive degree day estimates and a 20 year old plume model based on 4 CTD casts are not very convincing (or as well described).
There is no disadvantage in using old theories and models as long as they do not contradict basic physics. The advantage is that these approaches are simple and still provide solid answers to the questions we asked. The simple degree day model gives us the answer, that even for a large temperature increase (implying a considerably larger atmospheric energy transfer), the atmospheric conditions cannot explain the observed variability in ice thickness loss. The plume model provides information about the intensity of sub ice shelf fluxes, which is the basic parameter necessary for estimating oceanic energy exchange into the cavity. It is not the intension of this manuscript to explain detailed plume geometries, but providing basic potential causes for the observed thinning. Given that the data availability is very sparse for this region, the application of more sophisticated models without adequate input data would be even more questionable. We changed several parts of the manuscript to improve the arguments about the oceanic forcing. Please refer to our comments regarding reviewer #2.
• Clarity and context: This paper is possibly Nature-worthy if it was easier to follow and written more concisely. The first time I read the paper I thought the shear-zone analysis was going to be the major point of the paper. But, the main conclusion is the long-term thinning (which is an interesting result), and the shear zone is just one tool used to derive thickness change.
We still regard the shear zone migration a major result of the paper, because without this mechanisms it would have been impossible to derive the long-term thinning and it temporal variability. However, we tried to improve the clarity of the manuscript by better balancing the text between data and findings.
I've included some specific comments for the first few pages. However, most of these are editorial comments, so I did not continue to make the corrections for the latter part of the text. Throughout the text, the verb tenses are confusing, there are multiple typos and it doesn't seem to follow the Nature guidelines (for length, location of methodology, structure of abstract, or placement of figures).
Abstract: It is slightly confusing what the main question/problem is here. For example, "A considerable loss in ice thickness was observed" -is this your result or a previous observation? Per Nature guidelines, they like the summary paragraph to state the problem and then conclude with "Here we show…" We changed the abstract in order to comply better to Nature guidelines and clarify the contribution this manuscript provides to the research of NE Greenland glacier conditions. 15: The transition from "Based on the migration of a surface feature" to "ice thickness and bedrock data" is awkward (and missing some verbs).
We changed this sentence to clarify our contribution.
17: "for producing" -> to produce Changed 18: This statement seems overly confident…your results definitely suggest this conclusion, but not definitively.
We agree with the reviewer and have revised the abstract, using the formulation: " increased ocean heat flux is the most plausible cause of the observed thinning". Here we only state the potential contribution if the ice sheet disappears according to Morlighem et al., 2014. This is a common information to relate ice volumes of parts of the ice sheet to maximum consequences. We now included "in the unlikely case of complete melt down".
28: Add some more detail to this implication -how much does it contribute to freshwater flux? A significant amount? It's a pretty slow moving glacier that does not calve icebergs frequently.
This sentence refers to the entire section which provides a considerable fresh water amount. Calving is not a valid measure in this context, because subglacial melt is the dominating effect for 79 North Glacier and an important contribution at Zachariae Isstrøm. More details are now provided in this context.

30: early?
Changed 31: Need references for this statement

Missing a period
Added 37: "strong increase in ice flux" -by how much?
We added this information in the manuscript.

38: Glacier's
Done 39-42: This paragraph doesn't seem necessary, especially given the strict word limit The warming trends are essential for the energy availability in the region. We therefore prefer to keep this information in the manuscript. However, we removed the last sentence to shorten the paragraph.
44: "extensive cavity beneath the ice shelf" -does this just mean that the shelf is floating, or that there is a big bed depression under the ice shelf?
"Extensive" in this context described a bed depression with large regions being rather deep. The formulation has been changed to "Seismic measurements have revealed a deep ocean cavity beneath the ice shelf"

48: represents "a" remarkable…
Included 53: The transition to this last sentence is awkward This sentence was removed. The ATM data have been resampled to the resolution of the airborne radar sampling of 34 m, by using the arithmetic mean of the samples. Thus, it was easier to compare.