Contrasting thinning patterns between lake- and land-terminating glaciers in the Bhutanese Himalaya

Tsutaki, Shun; Fujita, Koji; Nuimura, Takayuki; Sakai, Akiko; Sugiyama, Shin; Komori, Jiro; Tshering, Phuntsho

doi:https://doi.org/10.5194/tc-13-2733-2019

Articles | Volume 13, issue 10

https://doi.org/10.5194/tc-13-2733-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-13-2733-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 13, issue 10

Research article

| Highlight paper

|

18 Oct 2019

Research article | Highlight paper |

| 18 Oct 2019

Contrasting thinning patterns between lake- and land-terminating glaciers in the Bhutanese Himalaya

Shun Tsutaki, Koji Fujita, Takayuki Nuimura, Akiko Sakai, Shin Sugiyama, Jiro Komori, and Phuntsho Tshering

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Final revised paper (published on 18 Oct 2019)
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Preprint (discussion started on 13 Feb 2018)
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Interactive discussion

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AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Review of Tsutaki et al', Anonymous Referee #1, 13 Mar 2018
- AC1: 'Reply to Referee #1', Shun Tsutaki, 15 May 2018
RC2: 'Review of Tsutaki et al manuscript', Anonymous Referee #2, 13 Mar 2018
- AC2: 'Reply to Referee #2', Shun Tsutaki, 15 May 2018
RC3: 'Review of Tsutaki et al.', Anonymous Referee #3, 28 Mar 2018
- AC3: 'Reply to Referee #3', Shun Tsutaki, 15 May 2018
EC1: 'Evaluation by handling editor', Francesca Pellicciotti, 09 Apr 2018
- AC4: 'Reply to Editor', Shun Tsutaki, 15 Jun 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Shun Tsutaki on behalf of the Authors (15 Jun 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (08 Jul 2018) by Francesca Pellicciotti

RR by Anonymous Referee #4 (14 Aug 2018)

Suggestions for revision or reasons for rejection

The manuscript by Tsutaki et al. combines surface elevation changes, surface flow velocities, changes in glacial area, and surface mass balance and ice dynamic modelling to investigate the difference in thinning rates of two neighbouring glaciers in the Bhutan Himalaya. One of these glaciers is lake-terminating, the other is defined as land-terminating; the aim of the study is to examine the influence of a proglacial lake on the thinning rates of the glaciers. The study is interesting and the figures are clear and well presented. The manuscript is mostly well-written, but various sections need to be better discussed, explained and justified so that it is clear how the authors have achieved their results. Although the results and conclusions appear to be well supported, there are large uncertainties in the modelling that make it hard to determine how well supported these conclusions are. It would be very interesting for the modelling predictions to be compared with what has occurred to Thorthormi Glacier since 2011, as suggested by a previous reviewer, although it is acknowledged that this would involve a lot more work.

General comments:
1. I find it quite difficult to follow the state of a proglacial lake (or not) at the terminus of Thorthormi Glacier, as contradicting information is drip-fed through the manuscript. Is there a proglacial lake, and when does it form? The timeline (to date) needs to be presented coherently in Section 2 and other mentions in the manuscript then need to correspond. This could also be helped by delineating the lakes in one of the panels in Figure 1. Although the authors made a case against this in their response as the lake area varies over time, even a visualisation of the minimum/maximum lake area for each glacier would be beneficial. A brief investigation of historical Google Earth imagery showed me that Thorthormi Glacier has a proglacial lake that has expanded up both sides of the glacier tongue, along the lateral moraines. I had not grasped this from the manuscript, having understood that there were a few limited supraglacial ponds at the margins.
2. The discussion in Section 5.3 of whether Lugge Glacier has reached floatation seems to be too little, too late. If the glacier tongue was near floatation in 2002, is it not possible it reached floatation during the study period? And if so, surely that may have a large impact on the results: how is it known whether changes in surface elevation are due to the glacier thinning, or changes in the lake volume? This is rather a large assumption to make, and needs justifying or debating earlier in the manuscript.
3. I’m not sure I see the value in including the change in glacial area as delineated from Landsat images. It involves quite large uncertainties, and in my opinion, detracts from a study that is assessing how proglacial lakes affect glacial thinning rates.
4. The comparison of the DGPS-DEM with the ASTER-DEM, after the ASTER-DEM has been calibrated with the DGPS data seems circular, and thus contradictory. If the ASTER-DEM has been calibrated with the DGPS data, it would be fairly obvious that the changes in elevation from each would be very similar. The suggestion from a previous reviewer was to compare the DGPS data with a DEM that has been externally verified, but ASTER does not have any ground-truthing, so it is not an ideal product for this. I suggest that the ASTER-DEM (calibrated with the DGPS data) is instead used for subsequent analysis of surface elevation changes, which would give elevation changes over a larger area and thus mitigate the large uncertainties involved with interpolating the DGPS data.
5. A number of the uncertainties that are reported are extremely large, and in some cases the errors are significantly larger than the values presented. Furthermore, the calculation and reporting of uncertainties is not consistent through the manuscript (e.g. DGPS DEM uncertainty calculations in Section 3.1 which are reported as something different in Section 4.1), some have not/cannot be given a value (such as the interpolation of the DGPS DEM), uncertainties are given as a range of values without explanation (L437), and other uncertainty ranges are discussed but not defined (L344), but yet the data do not lie within any uncertainty (one standard deviation?) of each other. Similarly, in one instance, calculated and observed velocities are reported as being within 7% of each other, yet in the Author Response this is reported as a mean and therefore only half the data will lie within this %. Other specific issues include the use of a quadratic sum (L134 & L239), which is not defined nor what Bolch et al. use, and the undefined extrapolation of the bedrock upglacier in the model inputs (L278), which must also have large uncertainties.
6. Debris cover is mentioned sporadically throughout the manuscript, but without any real weight or meaning. The authors clearly consider it important as it is mentioned in the abstract, a debris melt model is included in the SMB calculations, and debris-covered areas must have been calculated for different SMB values to be presented for debris and debris-free regions in Section 4.4. These values are certainly interesting, but without an idea of the debris thickness in the debris-covered surfaces, are not so useful (L368-371). The manuscript would benefit from a greater discussion of how the debris cover varies (expand the paragraph from L99 and refer to Figure S1), and what influence this might have on the conclusions drawn about ice dynamics.

Specific comments (by line number):
1: Suggest singularising the title and every other occurrence of “lake- and land-terminating glaciers” to “a lake- and a land-terminating glacier”, as you now only consider one of each type.
14: “supraglacial lakes” is not directly relevant, unless you specify that supraglacial lakes can evolve into proglacial lakes, which is what you consider in this study. Perhaps change to “proglacial lakes”.
23: “over half” – later in the manuscript, this value is reported as three quarters?
33: What do you mean by “the Bhutanese glaciers”? All Bhutanese glaciers?
37: Change “monsoon influenced humid” to “monsoon-influenced, humid”
38-40: This sentence would read better if it were condensed.
L43-46: This section would also benefit from a brief description of how proglacial lakes can be formed from supraglacial lake formation, growth, coalescence and downcutting, which is likely what has occurred at Thorthormi Glacier in recent years?
L51: No space between number and % sign, throughout manuscript.
L65-67: Two points are made here about the superiority of remote-sensing techniques: 1. that the surface of debris-covered glaciers can be highly variable due to cliffs and ponds, making access difficult to get large amounts of data; and 2. that UAVs can potentially obtain higher-resolution imagery than satellite-imagery, and thus resolve the highly variable thinning rates more accurately. Suggest restructure to make these points clear.
L68-69: DGPS is not remotely sensed, so this doesn’t follow on from the previous sentence unless it is explained why it is superior (higher resolution data/no permits required compared to UAVs/etc).
L69: Change “is” to “can be”.
L76-77: This sentence sounds like the only reason the glaciers were selected was because of their similar elevations. Any other reasons – debris cover, size, access? Suggest adding the sentence about safety and proximity to trekking routes, but surely the most important reason is the lake/developing-lake scenarios?
L88: If something thins at a negative rate, it is thickening. Remove negative sign. Same on L95.
L99: Needs more discussion of the ponds and cliffs on each glacier to later prove these don’t contribute to thinning rates. Google Earth shows a heavy amount of crevassing on both glaciers, which could be a reason why few lakes are found in the ablation regions.
L103-106: These are methodological details and would fit better in Section 3.4
L118: Move website to reference list, and reference instead. Same for L125.
L122-123: Refer to Figure S1.
L135: Change “In previous studies” to “Following previous studies”
L163: Is the 0.9 threshold picked according to information given by COSI-Corr, or some other method? Please specify. This and the next few lines are not clear: how many filters do you apply or are they all the same? Suggest rewrite to state, step-by-step, what you did and why. Should “attitude” be “altitude”?
L173-174: Remove “in a geographical information system” – manual delineation is sufficient to describe the method. Also change “Following to the previously” to “Following previously”.
L185: ‘Thick’ debris that suppresses ice melt is anything deeper than ~5 cm.
L248: “glaciers” should be singular.
L275: Why use yet another DEM when the first section describes four different DEMs? What year was this DEM from, and why was it necessary to “filter the elevations”?
L299-301: It is not clear how the conditions for creating a proglacial lake at Thorthormi Glacier were decided upon; they currently seem entirely random. How was it decided where to ‘put’ the proglacial lake for Thorthormi Glacier? It doesn’t look to be at the current terminus, so this needs some explanation. Similarly, how was a calving front thickness of 106 m chosen? And why would the surface level of the proglacial lake be identical to the supraglacial ponds in 2004? I understand that this is hypothetical and likely a good place to start, but surely it depends on the time of year, amount of melt, how well the hydrological system has developed, etc, as to the level of the ponds. Additionally recommend changing “assumed” to “simulated” to make it clear this is a hypothetical modelled situation.
L305: What years do you actually run the model from and to? The input data seems to be from a large number of different years… Also needs clarifying in Section 4.5
L331: Is this from the DGPS or ASTER DEMs? Needs specifying, and also in the caption for Figure 1a.
L335: Looking at Figure 2b, it seems that the most negative values are actually found (just) within the upper elevation bands.
L353: Remove sentence beginning “In this region…” as it is an interpretation, not a result, and belongs in Discussions. Same applies for all other instances, particularly of methodological details that are mentioned in the results, but not actually in the methods section.
L355: Report “0.99 years” in number of days to be consistent with start of paragraph.
L357: Change “and accelerated loss” to “which accelerated”
L374: The debris cover must have a more significant influence than this in order to produce 2 m w.e. less melt per year, as reported in the previous paragraph?
L381: I think the experiment names would be clearer as “Present terminus conditions” and “Reversed terminus conditions” as this is what you are changing (not the geometry).
L386: Change “In contrasted to the observed decrease” to “In contrast to the downglacier decrease”
L387: At what distance from the terminus is the 40 m/y velocity reached?
L402-404: Change “Although we assumed” to “Due to the assumption that” – by assuming the glaciers to be temperate, of course most of the ice flow will be due to basal sliding. But how can most of the ice flow be due to basal sliding, but also a “moderate amount” be due to ice deformation? Suggest rewording these two sentences to be clearer as to what you found, and whether the assumption of temperate ice had a significant influence or not.
L450: The repetition of these exact same measurements looks like a mistake; suggest remove the second and change “for the period” to “for both the periods”.
L501-503: Remove the reference to making hypotheses and just state what has been shown.
L506: Was the thinning accelerated?
L515: Change “less thinning” to “thickening”
L517: In Section 4.2, Lugge Glacier is described as having a convergent flow where the glacier width narrows. How might this contribute to, or affect, the stretching flow regime?
L531: Should the first 2000-2010 be 2000-2011?
L540: What are the implications of this?

Figure 1: The red and white centrelines of each glacier need more explanation, both in the figure caption and in the text. What is the difference between the red and white, and how is it used?
Figure S6: Needs error bars for the DGPS data – if these are already present, they are too faint and cannot be seen so need to be a darker colour than the ASTER error bars.

Referee Report: PDF

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RR by Martin Truffer (22 Aug 2018)

Suggestions for revision or reasons for rejection

This is a very interesting paper showing the difference in thinning between neighboring glaciers that have contrasting boundary conditions (lake or no-lake). The numerical study hints at some of the reasons for the differences and a second numerical experiment explores how the glaciers would develop under different conditions. The paper is generally well written and clear and comes to significant conclusions that warrant publication in TC. I have a few general comments that should be addressed, that revolve mostly around the use of calculated emergence velocities. The required revisions are somewhere between minor or major.

1) When discussing causes of thinning, a bit more care could be taken. The actual values of emergence velocities do not tell you whether the cause for thinning is dynamic or not (unless they are negative in the ablation area). Generally, I believe, attribution is really only possible when comparing to a steady state. In steady state, emergence velocities compensate for SMB and those values can be large or small depending on climate. When thinning starts one can then say whether it was more negative SMB or less positive emergence. Without that context attribution becomes much trickier. This could be explained better.

2) Calculating emergence velocities in numerical models is fraud with potential errors. Errors in ice thickness or sliding coefficients can result in errors in velocities, which can be amplified in the emergence velocities, because those involve the divergence of horizontal. It is therefore important to compare resulting elevation change rates with measured ones. In places where SMB and emergence velocities don't sum to observed thickness changes, one needs to be extremely careful with interpreting emergence velocities. Fig. 8b indicates that there can be several m/a difference between observed and computed dh/dt and this indicates that v_e has large errors. As a matter of fact, it might be possible to adjust the model to better fit observations by adjusting both ice thickness and the sliding coefficient to fit both velocities and thickness change rates.

3) Some global estimates of mass gain and loss terms would be useful. For example, how much flux enters the numerical domain at the upstream boundary and how does that compare to the mass flux at the terminus (for lake calving), the integrated SMB, and the integrated dh/dt? This would provide a good assessment of the overall role of ice dynamics, without relying on details of emergence velocity calculations.

Some detailed comments (in order in which they occur):

l.14: it is unclear why you mention supraglacial lakes, as the title is about proglacial lakes
l.22-24: I would rewrite this sentence as: The magnitude of dynamic thickening compensates for more than half of the negative surface mass balance.
l.194: a linear temperature profile implies steady state, and not 'no heat storage'
l.205/206: What are the ASTER images used for?
eqn 5: I don't understand this equation. Is M_d only non-zero over debris? What is the motivation for the first term (t_D H_L/l_m)? The equation looks like discharge is counted separately from melt? What is the source for the accumulation data? And, finally, should the opening parenthesis be after the summation sign?
l.256: delete: 'vertical component of the' (gravity only has a vertical component.
l.273: Make it clear that the modeling domain is in the ablation area (this caused me some confusion at first, because I assumed it was the whole glacier).
l.284/85: Give some detail about this. Do you assume a parabolic velocity profile and assign it as a Dirichlet condition?
eqn (12): It's a bit strange to convert emergence velocity to water equivalent and then convert it back in the next equation. It would seem more logical to just state the ice balance b in ice equivalent.
l.370: specify that this is not the mean SMB for the whole glacier (I think)
l.386: contrasted -> contrast
l.404: indicated -> indicates
l.465-468: it seems this could be more usefully displayed in a graph, otherwise there are too many numbers to make sense of.
l.546-548: I do not understand this sentence.
l.555: a decrease in effective stress does not enhance shear stress, it reduces shear strength of sediments
Fig. 2 caption: what does 'across off-glacier' mean?

Martin Truffer

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ED: Reconsider after major revisions (03 Sep 2018) by Francesca Pellicciotti

AR by Anna Wenzel on behalf of the Authors (06 Nov 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (10 Nov 2018) by Francesca Pellicciotti

RR by Anonymous Referee #4 (28 Nov 2018)

Suggestions for revision or reasons for rejection

The manuscript by Tsutaki et al. uses field- and satellite-derived measurements of a neighbouring lake- and land-terminating glacier in the Bhutan Himalaya to assess the impact of a proglacial lake on the thinning rates of each glacier. I very much enjoyed reading this version of the manuscript; it is much improved from the previous iteration, and is now a very neat study. The writing is generally good, but needs some correction to clearly communicate the content. I have provided examples of minor grammatical mistakes through the first two sections but this needs checking throughout; after this I only note specific instances where meaning is confused. I also have small queries about the discussion of the debris covers and a few other details. Otherwise, I consider it worthy of publication in The Cryosphere.
Specific comments
L21: Change “would be” to “is”
L22 and throughout: “dynamically induced” to “dynamically-induced”
L24: “One-thirds” to “one-third”
L39: Add “For example,” before “Mass loss”
L41: Remove “the” before “more insight for”
L46: “Suplaglacial” to “Supraglacial”
L55: Add “the” after “total ice thinning at”
L60 & 62: The phrases “beneficial to compute the ice flow velocity field” and “which require the ice flow velocity field” seem to contradict? Should the second be the surface velocity field? Or perhaps remove the first sentence of this paragraph.
L72: Change to “unmanned autonomous vehicles (UAVs) are”
L73: “satellite” to “satellites,” and “resolves” to “resolve” and “debris-covered surfaces”
L76: “the repeated DGPS” to “repeat DGPS”
L85: I don’t understand “grounding and fully contacting lake”. Perhaps either remove, or explain that one is lake-terminating and the other not.
L113: “show” to “shows” and “drain” to “drains”
L133: I don’t think you mean a change in debris thickness, just that the debris didn’t affect the surveys because the layer was very thin. Suggest change to “We neglected the influence of debris thickness”
L144: Repeated word “change”; suggest remove second instance.
L157: Change to “…survey are so many (n = 3893) that the standard error could appear too small.”
L170: Do you mean that the horizontal flow velocities are “at 60 m resolution”?
L178: “Between November 2000” and when? Needs a date here. Also check consistency through manuscript – the Results section says delineation was between 2000-2017, but Figure 4 still says 2000-2012.
L218: “three-visible” to “three visible”
Equations 4 & 5: “debirs” to “debris”?
L243: Change to “a snow layer” … and “climate condition nor at the elevation of the debris-covered area”
L251: “debris covered” to “the debris-covered”
L297: Would read more clearly as: “Model domain was from 5100 m and 2500 m to the termini … including the ablation and lower accumulation areas.”
L314: I don’t understand the second part of “We assume no basal sliding and quadratic function…”. I assume you did apply a quadratic function? Perhaps change to “and applied a quadratic..”?
L332: It is still not clear where this lake depth measurement was made, considering that Thorthormi wasn’t lake-terminating at the time of this measurement. Could the position be marked on Figure 1? Or described here?
L369: I understand your comment in the author response, but to be clearer in the text, suggest you do change this to: “found in the lower elevations of the glacier”
L374: The two vertical uncertainties aren’t height uncertainties, but the uncertainty in the elevation change rate, I think? This should be noted (“Vertical elevation change rate uncertainties…”)
L390: As you report mass balance values for both types of surface, why not just have this section title as “Glacier mass balance”
L398 and throughout: I’m still not convinced by the description of the debris cover as “thin and sparse”. I understand that a thick debris layer could reduce the SMB values by 2 m w.e. a-1. However, the images provided in Figure S1 actually show a continuous and very thin debris layer, which instead would greatly increase the melt rate. Where does this thin debris layer come into the debris-free/-covered categories for SMB – does it contribute to the high SMB for the debris-free areas? That would be wrong, in my opinion.
A “sparse” debris layer implies a discontinuous layer of debris (mostly clean ice), not what is shown in Figure S1. This thin debris layer is also the sort of debris layer I imagine from the methods, where the authors state that the debris cover was not thick enough to influence the surface elevations measured. Perhaps the thermal resistance results need reporting or showing in a figure to clear this up. If the debris layer is as shown in Figure S1, I suggest removing all instances of “sparse”, and just referring to the majority of the debris cover as thin.
L416: What does “within 16%” mean: ± 16% or ± 8% or that the calculated velocities were within 16% of the satellite-derived velocities?
L429: I still have issue with the phrase “regardless of ice temperature assumptions” – the ice deformation is small because of the assumption that the ice is temperate, so you can’t discard this assumption. I suggest you rephrase this either to follow the comment in the author response (that ice deformation is near the bed, so negligible) or simply that ice deformation plays a minor role in movement.
L441: Mean uncertainty of what?
L447: “and greatly negative value” doesn’t make sense; perhaps “becoming more negative”
L449: “within 4200 m of the terminus of Thorthormi”?
L480: Much greater than which values? The difference for Nepali glaciers is reported as 4x greater earlier in this paragraph, so not sure this sentence is valid?
L483: Suggest changing estimated to modelled through this section, and being very clear which dh/dt is being discussed at any one time
L484-5: I’m not sure what this sentence adds here? Nor do I understand the next sentence (“Although both SMB…”); could it be explained a little clearer?
L485: The argument would be better supported if the values were restated, rather than “Lugge < Thorthormi”; this makes a lot of work for reader. Write out the point in full and add important values in; same for instances below.
L488: Suggest start new paragraph after “would be plausible”
L495: Remove “rather” and change “accelerates” to “accelerate”
L503: Doesn’t this second sentence agree with the first? Suggest change “On the other hand” to something like “Furthermore”
L506: I don’t understand the start of this sentence as written – do you mean that the lake would have formed from this land-terminating condition if the model was run for longer?
L510: Proglacial rather than supraglacial lake?
L522: While some of this paragraph is necessary, I don’t think it fits well here; the previous paragraph would run into the next section well. Perhaps move, or condense this paragraph to a sentence or two and include in previous paragraph.
L541: Change “a less ice flux supplied” to “its smaller ice flux”
L566: Just use DGPS instead of spelling out acronym
L830: “enotes” to “denotes”
L846: Do you mean over “off-glacier areas”? Also after (c), “terminus” should be “termini”

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RR by Martin Truffer (13 Dec 2018)

Suggestions for revision or reasons for rejection

Re-review of Tsutaki et al., TC

This is a second review of the manuscript by Tsutaki et al. The revision has much improved the presentation and it is now much clearer in what has been done in the paper. I find the material interesting and relevant. On the other hand I still have several comments that need addressing. I apologize that some of these comments are things I did not clearly point out in the first review. The paper could also use more editing for language; I'll include some comments below.

My main issue with the paper is that the proposed models for both SMB and ice flow will necessarily come with very large errors; potentially much larger than what the impression is from the error analysis. I will explain in more detail below. As such I propose that the paper be reworded a bit. Mostly it requires a better explanation of the purpose of the model, which should be given at the end of the introduction. The way I see it is that this paper provides solid data that Lugge and Thorthormi Glaciers have different thinning rates and also quite different dynamics. This is observationally well constrained. The modeling serves more as an idealized case of how the presence or absence of a lake can alter thinning rates. The answers from the authors to the previous reviews make it clear that the models' purpose is NOT an accurate represenation of these glaciers; the necessary model complexity (2 vs 3D, for example) and input data is missing. I therefore suggest adding a paragraph at the end of the Introduction that explains that these models are there to illustrate the differences between a lake-calving and a land terminating terminus and that the model set up is meant to approximate the situation at Thorthormi and Lugge without making an attempt at accurate representation.

I think this would set a different tone for the paper. In particular, it would mean that the reader does not have to be worried about the very large differences in observed and modeled thinning rates.

Here is why I think these models have larger errors than stated:

1) SMB model: There are no observations that could be used for model validation, whether debris thickness or any measure of melt. As such, the model is entirely 'floating'. There is an error analysis in the paper, but it is very difficult to assess whether the reanalysis data works well for this purpose. The model serves well for the purpose of comparison between the two glaciers, because it is at least reasoable that the errors introduced from applying reanalysis data would apply to both situations.

2) Flow model: There are some validation data (surface velocities), but the model is severely under-constrained because of the lack of thickness data and the necessary restrictions from a 2D model in a valley glacier situation.

List of comments (in order that they occur):

l.24 one-thirds -> one third
l.46 form -> formed
l.69-71: I would split this into two sentences. Also, DEM differencing is routinely done, not just because the terrain is difficult to access
l.85/86: ... contrasting conditions at similar ... (delete 'the')
l.88/89: Here I would add several sentences explaining the purpose of the modeling exercise (as explained above).
l.114: drain -> drains
l.133: We neglected THE influence ...
l.156/158: Explain this a bit better: The issue is that using standard error assumes uncorrelated noise (which goes as 1 over square root n), while you assume systematic error. The truth is probably in between, where noise is correlated on some spatial scale (see e.g. Rolstad et al., 2009, J.Glac. or Motyka et al., 2010, J.Glac.)
l.204: I don't understand this assumption of a linear temperature profile. This assumes steady state. But a thin debris layer can never reach steady state when exposed to diurnal and seasonal boundary conditions. Also, what does the assumption of 'no heat storage' mean? Is it no 'change in heat storage'? The debris layer is at a certain temperature, that implies a certain amount of heat storage?
l.212: comma after resistance
l.218: three-visible -> three visible
eqn 2: should the H_L in the 'for debris' part be G_d? Also: spelling of 'debirs'. Finally: use rho_w instead of the number 1000 in the equation
l.238/39: How is the solid/liquid determination done? Is it a step function at 0 deg C?
l.242: ..when A snow layer ...
eqn 5: debirs -> debris
eqn 6: again, use rho_w instead of 1000. Also, do you need to go through this derivation? Couldn't you simply write eqn (6) and be done with it? Where do you actually need runoff values?
l.290: described -> fixed
l.296: Assuming temperate because no information is available seems like a bad justification. Is there other supporting evidence? For example, the occurrence of melt high in the accumulation area, which would lead to annual warming of the firn through refreezing.
l.300/301: Reword this sentence. For example: ...into the studied area, and it therefore excluded from the analysis of the results.
l.304/305: This requires more detail: The Farinotti method requires an 'apparent mass balance', which is SMB - dh/dt. What did you use here? The SMB calculated above and observed dh/dt? Also, there is an assumption about rheology, did you use a literature value for flow rate factor and no sliding? There is some circularity here, because the assumptions in the derivation of the ice thickness distribution affect the calibration of the slipperiness used to match surface velocities. This is one reason that the model results have to be treated with caution when applied to the glaciers, although the 'lake - no lake' comparison is still valid.
l.311/312: Did you do any convergence tests under element refinement?
l.313/314: Perhaps you could split this sentence, and explain it a bit better. Upper surface can mean the surface of the glacier or the upstream boundary condition. The surface of the glacier has a stress free boundary condition. The upstream boundary has a Dirichlet condition with an assumed parabolic velocity and no sliding.
l.319/320: Are those values of C consistent with the thickness inversion (see my comment above)?
l.325/326: Do you need to prescribe 'zero horizontal velocity'? Does this not come naturally at the land terminating boundary, due to ice thickness going to zero?
l.328: employed -> used
l.331: THE position ...
l.339: Same as earlier comment, do you need to prescribe this?
eqn 14: dh/dt should really be partial derivatives, otherwise this equation is not correct. Actually, I don't like the use of dh/dt anywhere in the manuscript (and in many other manuscripts as well). When you measure surface differences you measure Delta h, or actually really Delta z_surf (since you don't know anything that could happen at the base). If you want to put this as a rate it would be far better to write Delta h / Delta t (or Delta z_surf / Delta t). This clearly indicates that this is a measurement over a certain finite time span (you never directly measure a rate) and it avoids the issue that partial and total derivatives are not identical. Usually, this is clear from context, but why not be accurate? Also, in the equation it bothers me, because it's technically wrong.
l.354-357: The result in Truffer et al. (2009) that emergence velocities appear to be proportional to horizontal velocities are not stated in a universal way. That seems to be an observation at the terminus of the Taku Glacier. I do not believe this can be used as justification for assuming that errors in emergence velocities are proportional to errors in horizontal velocities. The vertical velocities are calculated from eqn (9), which involves derivatives of horizontal velocities. Because derivatives amplify noise, they can be large. Furthermore, the equation then needs to be integrated over the ice thickness, which also has large errors. That's why I believe the model might have much larger errors than stated here. Again, that's a problem if you claim to accurately model Lugge and Thorthormi Glaciers. I don't think it's a problem for comparing the two situations and for doing that 'lake - no lake' comparisons.
l.374/375: rewrite this sentence
l.391: As stated earlier, I have a hard time believing this error estimate. In fact, this is almost at the level of measurement uncertainty if you had a small stake network.
l.431/432: I think the RMSE between modelled and measured is meaningless, given some of my earlier comments. The model cannot be an accurate representation of these glaciers, so one should not worry too much about matching velocities. Furthermore, the velocities were used for model calibration, so it makes no sense to also use them for validation.
l.436: test -> tests
l.453: delete 'into'
l.486-488: Awkward sentence, rewrite.
l.490: ... the glacier BEING situated ...
l.493-496: You first say that the flow is surface parallel and then that the emergence velocity is negative, this seems contradictory.
l.506: I don't understand why the negative emergence velocity would have led to Lugge Glacier Lake being 'inevitably formed'?
l.510: supraglacial -> proglacial
l.519: delete 'accelerated' (negative emergence velocities imply thinning, but it doesn't imply accelerated thinning)
l.536: and THE glacier ...
l.541: .. that less ice flux cannot counterbalance ...
l.572: ... the MODELED SMB was ...

Martin Truffer

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ED: Reconsider after major revisions (13 Dec 2018) by Francesca Pellicciotti

Dear Shun, Koji and co-authors,

I have now received the re-review of you paper by the same two reviewers that provided the second round of reviews (we are now at the third round of reviews). One reviewer is happy with the revised version, and suggests a final round of very useful minor revisions. The second reviewer suggests major revisions, but offers a very clear and constructive way to address his main concerns. These were the concerns shared by all three reviewers in the first round of reviews, namely the very large uncertainties and errors in your modelling approach, and in the surface energy balance model and ice flow modelling in particular. I shared then and share now their concerns, and I think that the suggestion by Martin Truffer (the second current reviewer) to add a paragraph at the end of the introduction (that explains that the models are used to illustrate the differences between a lake-calving and a land terminating terminus and that the model set up is meant to approximate the situation at Thorthormi and Lugge without making an attempt at accurate representation) is an excellent one.

Please also consider and discuss the errors and lack of validation in both approaches (as in the reviewer's report).

I therefore strongly encourage you to revise the manuscript taking into account his main suggestions and detailed comments, together with the clear and useful suggestions of the first reviewer, and resubmit your manuscript. I anticipate that if you take into account those in a satisfactorily manner, the paper will be very close to acceptance.

Both reviewers provide a detailed list of important (but not major) comments that should be addressed.

I indicate major revisions (as suggested also by the second reviewer) because I would like to see again the revised manuscript, and the changes (albeit only to the text) require some major adjustments. I am confident however that they will not take you too much effort (as they do not require new analysis or calculations).

Please pay attention to the writing (both grammar and style), something both reviewers pointed at. You might have the manuscript read by a native speaker?

I very much look forward to receiving your revised manuscript, and I hope you will agree with me that the reviews have been very useful to improve the original submitted work.

All my best,

Francesca

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AR by Koji Fujita on behalf of the Authors (26 Feb 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (03 Mar 2019) by Francesca Pellicciotti

RR by Anonymous Referee #4 (22 Mar 2019)

Suggestions for revision or reasons for rejection

This is the third review of Tsutaki et al.’s manuscript. The manuscript is much improved again. As I am not a modeller, I have been largely unable to comment on the modelling section, however, I think the changes made based on the suggestions of Reviewer 5 to present the modelling as an idealised case has helped mitigate issues with the large uncertainties I had previously pointed out. I do think the idealised case should be restated in the conclusions section. Otherwise I have only a few minor comments, which I list below.
L16: change “glacier” to “glaciers”
L38: “monsoonal” rather than “monsoon-influenced”?
L55 and thereon: no space between a number and % sign
L80: suggest combining these sentences – “contrasting termini at similar elevations, which makes them…”
L131 and thereon: no dash between a number and m (denoting metres) – this has become inconsistent through the text and figure captions
L172: remove “the areal” (repetition of area)
L204-5: shortwave and longwave should be one word
L219 and thereon: no space between a number and degree sign
L230: add “the” before “debris-covered”
L240: add “the” before “melting”
L295: I still have issue with: i) the assumption of temperate conditions, and ii) the apparent (and later contradictory) assumption of no basal sliding in the modelling (L319). First, I don’t see how the air temperature over a lake determines the temperature of a glacier? Lakes obviously have a temperature > 0°C unless they are frozen through (which still wouldn’t represent the glacier’s thermal regime), and can additionally alter the local microclimate (Carrivick and Tweed, 2013), and I therefore don’t think this is a valid assumption. Second, if you do assume temperate conditions, there WILL be (at least some) basal sliding – which your results show (L427). The clause “We assumed no basal sliding” (L319) is thus unclear (at least to a non-modeller) and needs to be altered.
L304: “smoothing the elevations” rather than “filtering the elevations with a smoothing routine”?
L315: remove “and” before “several”, and “numbers” should be “number”
L380: is this flow uncertainty ± 12.1 or ± 6.05 m/a?
L404: “reversed” instead of “prescribed” for consistency with earlier in manuscript
L415: remove “within”
L430: add “to be” after “considered”
L475-6: if the difference between these glaciers and others in Nepal are similar, how can the role of ice dynamics be different?
L505: I’d be careful with this use of “thickening”, as the overall thinning rate is still negative – this clause implies to me that the thickening is greater than the negative SMB. This is expressed better in the final sentence of this paragraph, so I would suggest either wording more carefully (akin to L512) or just removing this final clause after “emergence velocity”. Similar for L23 – perhaps change “suppressed” to “minimised”?
L540: hyphenate “water-saturated”

Carrivick, J. L. and Tweed, F. S.: Proglacial Lakes: Character, behaviour and geological importance, Quat. Sci. Rev., 78, 34–52, doi:10.1016/j.quascirev.2013.07.028, 2013.

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RR by Martin Truffer (03 May 2019)

Suggestions for revision or reasons for rejection

This paper has improved a lot since its last iteration, particularly in grammar and language, which helps a lot with understanding. As I've stated before, the topic of the paper is interesting, the findings are significant, and I do hope that this will be published.
Unfortunately I still think that there are some issues that need to be addressed, and these issues revolve around the treatment of errors in both SMB and the flow model. I am not certain what the correct way is to address these errors, but they way it is done here is incorrect.

For the SMB the authors use the standard deviation of the SMB over the modelled area as an estimate of error. This is clearly incorrect, the spatial variability of modelled SMB is entirely unrelated to the error. A better way to estimate error would be if there are any independent estimates to compare to (even over short times), but this might not exist? Or a comparison of integrated SMB to geodetic balance for a land terminating glacier.

For the flow model, the stated error is clearly not correct, because measurements of velocity and simulated thickness change are outside the error range. There are a number of issues with modeled ice velocities that have yet to be addressed:
1) The issue of 'apparent mass balance' has not been addressed in the revision. This quantity is the SMB-dh/dt in the Farinotti paper. A negative thickness change contributes to mass flux and works opposite the SMB. In this case thickness changes are almost of the same magnitude as SMB, so the 'apparent mass balance' is much closer to zero, which would have an important effect on the calculated ice thickness.
2) The calculated emergence velocities show some clear errors, for example, the large positive values in Fig. 5b. If those were correct, the glacier would be thickening in those places at fast rates; this is not observed. I think that errors in emergence velocities are simply too large to say something meaningful about simulated thickness changes. It would make more sense to calculate emergence velocities from observed thickness change and modelled SMB.
3) Both Thorthormi and Lugge Glaciers show step changes in observed velocites that are not at all reproduced in the model.

These inadequacies are perhaps not such a big surprise. There are many things that the model does not consider, such as the influence of lateral stresses or spatial variation of sliding coefficients. The latter could be addressed, but in some sense the goal here is not to reproduce velocities. Rather, the authors should stress the changes that occur between experiment 1 and 2.

Smaller comments:

The thinning rate is sometimes stated as a positive number (l.114/115) and sometimes as a negative number (l.17/18). It is generally clear from the context what is meant, but you should at least be consistent. My preference is to always use thickness change, rather than thinning rate.

My previous comment about partial derivatives was slightly misunderstood: In eqn 14, you should use partial derivatives for h; this is an equation that is valid at each point in time. Otherwise, I like the changes, that is, measurements are now all refered to by Delta z/ Delta t. I think that's the most accurate representation. Basically what you do is to take a measurement Delta z/ Delta t as an estimate for the quantity partial h / partial t.

These comments are all addressable and I do hope that the paper can be published. I also apologize for the delay with the review; it came at a very busy time.

Martin Truffer

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ED: Reconsider after major revisions (06 Jun 2019) by Francesca Pellicciotti

AR by Shun Tsutaki on behalf of the Authors (14 Jul 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (05 Aug 2019) by Francesca Pellicciotti

RR by Martin Truffer (28 Aug 2019)

ED: Publish subject to technical corrections (10 Sep 2019) by Francesca Pellicciotti

AR by Shun Tsutaki on behalf of the Authors (13 Sep 2019) Author's response Manuscript

Short summary

We investigate thickness change of Bhutanese glaciers during 2004–2011 using repeat GPS surveys and satellite-based observations. The thinning rate of Lugge Glacier (LG) is > 3 times that of Thorthormi Glacier (TG). Numerical simulations of ice dynamics and surface mass balance (SMB) demonstrate that the rapid thinning of LG is driven by both negative SMB and dynamic thinning, while the thinning of TG is minimised by a longitudinally compressive flow regime.