General Comments

This is an interesting attempt to investigate, from in-situ

measurements, the basal meltwater generation under the Greenland ice

sheet during winter. While there is room for improvement, I think the

manuscript can be published after taking into account the comments

outlined below.



In Equation (1) the melt rate seems to be volumetric. This should be

explicitly stated (units for all quantities). Also state that this is

the conservation of energy in a small volume around the glacier bed.



The development in Equations (2) and (3) needs to be improved. Units

for the quantities should be given (is M_tot a volume, ice equivalent

or water equivalent, or mass?). As it is, it seems that volume (or

melted mass) and area are confounded in (3), and there are tacid

assumption on ice thickness. Also, it is not clear why all the

subscripts are needed. A small sketch of the geometry would help

clarify the situation.  Figure 8a shows the envisioned geometry, but

does not help in that respect since the quantities are labeled with

words, without relation to the symbols used in the equations.



Also, the formulas (2) and (3) seem to be unrelated to the results. It

seems that some kind of force balance is needed to properly calculate

melt rates and cavity size, as larger cavities lead to larger stresses

outside the cavities, and incresed melt rates there.



The whole process is also likely spatially heterogeneous due to

longitudinal and lateral stress transfer (e.g. Ryser et al, 2014

a,b). This might somehow be implied in the equations, but should be

made explicit.



One further point to take into account: The melt will be generated not

just at the bed (as assumed in Eq. 1), but also within the ice column,

especially where vertical shear rates are high. I know that at the

drill site this component is very small, but this might not be the

case on upstream or downstream obstacles. As a reference quantity, to

which these results could be compared to, it would be interesting to

caluculate total dissipation of potential energy. This is proportional

to u_avg * H * slope. This quantity would also give a good estimate on

the percentage of heat generated at the bed with respect to total heat

dissipated.

Specific Comments



40 This was estimated to be an order of magnitude higher in Lüthi et

al (2003).



46 What are storage sinks within the ice? Basal crevasses?



Figure 1, Caption: are all used data sets indicated here? Ordering

them according to data set would make this clearer (e.g. water

pressure at 27N, 27S and 33; GPS at 33 and 46).



Figure 1: dark blue on dark blue (station 46) is hardly visible.



113: The term "fitted" is better expressed as "instrumented with" for

an international readership.



116: Why not just use pressure? Then it is absolutely clear what you

are comparing.



125: What are the units of \dot{M}?



142: You could add some qualifying statements that with longitudinal

and lateral stress transfer could change local shear stress by a large

percentage below/above average values. But on the km-scale this is

likely to be averaged out. But then it is not clear, what the borehole

deformation measurements mean.



150: also Ryser (2014a)



151: In light of the above comment, this need not be true, and

internal deformation is likely exceptionally low at the drill site (as

compared to e.g. Ryser, 2013). It would be interesting doing the same

calculations with their results for comparison.



156: there is a stray "we"



184: This seems unintuitive. Melt only happens over \lambda - L_s,

\lambda being the wave length, and there is no melt over a cavity as

there is no friction. Then also Equation (3) is unclear. This is only

true if there if the water in the cavity has unit thickness.



M_tot is a volume, and C_a is an area, so units do not match.



Table 1: It would be useful (and more robust) to show total

displacement during the winter period. This displacement times

frictional stress gives the total energy released at the base, which

is readily transformed to total melt during that period.



240 more precisely: "the heat generated by sliding friction"



Figure 4b: squares are barey visible, consider using a better color



267 (also 397): typeset the number properly, not in computer coding



292: how are these values calculated. Give complete formulas that

allow the reader to repeat the calculations. Why is no reference made

to Eqs (2) and (3), where this whole development should be carefully

made.



297: step length should be named "wave length" as some kind of

periodic bed is assumed.



Figure 7, caption: This is not "heat", but "heating rate", "heat

production rate", or similar.



310: it seems that 2 cm of water are not hard to store locally in

sediment-filled basins or subglacial lakes in depressions. As water

pressure is very high everywhere, this is a possibility that should be

considered.



317: Here seems to be a confusion between water stored within the ice

matrix (Brown) and water stored in discrete cracks, e.g. basal

crevasses of some sort or other, sponge-like and large, void space

within the compact ice.



325: There are large depressions (100s of meters across) that could

easily accommodate large volumes of water.



330: But these might be unrealistic. Looking at the proglacial terrain

shows very irregular bed undulations with very large and deep valley,

deep and steep valleys etc. This looks very different from Kamb, Iken

etc theories, and also from all these model inputs. Such bedrock

topographies can, by moderate changes of water pressure, lift the ice

and easily accommodate very large volumes of water.



354: "whereas they are small or absent at other locations (Ryser,

2014a).



365: Or lower effective pressure in subglacial sediments leading to

liquefaction. A constant pressure and diffuse within the sediments,

and increase the vertical extent of "softer" sediments. Such a process

would readily explain the observed acceleration.



373: This strongly depends on the time scales of cavity formation and

cavity closure. It would be instructive to calculate approximate

values to understand their magnitude and their changes under changing

pressures and sliding speeds over winter.



Figure 8: step length could also be named wave length of the bed

This is an interesting attempt to investigate, from in-situ

measurements, the basal meltwater generation under the Greenland ice

sheet during winter. While there is room for improvement, I think the

manuscript can be published after taking into account the comments

outlined below.

In Equation (1) the melt rate seems to be volumetric. This should be

explicitly stated (units for all quantities). Also state that this is

the conservation of energy in a small volume around the glacier bed. 

The development in Equations (2) and (3) needs to be improved. Units

for the quantities should be given (is M_tot a volume, ice equivalent

or water equivalent, or mass?). As it is, it seems that volume (or

melted mass) and area are confounded in (3), and there are tacid

assumption on ice thickness. Also, it is not clear why all the

subscripts are needed. A small sketch of the geometry would help

clarify the situation.  Figure 8a shows the envisioned geometry, but

does not help in that respect since the quantities are labeled with

words, without relation to the symbols used in the equations.

Also, the formulas (2) and (3) seem to be unrelated to the results. It

seems that some kind of force balance is needed to properly calculate

melt rates and cavity size, as larger cavities lead to larger stresses

outside the cavities, and incresed melt rates there.

The whole process is also likely spatially heterogeneous due to

longitudinal and lateral stress transfer (e.g. Ryser et al, 2014

a,b). This might somehow be implied in the equations, but should be

made explicit.

One further point to take into account: The melt will be generated not

just at the bed (as assumed in Eq. 1), but also within the ice column,

especially where vertical shear rates are high. I know that at the

drill site this component is very small, but this might not be the

case on upstream or downstream obstacles. As a reference quantity, to

which these results could be compared to, it would be interesting to

caluculate total dissipation of potential energy. This is proportional

to u_avg * H * slope. This quantity would also give a good estimate on

the percentage of heat generated at the bed with respect to total heat

dissipated.

40 This was estimated to be an order of magnitude higher in Lüthi et

al (2003).

46 What are storage sinks within the ice? Basal crevasses?

Figure 1, Caption: are all used data sets indicated here? Ordering

them according to data set would make this clearer (e.g. water

pressure at 27N, 27S and 33; GPS at 33 and 46).

Figure 1: dark blue on dark blue (station 46) is hardly visible.

113: The term "fitted" is better expressed as "instrumented with" for

an international readership.

116: Why not just use pressure? Then it is absolutely clear what you

are comparing. 

125: What are the units of \dot{M}?

142: You could add some qualifying statements that with longitudinal

and lateral stress transfer could change local shear stress by a large

percentage below/above average values. But on the km-scale this is

likely to be averaged out. But then it is not clear, what the borehole

deformation measurements mean.

150: also Ryser (2014a)

151: In light of the above comment, this need not be true, and

internal deformation is likely exceptionally low at the drill site (as

compared to e.g. Ryser, 2013). It would be interesting doing the same

calculations with their results for comparison.

156: there is a stray "we"

184: This seems unintuitive. Melt only happens over \lambda - L_s,

\lambda being the wave length, and there is no melt over a cavity as

there is no friction. Then also Equation (3) is unclear. This is only

true if there if the water in the cavity has unit thickness. 

M_tot is a volume, and C_a is an area, so units do not match.

Table 1: It would be useful (and more robust) to show total

displacement during the winter period. This displacement times

frictional stress gives the total energy released at the base, which

is readily transformed to total melt during that period.

240 more precisely: "the heat generated by sliding friction"

Figure 4b: squares are barey visible, consider using a better color

267 (also 397): typeset the number properly, not in computer coding

292: how are these values calculated. Give complete formulas that

allow the reader to repeat the calculations. Why is no reference made

to Eqs (2) and (3), where this whole development should be carefully

made. 

297: step length should be named "wave length" as some kind of

periodic bed is assumed.

Figure 7, caption: This is not "heat", but "heating rate", "heat

production rate", or similar.

310: it seems that 2 cm of water are not hard to store locally in

sediment-filled basins or subglacial lakes in depressions. As water

pressure is very high everywhere, this is a possibility that should be

considered.

317: Here seems to be a confusion between water stored within the ice

matrix (Brown) and water stored in discrete cracks, e.g. basal

crevasses of some sort or other, sponge-like and large, void space

within the compact ice.

325: There are large depressions (100s of meters across) that could

easily accommodate large volumes of water.

330: But these might be unrealistic. Looking at the proglacial terrain

shows very irregular bed undulations with very large and deep valley,

deep and steep valleys etc. This looks very different from Kamb, Iken

etc theories, and also from all these model inputs. Such bedrock

topographies can, by moderate changes of water pressure, lift the ice

and easily accommodate very large volumes of water.

354: "whereas they are small or absent at other locations (Ryser,

2014a).

365: Or lower effective pressure in subglacial sediments leading to

liquefaction. A constant pressure and diffuse within the sediments,

and increase the vertical extent of "softer" sediments. Such a process

would readily explain the observed acceleration.

373: This strongly depends on the time scales of cavity formation and

cavity closure. It would be instructive to calculate approximate

values to understand their magnitude and their changes under changing

pressures and sliding speeds over winter.

Figure 8: step length could also be named wave length of the bed

Review of Harper et al. “Variability of basal meltwater generation during winter, Western Greenland Ice Sheet.

This manuscript by Harper et al. brings together previously-published datasets with new data and analysis to investigate whether subglacial cavity expansion caused by basal melt can explain the often-observed – but never satisfactorily explained – winter-time acceleration of surface ice velocity in Greenland. It makes an original and important contribution to solving this problem. The hypothesis that subglacial cavities become hydraulically isolated during winter is tested and the authors suggest that some interconnections must remain as melt volumes exceed plausible cavity storage volumes. Important points are made regarding basal melt variability, particularly that the majority of total basal melt is generated in areas with low and invariable basal melt rates, and that this will result in relatively constant winter-time discharge fluxes at the terminus. It follows that substantial perturbations in basal melt must represent the sudden release of subglacially stored water (e.g. drainage of subglacial lakes). The manuscript is concise, well written, well-presented and the arguments are framed well within the inherent limitations of the dataset. I have a number of comments detailed below.

General Comments

1. Further description of the GPS filtering and basal shear stress calculation are required to ensure reproducibility.
2. Expansion on the application of the Kamb (1987) analysis for determining cavity size could be helpful, for example by giving some of the original equations to explain the basis of the analysis. At present the description is limited to just two equations (Eq. 2 and 3).
3. Previous studies which reported and attempted to explain the winter-time acceleration in ice flow should be introduced in the Introduction – this would highlight to the reader the research gap that this investigation fills.
4. The Introduction (and discussion) could be expanded slightly to introduce current theory and modelling relevant to the behaviour of subglacial cavities during winter to set the scene for this study, and to show how this study contributes to our understanding.

Specific Comments

Please find minor typographical corrections and suggestions in the marked up PDF attached.

L1 – In the title “western” should be lowercase as there is no “Western Greenland Ice Sheet”. Also, this paper does more than just measure basal melt variability and its main take home point relates to cavity dynamics and subglacial hydrology – the title could be revised to reflect this better.

L15 - Can you mention in the abstract that you calculate cavity dimensions/dynamics and compare them to melt volumes to determine whether or not all basal meltwater can be accommodated by cavity growth. At present you just refer to “insights into subglacial hydrology”: I think you can be more specific. You might also mention in the abstract or introduction that you specifically test the hypothesis that cavities remain hydraulically isolated in the winter.

L36 – you should introduce here previous observations of, and explanations for, winter-time acceleration in ice velocity. You currently do this on L352-358 but it should come earlier as it is key to the data and analysis presented. The winter-time acceleration is evident in most measurements of ice velocity (e.g. Sole et al., 2013). Note that there are also detailed winter velocities from near your study site but 140 km inland that show winter acceleration presented in Doyle et al. (2014). Winter acceleration in ice velocity is also presented in Phillips et al. (2013; Fig. 4), which I believe is mis-interpreted therein as being caused by increased deformation due to heating of the ice due to warming ice temperatures. The first paragraph of the introduction could introduce the literature on this topic slightly better, which would set the reader up for the analysis to come.

L69 – delete “full”. All years have winter gaps due to power outage.

L73 – what is meant by “bed framework”?

Figure 1 caption and elsewhere – consistency with “basal water pressure” and “borehole water pressure” would help the reader who doesn’t know these are assumed to be the same thing.

L93 – The methods used to filter and differentiate GPS position data need to be detailed to allow the study to be reproduced.

L124 – why not rearrange to get M on its own on the LHS?

L126 – More detail on how the basal shear stress was calculated (e.g. the equation used) needs to be given.

L128 – there is avoidable repetition here with L142-144 and neither spell out why basal temperate ice presents a barrier to upwards heat conduction, which is due to the Clausius-Clapeyron gradient causing a reverse (and small) temperature gradient.

L185 – add an example reference to support the statement that cavities are often assumed to become isolated during winter. In general, slightly expanding the discussion of the theoretical understanding and modelling treatment of cavities and basal melt in winter would boost the significance of this papers’ findings.

Table 1 – “Site” needs to be taken out of brackets and put into a new column.

L199 – I’m not sure you mean “daily acceleration”, will “acceleration” suffice?

L209 – The seasons have strict definitions in meteorology, and it would be helpful to note early on that the terms “spring” and “winter” are being used more loosely than their normal strict definitions, that is to reflect the period at melt-onset and the period when the subglacial hydrology is in its “winter-mode”.

L213 – Move descriptions of water pressure results to the section on water pressure (or remove subsections altogether). It would be good to expand on the description of winter-time pressure variability due to its relevance for cavity opening.

L241, L255, L263 – “sliding friction”, “basal friction”, and “bed friction” should be “frictional heat from sliding”.

L269 – observations of inter-annual variability in winter-time acceleration in ice flow at 140 km inland are presented in Doyle et al. (2014, Fig. 2).  Can these measurements help quantify what is meant by “little to no winter acceleration”?

L323 – With the uninformed reader in mind, what are sliding speeds high relative to? Perhaps cite your previous work on this.

L328 – Note that cavities accessed (or even created) via drilling may not be representative of the majority of natural cavities. Analysis of the glacial foreground or subglacial topography in West Greenland would provide a better picture on the basal roughness; such analysis has been done (e.g. Lindback, 2015).

L367 – you could spell out for the reader even more clearly that previous explanations are not sufficient to explain all the observations.

L374/375 – mention that the studies reporting sediment are also from discrete sites (two of the references are even for the same site). The nature of the bed over large areas remains unknown. Therefore the capacity of the bed to store water in troughs and sediment also remains uncertain.

Additional References

Doyle, S. H., Hubbard, A., Fitzpatrick, A. A. W., van As, D., Mikkelsen, A. B., Pettersson, R. & Hubbard, B. Persistent flow acceleration within the interior of the Greenland ice sheet. GRL , 41, 899–905 (2014).

Lindbäck, K. & Pettersson, R. Spectral roughness and glacial erosion of a land-terminating section of the Greenland Ice Sheet, Geomorphology 238, 149–159 (2015).

Phillips, T., Rajaram, H., Colgan, W., Steffen, K. & Abdalati, W. Evaluation of cryo-hydrologic warming as an explanation for increased ice velocities in the wet snow zone, Sermeq Avannarleq, West Greenland. JGR  118, 1–16 (2013).