Togaibekov et al. report detailed measurements of glacier surface uplift inferred to be caused by hydraulic ice-bed separation from a dense array of GPS receivers on Glacier d’Argentiere. The results show the seasonal pattern of subglacial hydrological development and induced changes in basal sliding from winter-time distributed “weakly-connected” cavities to a system dominated by efficient subglacial channels in summer. The paper makes a strong and original contribution to the large body of work on the topic of subglacial hydrology and basal sliding, and in particular to the specific topic of ice-bed separation. The results are tentatively and appropriately put in to the context of similar studies in Greenland. I have four general comments; two of which request more detail on the GPS methods and a number of specific comments and technical corrections.

General Comments

1. Further justification for the use of static over kinematic carrier phase positioning should be provided. It is likely that a reference station is located closer than 110 km to Glacier d-Argentiere and this could allow kinematic position to be used, at least for comparison. The time period over which the receiver is assumed to be static is unclear from the methods and should be stated: from the text of the methods it appears to be daily but then the time series appears to be sub-daily. It is unclear whether the resulting position estimates were filtered in any way prior to differentiation to calculate velocity. I expect there will be good reason for using static processing and this should be stated.
2. As (nearly) stated on L118 of the manuscript using the standard deviation or RMS of a static site does not give an estimate of the precision of a kinematic site due to biases associated with the assumption that the moving site is static (King, 2004). On the next lines (L124-125) the RMS of a static bedrock-mounted site (ARGB) is used to estimate the velocity error of the moving on-ice sites. I think it needs to be stated that the error estimates based on a static site may be smaller than the true uncertainty of a kinematic site, as errors for example within ambiguity fixing may be caused by motion of the antenna.
3. Was vertical displacement resulting from sliding along the bed corrected for velocity (i.e. faster sliding results in faster vertical displacement)? Can you expand on the methods for linearly detrending to correct for sliding along the bed? What does this assume about the bedslope (e.g. that it is constant). These methods are central to the paper and conclusions and should be expanded on.
4. In Section 4.3, it would be good to see more discussion of the measurements of Andrews et al. (2014) in the context of the subglacial hydrological processes inferred from the spatial patterns of ice-bed separation.

Specific Comments

L7 – I was initially unsure whether it was the vertical velocity or the correlation that was positive or negative. Although it became clear when reading the corresponding section in the main text this should be clarified here. The directions of positive and negative can be defined either way.

L56 – Does Rothlisberger discuss glacier slow down? Adding an additional citation that does is worthwhile.

L83 -  do you specifically mean V-shaped here. Is the Argentiere valley not U-shaped?

L86 – is this water equivalent melt or ice equivalent? State either way. It is usual to give melt as water equivalent.

L103 – it’s unclear here that this threshold is an upper, rather than lower, measurement limit. State upper.

L104 – Expand on the vague phrase “more advanced measurement device” to state precisely how discharge was measured. Make clear here that this new device also allowed lower values to be measured (i.e. during winter, and as stated later in the results on L182).

L113 – Revise to “with double differencing and the ionosphere-free linear combination (LC; Bock et al., 1986) using the geodetic software GAMIT/GLOBK (Herring et al., 2018)”. Note the acronym LC is not used so could be omitted.

L115 – Move ‘13’ to before well-determined. Strictly speaking its not stated what is well-determined; can be assumed that this is the station position but this could be stated.

L121 – Add something along the lines of “Instead we estimate the precision by …” to make it clearer.

L130 – omit ‘bed-separation-induced’ as interpretation is better suited to the results and no evidence for this has yet been presented.

L146 – You switch between transmissivity and conductivity and while some readers may know that T = kh others might be able to follow the equations easier if this is defined, or if the term conductivity is used throughout.

L173 – this paragraph starts and focusses on the difference between sliding velocity and surface velocity and they do differ, but there are also periods of agreement that are worth highlighting, perhaps even before focussing on the differences.

L178 – frame this inference regarding the difference in basal shear stress: “with a different amplitude which previous studies (citation) have explained as due to higher basal shear stress”. Worth also commenting here on the difference in basal slope angle and surface velocity between the cavitometer and the GPS. It’s worth emphasising these differences as they are important to the interpretation

L182 – modify this sentence after including these methods details in the methods.

Fig. 2 – shading the melt seasons would make the plot easier to interpret. A horizontal line at 0 should be added for the vertical velocity axis.

L192 – Start sentence with ‘Although’ and change ‘but’ to ‘at’ and ‘the one’ to ‘those’. Summer is by definition a period so ‘period’ can be omitted. Make question plural. Finally expand on how the model and GPS measurements are different.

L197 – Expand this first sentence and show evidence for the second point.

L200 – you state two equations are used to plot a single line on Figure 3b. Expand on how these equations were combined.

L206 – mention stake measurements in methods.

L220 and L274 – change to ‘Figs’ with no full stop as it’s a contraction.

Figure 4 – include methods used to create this figure (i.e. what type of interpolation was used). HVC needs to be defined in the figure caption.

L223 – I see an increase in HVC gradient to the left bank which is the opposite to that stated in the text.

L231 – Just to highlight that this is a key point regarding HVC and uplift in winter that is worth emphasising in the abstract and conclusions.

L245 – Yes, depth-homogenous vertical strain rate may not be a valid assumption. The other potential problem here is that crevassing violates the continuity equation.

L259 – the conclusion regarding the requirement for running water here seems tenuous and would be best framed as speculation.

L307 – Hoffmann et al. (2016) is a modelling paper so although relevant here it is not quite the right reference. Andrews et al. (2014) could be cited as well or instead of Hoffmann et al. (2016).

L319 – consider introducing Moon’s Types II and III in the introduction or expand on what is meant slightly here. Only the informed reader will follow this.

Technical Corrections

L51 – Reorder citations so 2011 citation comes before 2016 citation.

L57 – add ‘usually’ before ‘cannot be measured’.

L89, L113, L115, – change ‘are’ to ‘were’ to use past tense.

L102 – move bracketed text later in the sentence where you describe the location of the gauge.

L129 – write out ‘… Figure 2’.

L135 – quantify number of decades

L142 – change to ‘the distance’

L143 – here and elsewhere fix the brackets for in text citations.

L204 – replace ‘right after’ with ‘immediately after’ and give a figure reference here.

L205 – state which year or state in both years.

L205 – change to “cavities shrunk when surface velocity was constant”. Note change to past tense.

L256 – revise ‘is required the transition’

L273 – delete bracketing comma.

L296 – delete ‘the’ and specify ‘surface ice motion’.

L316 – fix citation brackets.

This manuscript presents data gathered at Glacier d'Argentiere over a three year period in order to explore relationships between uplift, water discharge, and horizontal velocity fluctuations. The work follows similar studies at the same study site, now bringing together simultaneous observations of uplift and discharge.

General comments:

Some of the data is compared to a numerical model for sliding speed; the model description is not complete without a description of what the model inputs are, and associated assumptions that go into the model. Based on the description in Gilbert et al 2022, I assume the results presented here are also forced with the measured discharge, but I couldn't find a mention of this in the present paper. If so, then perhaps it could be that the assumption of constant hydraulic pressure gradient (required to link discharge to effective pressure - Gilbert2022) is what leads to the model-observations discrepancy in spring, noted in section 3.1.3 but not discussed in depth.

In Section 3.2.2 it's a bit unclear what HVC is defined as. Is it the difference between the current season and the season beforehand? So summer HVC is summer minus winter before, winter HVC is winter minus summer before? (Similarly for winter uplift).

It's a bit concerning that strain-rate derived thinning/thickening is predicted to be an order of magnitude larger than uplift/subsidence. Can the sign of uplift even be known given this uncertainty? What are the uncertainties in strain given the number of GPS sites?

The cavitometer is in a drained cavity by necessity; therefore there is no basal water pressure acting in this region of the glacier. Approximately how far from the terminus do you expect "basal water pressure" to be a well-defined property?

Specific comments:

L7: separation velocity is strange wording - rate of uplift perhaps better

L18: put into a geographical context - specifically alpine glaciers? or also Greenland - but not Antarctica!

L147: h acts as an effective water sheet thickness averaging over some region

L148 (or L153): p_1 and p_2 are fitting parameters

L191: include references to newer hydrology models (GlADS, SHAKTI)?

Fig2b: not a colorblind-friendly plot

Fig3bc: use same axis limits for consistency

L257: I am not sure I understand the importance of this distinction. Water pressure gradients = flowing water, no?

Review of “Seasonal glacier motion variations and underlying hydro-mechanical processes at the Argentiere Glacier, French Alps”

By Togaibekov and others

Submitted to The Cryosphere

Overview

This manuscript presents observations collected continuously over a few consecutive years at a mountain glacier, combined with modeling, to try to understand the spatial and temporal patterns in ice velocity and subglacial hydrology. 

In general, the paper is well written with nice figures. Please see below for general and specific comments. With minor revisions to further improve clarity and strengthen the paper, I feel this work will make an excellent contribution to the glaciological literature. 

General Comments

1. First, I will say that this is a valuable dataset of observations to understand the system that can serve as an excellent modeling target. It is especially interesting to see the documented observations of the winter hydrological influence as measured through the persistent winter discharge (lines 181-182) and the evidence of winter subglacial water pressure controlling winter velocity (Fig. 6), also demonstrating that summer behavior is more complicated to predict.
2. I have some questions about the nature of surface meltwater inputs to the bed at this glacier: Can you provide more details about location, timing, and magnitude of water inputs that likely reach the bed? The right bank of the surface is described as being heavily crevassed (line 225), but otherwise I don’t see any description of surface water features. Are there moulins? Supraglacial ponds? How do these features change in different regions of the glacier, and over time (seasonally and interannually)? Without measurements to constrain meltwater inputs beyond the discharge measured downstream, even a qualitative description of this possible distribution would be helpful, to give the reader a sense of where, when, and how much meltwater might drain from the surface to reach the bed. 
3. In Eqs. 3 and 4, how are the values chosen for average bed bump height, intrinsic conductivity, and the exponents? This would be helpful to explain and justify the choices, as well as discuss the implications and limitations of these assumptions. 
4. Discussion and interpretation of subglacial geometry refers to cavity size and cavitation rates, yet the summer velocity and pressure observations suggest that a highly connected or channelized drainage system likely develops. Do you have any observations of channelization? What does the outflow at the terminus look like?
5. I think it would be useful to add a “Limitations” section to the paper. This is currently missing, but would be a good place to discuss some of the assumptions involved in the observations and modeling methods, as well as opportunities for further research.
6. I am interested to see the documentation of short-term velocity pulses in the summer (line 311). More discussion or interpretation about what drives these pressure variations would be insightful. For example, can you connect them with higher temperature or rainfall events that contribute large amounts of water to the system? 
7. Finally, I am happy to see that you highlight the difference in seasonal behavior as observed at different parts of the glacier with different local characteristics. This shows that seasonal velocity and hydrology dynamics are more nuanced than how they are sometimes approached with different schemes of classification. This also raises the question of whether it is important to resolve these finer details across spatial and temporal scales, or not. That probably depends on the science question, but is something to consider, and this study nicely demonstrates that you can come to different conclusions about the nature of a glacier’s subglacial system depending on when and where you look.

Specific Comments

Lines 44-45: Remove either “although” or “yet” from this sentence

Line 100-101: About how thick is the glacier at each location? This would be helpful to mention here.

Fig. 1: You might consider adding an inset with a map showing the location of the glacier in a broader geographic area for reference, for those not familiar with the location.

Equations 3 and 4: How do you choose the average bed bump height, intrinsic conductivity, and the exponents used in these equations? See General Comment 3. 

Line 182: I’m not sure that “circulates” is the right choice of word here, as it might imply water moving around without flowing out, which is not the point being made with the observation of winter discharge. Perhaps it would be more accurate to say the water “moves” or “flows” or “travels” beneath the glacier year-round. 

Figure 2 is great to see all the measurements together.

Fig. 2b – interesting that the water pressure increases so much more significantly over the first instrumented winter (2019-2020) than the second (2020-2021), during which it remains more constant, also the big drop event during the first winter (any explanation?). How is water pressure measured?

Fig. 2c – difference in vertical velocity and vertical GPS displacement. How is vertical velocity measured? Is that at the icefall with the cavitometer? It would be good to clarify in the caption here for easy reference.

Line 319: Rather than referring to “types II and III” seasonal patterns, you might consider briefly describing each pattern in a few words, for readers not familiar with that classification (or for readers who always forget which is which)