In the present manuscript Roldán-Blasco et al. describe how they use glacier borehole inclinometer measurements to invert for the creep factor dependence on depth. From their measurements they infer interesting results about the seasonal variability of basal sliding and provide conclusive explanations for their observations. I evaluate the presented work as a thoroughly carried out analysis that is documented in detail and without any doubt relevant for the glaciological community. The strength of the manuscript lies, in my eyes, in combining field experimental data with realistic ice-flow modeling to learn about in-situ glacier ice viscosity, and to deduce reasonable physical mechanisms to explain their data. The weakness of the manuscript lies, in my opinion, in the long and comprehensive presentation of the study, where I am missing the conciseness.

I recommend the present manuscript for publication in The Cryosphere, 1) because I evaluate the analysis of this study to be done thoroughly and 2) due to the relevance of the results. Therefore, I only make very minor comments and suggestions below which might improve the comprehensibility.

Best regards,

Dominik Gräff

General Comments:

My foremost criticism of this manuscript links to my personal preference for short papers. This manuscript is not extraordinarily long for The Cryosphere. However, in my opinion the authors should try to focus more on the information that is important for the reader to get an overview over the experiment, understand the applied methods, and to retrace the derived conclusions. The present manuscript fulfills this, but it draws the attention of the reader repeatedly to details that are distracting and that make the flow of reading in some way humpy and hilly. Three examples:

• I’m very interested in instrumentation and even more in hot water drilling. However, I think the two paragraphs between L94-118 could be shortened for the main text by at least 75%. You might lose many readers by talking about the communication protocol that the tiltmeters used and it blocks the main massage of your study by entangling the reader in details. The same is in my opinion true for several paragraphs.
• Throughout the language of the manuscript seems convolved to me. L162/163: ‘Daily position time series are converted into horizontal velocity time series by subtracting successive positions over a 24 hours interval and dividing by the one-day time interval.’ could be phrased much simpler as ‘From the GNSS locations, we calculated daily horizontal velocities.’ without losing much of the information.
• Often additional information given is simply clear for the scientific reader: ‘In case the time interval of two successive positions is longer than one day (due to data gaps from missing measurements or removed outliers), no velocity is calculated. This avoids biased velocity estimates integrating position offsets unrelated to the glacier motion (e.g. re-installation of the antenna mast).’ This is like if you were explaining to a mechanic with which hand you are tightening a screw. Again, my personal opinion.

A scientific comment: You state in L364/365 that for explaining your measured seasonal variations in deformation velocity a change in water content of 60% would be needed and that this seems unrealistic based on strain heating. But why would you rule out that meltwater is pushed into micro-cracks increasing the interstitial water content. My colleagues and I measured at Rhonegletscher a daily increase of 90-180% of micro-scale water content in the glacier ice (Gajek, W. et al. Diurnal expansion and contraction of englacial fracture networks revealed by seismic shear wave splitting. Commun Earth Environ 2, 209 (2021). https://doi.org/10.1038/s43247-021-00279-4). If I understand it correctly, this effect could also explain the seasonal deformation velocity variations.

There are a bunch of typos throughout the manuscript or funny plotting issues (eg. Fig.6 180m depth label), that I leave for typesetting. Sometimes units are missing, which is particularly important talking about angles as the quantity could be in radians or degree. Overall, just cosmetics that can be fixed by thoroughly reading through the PDF again.

Nice to see such a comprehensive data and code repository on Zenodo!

As a last general comment, I would have loved to see a figure showing final borehole shapes like Fig.1b). Maybe even borehole shapes over time. The reason is, that this is in the end what the tiltmeters are measuring. They are located at a certain depth, and they record the inclination of the borehole at that given depth. This information would directly be shown in a depth over horizontal distance plot. I know this manuscript works a lot with the derivatives (eg. u), or even second order derivatives (du/dz). But derivatives intrinsically emphasize high frequency noise and pose some danger when integrating due to drift. I was relieved, when I came to Fig.6c, but then a bit sad that there were no data points at 20m and 0m and when I saw that the horizontal scale was in units of velocity. That’s all fine, but what you are measuring is a location at the surface (x,y,z) and inclinations at depth (theta). The shape would look identical, but there is this subtle difference in plotting recorded quantities and derived ones.

In the following, I list some comments and questions that might be helpful to improve the quality of the manuscript directly referring to line numbers of the manuscript:

Abstract:

Nicely written, concise and L9-11 stimulates to read.

1 Introduction:

L24: I’d say: Ice deformation is ‘commonly assumed’ to follow Glen’s flow law.

L34: This sounds like radar measurements are the only field method that exists to assess water content. Either pronounce that radar is an example or list other methods. (I’d prefer the former.)

L47: If you make ‘borehole inclinometry’ the subject of the sentence, it becomes much easier to read.

L56: ‘Since stresses cannot be measured, …’ That is formulated too general. Do you mean for the borehole case?

 2 Field site and instrumentation

L101-103: I don’t understand this. Why do you need to wait 1 month? Do you define your reference profiles to be the ones 1 month after drilling? Is that because the sensors freeze in? Or is that when you started recording? Please make this sentence clearer.

L149: I personally prefer Global Navigation Satellite System (GNSS), because you probably also used Galileo, Glonass and maybe Beidou satellites.

L150: ‘The GNSS receiver network ….’

L154-168: These lines are describing data analysis methods and are in my view neither ‘field site’, nor ‘instrumentation’ related.

3 Methods

L174-184: Contains results and interpretations. But I see that you try to explain why you applied the methods as you did.

L195: Why? Data gaps?

L214/215: Formatting of exponents. From what do you compute the discharge? Isn’t that measured at Argentiere?

L217: Unclear what you mean. Please clarify or leave this sentence out.

4 Results

L256-258: Nice! I’ve seen a similar behavior in boreholes at Rhonegletscher, also at an overdeepening.

L262-264: Please quantify.

L265: ‘… are very small’. How small? If you use quantifying language, make it concrete and state a number. Eg. 5% of the quantity you’re interested in.

L267-272: Is the shape factor f=0.646 a fit of the SIA to your full Stokes model, or does it come from the parabolic valley ratio?

L276: I had to read this a couple of times. You can make it clearer by saying:  ‘…and find that simulation with constant creep factor A for a given  Glen’s law exponent n=3,4,5 yield deformation …’

5 Discussion

L324/325: I can’t follow here. You measure that zigzag shape. That is your data, and the data doesn’t care if you neglect du/dx. Please clarify.

L347/348: Language problem.

L364: Either …, or …

L365/357: How do you calculate the 0.17% excess water content? Why

L387-390: Yes, but wouldn’t the increase in meltwater input also increase the interstitial water content due to increasing subglacial water pressures, resulting in enhanced deformation?

Figures:

Fig.1    a) The blue dots are the most important, but the green dots are plotted on top of them. Make the blue dots larger to improve their visibility.

Fig.4    b) How does the SIA including the shape factor look like?

Fig.6    c) You plot the velocity only to ~40m depth. I assume that is because you integrate du/dz over depth. However, you know the position of your cable reaching the surface and you have a tiltmeter at 20m depth. From this you get the shape of the borehole. Taking the time derivative also gives the velocity as a function of depth u(z). Is there a reason that you don’t show this data?

Fig.7    c) Typo in legend? ‘Model channel’

Tables:

Table 2: I think this table can go into the supplementary information, because it is not necessary to understand the paper. However, a histogram of water content values could be useful. That’s much easier to understand than a table.

Supplementary Information

Fig. S1-S3: I’m not sure if these plots are supporting the manuscript. But I'm ok with having them in the supplementary information.

Fig. S9/S10: Delta t labels hard to read.

S3: I think with machine error you mean a systematic uncertainty. Is that correct?

Fig. S16: Very hard to see orange line.