In this paper the authors compare the distributed SMB of well-studied Argentière Glacier calculated (1) by inverting an ice flow model and (2) using an enhanced temperature-index (ETI) mass balance model. With method (1) they find a higher spatial variability of SMB, especially higher accumulation rates  at the orographic left side of the glacier, which they attribute mainly to regular avalanching from adjacent steep headwalls. This is supported by the indication of avalanches in radar images and a conceptual snow redistribution scheme. To better describe the spatial variability of the SMB and especially account for the total effect of snow redistribution – in which avalanches are shown to be an important factor -  the authors come up with zonal precipitation correction factors.  Using these correction factors in the ETI-SMB model they find that the projected glacier volume by 2100 based on RCP 4.5 is higher than without including this effect and that more mass is conserved in the zones below the steep headwalls. Finally they conclude that SMB inversions have a high potential in deriving the spatial variability of the SMB.   

General comment:

This is a very interesting study, which is building up on a lot of previous work, taking advantage of the solid data base of Argentière Glacier and advanced glacier modelling. The authors take an impressive modelling effort to calculate the distributed mass balance of Argentiére Glacier and to better constrain the effect of avalanches on the mass balance. Especially the uncertainty analysis using three different ice thickness distributions and their effect on the inverted surface mass balance is very interesting. This study is an important contribution to better quantify the spatial variability of surface mass balance on a glacier and to attribute the observed variability to individual processes.

The paper is well written, well structured and generelly pleasant to read. Methods and results are described in a comprehensible manner, holding a good balance between detailness and readability. The supplement is very usefull in following the details of the analysis and the results. The authors discuss uncertainties and limitations of their study extensively and also put their findings in relation to the relevant literature.  

I have only some minor comments on the manuscript.

Minor comments:

L27: you could add the 20% of total mass input for the whole glacier as you did in the conclusions, as this is also a main quantitative finding.

L118: What do you gain by using 13 DEMs (of every year) and not just the DEMs of the beginning and end of the study period? Signal to noise ration should be best by using those two only. Could you add a line to explain why you are doing that.

L141: As I understand it, only two of the three different ice thickness modelling approaches are constrained by measurements at Argentière Glacier, while the Farinotti (2019) model is contrained by data from a also lot of other glaciers? Maybe you can be more specific here. Besides it would also be interesting to add a line, what was the intention to choose these 3 approaches? I guess to cover the uncertainty, that is introduced by the uncertainty in ice thickness distribution, but maybe there was also the idea to have different model complexities or applicability for glaciers without GPR measuements?

L373 – L376 Here you refer to different locations on the glacier by giving altitudes. Please label some contour lines in Fig.5, so that these locations can be identified faster by the reader.

L456 Here you write “46% less volume by the end of the century than for the corrected scenario”.  In L 459 (and also in L585) you write 71% lower in volume, obviously both values without the Tour Noir. This seems inconsistant to me. In the conclusion  L620 you write: “twice as much mass being conserved by 2100”, which seems to be constitant with the 46% of L456.  Maybe try to use the same measures throughout the paper.

L546 I guess text refers to Fig. S1 and not Fig. S10

L612 This location…  perhaps say “this area”

L615 “this” perhaps say “this process” or “avalanches”

Fig.3: For a faster readability perhaps add to the legend: 2020 and 2012 glacier outlines and stable terrain. Consider a color scheme that shows more details, especially in the elevation changes (a).

Fig S16(d): the distance along centerline is oriented from the snout upwards I guess. Please specify that in the x-axis label or in the Figure Caption.

Fig. 3,5,7,9 and also some Figs in the supplement: Maybe you can avoid repeating the phrase “The black outines indicate the glacier ourlines manually dreived from the … Pléiades..” by just stating the year of the glacier outline in the legend of the figures.

Maybe I missed it: Which ice thickness distribution did you use for the foreward modelling?

The manuscript by "Kneib et al." describes and demonstrates the calculation of a Surface Mass Balance (SMB) field for the Argentière Glacier in the Mont Blanc massif using high-resolution dh/dt fields (from Pleiades DEMs) and the calculation of ice flux divergence (using three different ice thickness datasets, a high-resolution velocity field, and two different methods to calculate the divergence). The resulting SMB field is then compared with results from an SMB model and stake observations, with the ultimate goal of obtaining a precipitation correction that better represents avalanche deposits. The impact of this correction on the glacier's future ice volume is subsequently examined using a 3D thermomechanical ice flow model.

The manuscript is very well-written, with a clear sequence of the steps undertaken by the authors. The reader can easily follow the process, which allows to apply a similar setup for other glaciers (highly appreciated). The various figures, both in the text and in the supplementary material, are well-chosen to represent the results obtained. In addition to the very detailed work carried out (including all uncertainties), the result is compelling and demonstrates the significant added value of the method.

In my opinion, this paper is definitely a valuable contribution to the glaciological community and is therefore highly recommended for publication in 'The Cryosphere.'

I have only a few textual comments and a couple of minor clarifications which I would like to see in the revised version. The only more substantial work I can see is calculating/presenting a mass balance derivation for each year in the studied period (2012-2021). How well does the mean specific mass balance obtained with the applied method represent the mean specific mass balance from the glaciological method and SMB model? And how does the mass balance of the stakes per year compare with the method used?

Specific comments:

• Line 15: “Particularly” might be removed here
• Line 16: High resolution (<-> high quality) as well?
• Line 18: A bit unclear if the approach to invert only uses three different ice thickness estimates or three different methods. Further, if formulated like now, it seems that the ice thickness setups show a good agreement, but it is the three different inversions that do show the good agreement.
• Line 19: After reading, the “consensus F2019 estimate” is not constrained by the ice thickness measurements?
• Line 20: Maybe mention the range of RMSE values?
• Line 21: “the” modelling approaches
• Line 23: “Avalanching” -> avalanche deposits
• Line 33: Accumulation zone
• Line 36: and extrapolation?
• Line 41: Compaction as well?
• Line 45: Remove “and”
• Line 52-53: Potentially add a reference to “Turchaninova A.S., Lazarev A.V., Marchenko E.S., Seliverstov Y.G., Sokratov S.A., Petrakov D.A., Barandun M., Kenzhebaev R., Saks T. Methods of snow avalanche nourishment assessment (on the example of three Tian Shan glaciers). Ice and Snow. 2019;59(4):460-474. https://doi.org/10.15356/2076-6734-2019-4-438
• Line 67: “ice flux”
• Line 67: Therefore -> subsequently
• Line 81: “which” does not have a direct link here. You probably mean that ice thickness and velocity is less constrained in the accumulation zone and therefore the uncertainty of the product is larger, butt this might need to be a bit clearer stated
• Figure 1: The colour scale is a bit large for the values of the SMB (especially the positive ones). Maybe limit this to +3 m w.e. yr-1 so that you can see a bit more the variations? The circles of the GPR locations are too large so that you cannot locate the individual points (it now seems to be more a line of GPR). Panel b, is it an option to zoom in somehow (e.g., to the Mont Blanc massif)?
• Line 132: Which software is used to compute the surface displacement, velocity?
• Line 141: You mention later that the F2019 did not use the GPR measurement, so it is a bit strange to mention here that the three methods use in situ data
• Line 184: There is some error between ice thickness (H) change (dH/dt) and surface elevation (h) change (dh/dt).
• Line 184: Formulating H₂O makes the equation for me a bit confusing. Consider writing just r_w and r_i.
• Line 185: Any evidence that internal and basal mass balance are negligible from previous studies?
• Line 188: Here you refer to ice thickness as H
• Line 211: Any estimate for y based on observations or modelling?
• Line 215: If formulated like this, it seems you calculate the ice flux divergence in three different ways. But as far as I understand, this is not the case? Three different ice thickness estimates are used, and two different approaches to determine the ice flux divergence.
• Line 223 and 224: Some repetition here of the ranges for the uncertainty (with lines 208-213).
• Figure 2: Like for F1, is it possible to limit the range of the colour scale for the SMB?
• Line 243: I do not completely get this 10% best SMB estimates. Can you clarify this a bit?
• Line 273: How does the exponentially decay of the albedo is determined? Which time scale is used?
• Line 341: Again, here you mean dh/dt I guess? The difference between dH/dt and dh/dt is not clear throughout the manuscript. I guess because bedrock elevation is considered to be stable, both are the same, but you should state this somewhere and from then on work always with dH/dt
• Line 343: The median of the 2012-2021 period for every grid cell?
• Figure 3: Both for the elevation change and the surface velocity, the colour scales could be optimized (wider for velocity, smaller for elevation change).
• Line 348: Median or mean velocity (<-> line 343)?
• Figure 5: You state different modelling approaches, but in fact it concerns two different ice flux modelling approaches and three different ice thickness estimates?
• How well can you invert the annual surface mass balance? There is only a focus on the multi-year average
• Line 385-389: I do not completely get this sentence (which I find too long).
• Figure 9: Very cool to see the impact of taking into account the avalanches. I wonder, however, if it is possible to show the flowlines. My first guess would be that the ice at the location of the avalanche deposits does not flow to the central trunk but moves along the headwall. But this must be different because the central trunk maintains more ice?
• Line 558: Is shading not included in the simplified energy balance model? By modifying the incoming radiation?
• Line 603: I guess also the ice thickness is crucial when the approach would be applied on larger scales? As you show in the sensitivity analysis
• Line 606: cf line 16 high-resolution vs high-quality (both are true…)