The manuscript by Reinthaler and Paul describes a glacier surface and extent reconstruction for the Little Ice Age maximum (assumed to be in 1850) and calculates area, thickness and volume changes from the LIA maximum to 2000 and 2015. The study makes use of numerous existing datasets and newly determines LIA outlines and surface topography for 19% of all glaciers in the Alps (>0.1 km²) for which outlines were missing in previous inventories. I find that the study uses generally robust methods to generate novel and significant findings. The manuscript is well-structured and well-written, the presentation is clear, and the results, analysis and discussion provide useful perspectives on acceleration of changes as well as uncertainties. I suggest the manuscript can be published after minor revisions. My comments are detailed below. I have some doubts about the method that is used to calculate the total volume error estimate, which I would like to see addressed. Other (minor) comments are mostly suggestions for textual revisions, added discussion, clarification and additional references.

Comments:

Volume uncertainty: The current error estimate of the volume does not seem correctly calculated. Summing squared relative errors and taking the square root is normally applied to calculate the total error of a variable that is the product (or division) of other variables with known errors (see e.g. https://www.statisticshowto.com/statistics-basics/error-propagation/). The total volume is however not the product of glacier outlines, surface reconstruction, and bed topography, but rather the product of the related ice thickness and area. Therefore, a better way to calculate volume errors is to apply error propagation on the product of area and thickness where relative errors of glacier area and thickness are individually defined. I think this formula could be used; eps_V = V*sqrt((eps_H/H)^2 + (eps_A/A)^2) where eps_V, eps_A and eps_H are volume (V), area (A) and thickness (H) errors, respectively.

L19-20: "Many glaciers have now only remnants of their former coverage left, which led to deglaciation of entire catchments.". Please specify how many glaciers this applies to and which catchments are affected, because now it is a rather hollow statement.

L20: "The new datasets should support a wide range of studies related to the effects of climate change in the Alps.". This is also rather vague. It could be good to specify types of studies / study fields that would benefit from the dataset.

L36-37: References and links to GLIMS and RGI should be included here and/or in the Data Availability section.

L40-41: "However, in contrast to other regions in the world, extent differences (e.g. between 1850, 1820 or 1600) are small in the Alps.". Is there a reference for this?

L51-54: "Whereas reconstructions ... European Alps.". This could be merged with / moved to the paragraph ending at L38.

L76-77: "Due to differences in interpretation of glacier extents by different analysts for the two datasets, we will only present glacier changes at a regional scale rather than per glacier.". This helps in case the observer errors are random, but not when they are systematic. Are there any indications for potential systematic errors between the two outline inventories?

L82: "As a starting point for the LIA outline digitizing, we used outlines from 1967-1971 (for France) and the RGI v7.0 from 2003 for the other regions.". What is meant by "as a starting point" here? Is it just to get a rough idea where the glacier is? Or is more information extracted than that?

L95-96: "A few glaciers that melted away before 2003 would lower this number by a few decimals.". What data is this statement based on? Is it possible to give an estimate of the number of glaciers that may have melted entirely since the LIA maximum?

L102-103: "The method calculates a scaling factor by dividing the gradient by the LIA elevation change (from interpolating outline points only)." This is not very clear. Please give a short summary of this method (as described in Reinthaler and Paul, in review) and how it compares to other methods.

L105: Please add a reference for the Topo to Raster toolbox.

L118-119: "Similarly, we have used the year 1850 as the date of maximum LIA extent.". This is a (justifiable) assumption of the timing of LIA maximum extent. It would be good to add this information already in the abstract or introduction.

L128: "This probably resulted in positive elevation changes in several accumulation areas (Figure S6).". Does this also explain differences with Sommer et al. (2020)?

 L144-145: See my previous comment about possibly incorrect quantification of the volume error.

L170: "15%". Is it coincidence that this is exactly the same value as the volume loss or is it inherent to the method that was used to reconstuct the surface shape back in time which preserves much of the modern glacier shape (i.e. area - thickness distribution)?

L171-172: "This is caused by differences in interpretation from different analysts, sensor resolutions (Landsat vs. Sentinel-2) and mapping conditions (snow, clouds and shadow) rather than by growing glaciers.".  Is there any reference for this? I also wonder whether a similar overestimation in 2015 likely also applies to the other (larger) glaciers?

L179-180: "Generally, elevation changes were largest at an elevation of around 1600 m (dominated by Region 6) and decreasing towards higher elevations (Figure 4).". Can this elevation also be calculated for P2 (2000-2015)? With glaciers retreating I would expect this elevation to migrate upwards as well with time.

L181-182: "The largest elevation changes (-105 m) were found at 1650 m in the western (Figure 4a) and at 2250 m (-65 m) in the eastern Alps (Figure 4b)". This does not seem consistent with the 1600 m for the entire Alps (?).

Figure 3: In the caption please indicate which period it applies to (P1 or P3).

L191: "238 km³". Why is the 5% for the missing glaciers only added to the upper bound and not to this lower bound?

Figure 4: This figure could be improved. The resolution is currently rather poor, reducing readability. Furthermore, the right axis is missing in both panels.

L210-212: "Overall, ... (Figure 3c).". Since these glaciers are not experiencing frontal ablation, elevation change rates, and trends of those, could be compared with longterm surface mass balance trends. I am not well up to date regarding available long-term SMB datasets for the Alps, but when available it would be interesting to compare long-term SMB trends with the surface height change trends presented here.

L216-217: "the regional variability ... Hugonnet et al. (2021).". It could be good to indicate the average relative changes compared to P1 for these as well.

L217-218: "Further research is necessary to investigate what causes the differences among the available datasets". It could be considered to include a comparison with surface mass balance studies, e.g. Davaze et al. (2020;  https://doi.org/10.3389/feart.2020.00149), in order to have some independent source to compare to. I would also like to see some more discussion on potential causes of the discrepancies between the available datasets.

L220: "The absolute volume change rates...". I suppose this is based on the use of Hugonnet et al. (2021) for P2? It could be good to clarify since in the previous paragraph different surface height change datasets were considered.

L265: "which is certainly not the case in 2015". I may be missing the point here. Why are 2015 conditions relevant for the Haeberli and Hoelze estimate (published in 1995)?

L277: "depending on the specific characteristics of  a glacier". It could be interesting to discuss these characteristics a bit further (as it might give some directions for future work).

L300: "an approximate regional average of 1850 has been used.". Larger response times of large (thick) glaciers will likely cause many of those glaciers to have a later LIA maximum extent date than small glaciers. Although this may be hard to account for in the approach, at least some discussion on the size dependence would be good.

L310-313: "The observed change in median elevation of 143 m would translate to a temperature increase of 0.84 to 1.43 °C, depending on the atmospheric lapse rate applied (Haeberli et al., 2019; Kuhn, 1989; Rolland, 2003; Zemp et al., 2007). This is lower than the 1.5° and 1.6° temperature increase determined by Begert and Frei (2018) and Auer et al. (2007) for Switzerland and the Alps, respectively.". This needs some clarification. I assume the temperature increase in the first sentence is purely due to the elevation drop. But what is the 1.5-1.6 deg C change in the second sentence referring to? Does it include both anthropogenic warming and elevation-drop induced warming?

L317-327: Interesting discussion on peak runoff!

Conclusions: The conclusions section gives a good summary of the work. However, I do miss some recommendations for future work. Would there for example be room for inverse (ice flow) modelling methods to generate physically more robust LIA surface topography? 

Textual revisions:

L10 (and elsewhere): digitising --> digitization

L17: In the mean --> On average

L18: 1600 m --> 1600 m above sea level (m a.s.l.)

L55: "first" --> "first complete"

L60: "Regional subdivision" --> "Study regions"

L99: "DEM" --> "Digital Elevation Model (DEM)"

L112: "the total glacier volume" --> "the contemporary total glacier volume"

L141: "Uncertainties of the bed topography impact" --> The impact of bed topography uncertainty"

L143: Add "volume" between "overall" and "uncertainty".

L160: "reconstructed to" --> "estimated at"

L170: "shrunk" --> "shrank"

L196: "altitude" --> "altitude range"

L201: "are" --> "is"

L203: "Increase in change rates". Please change to something more specific (indicating the variables it refers to).

L252: "if considering" --> "when including"

L261: "would" --> "could"

L269: "estimated" --> "estimate"

Figure 6b: Please mention that changes are negative.

L330: "coverage by area" --> "areal coverage"

L331: "these glaciers" --> "all glaciers" (otherwise it refers to the missing glaciers)

L356: "GILIMS" --> "GLIMS"

Dear authors and editor,

Please find the attached pdf file which includes my comments.



Best regards,

Arindan Mandal