Please find attached my review.

SUMMARY

This research by Paolo and colleagues analyzes 26 years of data from satellite observations of Antarctic ice shelf thickness based on a novel data fusion approach, advanced satellite-derived velocities, and a new surface mass balance model (GEMB). The changes in ice shelf thickness are subsequently related to (changes in) flow and basal melt rates. The study found a pattern of overall thinning around Antarctica, with a slowdown in thinning starting around 2008 (similar to earlier research of for example Adusumilli et al., 2020). The researchers attribute this slowdown to changes in external ocean forcing and potential negative feedback effects of i) accelerated grounded ice flow on ice shelf thinning rates and ii) thinning and melt rates. 

MAJOR COMMENTS

This research touches upon an important topic, is original with several novelties and provides new understanding of the melting of ice shelves. Therefore, I think the manuscript ultimately warrants publication in the Cryosphere if it manages to tackle some of the major and specific comments listed below:

    - Restructuring: although the paper is overall well written, I think the structure often is complicated to follow with data and methods that are often intermingled  and without a clear distinction of results and discussion. 

        ○ I think the paper would benefit from a more extensive Data section, where next to the Radar data, also the velocity data, GEMB model data and ECCO model data are described. These data sets now are gradually introduced throughout the manuscript and it is therefore sometimes difficult to keep the overview.

        ○ I think the paper would benefit from a more extensive discussion that actually zooms out, puts the results in a wider context (e.g. relative to the state-of-art) and reflects on the implications. Currently this reflection is very limited

    - Balance of detail: as a reader (and not a core altimetry expert) I was often missing the necessary details to understand the steps in the data processing and reproduce them. Therefore, I think it is key to provide much more detail on the processing methodology at several locations (especially for the steps that are at the core of the altimetry processing). At the same time, I had the impression that other parts (especially the GEMB model section) was very extensive and contained details that are less relevant for this paper (and can be looked up in the GEMB paper). I would therefore limit the GEM section to the core explanation and limit the description here to the steps that are specific to the paper (i.e. calibration of the densification parameters)

    - Reproducibility: due to the lack of detail on several processing steps (or an condensed explanation for their motivation) I think it is basically impossible to reproduce the method. I applaud the effort of the authors to make code available, but with this type of code a user cannot reproduce the paper. It is a collection of methods and example notebooks that are not related to the paper. I think it is key that the code is provided as such that the reader can at least see which functions are used for which steps etc. Currently this code does not help reproducibility. I would therefore advice to either provide a notebook that runs through a complete workflow (preferential) and/or clearly indicate how the different blocks of code were used in which steps.

    - Dynamic vs melting processes: the authors show two processes that could explain the slowdown (i.e. increased ice flow and thinning into cooler water), but fail to provide a consistent overview of the relative role of both (although they have the data to do so). Currently, they show individual examples for 4 ice shelves (Table 2) where they quantify the role of dynamic thinning vs. melting,. I suggest that they do this quantification for all ice shelves (in Table 3) and also add the role of dynamic thinning in all plots of time series to allow the reader to better understand the importance of both processes.

    

SPECIFIC COMMENTS

L50: I think it would be good to have a separate data section where next to the Radar data, also the velocity data, GEMB model data and ECCO model data are described

L80-85: this methodological step might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously. It would also be good practice to clearly show each of these steps in the available code (reproducibility). Now the reader has to guess what happens and also does not have the code to better understand what happens.

L92-96: again this methodological step might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously and/or to understand the motivation. It would also be good practice to clearly show each of these steps in the available code (reproducibility). Now the reader has to guess what happens and also does not have the code to better understand what happens.

L112 (but also later throughout the paper): when using text citations the brackets should be placed differently

L128-130 "Global MDT … ice shelves": not clear if this is in general or in this study?

L131-136: again this methodological step might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously and/or to understand the motivation. It would also be good practice to clearly show each of these steps in the available code (reproducibility). Now the reader has to guess what happens and also does not have the code to better understand what happens.

L144-147: again this methodological step might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously and/or to understand the motivation. For example it is not clear what robust multi-variate regression is (ref?), if it is done for every pixel separately?

L149-217: I think this section can be strongly reduced to keep only a condensed overview of GEMB (while refering to the GEMB main paper). Many of these methodological details are not relevant for this study (in contrast to other locations where the text is extremely condense on things that are important)

L223: what is the typical depth of 550 kg/m3? If it is not extremely deep, why would you need a spinup of 7750 years as the firn will be mostly dependent what happens in the last years of the spinup period.

L257: 28 seems reference is in wrong referencing system

L260: what are 5 month bins for every 3 months?

L259- 269: again these methodological steps might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously and/or to understand the motivation. It would also be good practice to clearly show each of these steps in the available code (reproducibility). Now the reader has to guess what happens and also does not have the code to better understand what happens.

L276: for readability it would help if the actual terms in the equation are repeated

L292-301: I do not understand the processing of the velocity data.  Again these methodological steps might need a bit more extensive explanation as it is currently very condensed and therefore not easy to interpret unambiguously and/or to understand the motivation. It would also be good practice to clearly show each of these steps in the available code (reproducibility). Now the reader has to guess what happens and also does not have the code to better understand what happens.

L305: what are insignificant changes? How insignificant are they?

L312 "mean rate of thickness change from both ends of the trend fit" Is it just first vs last value or are annual mean or so used?

L317: what is k? I guess the iterator over n?

Section 2.8: I  think the uncertainty quantification needs much better explanation. Currently many of the uncertainty terms fall out of the sky and their motivation and derivation is unclear. As such it is difficult for the reader to assess what these uncertainty terms are and/or what they mean.

Section 2.9 seems a section that is not properly placed. It is self-contained and contains results before even the main results are shown. I propose to move this section to supplementary material or appendix to allow the paper to focus on the main story

L438: I think it is good practice to separate results and discussion so the discussion can really reflect on the outcome of the results

L453-456: this is a methodological description and should not be part of the results

L484-486: this is a methodological description and should not be part of the results

L490-492: this is interesting and is probably the key of the paper. I therefore suggest that the separation of thinning factors is quantified for all ice shelves and not only done in an anecdotal way for only 4 ice shelves.

L496-497: I think this probably on overstatement as it might be read that it counts for all ice shelves. This might be true for Dotson, but is definitely not true for all ice shelves.

L498-502: I think the context and perspective is important here. By just showing the changes in time-variable melt, the reader only sees one part of the puzzle. Therefore, it is important to simultaneously show the (time series of) dynamic contribution so the reader can see both terms in perspective.

L517-520: this is a methodological description and should not be part of the results

L526-528: please provide references for these notions

L533-534: I think it is key for this paper that the relative contribution of this tandem should be quantified in order to understand the relative contribution of both processes

L539-542: again I think it is not good enough to hypothesize and hand-waive at this feedback mechanism. I think the authors have the data to quantify the relative contribution of both processes to asses their relative contribution

Conclusion: this section is written in a complete different style (all we sentences). It would benefit from a more general conclusion style

L556-561: I do not agree that these feedback mechanisms are not included. An ice sheet model advects ice (and hence thickness) and ice shelf draft plays a role in the melt parametrizations. Therefore, I do not see why the models should not account for these feedback processes.

FIGURES

Figure 1: I don't think this figure add a lot to the understanding of the methodology (especially not a)) and provides an unbalanced view of the methodology (e.g. why only a figure of this step) as it is very anecdotal. I think it would be much more insightful to have a flowchart (or equivalent) of the complete processing steps instead of an anecdotal figure.

Figure 3+4: I would also opt to remove this figure. They show GEMB results but are not necessary relevant for the key message of this paper.

Figure 5: it would be insightfull to also plot the data based on which these curves are estimated to give the reader an impression on how representative these estimates of decorrelation are

Figure 6: Scalebar? Location?

Figure 7: why is only half of Antarctica shown?

Figure 8: I would also opt to remove this figure. It adds very little to the understanding of the paper and it would be more insightfull to show figures that actually show the processing steps

Figure 10: what explains the enormous changes for Nivl and Lazarev between this study and Adusumulli?

Figure 11: nice figure!

Figure 14: It would be good to indicate in these figures how much can be explained by dynamic processes and how much by basal melt changes

Figure 16: for perspective it would be good to also plot the time series of the dynamic component to allow to put both processes into context