Dear Dr. Samsonov et al.,

Thanks for your thorough response to the three reviewer comments. The nuance of the novelty/history of the methodology proposed and its strength and weaknesses is now much clearer. Because of the breadth and depth of the overlapping concerns raised by the reviewers, upon receipt of the revised MS, I will evaluate whether it is sufficiently responsive to the concerns raised and then send it back out for review.

Regards,

Joe MacGregor
NASA/GSFC

Dear Dr. Samsonov et al.,

I've now received and reviewed three thorough reports from referees concerning your revised MS on a new derivation of 3-D glacier flow in Alaska from SAR from the same three referees. This is unusual and indicates the broad interest in the topic you've presented. However, all three indicate that major revisions are required, and no referee felt that any element of the manuscript could yet be rated excellent, so further revision is clearly still needed.

I agree that the manuscript is currently a bit dissonant with unusual complexity in the SAR methods and relatively little detailed discussion of the sometimes large signals observed. While reviewer #1 suggest breaking out the manuscript so that the glacier signals can be explored more fully, I leave it to the authors' discretion as to how to proceed. Please make a clear decision as to whether to highlight some of the unusually large signals observed and explain their possible physical origins more, or clarify whether they may be due to uncertainty in the method and require further future investigation.

A particular concern of referees #2 and #3 is the lack of a formal uncertainty analysis, which I agree is required for this relatively new combination of method + application. This also dovetails into reviewer #1's concern indicating that a simple smoothing might be just as good as the regularization. For these and other concerns, I expect them all to be addressed fully in a revised version, and I note that reviewer #2 indicated that some of their earlier comments were not fully addressed.

Figures 6-9 are overall quite effective, but I would like to see P1-9 labeled in the lower panels. In Figures 10 and 11, please indicate which glacier/distance P1-9 are associated with (e.g., Malaspina terminal lobe for P1). As they stand, the signals shown are quite complex and need some context without having to refer back to previous figures.

Regards,

Joe MacGregor
NASA/GSFC

Dear Dr. Samsonov et al.,

Thanks for your thorough revisions to your revised MS following the three referee reports. Your MS generated more intense feedback from the referees than I had initially anticipated, but all in cases they have stayed engaged with the peer review process and your MS has improved substantially. So, even though there is still some disagreement in approach between yourselves and the referees, it has been fairly debated and your MS will undoubtedly motivate further investigations into velocity time series from large volumes of SAR imagery. I will accept your MS to The Cryosphere once you address the following comments below.

NB1: Note that line numbers are in reference to your track changes version (tc-2021-257-ATC2.pdf).

NB2: WRT line 396, I *will not* accept this MS if the full data/code repository is not available for inspection beforehand. Include the final *public* URL in your next revision.

Abstract: Given that the primary advance of the MS is IMO the application of a new-ish method to a large volume of data regarding glacier flow, the abstract ought to give some clue as to what that method’s key advance actually *is*. Also, given the ferocity of the debate amongst the reviewers on this point, the abstract ought to address its uncertainty relative to earlier or contemporaneous methods. As it stands, the abstract is devoid of these highly relevant high-level concerns, which strike me as more important than satellite revisit times.

13: “Glacier dynamics” cannot be reduced solely to surface velocity. Strictly speaking their “dynamics” concern the evolving force balance. The downstream effects listed are an odd mix and not well supported when only considering surface velocity. Rethink this whole first sentence.

13: “intensity” is simply the wrong word here. “magnitude and direction” is in much more common usage and physically clearer. A referee brought this up previously and you responded that it was “corrected”… but it wasn’t.

38: “specifically” makes more sense here than “especially”

42: The GNSS acronym was introduced earlier, and GPS is left undefined. Use GNSS instead.

44: combined using the MSBAS technique.

59: remove “But”

61: Riel et al. (2021), who adopted some of the methods of Riel et al. (2014, 2018) and applied them

72: Figures should be referenced in the order they are presented. Either Figure 4 should move up to #1 or not be referenced here. I suggest the later approach.

77: using the speckle

91: incidence angle. (IMO “azimuth” does not need to be qualified with “angle”)

141: Passive voice. “We used a value of 0.1 for lambda.” Was this value selected using L-curve?
151: hundreds and often thousands of columns

156: “called from C++ code” does not seem relevant here

162: Passive voice

164: in the respective legends

165: 10% of what? I assume the harmonic’s amplitude but this origin should be made explicit here not just legend.

168: Now I’m confused. Did you add 10% of amplitude noise or 0/10/30? Reconcile with 165.

184: Is “cross-feed” the best term here? Not sure

186: Overall these tests indicate that

193: RGI Consortium

196: “pale in comparison” is strong language, especially given that parity is now effectively reached via ITS_LIVE and other international efforts. Reconsider this phrasing.

225: Does “lower” here mean “coarser” (larger value) or “finer” (smaller value)? Unclear.

228: A pers. comm. citation from the GAMMA developers is appropriate here.

229: using the TerraSAR-x

231: Filter width

236: This statement about data volume is odd and should either be further specified somehow or removed.

239-240: I don’t understand what “approximated to the actual glacier flow pattern” means. I assume OGGM uses a DEM for the flowlines, whereas you have actual surface velocities available. Clarify this statement.

243: intensity -> backscatter?

251: direction or sign?
303: Unless the authors have checked, it is unlikely that there are no GNSS stations on any of the studied glaciers during at least some part of the 5-year period. If not checked, I recommend moderating this statement to something like “we did not compare against GNSS)

305: “~4 m” not “four meters”

318: “they still show some agreement” -> “

334-347: As a referee pointed out, offending the solid earth community by implying they don’t understand Lagrangian vs. Eulerian reference frames is a strange and unnecessary stance. In recalling my own education, scientists in those disciplines learned these concepts right alongside myself. This paragraph should be shortened substantially by assuming that the likely reader is a glaciologist who is familiar with the two reference frames and by focusing on the argument the authors seek to make on the links between GNSS and SAR flow displacement time series for *glaciers*. A distinction for that link over deglaciated tectonically deforming surfaces should be made only as a final aside.

348-365: As the referees pointed out more than once, the ability to recover credible vertical displacements concurrent with horizontal displacements from large data volumes with MSBAS is a potentially valuable advance. However, the very large magnitudes reported (e.g., >200 m/yr) *require* further explanation, some of which was provided in the response to reviewers (e.g., ArcticDEM not available at coincident times, sparser ICESat-2 data). Without that further explanation, there is a risk of casual misinterpretation of the reported vertical velocities as rates of elevation change rather than evolving submergence/emergence velocities indicative of broader (and faster) changes in dynamic configuration than previously understood (and also much greater than short-term SMB fluctuations). This paragraph appears to be the right place for that clarification, as the discussion concerning Malaspina Glacier mostly works.

351: “is more concerning” reframe this qualification as it is already well established that most Alaskan glaciers are losing mass rapidly (e.g., Larsen et al., 2015).

367: Move Meier and Post (1969) citation to the group at the end of the sentence.

384, 395: Please be clearer here as to what you mean by “data”. The data you use are SLC Sentinel-1 images, but you’re probably not archiving those with the MS as they’re already at ASF. I believe the velocity dataset (over space AND time) is what is meant.

Figures throughout MS: It is odd to use the standard abbreviation for meters (m) but not that for year (yr) when showing speeds. Recommend changing unit abbreviation from m/year to m/yr.

Figure 4: Add a red arrow in inset map of North America so that small red box is more easily spotted.

Thanks again for choosing The Cryosphere for your work,

Joe MacGregor
NASA/GSFC

Dear Dr. Samsonov,

Thanks for your quick turnaround on these final revisions. I consider these responses satisfactory and have accepted your MS to The Cryosphere. Thanks again for considering this journal for your work.

Regards,

Joe MacGregor
NASA/GSFC