Dear authors,
I would like to thank first the two referees for their thoughtful and timely comments. Through the interactive discussion, you provided detailed responses and suggestions of how to address their comments.
To continue with the publishing process towards TC, I would like to ask you to upload a revised manuscript (ideally both track-changed and clean version) for a second assessment by me and, possibly, the referees.
I am looking forward to receive the revised MS.
Best wishes,
Etienne Berthier

Dear authors,

Your revised manuscript and your responses have been evaluated by both referees. One is generally satisfied with your answers. The second one expected more detailed answers and indicate that the revised manuscript would better reflect the points that have been discussed.

I would like you to consider thoroughly his comments and, as much as possible, make sure your answers percolate into the manuscript, its title and abstract. Although the entire review process is available after paper acceptance in TC, the article remains the master piece read by most colleagues.

I expect a point-by-point response to this new series of comments.

Best regards,

Etienne Berthier

Dear Authors,

Thanks for your point by point reply to the second round of comments. In general, you addressed satisfyingly the reviewer’s comments. I still have a few minor comments before the MS can be finally accepted (see below).

Do not hesitate to contact me if you have some further questions.

Looking forward to receive your revised text soon.

Best regards,

Etienne Berthier

L9. "climatological" would be acceptable if you had already applied the method over > 30 yr of data. "Decadal" or "10-yr" average velocity is a more appropriate way to describe in the abstract the period over which the method has been tested and validated (I understand there is in principle not technical hurdles to apply the method to the full Landsat archive, spanning > 30 yr, but this is has not been done yet, at least not in this paper).

L42. "global ice climatology" is ambiguous. I suggest "global ice dynamics" in this context.

Figure 1. Lines are thin and thus difficult to see. Make them thicker, especially the dashed black sinusoid.

L62. "climatological" is OK here given the > 30 periods of the Landsat archive. So there is indeed a potential to derive a "climatology" using your method. No change required.

L68. "see" is not needed.

L216. Add "(g-j)" here, just for clarity

L220. Add "(i,j)" here

L270. A reference would be welcome to back up the dramatic variability for PIG and Thwaites (Gourmelen, Mouginot or from others maybe?)

L290. "climatological" here suggests over 30-yr of data are needed before these short-term events are smoothed out. However, your case studies (Byrd, Russell) suggest that 10-yr of data is sufficient . What about “decadal average”?

L303. This statement suggest “several decades” (at least this is how I received it). Here I wondered whether there are enough Landsat image pairs between 1985 and 2000 so that the method can be applied and would also work? I think it is reasonable for a reader to ask this, because your Byrd and Russell glacier examples start both around 2007 / 2008. If the frequency of image pairs is as high throughout the Landsat archive then the statement can be left unchanged. Otherwise, authors should adjust the wording.

Dear Authors,

Thanks for taking into account my minor comments on the text.

I am delighted to accept your paper for publication in our journal. Thank you for choosing TC to publish your work.

My only remaining comment concerns Figure 1. The two sinusoids are very thin and hard to see (at least for me!). This is not an error so you keep it “as is” (I will not check) but the figure would gain readability by using thicker lines, and it is not an important figure after all.

Best regards,

Etienne Berthier