The revised version of the manuscript and the response letter is clear and well articulates the arguments that the authors have made. The both reviewers concerned the validity of sinusoidal fitting. The authors followed the suggestion of Dr. Gartner to use a bootstrapping technique and demonstrated that the best estimate of the sinusoidal approximation is robust. Also, the authors clarify in the response letter and the manuscript that it is likely that ice-flow variations are more complicated than the simple sinusoidal curve can capture. I am happy to see that these points are well presented. However, in my opinion, the authors do not adequately exclude a possibility that there is no seasonal variation of the flow speed at all. Thus, I would like to propose the authors to perform p tests with a null hypothesis that there is no seasonal variation of the flow speed. If this hypothesis is rejected with a very high confidence, it further supports the argument. In addition, I would request authors to include error estimates of individual flow-velocity measurements in Sections 2.1 and 2.2.

The authors presented the uncertainty quantification in Appendix A to keep the manuscript structure as close as possible to the original form, which was well received by the reviewers. However, depending on the outcome of the proposed tests above, please consider reorganizing the manuscript and present these uncertainty quantifications together at the end of Section 2.2.

Below, you find some very minor suggestions for improvement.

- Fig. 1: the calving front is also indicated by black, so revise the caption accordingly. Also, revise the second sentence in the caption to “Towards the ice calving front right bottom of the image…” so the shape and ice flow direction of TIS is clear for all readers. The label for the colorbar should be revised to “…. (m yr-1)” from “(m/a)”. Strictly speaking, velocity is a vector and speed is a scholar. I feel that the authors tend to describe both velocity and speed as velocity, which is acceptable for me. However, then please keep the terminology simple and uniform; consider changing “speed” in the colorbar label and elsewhere to velocity or at least check the clarity of the entire text one more time.

- Fig. 2: Unit of the ordinate should be “m yr-1”, not “m/yr”. And consider plotting the speed in the unit of km/a (to be more compatible with Figs. 3 and 7).

- P6L6-7 and P8L10-11: do you indicate the plus/minus one sigma (i.e. 2 sigma) or only one sigma? Remove the plus/minus signs from the sigma, or add this sign to the right hand side of the embedded equation as well.

- Fig. 5 caption: As far as I can read from the figure, I am not convinced that melt anomalies propagate in a clockwise fashion around the cavity. If this point is not important then please delete it. If important, revise the figure or explain more clearly.

- Spell out ECCO as “Estimating the Circulation and Climate of the Ocean” at least in the reference list of Fukumori et al.

- Fig. 6: add goldern ECCO location marker in the two most right satellite images taken in April and May 2016.

Dear authors,

The responses articualted in the ltter are adequate and I am happy to accept this article as is.
Thanks for sending the interesting work to The Cryosphere.

Kenny Matsuoka
TC/TCD Editor