Dear Authors,

the reviews on your manuscript were overall positive, with some concerns raised on the following questions:

1/ the manuscript was sometimes confusing, especially in the methods section: I believe this point has been addressed by the corrections provided, and the manuscript now reads much better.

2/ the issue of whether dynamically prone basins with large SMB signals are within the scope of this analysis, and the issue of whether dynamic and SMB related signals are really distinguishable: this is now much better addressed, with the focus now on large outlet glaciers where DMB is clearly larger than the SMB signal, and less focus on distinguishing SMB from DMB in areas where both signals are equally important and difficult to resolve.

3/ is the scope of this manuscript really Cryosphere related? This is in my opinion a non-issue. This manuscript is absolutely relevant to Cryosphere science, and will be of high interest to scientists who are trying to understand the implications of GRACE remote sensing data for assimilation into reconstructions of ice-flow dynamics, or assessments of the current mass balance of polar ice sheets.

4/ the issue of under-sampling in the model inversion: an increase of 6 runs to 50 runs was carried out, showing great responsiveness from the authors, and clearly addressing the concerns of the reviewers.

Given all the main concerns were addressed, and that the remaining minor issues were addressed in the new manuscript version, I am
comfortable accepting this manuscript for final publication in its current state. I commend you for a thorough work in answering the reviewers' concerns, and I'm looking forward to reading further quality work from your team.

Best regards,

Eric Larour