We thank the anonymous referee for this extensive review that engages deeply with our manuscript and provides constructive, detailed comments for improvements.

In the attached PDF, we respond to and propose changes according to the referee’s comments.

We thank the referee for their positive comments and suggestions for improvement. Below, we respond to and propose changes according to the referee’s comments. The editorial suggestions, especially in the introduction and methods, may become redundant due to more fundamental revisions based on other referee comments.

We will add references to the recently published DCG-MIP paper wherever appropriate, certainly in the limitations section (e.g., L618-621), maybe also in the introduction.

Minor corrections

L3: "The main aim of this study”

Will be done.

L35: “transported on the surface”

Will be done.

L41: “As debris is transported either”

Will be done.

L69: "cannot be considered”

Will be done.

L100: "magnitudes which”

Will be done.

L211: “we ensure that the Courant-Friedrich-Levy (CFL) condition is satisfied”

Will be done.

L233: “debris mass conservation”

Will be done.

L235: “discussion of the main model experiments”

Will be done.

L252: “debris start to emerge do the two surfaces”

Will be done.

L285: “which is the latter subtracted from the former”

Will be done.

L325: “to be only 18% slower”

Will be done.

L356: unbalanced parentheses

Will be corrected.

L389: "Note that the debris input area”

Will be done.

L403: “are almost completely halted”

Will be done.

L441: “leads to melt-out” – delete “that”

Will be done.

L588: misplaced (

Will be done.