The author has taken much care in responding to all reviewers' comments and has addressed (most of) the important issues in the revised version of the manuscript. In particular, the author has better detailed his version of the linear decline model by explicitly describing the associated set of differential equations and how they combine to form an integrodifferential equation. This greatly helps understanding not only its numerical implementation but also the behavior of its solution. By responding to reviewer 3’s suggestions, the author has also better positioned his work, which, in my opinion, greatly improves its potential impact. I also appreciate the improvement in the way the new algorithm is compared to previous ones. I only have one regret is that the author has elected not to follow one of Reviewer 3’s suggestion to compare its transient solution to a simple 1D analytical solution. It would have been very interesting to obtain more rigorous estimates of the error as a function of dt and dx. In his response, the author focused on the reorganization of the drainage factor as the main control/limitation on the time step size; I believe that a more thorough comparison with a simple 1D solution would more clearly characterize the method and help future users to assess its accuracy.

My recommendation is to publish subject to minor revisions to give the author another opportunity to incorporate a better assessment of the numerical accuracy of the method.

Many thanks for adding this section. I agree with you that it is not easy to find a useful analytical solution to compare to (1D is too simplified from a topological point of view and 2D are hard to come by or are over-simplified).

Lieber Stefan,

Thank you for working with AE Jean Braun and his referees to bring your manuscript into publishable form. I am happy to follow the AE's advice and accept your manuscript for publication in ESurf.

Your manuscript will now be handled by the copy editors of Copernicus. Your prompt response to their questions and instructions will help keep time to publication short.

Thanks for submitting your work to ESurf. I trust that it will get good attention.

Niels Hovius