Dear authors,

The same two anonymous reviewers have read the resubmitted version of your manuscript, along with the response to reviewers that you provided. They reach differing conclusions (reject vs minor revisions). It is my opinion that many of the points that reviewer 1 raises, are fair. Indeed there appears to be insufficient consideration of the concerns that this reviewer raised based on the first version of the paper. More changes are clearly required. Reviewer 2, although less critical, agrees at least on one point: that one of your most important formulae has wrong units. To my mind, this means that adaptation is required, and that model reruns with reconsideration of results are necessary. I translate this into a request for resubmission after major revisions.

Should you decide to resubmit an improved manuscript, please make sure to provide a detailed response that reflects the importance of reviewer 1's concerns.

I thank the authors for their second revision of this manuscript. Some of the issues that the reviewers flagged after the first revision have been solved, and this is to be commended. However, as the associate editor, I feel that not all issues and in fact few of the major issues have been dealt with to the extent that was expected. In some cases, I have the impression that no answer is given to reviewers' questions or criticism, and that instead merely a different point of view is presented. From my role safeguarding the process, I feel that it is therefore best to send the manuscript back to you without consulting the reviewers again. Below, I have attempted to provide more detailed guidance about a few points that I think you should focus on for a subsequent revision. However, I think that your entire response needs to be reconsidered. Given the importance of changes that I feel that you should consider, I see this as a "reconsider after major revisions" decision.

The first issue where I think no full justice has yet been done to a valid point of criticism, is reviewer 1's criticism of the value of parameters n4 and beta. You refer to an extensive sensitivity analysis and discharge data, but I believe these are not shown in the paper. Even if you insist on not showing them in the paper, it is a good idea to show them in your response to the reviewers, to convince them that this has been done successfully. When you show that, make clear what your criterion was for the ' best approximation' that you refer to on page 3 of your response document. I can imagine that it is worthwhile to pull into this response your intention with the two figures of diffusivity versus slope. You state that beta = 0.1 is needed to reproduce the observed topography, but is this topography a result of the aeolian setting? Is the current aeolian activity and diffusion in the landscape in equilibrium with the shape of the landscape? It seems you are making that argument, and if so, I would disagree with that just like reviewer 1.

There is heated discussion between you and reviewer 1 about how to model diffusion. There appears to be mutual misunderstanding or difference of opinion regarding the definitions of concepts such as routing, but I think the main point that the reviewer makes about diffusion modelling is that the results you show in the various figures have 45 and 90 degree angle elements that are likely model artifacts. I find that you should answer this point rather than go into a heated discussion about the modelling itself. As editor, I can live with differences in opinion about how the modelling is best done and best described, but results should be at the very least plausible. Please comment extensively on whether you agree that some of your figures show unrealistic patterns (I tend to agree here with the reviewer), and consider whether this should lead to an adaptation and rerun of your model - or to acknowledging to the future reader that this is unrealistic, but does not affect the main results of your study, which remain interesting. (As a scientist in your field, may I suggest that the apparent disagreement over routing may be resolved by adopting Dinf ' routing' with p=0? If I follow along correctly, then that that is functionally equivalent to the diffusion equation in your case.)

Thirdly, the basic form of two equations has been criticized, and I think the criticism has not been taken to heart. For Equation 4, the unit problem persists. After your small change in the manuscript in Eq 4, the units read: [m/y] =not [-/-][m/y][y]. This must be improved rather than defended, it seems to me. If you have a more elaborate algorithm that you summarize for readers' comfort, that is to be commended - but it should be correct. I did value the addition of Eq 5 in this context. (The changes to Equation 4 should be made in context of the discussion about diffusion above).

The other example of criticism of the basic form of a function comes from reviewer 2 who to my mind correctly points out that also your version of the humped equation is not correct in terms of units. Your response is not understandable to me, and appears to duplicate an earlier answer to reviewer 1 - which would indicate that the problem persists. Please provide responses and actual improvements for the next round of revisions.

As you consider whether you want to submit a further revision, please take into consideration that a novel answer to the reviewers' comments after your first revision is expected. They will not have received your current response.

I think the paper remains very interesting and deserves ultimately to be published - but that it requires a substantial amount of work to get there. I hope you have the opportunity and the continuing interest to make this happen. I wish you all the best with the revisions.

The changes made by the authors do justice to practically all comments made by both reviewers. Although authors and reviewers continue to disagree on some other aspects, I believe that the research presented in the paper is interesting and valid enough to merit publication. Continued discussion, perhaps with the reviewers, can then continue based on the published paper.

Dear Sagy, I am delighted to inform you that your ESurf manuscript has been accepted for publication as a final paper. Apologies for any delay - as noted by the associate editor.
All the best,
Tom