Dear referee, 

thank you very much for your review. 

Referee 2 send us some additional references that we will add to the manuscript as alternatives. Further we will tone down the applicability for practitioners, as referee 2 suggested as well. We will also try to discuss further developments clearer in the final manuscript.

Dear Executive Editor,



thank you very much for putting our attention on this issue. Since this module is part of a larger model/framework, we included our code in the supplementary materials.

We now also uploaded our code to Zenodo.org (https://zenodo.org/doi/10.5281/zenodo.10900454) and will update the respective part in the revised manuscript.



Best regards,

Matthias Rauter

Dear Dieter,

Thank you very much for reviewing the manuscript. We highly appreciate your opinion.

Curvature effects:

We mostly agree with your analysis, especially the misconception with Eq. (9). Luckily the code is not affected by this issue because it avoids expressing the curvature completely (that was the main selling point of Rauter and Tukvoic, 2018).

We tried to connect the curvature-free approach with methods that explicitly considering curvature effects, but made some mistakes along the way. We will correct or remove the respective sections in the revised manuscript.

We cannot follow the argument "This implies that [...] the surface derivative of scalar functions are of order (∆x)^2 and vanish in the limit ∆x -> 0" and don't think this is the case as the same argument could be made for any function.

Curvature effects beside det J != 1 are considered in the model. The velocity vectors are constrained to the tangent plane by the basal pressure (see Rauter and Tukovic, 2018). We checked the direction of the velocity vectors as a test for the correctness for the basal pressure (among other tests). The velocity was surface tangential at all points in space and time except for small numerical errors, both in the simple quasi-1D case and the more complexly curved cases (see Rauter and Tukovic, 2018). We interpreted this as prove that the basal pressure including centrifugal forces is correct. If there is an error in the basal pressure it has a big impact on results, see e.g., this bug, where a projections was wrong: https://develop.openfoam.com/Development/openfoam/-/issues/2979. We think this misunderstanding can be attributed to the mistake we made in Eq. (9) and the second problem you found.

Regarding the second problem you mention we fully agree with you. The main point we wanted to make is that the surface derivative can be split into a normal component (curvature effects) and tangential component. We first considered kappa as a placeholder which we didn't further specify, but wrongly connected it to Dieter-Kissling et al. (2015) at a later point. Of course it has to be a tensorial value and not the mean curvature. We will change this section.

References:

The work of Eglit, Grigorian, Yakimov and others is unfortunately not easily accessible and I usually end up in dead ends or being forwarded to Russian references (compare, e.g., references in Eglit et al., Geosciences, 2020). Conference papers are rarely available and complete in their description. Their influence on my work is very limited and I think that they are usually not the best references to send readers to. Foremost I miss applications, examples and simulations in the few publications that are available to me, something the other references provide. I also didn't study their work in detail and therefore feel not very comfortable citing it. So citing them is not without issues either. Anyway, we will add the review paper Eglit et al. (Geosciences, 2020) as a reference to developments in the Russian community.

We were not aware of their two-layer model, except for the theoretical ideas I read in Eglit et al. (2020). At the point of writing we would have been very happy for some more input, especially on the coupling models. We will cite the Eglit (1998) and Issler (1998) papers as examples for a two-layer model, although applications are missing in both.

Your newest paper looks great and I look forward to reading it. Is seems like a big source for ideas and inspiration. However, we would like to avoid references that were published after our work was finished because I think it will put many decisions we made in a different light. But we will of course consider this work in the future and add the respective submodels into OpenFOAM if possible.

Entrainment model:

We found in an earlier study that all entrainment models performed poorly. As before (Rauter and Köhler, 2020) entrainment is basically regulated by the available mountain snow cover and the exact entrainment relation does not have a big impact on results.

We agree that the entrained snow masses have to be accelerated to the avalanche velocity. This is taken into account, at least to some extent, in the conservation equations: If the flow depth h grows due to entrainment, and the momentum hU is conserved, the velocity U decreases. We are not sure to which extent this covers your suggestion.

What I personally like about the applied model is that the idea is somewhat consistent with damaged plasticity model (e.g. https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch04s05ath120.html).

Thank you for the hint on the manual. Since it is a minor change I will wait for the next release (v2406) to correct it.

User friendliness:

We agree that many practitioners might be intimidated and overwhelmed by the complexity of OpenFOAM. Some (mostly students) are using it, but considering the support requests I get, there is some improvement to be made with user-friendliness. We will tone down the respective statements in the revised manuscript.