The preprint presents a potentially interesting contribution to numerical modelling of coastal and oceanic flows. The overview of the literature is broad (even though it could be further improved) and the level of detail in the description of the proposed numerical procedure is appropriate for the scope of GMD. The proposed technique could be very useful for the improvement of the results of coastal and oceanic simulations and deserves to be made  available to the community doing research on numerical models for coastal flows, along with a comprehensive assessment of its performance.

However, the detailed description of the numerical method is strongly affected by a number of unclear statements, undefined symbols and imprecise definitions. This makes the paper hard to read in its present form and its real value difficult to assess even for an experienced reader. The authors claim that the method they propose has superior stability properties with respect to those available in the literature, but no stability analysis is provided. The authors' attempt at generality in considering apparently several z-coordinate approaches  in the same framework unfortunately  ends up making the preprint more obscure, since it is often unclear  whether the whole approach has general validity or whether parts of it only apply to some  specific z-coordinate formulation. Finally, the truncation error analysis of the vertical discretization appears to be only marginally related to the main topic of the  preprint and is affected by several mathematical inconsistencies. The authors may consider removing this part from the revised version of the preprint.

The preprint can be considered for publication after major revisions,  that are detailed in the attached file.

The authors present a novel alternative to existing z-coordinate type models for the simulation of multi layer shallow water systems. The main novelty is given by the use of a feature that allows the insertion and removal of vertical layers. The paper is interesting and the algorithm well developed. Extra significance is provided by the ability of the proposed method to recover other types of z-coordinate models by appropriately tuning some of the parameters of the novel method.

I recommend the paper be accepted after the authors have properly complied with the following requests (I have attached a PDF with inline comments, this PDF will be referenced next).

Major points:

1. The paper is currently suffering from a lack of mathematical rigor and the presentation is sometimes confused. The notation is often unnecessarily complex and some definitions are missing. Please refer to the comments in the attached PDF document and revise the presentation (especially in Section 2).

2. The authors are doing a good job in the numerical results with showing that the proposed method is well behaved and that it does not perform worse than z-star. Although it is my opinion that additional results are missing to show that the extra hassle of introducing or removing layers is actually beneficial for some application. The authors should include at least one additional test case to show that their method enables simulations that are currently not possible with other existing z-type coordinate models. If this is deemed unfeasible, please show at least that there exists one relevant test case for which your model clearly outperforms existing z-coordinate models.

3. The computational peformance of the method is relegated to the last 4 lines of the numerical results section. Parallel performance is clearly of paramount interest for your readers so a more detailed analysis should be included in the paper. Currently, in the serial runs reported, the overhead of the present method is 8% over z-star. Would that get worse in parallel? If so, what are possible avenues for mitigation?

Minor comments:

Please see the attached PDF. NOTE: I do not expect the authors to supply a point by point response to all the comments in the PDF as that would take too long. As far as I am concerned, it is enough for them to provide a written answer to just the three major points above. However, I expect to see amendments in the revised manuscript addressing all points mentioned in the PDF. In case there is something the authors do not agree with, please include your comment in the written response along with the response to the major points. Thank you.