This is the first time that I have not requested any corrections.This is a terrific paper that clearly describes a new, challenging test case for dynamical cores with simple microphysics. The test case is discussed relative to meteorological phenomena and relative to numerical methods and artefacts, bringing in a wealth of insight. The graphics are beautiful. I haven't checked all of the equations and I haven't tried to run the test case myself so I cannot be sure that it is fully described.

I have some comments which the authors can consider.

1. In 2.3 you describe the method of initialising w for non-hydrostatic models which, you say, doesn't have much impact. I would imagine that, if you did need to get rid of initial condition shocks then you would need to apply a projection to get discretely divergence free initial conditions.
2. On lines 399-403 you talk about comparing area averages of precipitation. However it is not clear at this stage that this is what you are going to do. The relevance of the paragraph is not clear.
3. On line 480 I would say "compares" rather than "intercompares".
4. On lie 485, "the" rather than "to".
5. On line 502, "have" rather than "has"
6. On line 503, "compact" rather than "concise".
7. The paragraph including line 530 sounds important, describing how you can remove spurious oscillations. I would think that you should show evidence for this.
8. Line 548, why is damping out a Lamb wave considered to be more desirable than maintaining a Lamb wave.
9. Loine 579 you say that you have "discussed the impact of diffusion on the flow and precipitation". You haven't discussed this much.
10. Line 589, this is not clear. Say from the start of this topic that you are referring to work does by Skamarock et al 2021. Otherwise you seemed to be saying things without evidence.

Publisher’s note: the supplement to this comment was edited on 17 July 2023. The adjustments were minor without effect on the scientific meaning.

Please refer to the attached file. Only the general comments are pasted here:

General comments:

This manuscript proposes a new test case for atmospheric general circulation models for the evolution of baroclinic waves over topography. The proposed test case aims to examine the model performance of baroclinic waves over topographic mountains with or without moist processes. The description of the experimental design is presented except for cloud microphysics processes (see below). This paper is valuable for readers who can easily set up the test case by referring to this paper.

Although the description of the experimental design is clear, the purpose of the new test case is not clear enough, and the paper's purpose should be more focused. The experiments include the evolution of baroclinic waves, synoptic flow over mountains, and the moist effect on both. These are separately examined by the previous individual test cases. One new proposal might be the introduction of a ridge-type mountain. The authors may focus on the interaction of the flows over the ridges.

The moist process is an interesting aspect, but the inclusion of the moist process seems too much in this paper. The reviewer suggests the omission of the moist process from the paper. The proposed test case is conducted in a moderate resolution of AGCMs, and convective parameterization is generally used for moist convective processes. Most AGCMs generally do not have a rain category of the prognostic variable, and they cannot introduce the Kessler scheme. A more general and simpler choice for the moist process is the moist adjustment or the large-scale condensation with the saturation adjustment.

If the authors nevertheless choose to introduce the Kessler scheme, the details of the scheme should be clearly defined in this manuscript. The original Kessler is shown in the cgs unit, and Klemp et al. (2015) do not clearly show the parameter values except for the FORTRAN code. The authors should describe how to implement the Kessler scheme in AGCMs where a rain particle is not included as a prognostic variable.

Section 5.3 should be omitted. The readers are not interested in the model-specific namelist in the main text. This physics-dynamics argument does not seem to be a generic character. More examination must be added.

The four dynamical core results are presented in this paper. The results are just for comparison, and no physical insight is presented. Any test case is designed to know some specific characteristics of the models. The authors must extract and summarize the models' advantages and disadvantages. The test cases should generally be presented with standard analytic methods and a reference solution. These are not presented in this paper, and the readers cannot know how to evaluate their model results using the proposed test case.