Page 2, line 22. Unusual to refer to a "grid mesh". People ususally use either mesh or grid. (Either are fine but be consistent)

Page 8, line 15. Line 14 says that the Laplacian is on coordinate surfaces. The following lines discuss a horizontal Laplacian but the metric terms are not present. So I assume that you mean Laplacian is on coordinate surfaces. Please do not call this a horizontal Laplacian.

Page 28, line 28. You use centred differences in the vertical. So if you used non-uniform vertical spacing you would get 1st-order accuracy. The vertical resolution is uniform so these centred differences will certainly contribute to the second-order convergence with resolution.

Page 16, line 30. The sentence is not finished.

The lines for 5th order and 8th order in fig 9 are pretty much on top of each other. I therefore dispute your claim that "The above results suggest that the numerical solution can be converged more rapidly by using a higher order of basis polynomial". I think that your eye was seeing what it wanted to see when comparing figs 7 and 8. Plotting errors instead of/aswell as absolute values would resolve the issue.

Page 19. Based on the statement: "Although this amount of diffusion might seem excessive, it was chosen because it allows the model to remain stable even after the bubble reaches the top boundary."
I would change a sentence in the abstract:
"The results from these tests demonstrated that the horizontally spectral element vertically finite difference model is accurate and robust provided sufficient diffusion is applied."

One of the reviewers also asked if you could report maximum Courant numbers. Do you still have this information? Could you reproduce it?

Due to a misunderstanding, you did not do a resting atmosphere over orography test case which is a shame. Please note in the manuscript that this will be the subject of future work.

Many thanks for your continued improvements to this manuscript. The quantity of additional test cases and clarifications is much appreciated. However I am afraid that I still have some more comments that need to be addressed before publication.

On page 10, lines 12-14 you say:
"We validated the 2D NH model with five test cases: linear hydrostatic mountain wave and tracer-advection and gravity-wave tests over Schär Mountain, as well as density current, inertia–gravity wave, and rising thermal bubble experiments."

That sounds like 6 test cases. But what about the resting atmosphere over orography? That would make 7.

On page 12, lines 22-24 you say:
"Additionally, we conducted a simulation for a resting, stratified atmosphere over Schär Mountain to show how spurious velocities are leaded by the model."
Do you mean "created" rather than "leaded".

Section 4.2 is difficult to follow as you are describing the results of 3 different test cases and sometimes you describe 2 different test cases within one paragraph. Might it be easier to split these test cases into 3 separate subsections? One of the reviewers has given me further comments about your discussion of the resting atmosphere test case:

The corresponding text, at page 14 is: "Fig. 5 shows the time evolution of
the maximum vertical velocities for the resting atmosphere simulation. We
observe that the maximum vertical velocity abruptly increases by 0.08 ms-1
at 1.5 h. But, it is noted that after 2 h the maximum vertical velocity seems
to reach a state of equilibrium by about 0.29 ms-1 and tends to increase
steadily until 25 days."

It is not clear to me how to relate what they write to the Figure. First of
all, is the x-axis unit days or hours? For the last sentence, it seems the
former, but the comment on the growth would hint at the latter.

Moreover, the maximum attained velocity is about 0.03 m/s, so I don't quite
understand where they take the 0.08 m/s growth from. I also personally find
the phrasing "state of equilibrium" misleading in this context. Finally,
leaving the reader with the sentence " tends to increase steadily until 25
days" might actually leave open a potentially more serious growth at later
times.

I have some further points about your presentation of this test case:

You have created a new test case for a resting atmosphere over orography. Klemp (MWR 2011) presented a test case with a region of higher stratification above the mountain in order to excite spurious vertical velocity. Botta et al (JCP 2004) presented a resting atmosphere test case with regions of higher stratifictation and with a much steeper mountain. Zangl (MWR 2012) also presented results with a very steep mountain. Your test case is easier than these and I see no merit in presenting this new test case rather than using an existing one.

You use a large viscosity for this test case and then, not surprisingly, get small spurious velocities. If you cannot run this test case without viscosity, then you should present potential temperature contours (as in Klemp, MWR 2011) in order to see the effect of the spurious motions. With this much viscosity, I would expect the spurious velocities to die down. There must be a large spurious source of energy for this spurious motion to keep going indefinitely.

A minor comment - the y-axis of figure 5 needs units (m/s)?

It seems that your presentation of the resting atmosphere test case opens up alot more questions and a considerable amount more work would be needed to first use an existing test case and then work out why your model is not stable without so much viscosity. I would recommend removing these results from the paper and making a comment that, achieving stable results for a resting atmosphere over steep orography with minimal diffusion will be future work.

At the top of page 16 you discuss the difference between the 5th and 8th order basis polynomials for the cold bubble test case. You still insist that the 8th order basis polynomials give better results but from the results that you present, this is not the case. The results in figures 7 and 8 are extremely similar. The results in figures 9 and 10 confirm that the results for 5th and 8th order are extremely similar. I agree that on figure 9 and 10 I can see some very small differences. But these seem so small that you cannot possibly suggest that 8th order is beneficial.

Having re-read the paper and the conclusions I would say that the conclusion:
"The numerical results showed that the present dynamical core is able to produce high-quality solutions comparable to other published solutions."
is not proved. I would say that a more accurate statement is:
"By varying the viscosity between test cases, the numerical results showed that the present dynamical core is able to produce high-quality solutions comparable to other published solutions."
In order to show that your dynamical core can produce good results for all test cases, really you should use the same viscosity for all test cases. I am not asking you to do this. I am just asking for a modifier to your conclusions.

Many thanks for this illuminating article