Great study! I only have few minor comments for the authors.

General Comments

In the manuscript, the authors conduct a careful and systematic study of the influence of boundary damping on gravity waves in the perturbed atmosphere. The emphasis is on the strength of the damping, the thickness of the damping layer, and the domain size and the influence of these quantities on the reflection of gravity waves. Two configurations are considered: a simple hill, where the gravity waves can be computed a priori from an analytical solution, and a wind farm canopy. The former seems to give a more conservative constraint on the parameters, which is promising. Overall, the work shows that domain sizes must be larger than the dominant wavelengths of the gravity waves, likewise for the thickness of the damping layers, and the damping coefficient, normalized with the BV frequency, should be order unity to order ten.

The work is worthy of publication for providing clear guidelines of avoiding spurious gravity wave reflection, and the authors are encouraged to consider the following detailed comments in revising the work.

Specific Comments

1. What is role of grid resolution in the conclusions? Certainly, the domain size conclusions will be unchanged, but is the damping strength dependent on grid resolution?

2. Why are the simulations three-dimensional? There are only five grid points in the third dimension without any inherent three-dimensionality in the geometry or inflow, so the flow is almost certainly two-dimensional.

3. In various places in the manuscript, the authors mix discussion of dimensional terms and non-dimensional terms. Everything seems to be able to be expressed in non-dimensional terms, and I encourage the authors to rewrite the commentary and replot the figures as such where possible. Doing so could also reduce the total number of figures and lines on figures needed. (The need to demonstrate dynamic similarity also seems unnecessary.)

4. A key conclusion of the manuscript is the need to scale the domain size and damping layer dimensions by the wavelengths. However, the actual discussion of the wavelengths from the semi-analytical solution for the hill is somewhat limited. The vertical wavelengths are not actually quantified or plotted, in fact. To make the manuscript more useful, the authors should include expressions for the (non-dimensionalized) wavelengths or similar plots as a function of the relevant non-dimensional parameters. That will allow other researchers to consult this work in order to scale their geometries.

5. While the authors allude to other effects of interest (turbulence, ABL, etc.), for future work, this leaves the reader wondering how relevant this work really is. For example, no wind farm is strictly in the free atmosphere, and this seems to be intended application of the authors. How then would the ABL influence the conclusions of this manuscript? While the authors may not have the quantitative answer yet, some scaling argument to demonstrate that the present results would, for example, be a conservative constraint on more complex flow situations would be beneficial.