Overall, this paper can be considered a companion to Harnik and Wirth (2025). While Harnik and Wirth (2025) focused on obtaining solutions for a leaky waveguide, and the effects of a leaky waveguide are somewhat analogous to wave damping, the present paper emphasizes the features of Rossby wave resonance. The authors provide a thorough review of the historical context of Rossby wave resonance in the literature, return to the linear barotropic model with pseudo-topography as forcing, derive analytical solutions, and present corresponding numerical solutions. This study suggests that, under realistic conditions, the only possible resonance solution within a linear framework corresponds to the first meridional mode.

It is a pleasure to review this paper. The main body of the manuscript is well-written and clear. I have only a few minor comments and suggestions:

Minor comments:

1. Line 2: “westery jets” should be corrected to “westerly jets.”
2. In the Introduction, I would really appreciate the authors including a more detailed comparison with several relevant papers on resonance, such as Charney and DeVore, Tung and QRA, to better position this work in the existing literature.
3. From equations 5 to 8, it seems that h hat is not dimensionless if D=500 km, in equation 7, which appears inconsistent with the units in equation 8. I would suggest adjusting the delta function to have the dimension of (length)^-1. Additionally, a brief explanation of the forcing expression of pseudo topography could be helpful for readers less familiar with this formulation.
4. In Figure 1, the annotation for “meridional wind” need to be corrected to “zonal wind.”
5. I suggest adding more explanation regarding the psi value in equation 29, for example, by showing how it is derived by substituting back into equation 17.
6. When discussing the physical interpretation or the limitations of the n=0 solution, either in the Results or Discussion sections, it may be helpful to explicitly note that the presence of singularities indicates that, beyond analyzing wavenumber, amplitude, and phase, the linear equations may no longer be valid for the solution.
7. Line 343 ‘reminscent’ should be ‘reminiscent’
8. Line 375 ‘analysical’ should be ‘analytical’
9. However, it seems that a zonal resonance solution (n=0) is not necessarily impossible in realistic conditions. For example, in line 557, the jet corresponding to the n=0 solution is described as “unrealistically wide,” yet Figure 6 still shows a solution with Ly=1500km, though its amplitude is weaker. Some clarification of this point could strengthen the discussion.
10. In equation 40, I assume that sigma is not explicitly defined earlier. While its meaning (related to jet width) can be inferred, a brief definition would be helpful for clarity.

Overall, I found this paper to be well-structured, informative, and a valuable contribution to the literature on Rossby wave resonance. I hope the paper can be published soon.

I enjoyed reading this paper; it presents a thorough pedagogical exposition of Rossby wave resonance in a orographically perturbed linearised barotropic vorticity equation.

As far as I could see there are no technical issues with the paper, the literature is appropriately referenced for a non-review paper, and the exposition is clear, if a bit longwinded. From that point of view, the article could be accepted as is, subject to some minor technical corrections, and I would be quite happy for this to be the outcome of the review process.

I must admit I have a problem with the manuscript, which the Editor is free to ignore if they think this does not represent a serious enough issue.

Firstly, I was not immediately struck by the originality, surprise, or novelty of the results. It seems to be a bit of an exercise in relatively straightforward applied mathematics with some linear model well-explored. It is then not so clear to me what I really did learn from the manuscript that I did not already know or could guess. It clearly does add colour and detail to our understanding of the forced, linearised barotropic vorticity equation applied in a beta-channel setting, but I am rather less convinced it actually helps us understand the atmosphere any better.

The authors point out some of the caveats of the setup, but I might add some further caveats: the BVE is linearised, but partial wave reflection at a jet edge in any dynamical setting would be accompanied by nonlinear filamentation. The authors point out that the jet is considered zonally symmetric but the real jet is importantly deformed by the nonlinear planetary waves that the paper is about. The detailed nature of the boundary conditions is important, but in reality this would vary on the zonal scale of the planetary waves themselves. The atmosphere is not barotropic, and would, at the least, involve a finite Rossby radius; after all, the compression of the column by the orography is the key forcing mechanism. Any nonlinearity would immediately introduce wave-wave interactions in which case the whole spectrum of the forcing becomes important. I am sure that further analyses could address some, perhaps all of these caveats, but that is not done in the present manuscript.  The detailed results in the manuscript seem at face value strongly dependant on the rather strongly simplifying assumptions in the setup, but these same assumptions move the model quite far away from the observed atmosphere.

In summary, the details resulting from the analysis of a model with so many idealisations probably have rather limited applicability to the real atmosphere: which of your detailed conclusions would stand up to more realism?

If the idealised model actually solves a question we had about planetary waves then we learned something about the atmosphere using the model, but I do not believe that is the case in the present manuscript; at least that is not what is presented. As it stands the model analysis appears to just answer detailed questions about the model.

Would this type of analysis perhaps be better suited for an applied mathematics journal?