Review of "Process-Oriented Evaluation of Stationary Rossby Waves and Their

Impact on Surface Air Temperature Extremes in Dynamical

Downscaling over North America" by   Sakaguchi et al

This paper assess the ability of three different dynamical downscaling methodologies to simulate how quasi-stationary Rossby waves from remote regions lead to regional temperature anomalies and extremes over North America during summer. The three classes of models differ in how the large-scale forcing affects the downscaled domain: a LAM constrained only by lateral boundary conditions, a LAM with spectral nudging to maintain consistency in large-scale dynamics with the forcing data, and a global variable-resolution model with smoothly varying grid spacings. The model with spectral nudging is shown to perform best. The global variable resolution model suffers from time-mean biases in the upper-level circulation, leading to incorrect Rossby wave propagation. The LAM with just lateral boundary constraints also has biases in the large-scale flow and also abrupt changes in winds near the boundaries, again leading to incorrect Rossby wave propagation. Finally, the paper demonstrates that getting correct Rossby wave propagation and accumulation of wave activity is essential for surface temperature anomalies over the Southern Great Plains, an effect only captured with spectral nudging.

This was an interesting and well-written paper, and is well on its way to being suitable for publication. Nonetheless, I think the paper could be improved somewhat as described in my comments below. I should note that my background is in Rossby wave dynamics, and not in downscaling, which certainly is reflected in my comments below.

Major comments

1. When the authors compute the WA fluxes, they apply a 25-90 day bandpass filter. Given that they are focused on the development of heat extremes on subweekly timescales, this seems to be too heavy of a filter. Specifically, because of this filter, the causality of the connections inferred in Figure 1 and in Figures 11-14 is somewhat ambiguous, as all of the changes should happen simultaneously if you filter out <25 day variability. Are these results sensitive to this heavy filtering?

2. I have a few questions about how ray-tracing is implemented here as compared to Hoskins and Karoly 1981.

2a. Equation 1: in classic ray tracing in Hoskins and Karoly 1981, k is kept constant. Why in the current formulism is it allowed to be a function of location? How much does k change as the wavetrain propagates away from the source region? More generally, please add a citation that derives equations 1 and 2.

2b. In line 290, the authors say that their implementation of ray tracing gives no information on the wave amplitude. While I can't say whether this is true of their implementation, it is clearly not true of the wave tracing WKB theory from Hoskins and Karoly, as they do diagnose wave amplitude. See their section 5. If the statement in line 290 is a typo and it is possible to infer wave amplitude, this would be an interesting addition to the (very long) paper as it directly relates to heat extremes. If the statement in line 290 is correct, please explain why things are different from HK81.

Minor comments

1. The paper refers to these wavetrains propagating into North America on subseasonal timscales as stationary Rossby waves. I think a more suitable terminology is "quasi-stationary Rossby waves", as typically stationary waves are averaged over an entire season (or at least over an entire month). See e.g., White et al 

2 . Line 31: the sentence "Since phase speed is inversely proportional to wavenumber, larger waves tend to have greater phase speed." Is an oversimplification, and depending on how it's interpreted incorrect. I suggest deleting

3. Line 342: "creates" isn't precise. It seeds relative vorticity, but doesn't create any vorticity per se.

4. Figure 8-10 demonstrate that there exists a waveguide in the climatological circulation (e.g., a North Pacific subpolar waveguide appears to trap k=6 or k=8). Previous work has diagnosed such a waveguide using K_s (as the authors later note), and while K_s has many suspect assumptions underlying it, it is a more intuitive tool than the more comprehensive but black-boxy tools used in this paper. If my intuition is correct and there is a waveguide formed via a K_s local extrema, I think the paper would be clearer if this was shown explicitly.

5. Figure 8: please fix the panel titles. Also, the caption doesn't appear to accurately reflect the figure contents.

6. Line 433: **to** travel north

7. Equation C11 and C13. The authors jump from \eta_y and \eta_x to q_x and q_y. I assume this is just a notational issue, as the authors are neglecting stretching vorticity/divergence. If yes, please keep the original notation.

              White, R. H. and Mareshet Admasu, L.: Temporally and zonally varying atmospheric waveguides – climatologies and connections to quasi-stationary waves, Weather Clim. Dynam., 6, 549–570, https://doi.org/10.5194/wcd-6-549-2025, 2025.