See attached .pdf file.

The study describes a detailed analysis of the propagation of waves into 

the lower stratosphere, bringing evidence that lateral propagation of several 

thousand kilometers can be common already at lower stratospheric heights. 

The methodology is well explained, the figures are clear, the analysis 

and the discussion are convincingly carried out. The illustration of this 

lateral propagation and the conclusions are of great interest to the community

interested in gravity waves, their parameterization and their impacts on 

stratospheric circulation. However, some of the choices

in the methodology would need to be further justified, or sensitivity 

to these choices should be explored a bit: using temperature perturbations 

as the key variable for identification of the waves (point 1), the 

calculation of the gravity wave momentum fluxes (point 2), the choice 

of the analysis altitude (point 3). The discussion of the origin of 

the waves should be strengthened slightly (point 4), even if a detailed 

discussion is outside the scope of the present study. Once these concerns 

have been addressed, this study should constitute a valuable reference

for the understanding and modeling of atmospheric gravity waves. 

Major Points

1. The investigation is carried out with the identification 

of gravity wave packets as a starting point. This identification

focuses on temperature. This makes sense and is related to the 

relevance of this variable and the corresponding dignostic tools

in observations. However, since the analysis is carried out on 

model data, other variables could be used. The vertical velocity

in particular is available, and variations will naturally be 

dominated by gravity waves (no or much less need to remove 

background large-scale gradients). What are the results of the S3D

method on the vertical velocity field (or on other fields, e.g. 

meridional wind, ageostrophic wind, divergence..)? What is the 

sensitivity of the method to the choice of the reference variable

for the identification of wave packets and what does this imply 

for the overall interpretation? 

2. The gravity wave momentum flux (GWMF) is calculated, it seems, 

from the wave characteristics ('GWMF depends both on the squared

temperature amplitude and the ratio of horizontal to vertical wavelengths',

line 264). Yet from the model output there is much more information

available, allowing a direct calculation of the momentum fluxes from 

the different variables involved, including velocity components. Although

such validation is not the focus of the manuscript, a comparison of the

two estimates would bring much more confidence to the estimates of GWMF, 

which is a central quantity in the study of gravity waves. Reducing the 

uncertainty on the estimate of these fluxes is important and worthwhile. 

3. Although the tool used for ray-tracing does not require validation, 

as it has been used and its relevance demonstrated many times, it could 

be useful to explore a bit the sensitivity of the analysis to some 

of the methodological choices: if the analysis of the waves is carried out 

at 30 km instead of 25 km, or at 20 km, are the results essentially unchanged? 

How well do rays launched from 30 km correspond to the wavefield present at 20 km

when they have propagated down to 20 km (with the reserve in mind that part 

of the waves present at 20 km do not propagate up to 30 km)? Of course, 

the questions suggested here would require more work than is reasonable, 

but it would be useful to give some indications for the sensitivity of the

analysis to different choices that need to be made in the process. 

4. The origin of the non-orographic waves deserves some more 

discussion. Although it is quite acceptable that "A detailed discussion 

of the source processes is however beyond the scope of this study," (l359)

some indications of what the sources could be, and some references, should 

be included. In particular, some information may be present in the output 

of the ECMWF-IFS. In addition to the vertical velocity plotted in figure 11, 

the divergence of the horizontal wind should be plotted. It highlights a 

different part of the spectrum relative to vertical velocity, and is 

particularly relevant for non-orographic waves, which often have low intrinsic 

frequencies. 

Minor Points

l4 parts of the discrepancy -> part of the discrepancy

l17 remove e.g.? 

l49-50: this is slightly misleading because the distances 

over which horizontal propagation will matter are much larger

than those over which vertical propagation matters. The propagation 

is in line with the aspect ratio of the wave. 

l70-74 another study investigating such wide lateral propagation from 

observations is the study by Thurairajah et al (2017)

p8, Fig 2: please find a way to add a fine line indicating the 

locations of the two cross-sections on the maps, this will be 

helpful (of course the latitude and longitude suffice in 

principle, and it is good not to overload figures, but it 

should nonetheless be helpful)

l256 expected wavelengths for GW range between 5 and 20 km: should it be added 

'in the present case', to remove ambiguity. The sentence may otherwise read as 

a generality, although GW with shorter vertical wavelengths are common

l271-280: is it the right choice to represent the ground-based period (or 

frequency)? The intrinsic period will be related to the horizontal and vertical 

wavelengths. These have variations within the ellipses I, S and E, but seem 

rather smooth nonetheless. In contrast, the ground based period (Fig 3e) shows

very large variations within region I (strongly positive and strongly negative

values are present side by side). If the ground based frequency is calculated 

from the estimation of the intrinsic frequency, the wavevector, and the background 

wind, the multiple sources of uncertainty can lead to large uncertainty. 

l287: 'an intermediate, positive ground-based period': figure 3e rather 

suggests an ill-defined ground based period, with strong spatial variations

l293: 'the influence of imperfections in the background removal is less important for higher amplitude waves': as propagation is linear, why would this be the case? 

Is it rather that characterization of the waves is less uncertain for higher 

amplitude waves, for obvious reasons that the signal is clearer for higher 

amplitude waves?

l296: missing citation

l300-305: no reason to separate the two paragraphs

l317-318: could the authors recall the time resolution available to interpolate 

in time? How sensitive are solutions to this time resolution and to the 

interpolation?

l325-330: Are the ray-tracing results sensitive to the choices described in 

section 2.3 to define the background flow? 

Legend of figure 4: it is slightly odd to start by describing the right column 

then the left one; would it be better to change the order in the figure, or in 

the caption? Also, the percentage of stratospheric GWMF is in the upper-right 

corner of the figures (of the right column). 

l381: non -> none ; where -> were

Legend of figure 10: mention the unit for the pressure contours

l453: what is the apparent contradiction mentionned here, between the 

numerical and observational studies referred to? 

l541-543: paragraph containing a single sentence - should this not be avoided? 

l545-549: the balloon observations have also been investigated to relate the 

observed waves to background wind speeds: it has been found that gravity wave

momentum fluxes are systematically enhanced in the regions of stronger 

background wind speed in the balloon observations (Plougonven et al 2017).

This makes the statement put forth by the authors more precise: it is not just 

a geographical statement (balloons observed GWMF at 60°S), but a dynamically

meaningful statement (balloons observed enhanced GWMF in the jet) which is 

consistent with the findings of the manuscript. It supports the generality of  

the findings obtained from the detailed investigation of the propagation paths

carried out in this case study. 

l573-575: this point is very interesting and should perhaps be more emphasized.

Are the waves that end up at 25 km those that have found strong winds to 

propagate into successively in the troposphere and the stratosphere? (It is 

mentionned that both jets are strong, but they are not colocated in latitude..)

==================

Plougonven, R., A. de la Camara, V. Jewtoukoff, A. Hertzog and F. Lott (2017).

On the relation between gravity wave and wind speed in the lower stratosphere.

J. Atmos. Sci., 74, p1075-1093, 10.1175/JAS-D-16-0096.1

Thurairajah, B., D. E. Siskind, S. M. Bailey, J. N. Carstens, J. M. Russell III, and

M. G. Mlynczak (2017), Oblique propagation of monsoon gravity waves

during the northern hemisphere 2007 summer, J. Geophys. Res. Atmos., 122, 5063-5075, doi:10.1002/2016JD026008.

*REVIEW OF Strube et al.: Propagation paths... (ACP160)*

** Summary

The authors study the propagation of gravity waves in ECMWF-IFS analyses for an event (31 July / 01 August 2014) during the DEEPWAVE campaign. They apply established methods and concepts. I am missing a dedicated discussion of achievements with respect to former publications. Further, the appendix needs thorough correction. Thats why I recommend major revision.

** Major ccomments

Paramount importance: In line 496 ff you write about the "paramount importance of the relative wave direction for the distance..." in contrast to the wave-refraction effects. Do you mean those waves in Fig. 8 which travel more than 4000 km which are opposite to the wind? This needs to be elaborated and made more pronounced. 

Long waves: You show long waves travel long - as may be verified with the ratio of horizontal and vertical group velocities. Jiang et al. (2019) show similar effects as well as Ehard et al. (2017). This needs to be included in the discussion. Are these long-travelling waves the "paramount" waves oriented against the wind?

Mountain-wave directions: In the appendix you show that ground-based (apparent) group velocity is perpendicular to the wavenumber vector respectively parallel to the phase lines (or the mountain ridge). Can this detail be used to interprete the wave propagation? What was your intention to show Fig. A1 when you do not refer to it in the main text?

225 Degree: What is the reason for the major wave orientation seen in Fig. 9? It is not apparent in Jiang et al. (2019), but is also present in Ehard et al. (2017). They argue it is a refraction effect. Please, dicuss this issue.

Appendix: This part of the paper has to be rewritten because it contains a number of mistakes. For example, equation (A1) is wrong because phase velocity is the ratio of frequency and wavenumber and it is NOT parallel to the wavenumber vector ( k, l ). In the text, you write in line 595 that the phase and group veocity are equal but you do not give a dispersion relation. For mid-frequency waves with

  omega_hat = N k_h / m

it is definitely NOT. While eq. (A2,A3) is formally correct for such waves, it might be easily extended for arbitrary wavenumbers ( k, l ) and winds ( u, v ). Also figure A1 needs revision: there should be intrinsic (flow-relative) group velocity instead of "horizontal phase speed vector" because the vector addition is fo the group velocity. Further, I suggest to extend the consideration with a decomposition of the group velocity in a component parallel and perpendicular to the wavenumber.

** Technical comments

Abstract: Please, specify the event you analyzed.

L201: Do you refer to Fig. 2b? Please, specify.

L207: May be, "localized" or "confined" is a better word than "restricted"?

L318: "through" --> "of"

L321 (Eq. 6): The formula is corrupted - please, indicate the time derivatives correctly - either with "\partial" or subscripts.

L546: You write "apparent contradiction" while you refer to different situations. I suggest to write "There are different situations..." or "There is not a universal picture..."

Fig. 4: Please, change positions of "Right column: ..." and "Left column: ..."

** References

Ehard, B., B. Kaifler, A. Dörnbrack, P. Preusse, S. D. Eckermann, M. Bramberger, S. Gisinger, N. Kaifler, B. Liley, J. Wagner & M. Rapp, 2017: Horizontal propagation of large-amplitude mountain waves into the polar night jet. J. Geophys. Res. Atmos. 122,  3: 1423-1436, doi:10.1002/2016jd025621.

Jiang, Q., J. D. Doyle, S. D. Eckermann & B. P. Williams, 2019: Stratospheric Trailing Gravity Waves from New Zealand. J. Atmos. Sci. 76,  6: 1565-1586, doi:10.1175/jas-d-18-0290.1.