This paper presents and tests a mountain wave (MW) model that aims to represent the characteristics of orographic gravity waves generated by the Earth's mountain ranges, with a particular emphasis on those that have horizontal propagation, and thus that may exert drag remotely from the regions where they are generated. This aims to address a deficiency in current MW parametrizations which use a single-column approach. The model represents the MW field as the superposition of 2D waves generated by elongated ridges adjusted to optimally fit the main mountain ranges, and a ray tracer algorithm GROGRAT to compute their propagation, and is tested using HIRDLS satellite observations and ECMWF IFS model data. While this is an important and interesting topic, and the science presented in the manuscript appears to be sound, it is difficult to be certain about this, as the presentation is at times unclear and confusing, omitting important details, lacking references, and phrasing explanations in an unnecessarily complicated way. I believe these presentation issues are sufficiently profound to require major revisions.

Comments

Line 9: "This study presents the MWM [mountain wave model] itself". This is not done in sufficient detail. For example, the mathematical expression for the GWMF (gravity wave momentum flux) is not presented anywhere (unlike the expression for the residual temperature, Eq. (8)), and this is an unacceptable omission, given that a large portion of the results are fields of the GWMF.

Lines 20-21: "Various studies also argue for a significant role of gravity waves in the occurrence of Sudden Stratospheric Warming (SSW) events [...] and even their shape". It is not clear what is meant here by "their shape".

Lines 26-27: "small scale GWs caused by the sub-grid-scale orography and convection are approximated by a parametrization scheme". I have strong reservations whether the waves under focus in this study (with horizontal wavelengths above 80 km) can be considered "small scale" and if they need to be parametrized, except in climate models. This should be more clearly emphasized.

Lines 38: "(Polichtchouk et al., 2018)". The left bracket should be immediately before 2018 instead.

Line 47: "In the middle atmosphere they [MWs] can be measured from satellites". In this paper, the terminology "gravity waves" is used indiscriminately for waves affected by rotation, which I would classify as "inertia-gravity waves instead". Only waves with horizontal wavelengths of at most a few 10s of km are purely gravity waves. But in Table 1, the lower boundary of the shortest band-pass interval is 80 km. Waves with this wavelength will typically always be affected by rotation of the Earth, which is reflected in their dispersion relation, Eq. (5).

Lines 91-92: "This data set models the earth's surface, including ocean bathymetry, on an 1 arc-minute resolution". For the reader to get a more intuitive view, express this in km as well.

Line 96: "sampled on a 0.3º x 0.3 º grid. Again, express this in km as well, for greater clarity.

Line 99: "cutoff zonal wave-number of 18". How many km does this correspond to? Please specify.

Line 101: "the smoothed background is sampled onto a grid of 2º latitude and 2.5º longitude". Again, express this in km as well, to aid the reader.

Line 110: "HIRDLS temperature measurements". This would be a good point to specify the horizontal resolution of these measurements.

Lines 119-120: "For this paper, GWMF is binned within rectangular overlapping bins of 15º in longitude and 5º in latitude sampled every 5º in longitude and 2.5º in latitude". This would be a good point to specify the horizontal resolution of these data, which I believe is higher than 5º or 2.5º.

Lines 130-131: "horizontal wavelength, amplitude, orientation and location". This description suggests that each of these waves (generated by each ridge) are represented as monochromatic waves (as seems to be confirmed later on). If so, this would be a good point to mention it.

Line 133: "overlapping slices of 10º in latitude and every 7.5º spanning the full globe in longitude. Does this correspond to the maximum length of each ridge?

Line 149: "The cross section of the idealized Gaussian ridges is given by:". It should be noted that, in reality, a Gaussian ridge would produce waves that, although 2D, are not monochromatic, unlike what seems to be assumed in the MWM.

Lines 157-158: "The amplitude is taken as half the height h". Given that a correction is introduced for the effect of low-level flow blocking by Eq. (2), is there a justification for taking h/2 as the amplitude instead of h? This should be commented on in the text.

Line 159: "the horizontal wavelength is set to ...". This presupposes monochromatic waves (for each ridge source). This approximation should be mentioned explicitly.

Line 190, Eq. (3): In this equation U_amp appears to be the horizontal velocity perturbation associated with the wave, and should be identified as such in the text. But this is not currently done.

Lines 195-196: "Lagrangian derivative". Is this defined following the mean flow, or following the total flow (including the wave velocity perturbations? Please mention this.

Line 198: "H the scale height". It is not obvious to the reader that scale height this is. Please briefly specify what it means.

Line 218: "residual temperature structures". It is not at all clear at this point what "residual temperature" means. Later, it becomes clearer that it is the temperature perturbation associated with the waves. But it needs to be explained at this point what it refers to.

Line 228-229: "phi is the current phase at the ray-path of the wave given by the ray-tracer". How is this determined? It is not clear from Eqs. (4)-(6).

Line 229-230: The last term accounts for linear frequency modulation in the vertical with chirp rate ...". What is the physical basis for this? A relevant reference should be cited.

Line 233: "symmetric Butterworth function". How is this defined? Is it the function involving the 12th power in denominator in Eq. (8)? If so, this should be made explicit.

Line 247: "the momentum flux of each wave packet is distributed across the specified data grid using Eq. (8) analogously for GWMF". It is not clear how this analogy works. As mentioned earlier, it is necessary that an expression for the momentum flux is presented, and it is explained where it comes from.

Line 248: "since GWMF ~T^2". Where is this shown? A backing reference is necessary.

Lines 251-252: "we are supersampling the GWMF of each wave on a finer grid (3x3 subgrid resolution for each grid point)". Is there any particular reason why it is 3 x 3? Please explain.

Line 257: "the footprint of the grid cells of the horizontal distribution". It is not clear what this means. Please explain in the text.

Lines 266-267: "reconstruciton" should be "reconstruction" instead.

Lines 308-309: "The operational analysis data set is provided on a 0.1º resolution and capable of resolving mesoscale gravity waves". In km this is around 10km, I think, and this should be mentioned in the text.

Line 313: "smaller scale MWs". Smaller than what? Please specify.

Line 316: "spontaneous adjustment". This expression is thrown in here, as if it was obvious what it refers to, when in fact this phenomenon may not be known to a sizeable part of the readership of this paper. Please briefly introduce the concept, possibly backed with a reference.

Lines 326-327: "The IFS, however, seemingly does a better job of resolving very small scales". Better than what? Please be more explicit.

Line 327: "towards towards". Eliminate this repetition included by mistake.

Lines 349-350: "the change in wave field characteristic is not happening due to filtering of westward facing GWs". Filtering by what process? Please be more specific.

Line 360: "GW filtering due to wind conditions". What is the mechanism that causes this filtering. Please specify it in the text.

Figure 5: It should be mentioned in the caption whether the results shown in this figure are for the whole globe, or in some localized region, e.g. the Andes.

Line 373: "spontaneous imbalance". Again, add a relevant reference to this topic.

Line 386: "decreases in strength stronger". This does not seem to be correctly phrase. Please rephrase this passage.

Line 418: "oblique propagation". In what direction? This is not specified, but it should.

Line 433: "the criterion of waves blocking". Does this refer to wave absorption by critical levels? If so, it would perhaps be better to include standard terminology. Usually, blocking is used in the context of low-level blocking, as described by Eq. (2). The process I think the authors are referring to is attenuation or suppression of gravity waves by critical levels, and perhaps it should be named so.

Lines 440-441: "These contours have been superposed from the surface to 25km altitude and divided by the number of contours". This is phrased in a rather confusing way. It is unclear what contours the authors are talking about. Please clarify.

Line 442: "the percentage of altitude". Again, this concept is unclear, and the authors need to be more explicit in explaining it.

Lines 482-483: "The MWM shows, that parts of the GW spectrum refract to very short vertical wavelengths, which makes them hard to be detect by the satellite". How can this process be distinguished from wave breaking, it that is possible?

Line 486: "total breakdown of GWs reaching saturation". In what sense is this process different from what the authors call "blocking" (around Eqs. (10)-(11))?

Line 490: "obsrvations" should be instead "observations".

Caption of Fig. 9, line 2: "percentage of altitude levels". It is unclear what this means.

Line 517: "far to little" should be instead "far too little".

Line 518: "we can attribute this feature in the observations to MWs due to katabatic flow". Can the authors explain in more detail why these MWs are not represented in the MW model?

Line 519: "like spontaneous imbalances of the polar jet or ". The end of this sentence is incomplete.

Lines 534-535: "Weak GW activity above the northern Rocky mountains, Greenland and the Japanese Sea can be assigned to structurally agreeing counterparts in HIRDLS". It is not clear what "structurally agreeing counterparts" means. Can this be expressed more simply?

Line 547: "due to clouds and the tropopause". It is unclear in what way the tropopause will produce these gaps. Can the authors explain this in more detail?

Line 560: "due to shift of MW parameters towards better observable values". it is not clear what this means. Does it refer to longer vertical wavelengths? In any case, please be more explicit.

Lines 569-570: "due to the observational". A word seems to be missing after the word "observational". Please check and correct.

Lines 591-592: "As presented, model allows" should be instead "As presented, the model allows".

Line 620: "The distributions agree to the findings" should be instead "The distributions agree with the findings".

Line 700: "the corresponding sigma of the kernels". Not clear at all what this is. What does sigma represent. Add this information.

Line 707: "rectangular cutout". Not clear what "cutout" means in this context. The authors need to provide more details.

Section A2 of Appendix A is, as a whole, quite difficult to follow. Some additional information would help.

Line 718: "it's probabilistic variant" should be instead "its probabilistic variant".

Line 721: "Radon transformation". It is not obvious to the reader what this is. Please add a reference that explains it.

Line 725: "empty accumulator". Again, it is not clear at all what this refers to. What is an accumulator? Why is it empty?

Lines 725-726: "this matrix". It is not clear what "matrix" refers to? The accumulator? If so, please mention before that the accumulator is a matrix.

Lines 728-729: "(that pixel in the input image basically gives a 'vote' for all straight lines passing through it)". This explanation is quite unclear. It is unclear what "pixel" the authors are talking about, and what this "vote" signifies. Please clarify.

Section B1 of Appendix B as a whole is also quite hard to understand. Please not only improve the description, but also add relevant references that may aid the reader.

Lines 766-767: "All authors provided scientific input and reviewed the manuscript". However, it is not mentioned who wrote the manuscript (presumably the lead author). Please add that information.

The present manuscript "A mountain ridge model for quantifying oblique mountain wave propagation and distribution " submitted by Sebastian Rhode and coauthors presents good research on the constraining observation of internal gravity waves through phase space modelling of said waves. I think it will be a valuable contribution to the community but needs a major revision before it can be recommended for publication.

In general I have the following criticism:

(1) The underlying model GROGRAT has known errors which can have significant impact but can be easily mended. If the coauthors use - as stated in the text - the original version from 1997 (Eckermann and Marks) they would need to revise several structural dficiencies before applying the ray-tracing algorithm.

(2) A lot of details are missing in the description of the methodologies which hinders the understanding fo some crucial parts of the work. As an example it is unclear in how far the time dependency of the mean flow is taken into account and how it propagates into the ray paths. That makes the interpretation of the presented yearly cycle difficult.

(3) Many statements in the text need sources to be backed up. For instance the ridge detection model utilizes the probabilistic Hough transform which is very briefly described but lacks referencing. Without any source and only a brief explanation - as in the scope of this manuscript - the work is not reprodicible to the reader.

(4) The text needs a general revision. Several references to figures are wrong, there are many typos and slips of the pen.

In the following I will list my line-by-line comments. Note that I omit many of the small typos and gramar mistakes as they are numerous and would make the review longer than necessary.

Abstract

- general - The abstract lacks the general purpose of the work. It seems that would be the analysis of wave propagation / transiaent non-linear waves to better understand gravity wave observations. The comparisons are extensively done in the manuscript but are not mentioned here. In return, the deiciencies of the GCMs that arementioned but not adressed may be removed (e.g. cold pole bias, polar vortex breakdown / final warming date).

- L6f - "This model [...]" i do not understand this sentence. What exactly is associated to what and why?

Section 1 - Introduction

- general - While the first paragraph mentions the roe of internal gravity waves in the atmosphere in gerneral, the second and thir paragraphs focus on the deficiencies of current GCMs. I the following two paragraphs it is explained what the role of orographic waves is and what the presented model is capable of, but not why. Thus the impression is that the presetn study tries to mend deficientcies oin GCMs which is, however neither the scope of the manuscripot nor it is easily transferred to being an SSO parametrization. It would be a lot better to focus less on GCMs but rather focus on the interpretability of observations with respect to detailed wave parameters and sources.

- L15gf - "ehy are [...] clouds." These statements need referencing.

- L16ff - "Since they propagate [...] and lower thermosphere" This sentence suggests that the waves are propagating dominantly in the vertical. However, the opposite is shown in the manuscipt.

- L26 - "are approximated" -> "are typically approximated"

- L42ff - "Both processes could [...] models." This sentence is redundant to the previous one and should therefore be removed. 

- L51f - "In order to understand this low stratóspheric GW activity [...]" It is unclear what is meant with this sentence as no wave activity in the Stratopshere was discussed before. At the same point the combination of observations with model studies seems to be the main point of the work. So this should be expanded / explained in more detail.

- L64 - "wind blocking" The term blocking is not used consistent throughout the manuscript. In the context of orographic (Lee) waves blocking is typically referring to blocked flow over the mountains. However, here it is used as "wind blocking" referring to both the flow blocking at the surface and critical layer filtering of waves due to wind shear. I suggest to either consistently distinguish between flow bnd wave blocking or, even better, use critical layer filtering instead of "wave blocking" as used by Taylor et al. (1993).

- L79ff - "Predicted GW parameters [...]" I do not understand this sentence.

Section 2 - Data

- L84ff - The formulation of this sentence is unclear. I am guessing that the authors want to describe at which points they require data for their consideration? Also there is at least some detail missing on what is meant by data for "atmospheric winds and temperature(s)". From the latter subsections one may later find out that the authors are referring to the ERA 5 reanalysis.

Section 2.2 - Atmospheric Background

- The authors describe how they use the the ERA5 reanalysis data as background field for the ray tracing algorithm. Hower, several information is missing:

(1) What is the temporal resolution? How does the spatially filtered data change over time? Are there temporal filters or interpolation?

(2) The ERA5 dataset is also used for the detrending of the HIRDLS dataset (as explained below). However the spatial filters are different as compared for the ray tracing. There are two questions arising: In how far are perturbation solutions of the MWM and the perturbations from HIRDLES independent of each other when the underlying data is a differently filtered version of the EAR5 data? What is the effect of the different filers? Why are they not the same?

(3) The authors are using IFS data from the operational forcast using a similar kind of filter as for the ERA5 data used for the ray tracing. This dataset is not mentioned here and the impact of the different resolutions in combination with the filtering remains unclear. It would be preferred to explain the differences to clarify the later comparisons and give them a better context / understanding.

Section 2.3 HIRDLS sat data

- L119ff - The authorts explain that the data is horizontally filtered through overlapping but fixed size bins in latitude and longitude. These bins are therefore not equal in physical size and thus a spatially dependend but strong autocorrelation is introduced into the dataset. What is the impact of the latter?

Section 3.1 RIDGE Identification

- L133f - I do not understand the projection of the orographic data. Are these slices overlapping as well? Or is there an approximation at the boundary between the slices? 

- L135f - It remains unclear how the data is filtered. is the Gaussian filter 2-dimensional? Or is the filter applied successively in several directions? How is dioes the filter depend on the projection?

- L143 - The Hough transform urgently needs a reference to a source or a more detailed explanation in the appendix as it is not sufficiently explained there. Otherwise the transform remains somewhat a blackbox to the reader.

- Fig. 1d - This image seems to be very different from the data shown in the appendix (compare Fig. B1), why is that? After studying the appendix it beacomes clear that the used parameters for the Hough transform are not shown in the appendix but also the point data does not seem to coincide in structure. Maybe this is a matter of visual representation?

- L154ff - The meaning of the position and lengths (X,Y,L) as well as the angle (θ) are unclear because the projection is not clearly described before. Does the algorithm work with a local Cartesian space? If so what si the effect of interpolations?

- L158 - The displacement being half the mountain height seems arbitrary here, I am guessig it is derived using linear theory? Please clarify.

Section 3.3 Ray tracer

- general - Do the authors use the GROGRAT ray tracer as published in Marks and Eckermann (1995) and Eckermann and Marks (1997)? It is well known that this model has several severe shortcomings. Explicitely these are

(1) The model does not contain the metric terms necessary to compute ray traces on a sphere. It is therefore only capable of solving traces for local Cartesian applications which are, however, bound to have errors for larger horizontal paths as in the present work.

(2) GROGRAT suffers from the occurence of caustics as the wave action equation is not expanded in phase space as for instance in Muraschko et al. (2015). Overlapping wave action densities are therefore not meaningful.

(3) The wave action equation is solved in terms of wave action fluxes. However, some arising term on the right hand side is simply neglected and thus the wave amplitude is not energy preserving.

(4) The ray tracing supposedly uses the Boussinesq approximation (c.f. L203). That would, however, neglect the anelastic amplification which is cruical for predicting the growth of gravity amplitudes with altitude.

On the one hand a quantification of the errors remains unpublished, on the other hand there is a range of publications suggesting rather simple fixes for the deficiencies (e.g. Muraschko et al., 2015; Hasha et al., 2008). Working with an unrevised GROGRAT does therefore not follow state of the art practice and makes the presented results unreliable with respect to the predicted temperatures and momentum fluxes.

- general - The lower boundary condition of the ray tracer is not described here. It thus remains unclear how the ray tracing is launching rays in space and time. Only through the analysis one may guess that there is one ray ray per ridge (launched in the center?) with unknown distribution in time.

- L177f - "[...] the ground based frequency of all our waves is assumed to be zero [...]" This contradicts later considerations and the notion that the used ray tracing supposedly considers temporally changing background fields. Maybe the author refer to the lower boundary condition? If not this may be a major contradiction.

- L185, Eq. 2 - While the formulation is rather standard, the authors use a tuning constant of 0.32 but do not explain reason for the choice or even the fact that it is a tunin constant. Please clarify.

- L194, Eq. 4 - The coordinate system of the equation system is not clear. The absence of metric terms (c.f. Hasha et al., 2008) suggest a local Cartesian system but no procedure for projection is mentioned. This nmeeds clarification. If the integration is done on the sphere it needs revision.

- L198ff - It is unclear how the ray tracing is generating time series of wave eave perturbation quantities. Do the authors continuously launch rays at the source location taking into account the changing background? If not, how do the authors justify temporatl changes in the background winds and overlapping structures given the transient nature of IGWs (c.f. Bölöni et al. 2021)? This problem propagates into the understanding of the time series in the analysis as the meaning is unclear.

- L203 - Do the authors really use the Boussinesq approximation? If so, how do they justify neglecting the anelastic amlification effect?

- L207 - This is misleading. GROGRAT, according to Marks and Eckermann (1995), does not solve this equation but a prognostic equation for the wave action flux instead (c.f. Marks and Eckermann, 1995, Eq. 4). Moreover the wave action is not conserved along the path. Moreover Eq. (6) is a flux equation rather than a transport equation and in this formulation the wave action density, A, is not conserved along the path even when there is no turbulent damping. Only when expanding into a phase space wave action density this may be the case. In that case, however, the physical extend of the wave packet surrounding the carrier ray (in other words the phase space ray volume) may change its shape along the ray trace (c.f. Muraschko et al., 2015).

Section 3.3 Representation of ray-tracing data

- general - As before this section suffers from missing information on the methods used. In particular it is unclear when the traces, reconstructed at a specific time and position, were started in time. Moreover, as before the projection remains unclear. 

- L221 - L224 - As the temporal scheme is unclear from the description of the ray tracing algorithm it remains unclear what traces would be taken into account for the reconstruction. This needs clarification.

- L226, Eq. 7 - To reconstruct the wave phase the authors utilize a second order Taylor expansion but neglect several second order terms. In particular both terms with horizontal gradients of both the horizontal and vertical wavenumbers are not taken into account. 3D oblique porpagation would suggest that as long as the horizontal gradients act on the scales of the wave packets these terms are non-zero. The fact that the vertical term is non-zero reflects on the very same argument. Based on L292ff the ridge lengths are of the size between 75 and 500km. While the approximation that the horizontal wavenumber may not change throughout a wave packet might hold for small horizontal distances it breaks down for larger packets. If so, also the assumption that the wave packet extend does not shear in the horizontal but stays a rectangle breaks down as well. This simplification potentially poses an important error source and therefore needs mentioning and explanation in the text.

- L229ff - The authors mention that the chirp rate is reconstructed from the closest time steps near the target altitude. Does that mean that the chirp rate is calculated on the characteristic of the ray (total derivative in time) rather than in the vertical (partial derivative in the vertical)? What is the error of that? How would the results change if only the linear term in the vertical would be considered?

- L237, Eq. 8 - As before the reconstruction of the temperature field is statically coupled to the exciting ridge in terms of physical extent and and shape. The assumption of a static wave packet shape is inconsistent with a WKB theory assuming slowly varying background fields and thus needs justification.

- L248 - The authors mention that the (pseudo?) momentum flux scales with the square of the temperature. It would be important for the reader to know what formulation the authors use to calculate the momentum fluxes. If, in accordance with linear theory, they calculate the pseudo-momentum flux the terminology should be adapted accordingly (c.f. Achatz et al., 2017 and Wei et al., 2019).

- L255, Eq. 9 - The authors explain that they compute an integral average of the momentum flux from the Lagrangian reconstruction over the target grid cell. While they mention integrating over cells in a sub grid it remains unclear how the integral is actually computed. I am guessing that the authors approximate the integral as a sum of the cell centered values multiplied with the cell areas. In that case I would like to see a statement on the convergence of the area integral with only 9 values (3x3 sub grid). How large is the error of the integration scheme and how does it compare to the error introduced by assuing a static geometry of the reconstructed field?

Section 4.1 Detected structures and scales in the MWM

- general - I think this part is important as the misrepresentation of the mountains in terms of spectral power can lead to both - over and underestimates of the excited gravity wave energy. The chosen comparison, does however, leave a couple of questions open. It would also be nice to show the Tibetan plateau as well as the orography in southern Africa as these are mentioned explicitly in the analysis.

- L265ff - The comparison in Fig. 2 is made between the raw dataset and the reconstruction isolated by scales. It would be nice to reorder the comparison so that it shows the raw orography, the filtered orography as used for the ridge construction and sum of the constributions of small and large scales. Then, in a second step, the large and small scales could be analyzed. This procedure would have the advantage that the reader wold get a much better feeling for included and filtered scales of the ridge construction algorithm. Moreover, I am wondering: Does the ridge reconstruction into a full orography field demand a maximum of all overlaying detected ridges rather than a sum? This could possibly deal with the representation problem the authors mention in L268ff.

- L290ff - The presentation of the statistics of the detected ridges (Fig. 3) is hard to read and therefore the description is difficult to understandFor instance the statement that longer ridges are associated to large scales and small amplitudes (L294) is not visible from the figure. I therefore suggest to make a scatter plot for the horizontal scales (L, λ_hor) and color code the dots with the feature height, h. This would give the reader a much better understanding of the statistics and the relationships between the different detected parameters.

- L301ff - "[...] the MWM does a good job in representing features on variaous scales." It seems odd to testify a "good job" while several shortcomings are described leading to very large descripancies in the reconstructions as shown in the example plots (c.f. Fig. 2a and c, at ~46°S). This might either be mended by an improved representation / reconstruction (see comments above) or by focusing on whether the detection is appropriate to determine orographic waves.

 

Section 4.2 Residual temperature as compared to ECMWF operational analysis data

- general - At some parts of the comparisons the authors seem to mix up the comparison and evaluate the IFS rather than evaluating the MWM agains the IFS. Being more clear about it would make the point the authors want to make a lot stronger. Also, how do the ampülitudes compare well if the MWM uses Boussinesq dynamics and neglects the anelastic amplification? Is it negligible or do the authors actually take the amplification into account? The amplitues suggest the latter, this needs clarification.

- L321 - "[...] which can be associated with a similar pattern in the IFS data." I do not understand how the patterns are associated, In particular as there are patterns all over the oceans in the IFS data. I suggest to connect the observation of the pattern above the Atlantic at 8km altitude observed by the MWM with the leading argument on structures above the ocean in L315ff. 

- L326f - "The IFS, however, seemingly does a better job of resolving very small scales." I was under the impression that the IFS data was considered the "truth" to be compared against based on the data assimilation it is based on. With this sentence the authors seem to evaluate the IFS based on the MWM, which is however the model which is to be evaluated against the proven IFS results. Please reformulate.

- L332ff - "We see significant GW activity over both the Pacifi Ocean as well as the Atlantic Ocean in the IFS data, which can be mostly explained by oblique propagation of MWs from the Southern Andes as indicated by the MWM data." Again, it would be better to strictly seperate arguments here. Explaining the patterns of the IFS with the MWM is not the objective here. Rather the MWM needs evaluation when comparing to the IFS data.

- L336ff - For which height is the inverse ray tracing done? Does that refer to the patterns at 30km height?

- L340 - The location is missing.

- L345 - The authors refer to Fig. 4 but mention Fig. 5.

- L347, Fig. 5 - For which are region at what time is the analysis of the momentum fluxes done?

- Fig. 5 - What does the ray count entail? Related to the question concerning the temporal dependency of the lower boundary condition (see discussion above) of the MWM it is not exactly clear what the ray count represents. Are those rays from strictly different ridges, or are these overlays from dleayed times due to the transient propagation in a slowly varying medium?

Section 5.1 Global distributions of momentum flux

- L365ff - The authors hint at errors in the HIRDLS data. This would need references or data showing the deficiency.

- L379 - How is the MWM data "binned" after applying the observational filter? Does that mean the intefgal over the GWMF is sinply done over other cells (c.f. Eq. 9)?

Section 5.1.1 January 2006

- general - This section is partly difficult to read and understand due to three reasons. First, the meaning of a monthly mean is unclear as the time dependence of the MWM lower boundary is unclear (mentioned above). Second, some of the mentioned conclusions from the datasets seem speculative. Third, the representation of the data on logarithmic (nowhere mentioned) levelsets with very few levels is quite hard to read and interpolates over many details. I therefore recommend to streamline the section and change the data representation to pseudo color plots. Moreover I recommend linear color scales for the horizontal maps in Figs. 6 and 10 as the currently shown levels are barely covering 2 orders of magnitude and the features in HIRDLS are hard to distinguish in the flat color scaling.

- L395f - "There are two possible reasons for the GWs missing in the satellite observations at higher altitudes." This claim needs justification / references of reported descripancies. Moreover 

- L405f - "There is also a minor southward shift of GWMF towards California visible which is also picked up by the satellite data." This seems highly speculative. The supposed shift is located at the edge of the observations and thus it is unclear what influence structures in the not observed regions have. Moreover there are no structures visible beyond the global GMF band in the HIRDLS data.

- L409ff - "Therefore

the strong signature in the MWM data could be another hint at this or another process missing in our current understanding of GW physics." This, too seems speculative. The quantitative correctness of the MWM over the Rockies was not shown. Instead it is stated that the momentmum flux results of the MWM are too strong at lower altitudes. Moreover some known and cited physical mechanism (total breakdown of the waves) explaining the amplitude behavior not captured by the MWM are mentioned. This context rather suggests that some of the many simplifications of the MWM are not covering the dynamics here, rather than some unknown GW physics.

- L414f - "Another strong feature predicted by the MWM are local maxima in the Southern Hemisphere above New Zealand and the southern Andes, which are matched by the observations." Again, this seems speculative. I cannot see any particular structure over New Zealand in the HIRDLS observations. While the HIRDLS signal over the southern Andes could be interpreted as originating from the mountain waves its magnitude is significantly lower than the momentum fluxes predicted by the MWM.

- L418f - "However, their persistence at 25 km altitude in the observations is not consistent with them being MWs." I suggest a reformulation of this statement as the waves observed at higher altitudes and inside the polar vortex are most likely originating at different locations (possibly from other sources), given they are advected by very high wind speeds. These waves are therefore most likely not "persisting" to higher altitues as suggested.

- L420 - 427 - This paragraph is somewhat confusing as it is not clea when the authors refer to HIRDLS and when to the MWM. Particularly the sentence in L425 was very confusing to me at first. I suggest a streamlining of the whole paragraph clearly laying out the differences.

- L433 -  As mentioned above. Beyond the coined name blocking diagrams I suggest to use the term critical layer filtering to distinguish flow blocking from wave filtering to clarify the refferred to physics to the reader.

- L435, Eq. 11 - This equation is singular for the extrinsic frequency / the phase speed being nearly zero which is notably true for orographic waves near the surface and where the wind is approximately static throughout the propagation path. I would thus suggest to emphasize that by the curves for ω_intr=0 only occur where ω_gb is non-zero.

- Fig. 9 -  It would be helpful if the considered time interval (Jan 2006) was added to the caption of the figure. 

- L443 - The authors note that the blocking diagrams only show critical layer filtering for ω_gb=0. I suggest to add a statement that this is true where the wind profile is approximately constant and near the topography where the refraction is not strong enough, yet.

- L456 - "This total breakdown of saturating waves is not represented in GROGRAT simulations, but could be a reason why HIRDLS sees less activity above the Himalaya (Fig. 6)" I suggest to reformulate this statement as it is not the MWM leading to patterns being observed in HIRDLS. Rather than that the observations hint at missing effects in the MWM, which I suspect the authors meant to say.

- L474 - There are no yellow lines in Fig. 9d anf f? I suppose the authors refer to the red lines?

- L475 - The authors refer to the wind reversal, I suppose at very low altitudes. This is difficult to see so I suggest the altotude is mentioned in the text so that the reader will not have to search for the detail in the plots.

Section 5.1.2 July 2006

- L495ff - Here the authors state to see eastward propagation in the HIRDLS dataset. Albeit this being the likely reason there is no propagation information in the data. I thus suggest to reformulate the paragraph arguing that the MWM suggest this to be the reason for the patterns observed in the HIRDLS dataset. Moreover a hint at why the contribution from the Antarctic Peninsula is missing in the (filtered) MWM would be helpful and complement the argument.

- L511 - What is meant with the "assumption"? The reference needs to be fixed, maybe be more specific.

- L517ff - The attribution of the momentum flux to spontaneous from jet imbalances or katabatic flows seems somewhat ad hoc. That would be generally fine but has to be formulated witout a clear attribution. On a site note: If the ray tracing does not contain the necesseary metric terms it will have particularly strong errors near the pole. Should this be the case (as in the equations of Marks and Eckermann, 1995) it is a possible candidate for the missing northward propagation.

- L522f - "The location and strength of local maxima fits nicely between the two." Does that refer to the comparison between the MWM and the observations by HIRDLS? If so it would be contradictive as the following sentence states (and I agree), that the effect is not seen in HIRDLS as it cannot be separated from the background. Since no definite statement can be made about the considered structures in the observations I suggest to leave them out entirely.

- L534ff - "Weak GW activity above the northern Rocky mountains, Greenland and the Japanese Sea can be assigned to structurally agreeing counterparts in HIRDLS. Note however that the baseline of HIRDLS is much higher than the predicted GWMF of the MWM and these features might as well not be visible in the observations at all" This statement is contradictive. If the structure cannot be seen in the HIRDLS data there is no attribution of any structure in the HIRDLS data with respect to orographic waves. I suggest to remove the comparison entirely.

Section 5.2 Zonal mean momentum flux distributions

- L548 - Unclear. Black contour lines in which plot (Fig. 12 I suppose) and from which dataset?

- L552f - "Another low altitude maximum at 30°S in the observations is probably not robust, [...]" This statement is not backed up and needs an argument. The HIRDLS data quality threshold permitted the structure and so the fact that it lies inbetween data that was flagged invalid is not enough to make that claim.

- L557-567 - In this paragraph it is not always clear which dataset the authors refer to. Some streamlining would help understand the points better.

- L560f - "Below about 20km, there is also southward propagation towards 60°S." The presentation of zonal mean absolute momentum flux does not show any meridional propagation. Can this claim be backed up (for instance by showing meridional fluxes)? If not, remove it.

- L570 - observational -> observational filter

- L585f - "Since the observations are limited due to clouds, this is only seen in the model data, but since this feature almost completely vanishes after application of the observational filter, HIRDLS would probably not have observed this." This is very speculative claim which adds little to the discussion. I suggest to remove the second part of the sentence and write: "Since the observations are limited due to clouds, this is only seen in the model data."

Section 5.3 Time evolution of GWMF distributions

- L596 - "this is usually happening" Needs a reference.

- L609 - "zonal propagation"  -> "zonal propagation and advection"

Section 6 - Conclusions

- L651 - "a study of blocking and wind filtering" Here it is unclear what is meant by blocking. Is it flow blocking in the PBL or critical layer filtering? See note on consistent terminology concerning blocking.

- L666f - "Another finding is that it could be worthwhile to implement katabatic MWs in order to obtain increased fluxes northward of Antarctica and southward of Greenland." This formulation is somewhat misleading. I suppose the authors would like to improve the predictions at these locations rather than just obtain an increase.

- L691 - When you suggest ray-tracing as a gravity wave parametrization for GCMs it would be useful to reference works that have shown first implementations, strengthening the feasability of the idea. In particular I suggest to refer to the recent works of Bölöni et al. (2021) and Kim et al. (2021).

Appendix A2 -  Mountain wave fit

- L711 - Do I understand correctly that the function R is equal to the function f from Eq. 1?

- L716 - How many parameters are fitted to the ridge? I suppose it is the mountain height as well as the half width? Please clarify what R depends on.

Appendix B - The (Probabilistic) Hough Transformation

- general - This appendix is very interesting but also brief. Given the scope of the manuscript that is to be expected, however, it urgently needs references for further reading and understanding.

Appendix B2 - Sensitivity of the probabilistic Hough Transform

- general - The Hough transform seems to be done on a local Cartesian coordinate system, however the details about the projection are not mentioned. I suggest expanding on that.

- L752 and Fig. B1 - This is interesting and a nice overview but needs some consistency. It would be helpful to order the subplot along the changes in the two length scales (so that one row or column has one constant parameter) and also show the optimal values used. Finally: Why does Fig. 1d look very different from all figures here? Aren't they both the southern Andes region?

Appendix C - Alternative representation of ridges as used in previous studies

- general - This section does not seem to add much to the manuscript and could be removed.

References:

Achatz, U., Ribstein, B., Senf, F., and Klein, R. (2017). The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: weak and moderately strong stratification. Quarterly Journal of the Royal Meteorological Society, 143(702):342–361.

Bölöni, G., Kim, Y.-H., Borchert, S., and Achatz, U. (2021). Towards transient subgrid-scale gravity wave representation in atmospheric models. Part I: Propagation model including direct wave-mean-flow interactions. Journal of the Atmospheric Sciences.

Hasha, A., Bühler, O., and Scinocca, J. (2008). Gravity Wave Refraction by Three-Dimensionally Varying Winds and the Global Transport of Angular Momentum. Journal of the Atmospheric Sciences, 65:2892–2906.

Kim, Y.-H., G. Bölöni, S. Borchert, H.-Y. Chun, and U. Achatz (2021). Toward transient subgrid-scale gravity wave representation in atmospheric models. Part II: Wave intermittency simulated with convective sources. J. Atmos. Sci., 78, 1339–1357

Muraschko, J., Fruman, M. D., Achatz, U., Hickel, S., and Toledo, Y. (2015). On the application of Wentzel-Kramer-Brillouin theory for the simulation of the weakly nonlinear dynamics of gravity waves. Quarterly Journal of the Royal Meteorological Society, 141(688):676–697.

Wei, J., Bölöni, G., and Achatz, U. (2019). Efficient modeling of the interaction of mesoscale gravity waves with unbalanced large-scale flows: Pseudomomentum-Flux Convergence versus Direct Approach. Journal of the Atmospheric Sciences, 76(9):2715–2738.