Time-varying Atmospheric Waveguides &ndash; Climatologies and Connections to Quasi-Stationary Waves

White, Rachel H.

doi:https://doi.org/10.5194/egusphere-2024-966

Preprints

https://doi.org/10.5194/egusphere-2024-966

Preprints

04 Apr 2024

| 04 Apr 2024

Time-varying Atmospheric Waveguides – Climatologies and Connections to Quasi-Stationary Waves

Rachel H. White

Abstract. Atmospheric waveguides have been linked to amplified atmospheric Rossby waves and therefore to extreme weather events in the mid-latitudes. Waveguides have often been calculated on zonal-mean data, and/or on timescales of a month or longer. Here, I develop an objective algorithm to detect barotropic waveguides, and create a dataset of time- and spatially-varying waveguides in both summer and winter for both the Northern and Southern Hemisphere (NH/SH), including a metric of waveguide depth. In this dataset, waveguides for waves of zonal wavenumber 5 exist in the extra-tropics on more than 40 % of days across many longitudes, with the frequency of occurrence reducing for higher zonal wavenumbers. Waveguides tend to be more frequent, and deeper, in summer than in winter, and more frequent in the NH than the SH. Composites of days with high spatial mean waveguide depth over particular regions show a double jet structure associated with strong waveguide occurrence, consistent with previous research. Significant positive correlations exist between waveguide depth and the presence/strength of quasi-stationary waves. In the SH these correlations are strong across much of the mid-latitudes in both seasons, whilst in the NH significant correlations are found only over the Atlantic, Europe and Asia during NH summer, with the strongest correlations over the Atlantic and western Europe, a region notable for its strong positive trend in extreme heat temperature events in recent decades.

Received: 30 Mar 2024 – Discussion started: 04 Apr 2024

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Journal article(s) based on this preprint

16 May 2025

Temporally and zonally varying atmospheric waveguides – climatologies and connections to quasi-stationary waves

Rachel H. White and Lualawi Mareshet Admasu

Weather Clim. Dynam., 6, 549–570, https://doi.org/10.5194/wcd-6-549-2025,https://doi.org/10.5194/wcd-6-549-2025, 2025

Short summary

Rachel H. White

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-966', Anonymous Referee #1, 26 Apr 2024

The paper investigates characteristics of Rossby waveguides in the Southern and Northern hemispheres (SH/NH) during summer and winter and relationships between waveguides and quasi-stationary wave amplitudes. Several recent studies emphasized that waveguides are related to high-amplitude waves but the causality between the two is still a matter of debate. The originality of the paper is to develop a method to detect systematically at each longitude and each time the presence of waveguide based on the detection of turning latitudes where the stationary wavenumber Ks of the barotropic Rossby wave dispersion relation is equal to the zonal wavenumber k. The stationary wavenumber has been introduced in Hoskins and co-authors papers but only applied to a time-mean flow. In the present paper, it is adapted to get waveguides as function of time. The stationary wavenumber is computed by defining a background zonal flow using a spatial and temporal filter of the zonal wind. The paper also introduces the notion of waveguide depth which is somehow close to the number of zonal wavenumbers for which a waveguide exists. Quasi-stationary wave amplitudes are computed by considering the amplitude of the wave envelope where the quasi-stationary wave is here defined as the deviation of the 15-day running mean meridional wind from its climatology for each wavenumber. The definitions of the waveguides and quasi-stationary waves amplitude are appropriate and well thought. But since the 15-day running mean is used for the computation of both the background flow and the quasi-stationary waves, it is the separation in spatial scale that makes the difference between the two parts of the flow (k<2 for the background flow and k between 4 and 15 for the quasi-stationary waves). Results show that waveguide frequencies are higher in summer than winter in the NH and more frequent in the NH than in the SH. It would be good to detail more the physical interpetation for those statistics (see main comments below). Composites of high and low waveguide depths indicate that high waveguide depths are associated with a double jet structure and in that sense confirm previous studies. However, I am not entirely convinced because they rely on Figures 6 and 7 where anomalous composites are shown so a double jet structure in zonal wind anomalies does not necessarily mean a more pronounced double jet structure for the high waveguide depth than for the low waveguide depth (see main comment below where I suggest to show the composites of the low and high waveguide depths separately). Then correlations between waveguide depths and wave amplitudes are investigated. Even though the correlations are weak, there are several regions and seasons for which the positive correlations are significant. It concerns the SH and the NH summer over the Atlantic and Europe. The results are interesting in themselves but it would be good to add some comments related to previous studies and also related to the maps of waveguide depths (see below for more details). Finally sensitivity tests made by changing some values of the parameters used for the waveguide detection show that the results are quite robust. I think changing the pressure level to detect waveguide could be also another sensitivity test worth making. To conclude, the paper is well written and well organized, the results are new and interesting. However I have several major comments that need to be addressed before I recommend publication of the paper.
Major comments:
a) Abstract: the notion of waveguide depth is obscure there. When I read the abstract I thought it was considering the depth in altitude. It would be good to add words to qualitatively define the waveguide depth. For me, the waveguide depth is closely related to the number of zonal wavenumbers for which the waveguide exists.
b) Introduction (lines 25 to 29). It would be good to add some physical interpretation of why people think there is a link between waves amplitude and waveguides. In my opinion, this is potentially because waves are not dissipated as there are no critical latitudes in a waveguide. But I am not sure this is what the papers cited in line 28 have argued.
c) Method: it would be good to highlight that the background flow and the waves are separated by the spatial scale (k<2 for the background flow and k between 4 and 15 for the quasi-stationary waves). Since the 15-day running mean is used for the detection of both the background flow and the waves, the reader might be confused by the separation between these two parts of the flow.
d) Section 4.1 and waveguide frequencies:

- before starting that section it would have been nice to show Ks for the time mean flow of JJA and DJF, i.e repeat Figures 3c of Hoskins and Ambrizzi (1993) and 11c of Ambrizzi et al (1995). Maybe it would be good to do it by considering the climatological flow for k<2 to be close to what is done in the present paper for the time-evolving waveguides. Such additional figures could help to better visualize the difference between summer and winter and between SH and NH. The argument made lines 160-165 to qualitatively explain why the summer NH has more frequent waveguides than the winter NH could be better understood by showing the time mean U and Ks for both seasons. Furthermore, maybe the additional argument is the fact that the jet is probably narrower in summer than winter and both the planetary vorticity gradient and relative vorticity gradient play a role in the difference between summer and winter.

- I am surprised that the SH has less waveguides than the NH as the double jet structure (separation between subtropical and eddy-drivent jet) is more marked there, at least in the climatologies.
e) Section 4.2: this is the part of the results where I am less convinced by the conclusions. For instance, Figure 6a shows an anomalous tripolar pattern in zonal wind when computing the difference between high and low waveguide strengths. This anomaly could be the result of different changes: a more pronounced double jet structure is one possibility but it could result from a widening of the jet or some latitudinal shifts. So it would be very nice to compare composites of high waveguide strengths and low waveguide strengths separately before (or rather than) showing the difference.
f) Section 5: It is suprising that the correlations are strong in the Atlantic and over Asia and not in the Pacific while the waveguide depths are similar in the North Atlantic and North Pacific. What would be a possible explanation for that ? Or if you do not have hypothesis it would be nice to comment these results by referring to other studies. Were the studies on the relationship waveguide-wave amplitude focused in the North Atlantic and Asian regions. Do you know studies that also considered that relationship in the North Pacific ?
g) Sensitivity tests: I think it would be good to have a sensitivity test by changing the mean pressure level (e.g. 500 hPa?). Held et al. (1985) computed a barotropic equivalent level near 425 hPa and Charney (1949, see section 6) found a barotropic equivalent level closer to 550-600 hPa.
Minor comments:
1) Line 125: maybe add "temporally and zonally filtered U following the method described in section 2.1"
2) Line 130: it would be good to have a qualitative description of what the waveguide depth means. We understand mathematically in the main text but this would be useful for the abstract.
3) Line 134 and thereafter: why is cut-off latitude used rather than turning latitude ? I think turning latitude is the classical term
4) Figure 2: what are the black contours. Zonal wind at 300 mb ? Same question for Figure 4 but they disappear in Figure 5.
5) Line 178: I do not understand the end of the sentence "latitudinal cut-off ... latitude of the jet".
6) Lines 187-188: I do not understand what is meant by "Latitudes are weighted equally". Do you mean that multiplication by the cosine of latitude is applied to do the regional averages?
7) Line 196: I would add "a 'double jet structure' in anomalies is present
8) Lines 204-206: here again it would be better to see both composites rather the difference between composites
9) Figure 7: the magenta contour is difficult to see in the red-brown areas.
10) Lines 260-265: Here the importance of narrow jet is highlighted but this has not been the main argument mentioned in the main text when describing the difference between summer and winter in the NH (lines 160-165). The story of the equatorward displacement of the jet was emphasized. So please be more precise why there is a difference between summer and winter. How important are the jet width and latitude in that story ?
11) Caption Figure 9: please provide units for dimensional parameters.

Citation: https://doi.org/10.5194/egusphere-2024-966-RC1
- AC1: 'Reply on RC1', Rachel White, 13 Jun 2024
  
  I thank the reviewer for their helpful comments and suggestions for improving the paper – your comments will lead to a substantial improvement in the manuscript. I agree with all of your suggestions, and will implement them in a revised manuscript. More detailed responses to your major comments are given in the attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC1
RC2:
'Comment on egusphere-2024-966: Some serious issues', Volkmar Wirth, 06 May 2024

see attachment

Citation: https://doi.org/10.5194/egusphere-2024-966-RC2
- AC3: 'Reply on RC2', Rachel White, 14 Jun 2024
  
  I would like to thank Volkmar for his review, as it has helped me think more deeply about, and subsequently refine, some of the points of the paper, which will lead to substantial improvements in the manuscript. The attached pdf responds to his major comments, and I believe a revised manuscript would be able to address all of his concerns.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC3
RC3:
'Comment on egusphere-2024-966', Anonymous Referee #3, 06 May 2024

The atmospheric waveguide has a profound influence on the propagation path of stationary Rossby waves, thereby affecting when and where these waves impact surface weather and climate. In recent years, studies on the atmospheric waveguide have gained popularity among the climate community due to its significant connection to extreme events. The investigation of waveguides can be traced back to early works, notably Hoskins and Karoly (1981), followed by Hoskins and Ambrizzi (1993) and Ambrizzi et al. (1995). This current study aims to extend previous research by examining the waveguide in the context of spatially and temporally varying mean flow. Most of the analysis is focusd on this issue.

This is a nice manuscript that uses refractive index as a perspective to understand atmospheric waveguide and its connection to stationary Rossby waves. In my opinion, it holds the potential to be considered for publication in a WCD. However, I have several major concerns about the methodology and interpretation of the results. I have listed my major comments below and would like to invite the authors to address them:

1. The separation of mean flow and perturbations is always a controversial issue when studying wave-mean flow interactions. This issue becomes even more critical when large-amplitude eddies appear in the mean flow (e.g., Wirth and Polster, 2021). However, the present study heavily relies on the separation method, and most of the findings are based on the assumption that the waveguide and Rossby waves are well-separated and independent. Therefore, I question the significance of the results, as many intraseasonal waveguide behaviors are actually reflected by long-lasting waves.
2. Regarding the methodology, using the traditional turning point perspective to identify the waveguide could be misleading, despite its extensive use in recent studies such as Petoukhov et al. (2013) and many subsequent papers. The limitations of this method have been thoroughly discussed by Wirth (2020). Therefore, the authors need to demonstrate the limitation of the method used here is nontrivial and confirm the appropriateness of the method.
3. I doubt about the characterization of the atmospheric circulation associated with the waveguide strength as "double jet streams" (Figure 6), as the zonal wind anomalies are only confined to a local scale. Additionally, as related to my major comment 1, long-lasting waves might play a role in this structure. Therefore, it is possible that the pattern seen in Figure 6 is not "double jet streams", but prominant Rossby wave activity itself.
4. The current study primarily focuses on the waveguide effect along the subtropical jet, based on the refractive index, which essentially represents the gradient of absolute vorticity. However, recent studies (e.g., Xu et al. 2019, doi: 10.1175/JCLI-D-18-0343.1; Xu et al., 2020, doi: 10.1175/JCLI-D-19-0458.1) have presented compelling evidence of the existence of stationary Rossby waves along the eddy-driven jet, where the waveguide effect arises due to the gradient of potential vorticity. As mentioned by the author herself, this important aspect has been neglected due to the limitations of the methodology used in this manuscript. The authors briefly touch upon this issue in the manuscript, but in my opinion, more in-depth discussion is required.

Citation: https://doi.org/10.5194/egusphere-2024-966-RC3
- AC2: 'Reply on RC3', Rachel White, 13 Jun 2024
  
  I thank the reviewer for their helpful comments, which will lead to improvements to the manuscript. More detailed responses to your major comments are given in the attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-966', Anonymous Referee #1, 26 Apr 2024

The paper investigates characteristics of Rossby waveguides in the Southern and Northern hemispheres (SH/NH) during summer and winter and relationships between waveguides and quasi-stationary wave amplitudes. Several recent studies emphasized that waveguides are related to high-amplitude waves but the causality between the two is still a matter of debate. The originality of the paper is to develop a method to detect systematically at each longitude and each time the presence of waveguide based on the detection of turning latitudes where the stationary wavenumber Ks of the barotropic Rossby wave dispersion relation is equal to the zonal wavenumber k. The stationary wavenumber has been introduced in Hoskins and co-authors papers but only applied to a time-mean flow. In the present paper, it is adapted to get waveguides as function of time. The stationary wavenumber is computed by defining a background zonal flow using a spatial and temporal filter of the zonal wind. The paper also introduces the notion of waveguide depth which is somehow close to the number of zonal wavenumbers for which a waveguide exists. Quasi-stationary wave amplitudes are computed by considering the amplitude of the wave envelope where the quasi-stationary wave is here defined as the deviation of the 15-day running mean meridional wind from its climatology for each wavenumber. The definitions of the waveguides and quasi-stationary waves amplitude are appropriate and well thought. But since the 15-day running mean is used for the computation of both the background flow and the quasi-stationary waves, it is the separation in spatial scale that makes the difference between the two parts of the flow (k<2 for the background flow and k between 4 and 15 for the quasi-stationary waves). Results show that waveguide frequencies are higher in summer than winter in the NH and more frequent in the NH than in the SH. It would be good to detail more the physical interpetation for those statistics (see main comments below). Composites of high and low waveguide depths indicate that high waveguide depths are associated with a double jet structure and in that sense confirm previous studies. However, I am not entirely convinced because they rely on Figures 6 and 7 where anomalous composites are shown so a double jet structure in zonal wind anomalies does not necessarily mean a more pronounced double jet structure for the high waveguide depth than for the low waveguide depth (see main comment below where I suggest to show the composites of the low and high waveguide depths separately). Then correlations between waveguide depths and wave amplitudes are investigated. Even though the correlations are weak, there are several regions and seasons for which the positive correlations are significant. It concerns the SH and the NH summer over the Atlantic and Europe. The results are interesting in themselves but it would be good to add some comments related to previous studies and also related to the maps of waveguide depths (see below for more details). Finally sensitivity tests made by changing some values of the parameters used for the waveguide detection show that the results are quite robust. I think changing the pressure level to detect waveguide could be also another sensitivity test worth making. To conclude, the paper is well written and well organized, the results are new and interesting. However I have several major comments that need to be addressed before I recommend publication of the paper.
Major comments:
a) Abstract: the notion of waveguide depth is obscure there. When I read the abstract I thought it was considering the depth in altitude. It would be good to add words to qualitatively define the waveguide depth. For me, the waveguide depth is closely related to the number of zonal wavenumbers for which the waveguide exists.
b) Introduction (lines 25 to 29). It would be good to add some physical interpretation of why people think there is a link between waves amplitude and waveguides. In my opinion, this is potentially because waves are not dissipated as there are no critical latitudes in a waveguide. But I am not sure this is what the papers cited in line 28 have argued.
c) Method: it would be good to highlight that the background flow and the waves are separated by the spatial scale (k<2 for the background flow and k between 4 and 15 for the quasi-stationary waves). Since the 15-day running mean is used for the detection of both the background flow and the waves, the reader might be confused by the separation between these two parts of the flow.
d) Section 4.1 and waveguide frequencies:

- before starting that section it would have been nice to show Ks for the time mean flow of JJA and DJF, i.e repeat Figures 3c of Hoskins and Ambrizzi (1993) and 11c of Ambrizzi et al (1995). Maybe it would be good to do it by considering the climatological flow for k<2 to be close to what is done in the present paper for the time-evolving waveguides. Such additional figures could help to better visualize the difference between summer and winter and between SH and NH. The argument made lines 160-165 to qualitatively explain why the summer NH has more frequent waveguides than the winter NH could be better understood by showing the time mean U and Ks for both seasons. Furthermore, maybe the additional argument is the fact that the jet is probably narrower in summer than winter and both the planetary vorticity gradient and relative vorticity gradient play a role in the difference between summer and winter.

- I am surprised that the SH has less waveguides than the NH as the double jet structure (separation between subtropical and eddy-drivent jet) is more marked there, at least in the climatologies.
e) Section 4.2: this is the part of the results where I am less convinced by the conclusions. For instance, Figure 6a shows an anomalous tripolar pattern in zonal wind when computing the difference between high and low waveguide strengths. This anomaly could be the result of different changes: a more pronounced double jet structure is one possibility but it could result from a widening of the jet or some latitudinal shifts. So it would be very nice to compare composites of high waveguide strengths and low waveguide strengths separately before (or rather than) showing the difference.
f) Section 5: It is suprising that the correlations are strong in the Atlantic and over Asia and not in the Pacific while the waveguide depths are similar in the North Atlantic and North Pacific. What would be a possible explanation for that ? Or if you do not have hypothesis it would be nice to comment these results by referring to other studies. Were the studies on the relationship waveguide-wave amplitude focused in the North Atlantic and Asian regions. Do you know studies that also considered that relationship in the North Pacific ?
g) Sensitivity tests: I think it would be good to have a sensitivity test by changing the mean pressure level (e.g. 500 hPa?). Held et al. (1985) computed a barotropic equivalent level near 425 hPa and Charney (1949, see section 6) found a barotropic equivalent level closer to 550-600 hPa.
Minor comments:
1) Line 125: maybe add "temporally and zonally filtered U following the method described in section 2.1"
2) Line 130: it would be good to have a qualitative description of what the waveguide depth means. We understand mathematically in the main text but this would be useful for the abstract.
3) Line 134 and thereafter: why is cut-off latitude used rather than turning latitude ? I think turning latitude is the classical term
4) Figure 2: what are the black contours. Zonal wind at 300 mb ? Same question for Figure 4 but they disappear in Figure 5.
5) Line 178: I do not understand the end of the sentence "latitudinal cut-off ... latitude of the jet".
6) Lines 187-188: I do not understand what is meant by "Latitudes are weighted equally". Do you mean that multiplication by the cosine of latitude is applied to do the regional averages?
7) Line 196: I would add "a 'double jet structure' in anomalies is present
8) Lines 204-206: here again it would be better to see both composites rather the difference between composites
9) Figure 7: the magenta contour is difficult to see in the red-brown areas.
10) Lines 260-265: Here the importance of narrow jet is highlighted but this has not been the main argument mentioned in the main text when describing the difference between summer and winter in the NH (lines 160-165). The story of the equatorward displacement of the jet was emphasized. So please be more precise why there is a difference between summer and winter. How important are the jet width and latitude in that story ?
11) Caption Figure 9: please provide units for dimensional parameters.

Citation: https://doi.org/10.5194/egusphere-2024-966-RC1
- AC1: 'Reply on RC1', Rachel White, 13 Jun 2024
  
  I thank the reviewer for their helpful comments and suggestions for improving the paper – your comments will lead to a substantial improvement in the manuscript. I agree with all of your suggestions, and will implement them in a revised manuscript. More detailed responses to your major comments are given in the attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC1
RC2:
'Comment on egusphere-2024-966: Some serious issues', Volkmar Wirth, 06 May 2024

see attachment

Citation: https://doi.org/10.5194/egusphere-2024-966-RC2
- AC3: 'Reply on RC2', Rachel White, 14 Jun 2024
  
  I would like to thank Volkmar for his review, as it has helped me think more deeply about, and subsequently refine, some of the points of the paper, which will lead to substantial improvements in the manuscript. The attached pdf responds to his major comments, and I believe a revised manuscript would be able to address all of his concerns.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC3
RC3:
'Comment on egusphere-2024-966', Anonymous Referee #3, 06 May 2024

The atmospheric waveguide has a profound influence on the propagation path of stationary Rossby waves, thereby affecting when and where these waves impact surface weather and climate. In recent years, studies on the atmospheric waveguide have gained popularity among the climate community due to its significant connection to extreme events. The investigation of waveguides can be traced back to early works, notably Hoskins and Karoly (1981), followed by Hoskins and Ambrizzi (1993) and Ambrizzi et al. (1995). This current study aims to extend previous research by examining the waveguide in the context of spatially and temporally varying mean flow. Most of the analysis is focusd on this issue.

This is a nice manuscript that uses refractive index as a perspective to understand atmospheric waveguide and its connection to stationary Rossby waves. In my opinion, it holds the potential to be considered for publication in a WCD. However, I have several major concerns about the methodology and interpretation of the results. I have listed my major comments below and would like to invite the authors to address them:

1. The separation of mean flow and perturbations is always a controversial issue when studying wave-mean flow interactions. This issue becomes even more critical when large-amplitude eddies appear in the mean flow (e.g., Wirth and Polster, 2021). However, the present study heavily relies on the separation method, and most of the findings are based on the assumption that the waveguide and Rossby waves are well-separated and independent. Therefore, I question the significance of the results, as many intraseasonal waveguide behaviors are actually reflected by long-lasting waves.
2. Regarding the methodology, using the traditional turning point perspective to identify the waveguide could be misleading, despite its extensive use in recent studies such as Petoukhov et al. (2013) and many subsequent papers. The limitations of this method have been thoroughly discussed by Wirth (2020). Therefore, the authors need to demonstrate the limitation of the method used here is nontrivial and confirm the appropriateness of the method.
3. I doubt about the characterization of the atmospheric circulation associated with the waveguide strength as "double jet streams" (Figure 6), as the zonal wind anomalies are only confined to a local scale. Additionally, as related to my major comment 1, long-lasting waves might play a role in this structure. Therefore, it is possible that the pattern seen in Figure 6 is not "double jet streams", but prominant Rossby wave activity itself.
4. The current study primarily focuses on the waveguide effect along the subtropical jet, based on the refractive index, which essentially represents the gradient of absolute vorticity. However, recent studies (e.g., Xu et al. 2019, doi: 10.1175/JCLI-D-18-0343.1; Xu et al., 2020, doi: 10.1175/JCLI-D-19-0458.1) have presented compelling evidence of the existence of stationary Rossby waves along the eddy-driven jet, where the waveguide effect arises due to the gradient of potential vorticity. As mentioned by the author herself, this important aspect has been neglected due to the limitations of the methodology used in this manuscript. The authors briefly touch upon this issue in the manuscript, but in my opinion, more in-depth discussion is required.

Citation: https://doi.org/10.5194/egusphere-2024-966-RC3
- AC2: 'Reply on RC3', Rachel White, 13 Jun 2024
  
  I thank the reviewer for their helpful comments, which will lead to improvements to the manuscript. More detailed responses to your major comments are given in the attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2024-966-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Rachel White on behalf of the Authors (18 Aug 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (31 Aug 2024) by Nili Harnik

RR by Anonymous Referee #3 (16 Sep 2024)

RR by Anonymous Referee #1 (16 Sep 2024)

For final publication, the manuscript should be

accepted as is

accepted subject to technical corrections

accepted subject to minor revisions

reconsidered after major revisions

rejected

Were a revised manuscript to be sent for another round of reviews:

I would be willing to review the revised manuscript.

I would not be willing to review the revised manuscript.

Suggestions for revision or reasons for rejection

The paper has been deeply modified since the first submission. The paper now contains a systematic comparison between two notions of waveguides: one based on the classical stationary wavenumber, which was present in the initial submission, and the other on potential vorticity gradient that has been recently introduced by Wirth and Polster papers and inserted in the revised version of the paper. I think this comparison made the paper much more attractive and I enjoyed reading it. Additionally, all my comments have been carefully considered by the authors. Therefore, I recommend publication of the paper once the following minor suggestions have been taken into account:

1) The waveguide strength is a new diagnostic on which many figures rely on but its definition is not entirely easy to find. Line 165, the maximum waveguide strength W_s=K_s-k is introduced. But in order to build composites from Figures 4 to 9, the text says (line 218) that the waveguide strength is the sum of all K_s-k for k between 4 and 9. Why did you choose the sum of K_s-k for the composites and not the maximum K_s-k ? Since all the composites rely on that parameter it would be good to introduce a mathematical notation for that parameter. This would help to clarify the captions of Figures 4 to 9. Different wordings are used to say the same thing: in Figures 4 to 7 "strongest waveguide presence" is used, in Figure 8 "strongest average waveguide strength", Figures B1-B5 "strongest ... average waveguides". Please keep the same wording or use a specific notation.

2) Line 227: "in the appendix B"

3) Line 270: I do not understand the end of the sentence "however, these results .... background flow"

4) There are two groups of sentences in the discussion (lines 418-422) and in the conclusion (lines 434-438) saying roughly the same thing. I would suggest to suppress one of the two.

Hide

RR by Volkmar Wirth (27 Sep 2024)

For final publication, the manuscript should be

accepted as is

accepted subject to technical corrections

accepted subject to minor revisions

reconsidered after major revisions

rejected

Were a revised manuscript to be sent for another round of reviews:

I would be willing to review the revised manuscript.

I would not be willing to review the revised manuscript.

Suggestions for revision or reasons for rejection

The author has revised the manuscript very substantially. She impleented a suggestion from my previous review and included a comparison with the novel rolling zonalized PV waveguide definition of Polster and Wirth (2023). The paper has more or less turned into a comparison between two different definitions of (zonally varying) waveguides on a statistical level. I think that this is good progress, and the results are interesting and worth a publication. In most parts the text is very well written, and the figures are very well prepared.

However, I still have two major issues regarding the interpretation (see below). Either the author can give convincing arguments in defense of her own interpretation, or she would have to reframe her interpretations into a different direction. If either of these is done satisfactorily, I suggest that the paper can be published.

Mainz, 27 September 2024
Volkmar Wirth

Major comments:

A key result of the revised manuscript is the fact that the two different waveguide definitions are associated with rather strong differences in their climatological/ statistical properties. As I said, that’s interesting and worth a publication, given the fact that the Ks-waveguide has been used extensively in the past. However, I disagree with the author’s interpretation saying that “it is unclear which [of the two] is the more ‘accurate’ description [of reality]”; such or related statements appears several times in the text (occasionally somewhat indirectly). First of all, the Ks-definition is based on assumptions that are badly violated in reality (Wirth 2020). It does, therefore, not come as a surprise that the waveguidability diagnosed with the Ks-algorithm is unable to explain properties of true waveguidability (Wirth, 2020). Moreover, Wirth and Polster (2021) have shown that the Ks-method is prone to artefacts in the presence of large-amplitude waves. In fact, the current work corroborates the existence of such artifacts by showing that certain “double jet features” co-occur with blocking-like flow patterns, and the abstract of this manuscript says that the “Ks-methodology…. does not sufficiently separate waves from the background”. Given this body of earlier work and the authors own statement in the abstract, a more logical interpretation of the substantial differences between the two methods would be saying that the current work corroborates earlier indications that the Ks-definition may be inappropriate to diagnose waveguides.

My second issue is related to the first issue. It concerns the authors “explanation” (“this can be understood…..”) of the differences between the two waveguide detection algorithms, most notably the fact that the definition of Ks implies a division by the wind speed U, while the PV-gradient method does not. Obviously, the division by U explains some of the differences between the two statistics on an algorithmic level. However, the current text conveys the impression that both methods are equally valid, suggesting that the jury is out which of the two methods is better suited (see above, my first major issue). More explicitly, in her reply the author says: “We do not consider this [i.e., the differences in the seasonal and hemispheric behavior between the two waveguide definitions] necessarily to be a weakness of the Ks-waveguides, however, as the results are consistent with the mathematics that the zonal wind strength appears in the denominator of the Ks equation”. I disagree, because this argument lacks logic. Of course, the differences in the statistics can be traced back to differences in the algorithms, but this exercise does not make any statement about the appropriateness of an algorithm to represent reality. For the reasons given above, I think that the Ks-algorithm is not a good waveguide diagnostic. A proof that an algorithm does what is it supposed to do cannot save it from being inappropriate.

Minor comments:

Line 5: what is an “objective algorithm”?

Lines 6,7: given that the concept of “waveguidability” is more appropriate than a binary decision between “waveguide” or “no waveguide”, such a number (“40% of all days”) is meaningless, because it sensitively depends on the threshold chosen in the definition of a waveguide.

Line 34: does this argument apply only to quasi-stationary waves, or does it also apply to travelling waves?

Line 44, “there are two main methods….”: this formulation suggests that both methods are well established and equally valid. I would argue that this is not the case: the Ks-method was shown in earlier papers to be fraught by a number of issues (see my first major issue)

Line 61, “without this clear separation….”: I would argue that without a scale separation, the entire concept of a waveguide breaks down, which is much worse than what is suggested by the simple phrase “care must be taken”.

Line 180, “however”: this sentence lacks logic (see my second major issue). The word “however” suggests that the argument that follows solves the riddle that was given in the previous sentence. The previous sentence refers to the fact that summer has generally weaker jets than winter, and that according to previous work weaker jets are weaker waveguides. The argument given in the following sentence CANNOT resolve this issue, as it only shows why the Ks theory yields a stronger waveguide in summer than in winter; one might just as well conclude that for this reason Ks-theory is inappropriate, because it contradicts the previous wisdom that weaker jets are weaker waveguides.

Line 183, these idealized tests: I do not quite understand the result of these tests, because they contradict the following simple asymptotic argument. If you increase the strength of the jet and leave the width of the jet constant, I expect that Ks saturates to some finite value, but it should not decrease. Basically, in this limit one can neglect the first term on the right-hand side of (2), and Uyy divided by U essentially yields a meridional wavenumber that characterizes the meridional width of the jet.

Line 213: I suggest to change “much more” to “more”

Line 214, “U in the denominator…”: again, this only makes plausible that algorithmically the differences are due to the U in the denominator, but it does not make any statement about which of the two options is more realistic (see my second major issue). Similarly on line 345 and 409, “…. This can be understood…”: yes, algorithmically the difference can be “understood”, but the more important question would be which of the two definitions is more realistic. You simply write that “further study is required”; however, I would argue that the Ks-definition has already accumulated a significant amount of criticism, including the fact that the underlying assumptions are badly violated (see my first major issue). For that reason, one could conclude from these differences that the Ks-definition is less realistic. In your text you make the reader believe that the jury is out (see also lines 356, 357, or on line 411 “it is unclear which is the more ‘accurate’ description….”), but in my eyes is really isn’t.

Line 237, “…. Enhanced zonal wind inside the waveguide region”: I cannot verify this statement on panels 4c, g, i

Line 248: could you point to those panels in Fig 4 where this “double jet feature” is clearly visible?!

Line 303: suggest to change “much stronger”  “stronger”

Line 432,433: I disagree. I think here one can dare a statement about causality. One important advantage of the rolling zonalization approach is the fact that the so-obtained background state is (almost) independent of the waves that may be present on the background state (see Wirth and Polster 2021). For this reason, one may at least hypothesize that the strength of the waveguide has an impact on the strength of the waves, but not vice versa!

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ED: Publish subject to revisions (further review by editor and referees) (02 Oct 2024) by Nili Harnik

AR by Rachel White on behalf of the Authors (15 Dec 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (17 Dec 2024) by Nili Harnik

RR by Volkmar Wirth (06 Jan 2025)

For final publication, the manuscript should be

accepted as is

accepted subject to technical corrections

accepted subject to minor revisions

reconsidered after major revisions

rejected

Were a revised manuscript to be sent for another round of reviews:

I would be willing to review the revised manuscript.

I would not be willing to review the revised manuscript.

Suggestions for revision or reasons for rejection

Recommendation: Accept with very minor revisions

The manuscript has been revised very thoroughly. The revised version contains a comparison between two different methods to diagnose Rossby waveguides. Apparently, the two diagnostics yield rather different results in several aspects such that at least one of them must be considered as unreliable or even inappropriate. In my eyes, the revised text gives a fair account of interesting new results and puts them well into the context of previous published work. I have only a few very minor suggestions that may help to polish the manuscript into a final version.

January 6, 2025
Volkmar Wirth

Minor comments

Abstract line 6 and main text lines 86/87: The text reads as if the technique of rolling zonalization precludes the computation of Ks-waveguides. This is not really true. Assuming a balance condition, the knowledge of PV allows one to compute the wind through so-called PV inversion. Of course, PV inversion in the framework of the primitive equations is cumbersome (see e.g., Nakamura and Solomon 2011), but at least in principle it would be possible. Having said this, I do NOT suggest that this should be done here.

Figure caption Fig 2: Units of \nabla ln PV must be m-1

Line 185, the definition of w_s: this seems somewhat unclear, since K_s is a function of latitude. Are you considering the maximum value of K_s-k over the waveguide, i.e., the range of latitudes where K_s>k?

Line 257: the formula given for W_s is somewhat ambiguous: do you mean the sum of (K_s-k) or do you mean the (sum of K_s) minus k?

Line 283, what is the “second meridional gradient”? Do you mean the second derivative of U in the meridional direction?

Line 348: what is an “in-season seasonal cycle”?

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ED: Publish subject to minor revisions (review by editor) (11 Jan 2025) by Nili Harnik

AR by Rachel White on behalf of the Authors (01 Feb 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (03 Feb 2025) by Nili Harnik

AR by Rachel White on behalf of the Authors (13 Feb 2025)

Journal article(s) based on this preprint

16 May 2025

Temporally and zonally varying atmospheric waveguides – climatologies and connections to quasi-stationary waves

Rachel H. White and Lualawi Mareshet Admasu

Weather Clim. Dynam., 6, 549–570, https://doi.org/10.5194/wcd-6-549-2025,https://doi.org/10.5194/wcd-6-549-2025, 2025

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Rachel H. White

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Mid-latitude atmospheric jet streams sometimes create 'waveguides', thought to increase the chance of quasi-stationary waves — atmospheric circulation patterns that lead to extreme weather events. I describe a new algorithm for identifying atmospheric waveguides, and show maps of waveguide frequency and strength. Waveguide strength is associated with an increased probability of quasi-stationary waves, although not in all regions; the connection is particularly strong over Europe during summer.


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