the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Feb 2025
A Novel Identification Method for Stratospheric Gravity Waves in Nadir Viewing Satellite Observations
Abstract. Atmospheric gravity waves (GWs) are an important mechanism for vertical transport of energy and momentum through the atmosphere. Their impacts are apparent at all scales including aviation, weather, and climate. Identifying stratospheric GWs from satellite observations is challenging due to instrument noise and effects of weather processes, but they can be observed from nadir sounders such as the AIRS instrument onboard Aqua. Here, a new method (hereafter ‘neighbourhood method”) to detect GW information is presented and applied to AIRS data. We describe the concept of the neighbourhood method and use it to investigate GW amplitudes, zonal pseudomomentum fluxes, and vertical wavelengths over 5 years of AIRS data. We compare these results to those calculated from GWs detected using another widely used method based on a defined amplitude cutoff. The neighbourhood method reveals GW patterns in seasonal means that are not visible when using the amplitude cutoff method. Time series analysis suggests that GWs have a larger impact than was previously analysed from the amplitude cutoff detection method. ∼ 25 % of waves detected using the neighbourhood method have amplitudes lower than is visible using the amplitude cutoff method. Three regions are studied in greater depth: the Rocky Mountains, North Africa, and New Zealand/Tasmania. GWs detected using the neighbourhood method have realistic wave phase propagation angles, which are consistent with surface-levels winds from ERA5 climatological reanalyses. Using the neighbourhood method produces new statistics for regional and global GW studies, which compares favourably to the amplitude cutoff GW detection method.
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RC1: 'Comment on egusphere-2025-455', Anonymous Referee #1, 11 Mar 2025
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Review of A Novel Identification Method for Stratospheric Gravity Waves in Nadir Viewing Satellite Observations by Peter Berthelemy et al. (2025)
General comment:
The authors of this paper present a new methodology for identifying GWs in AIRS observations in the stratosphere. They use a well-known method based on the 3D Stockwell transform and extend it by adding a filter that requires the horizontal wavenumber to remain approximately constant over a defined area. The application of this filter enables the detection of GWs with amplitudes lower than the thermal noise of the instrument and excludes wave amplitudes that are associated with atmospheric noise in an outdated approach. The authors conduct statistical analyses over a period of five years and compare the new methodology with the outdated one. It becomes clear that the new methodology offers many advantages. Regarding methodology and results I would recommend to publish this work. However, several issues regarding the explanation of methods and contextualization of results need to be resolved, which warrants a major revision.
My main points of criticism are:
1. Clarity and precision
The manuscript contains ambiguities in many places. Often, general phrases are used, unclear links are made, or the sentences are overly complex. This makes it difficult to understand the text. Unfortunately, the references are also often not chosen appropriately.
2. Definition of key terms
At the core of the paper, three different methodologies for determining GW amplitudes, momentum fluxes, and vertical wavelengths are compared. Unfortunately, the three methodologies are not described in sufficient detail. A brief comparison, for example using a table, would enhance the paper.
3. Treatment of measurement uncertainties
While it is clear that the new methodology is more robust against the Gaussian noise of the instrument, it is not explained how the measurement uncertainty affects the spectral analysis and hence, determination of wave amplitudes, wavelengths, and ultimately the momentum flux.
In the following you will find my detailed review. I hope for a good discussion and look forward to seeing the results soon in an improved and clarified form that does justice to the hard work that has been put into this.
1. Introduction
Short but good. Quickly funneling down from “gravity waves are important” to “We present a novel method to identify GWs in AIRS data”. However, often times it is not clear what the authors are getting at. So, the introduction could need some polishing. In that sense, have a look at my suggestions below.
Line 18: Please add at least one reference for every mentioned impact of GWs.
Line 19-20: Technically not wrong, however, I suggest to rephrase the sentence in the following way: “GWs propagate throughout the atmosphere, but have their largest effects at higher altitudes, as according to linear theory conservation of energy and the exponential drop in density enforce their amplitudes to grow exponentially with height.”
Line 21: I do not agree with the statement that “by far the most important” mechanisms are the excitation by orography and deep convection. For one, it depends on the altitude range one is interested. Second, these are “by far the most studied” mechanisms. Does that mean, they are the most important mechanisms? I’d suggest to weaken that statement a bit or find a proper reference quantifying the dominance of these mechanisms over the other.
Line 21: The Smith and Lyjak (1985) reference is not a good one for orographic GWs. There are plenty better ones, like the very first works by Kuettner from the 1940s, Dörnbrack et al. (2002), Ehard et al. (2017), Hecht et al. (2018), Pautet et al. (2021), etc.
Line 23: Please add a more specific reference like Fritts and Luo (1992).
Line 24: Please add a reference for non-linear wave-wave interaction.
Line 25-29: That is a bit irritating. I’d suggest to simply state: “These diverse mechanisms can lead to large differences in the wave properties, with the vast majority of GWs having horizontal wavelengths in the range of a few kilometres up to thousands of kilometres (Choi et al., 2012; Kalisch et al., 2016; Trinh, 2016; Hájková and Šácha, 2023) and periods from hours to days (Dunkerton, 1982; Baldwin et al., 2001; Ern et al., 2021).”
Line 35: Please change that to “This allows for 3D measurement of temperature and hence, detection of GWs.”
Line 37: I suggest to rephrase this line in the following way: One problem previous studies were dealing with is the proper filtering and identification of GW signatures in AIRS temperature data.
Line 37-40: At this point it’s not clear what an “AIRS temperature perturbation footprint” is. Maybe it's more clear to say: "Hoffmann et al. (2013) calculated the temperature variance in a running fashion over regions of 100km radius and compared the result with a predefined threshold in order to identify GW signatures."
Line 40-42: I suggest to say: “Hoffmann et al. (2016) improved on this by taking variance differences between two boxes, one over an orographic hotspot and the other upwind of this hotspot to define a background or reference variance.”
Line 42-43: Please erase “This was used to identify whether orographically generated GWs exhibited larger variances downstream of the mountain than upstream.”
Line 46-47: Please change to: “This resembles a continuous wavelet transform except for the fact that the complex phase is kept constant.”
Line 48-49: Please erase “Such an analysis assumes that a wave is present at all locations in the data, and so will fit wave properties even if there is no wave.”
Line 49-54: Please rephrase these lines. The term “voxel” was not properly introduced yet and it remains unclear what it refers to. Also, the “amplitude-cutoff method” is not properly introduced. Is that the “amplitude-cutoff approach” by Ern et al. (2017)? Please make more clear how the ST separates between GW and noise features. It seems like the convolutional nature of the ST considers multiple independent data points and therefore the noise floor is lowered, right?
Line 55-56: S-transform was already introduced. Please abbreviate it with “ST”.
Line 56: Please be more concrete here and tell the reader what kind of wave properties you have in mind.
Line 58: I suggest to use “constant” instead of “stable” in that context.
2. Data
Perfect as is.
3. Methods
3.1. Preprocessing
Very well written. Please highlight that a granule is a 3D data array with 128 x 135 x ??? pixels and introduce the term voxel in that context. Also, the bias mentioned in Section 4.2 surprised me that late in the manuscript. Since you mention the sensitivity to GWs with wavelengths in the range 30/80km to 600km, I would like to see a more precise statement maybe about the sensitivity of zonal and meridional wavenumbers separately.
3.2. S-Transform Method
This paragraph is too short and lacks clarity. Please recall what the S-Transform is and state the equation, how to compute the ST. How is the wavelet normalized? Do the results differ significantly when using another wavelet normalization?
Line 104: Please explain, how you characterize the properties of dominant waves in each voxel. Why is the ST applied to two and not one granule at a time?
Line 106: Be concrete. What is meant by “the full three-dimensional dataset”?
Line 107-108: How exactly do you constrain the 2D+1ST approach using only those spatial frequencies with the greatest spectral magnitude in the 3DST output? Is that documented in another publication?
Line 114: It might be worthwhile to mention that Reichert et al. (2021) found that 20% of the detected GWs are apparently downward propagating in the stratosphere over the Southern Andes.
Line 117-119: These two sentences seem contradictory. Please rephrase. Also, this is not a good place to mention “neighborhood method” for the first time in the manuscript since it is not explained yet.
3.3. Wave Detection
Line 121-122: Not a good opening. The reader doesn’t know what the “neighborhood method” is, yet. State the problem and how you are gonna solve it.
Line 128-129: It is suggested to rephrase these lines for clarity: “The ST method is applied to the concatenated granules providing wavenumbers along-track, cross-track and in the vertical as functions of space. After that, the satellite track referenced wavenumbers are projected into zonal, meridional, and vertical wavenumbers k, l, and m.
Line 136: Please change as suggested: “Regions where wavenumbers are very similar in a 5x5 neighborhood, which is consistent with our requirement for an extended GW field.
Line 147: Please use either “point”, “pixel” or “voxel” consistently.
Line 147-155: Please create a subsection for the computation of momentum flux.
Line 153: g=9.69m^2/s^2 at 39km altitude. (Just for physical correctness, I am not asking you to redo the analysis.)
Line 153: Is N measured or assumed?
Equation 1: This is a simplification of Ern’s formula. Please argue why you can use this simplified version.
4. Results
Please change the section title to “Results and Discussion”.
Line 159: Please change the citation style.
Line 161-164: Please erase “Specifically, it shows the mean amplitudes of detected GWs during local winter months, November-February (NDJF) for the Northern hemisphere and June-September (JJAS) for the Southern hemisphere. The difference (g,h,i) and ratios (j,k,l) between the two methods are also presented.” This improves readability since this information is in the caption of the Figure.
Line 168: I would expect the mean of the noise to be zero. Do you mean the mean of the noise amplitude?
Line 173: I wouldn’t use “especially” here, since both “GW belts” nicely show up in the maps.
Line 175-176: The statement makes sense. However, please deliver more proof that wave activity is more persistent over the Antarctic peninsula. Figure 12 in Wright et al. (2017) shows an enhanced Gini coefficient for southern hemispheric winter months over the Antarctic peninsula, indicating not constant but intermittent GW activity! Therefore, I would expect a stronger deviation between the amplitude cutoff and the neighborhood method.
Line 180-186: Concerning Figure 3: Please provide a linear color scale to enable a fair comparison with Figures 6 and 7 from Hoffmann et al. (2017).
4.1. Histograms of Latitude Bands
Line 188-189: You never properly introduced the amplitude cutoff method. (I’m still assuming it is the amplitude-cutoff approach by Ern et al. (2017)) Now a third method is mentioned without introducing it, the ST. Please provide proper descriptions of the three different methods in the methods section.
4.1.1. Amplitude (A)
There is not a single reference in this subsection. Please provide some contextualization. The novel neighborhood method retrieves smaller wave amplitudes in the tropics than the old amplitude-cutoff method. Is that closer to reality? Is that in better agreement to other studies?
4.1.2. Zonal Momentum Flux (MFx)
How is the wavelength and hence momentum flux derived in the case of the amplitude-cutoff method?
Line 209: A bit irritating, maybe just say: “When the GW’s horizontal phase speed equals the horizontal wind speed […]” and cite Lindzen (1981).
Line 216: instead of “the Hindley study” use \citet{Hindley_reference}.
Line 222-224: That is not clear. I understand that the 3DST samples discrete angles, however, the 2D+1ST computes the vertical wavelength from a phase shift. So, technically, an infinite vertical wavelength would be retrievable. What do you mean by “uncertainty bounds” in that context? Please elaborate. In case of very long vertical wavelengths, the Ern formula (equation 1) does not hold anymore since the wave’s intrinsic frequency approaches N and the momentum flux drops to zero.
Line 226: GW activity is not a vector quantity and cannot be directed eastward/westward. Please change that.
Line 227: Please change “the Hindley et al. (2020) study” to \citet{Hindley_reference}.
Line 228: Please be more specific.
Line 231-233: Please change that to “The low percentage of data close to 0mPa can be attributed to the fact that the neighborhood method cannot identify waves with arbitrary small amplitudes due to the noise floor of AIRS. Another explanation might be that the waves mostly propagate in zonal direction and hence, k is never close to 0.” (Although we will later find out that there is a bias problem with zonal wavenumbers.)
4.1.3. Vertical Wavelength
Again, please provide contextualization.
Line 237: Please change “curves” to “distributions”.
Line 241: These winds allow westward propagating or stationary GWs to
propagate into the stratosphere. Their stratospheric penetration does not depend on their vertical wavelength.
4.2. Regional Studies
Line 246: Misleading reference of Zhang et al. (2013). Better use Rapp et al. (2021) and Reichert et al. (2021).
Line 253-258: Erase everything except “Figure 6 shows the annual cycle of GW activity over each region.” The other information is in the caption.
Line 261-263: Change to “This is due to the stratospheric wind reversal close to 20km in summer limiting the vertical propagation of orographic GWs.”
Line 272-273: It can be excluded that the signal is due to orographic GWs. But please elaborate on why more stable winds or the Southern Ocean storm belt are responsible for enhanced summertime lower stratospheric wave activity over New Zealand.
Line 286: Use \citet{Hindley_reference}.
Line 290-293: Erase except for “We next consider Figure 7, which shows polar histograms of wave phase propagation angle over the three regions during wintertime.“ The other information is given in the caption.
Line 294: Why do you expect propagation against the background wind?
Line 295: is “eastward” attributed to the wave propagation or the background wind?
Line 315-320: What a kick in the teeth. This issue should be mentioned earlier in the manuscript. Moreover, effects on the momentum flux retrieval should be discussed. Does this lead to an underestimation of momentum flux? Could this problem be resolved using only one granule at a time?
5. Conclusions
Line 324: I’d prefer “constant” or “homogenous” over “stable” in that context.
Line 332: Be more specific. How large is the fraction? Give me a number.
Line 333: Be more specific. How much larger are wave amplitudes on average?
Line 335: The color scale ranges from -1 to +1 Kelvin. I cannot follow where the maximum amplitude difference is 3K.
Line 346: What do you mean by “reliable ST output”?
Citation: https://doi.org/10.5194/egusphere-2025-455-RC1 -
RC2: 'Comment on egusphere-2025-455', Anonymous Referee #2, 13 Mar 2025
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This paper proposes a method for improved noise removal and GW identification from satellite observations, by utilizing the spatial homogeneity of spectral wave characteristics. This method enables the detection of small-amplitude waves that were previously excluded by the existing amplitude-cutoff method to avoid noise contamination. The identified waves also exhibit a realistic seasonality with asymmetry in the direction of zonal momentum flux, which is highly encouraging. I recommend this paper for publication after revision, considering the following issues .
- Discrepancy with the literature. The advantages of the proposed method are demonstrated through a comparison with the results from the existing amplitude-cutoff method presented together. However, these results appear largely unrealistic in terms of phase direction. This contrasts with previous studies that have employed similar methods and reported more reasonable results. For more details, please see Specific comments on Figs. 4 and 7 below.
- Statistics including no-wave events. It would be valuable to assess the amplitude and momentum flux averaged over all observations including no-wave events (with zero amplitude and momentum flux where waves are absent). However, the results presented in this study are averages only over detected cases. This approach limits its applicability to GW parametrization and makes it less straightforward to evaluate the GW impact on circulation. I recommend including results that incorporate no-wave events. Additionally (and optionally), including no-wave events in the statistics could provide valuable insights into wave intermittency, particularly since the proposed method effectively remove noises without artificially truncating all small-amplitude signals.
- There are several instances where the explanations of the presented results lack clarity (see Specific comments below). These should be clarified to ensure better understanding of the findings.
[ Specific comments ]
L9-10: Examining the GW impact requires the results integrated over all observations including no-wave events (see General comment #2). In the following sentence (L10-11), it is stated that small-amplitude waves can be additionally detected by the new method, which partly supports the argument in L9-10; however, how much noises were falsely detected as waves in the existing method (leading to an overestimation of GW impact) has not been presented in the current manuscript.
L13 “consistent with surface-levels winds”: I found several places in the main text where the stratospheric winds are discussed, but could not find a discussion with surface-level winds.
Fig. 1: The unmasked regions in panel (d) are slightly larger than those in (c). Has the neighbourhood been unmasked in (d) ? If so, this information should be included somewhere around L141. If this is not the case, please provide the reason for the different sizes.
L132: It should be clarified whether the absolute difference is in wavenumber vectors or in each of k and l.
L135 “C”: I would expect that a more broadly effective tolerance might be relative to the horizontal wavenumber (e.g., C ~ kh / 10, or so) rather than a constant for any waves. Is this constant approach because AIRS-detectable GWs have a limited range of wavelength spectrum ?
Eq. (1): This seems to omit the minus sign on the right-hand side. (m < 0 in the authors’ convention: L114)
L172: From here onward, the detected GW activity is often discussed in relation to the polar jet. At least once here, please provide a brief description of how the GW detection is linked to the jet. Does this refer to upward refraction by the jet, which increases vertical wavelengths, making them more detectable by AIRS ?
Fig. 4: It is very encouraging to see the realistic asymmetry in the direction of zonal momentum flux derived using the new method. On the other hand, in the results of the amplitude-cutoff method, it is surprising to see that eastward/westward momentum fluxes are rather symmetric in the extratropics. This seems to contradict previous studies that have shown the realistic direction of zonal momentum flux using the amplitude-cutoff method (e.g., Hindley et al., 2020). What am I missing ? In the authors’ work, the advantages of the new method are demonstrated by comparing it with the amplitude-cutoff method shown together. If the latter is not fully representative of others’ results in the literature in some way, that should be explicitly stated.
L203-204 “during austral winter, …”: What is discussed here seems to be true in both winters.
L214: Please clarify the levels: near-surface or stratospheric winds ?
L229: (1) Because the period of 2010–2014 fully covers two QBO cycles, I would not expect to see the QBO effect in the statistics integrated over this period if this effect simply refers to QBO-phase dependence. Or, if it refers to another aspect (e.g., phase asymmetry or some seasonality?) of the QBO, this should be clearly described to justify the attribution to short vertical wavelengths. (2) Again, it was nice to see the realistic asymmetry in the direction of momentum flux with seasonal dependence. Therefore, if it is also possible to include a result showing GW responses at ~39 km (or any other level) to the QBO, that would be great. Comparing any given month in 2012 to the same month in 2013 (or, even the 2012 annual mean to the 2013 mean) might be interesting, as the months in 2012 are dominated by stronger easterlies in the QBO domain, compared to those in 2013. However, this suggestion is optional, as such a result could be subject to uncertainty due to the limited statistics.
L239-241: There is an inconsistency in logic between these two sentences. The first sentence attributes the long vertical wavelengths to the strong winds. However, the second sentence suggests that such waves with long vertical wavelengths already exist and they need that favorable wind condition (strong winds) to reach the stratosphere. Please re-write these sentences.
Fig. 6 caption “Histograms for each day”: Does this mean daily-mean values counted into monthly bins or shorter-term (instantaneous?) values into daily bins ?
L263: “This also indicates that these regions have similar drivers of GWs”: This argument seems to be logically weak, as different sources could exhibit similar seasonality (e.g., being more active in winter). Additional evidence or reference would be needed to support the claim that the GW sources are similar across these regions.
L268-270 “On average, ...”: This information, which refers to the average rather than local or seasonal features, would align better with Fig. 4. I suggest moving it to Sect. 4.1.
L273: While the cited reference (Chapman et al., 2015) explained the interaction of the Southern Ocean storms with topography, I could not clearly find an explanation for why such an interaction is weaker with the Rocky Mountains.
L278 “as discussed in Figure 4”: I though that the lack of near-zero flux discussed in Fig. 4 (L231-233) was for the results using the neighbourhood method (where very small amplitude noises were filtered). However, the current paragraph explains the amplitude-cutoff results. The lack of near-zero flux in the amplitude-cutoff results shown in Fig. 4 (although I am not sure whether it was discussed) may be due simply to the cutoff. Consider clarify or adjust the text to avoid potential confusion.
L284-287: (1) Logically, the use of a cutoff cannot be the reason for detecting more waves of low amplitudes (as it cuts off). The neighbourhood method filtered the low-amplitude noises, leading to relatively larger mean fluxes. (2) I guess MFx in this line refers to the net zonal momentum flux, as this is the quantity presented in Hindley et al. (2020). The authors have showed the predominance of westward momentum fluxes over eastward momentum fluxes in winter (e.g., ~88% over the Rocky Mountains), while this was not the case for the amplitude-cutoff based results (please also see my comment on Fig. 4 above). If this was also the case in Hindley et al., where the amplitude-cutoff method was used, the cancellation between the nearly symmetric eastward and westward fluxes could be the primary reason for the 10 times smaller MFx.
L289 “lower proportion of low value MFx”: Does this mean that the low-flux part is relatively smaller in this region than in the other regions when the eastward-momentum fluxes in the summer season is scaled (normalized) in each region ?
Fig. 7: In the amplitude-cutoff results, the meridional propagation is surprisingly predominant over zonal propagation. In L315-320, this is explained as a bias due to several factors, including the across-track fourth-order polynomial filtering. This factor is said to be a standard. Does this mean that results of previous studies in the literature were also affected by this bias ? I am confused because in those studies, the zonal flux was found to be much larger than the meridional flux (e.g., Fig. 3 in Hindley et al., 2020).
L306: How can the African easterly jet account for the westward propagating waves ? (In many parts of the manuscript, observed waves have been thought to propagate against the winds.)
L340 “~40× greater”: This specific information has not been mentioned in the Result section.
L343-345 “… consistent …” / “and consistent …”: (1) The former part seems to be repetitive if it refers to the global morphology of flux directionality, which was already mentioned in L341-342. If it refers to another aspect that is consistent with the linear theory, please specify it. (2) For the latter part (“and ...”), its meaning is unclear. Please rewrite this.
Figs. A1-2: I would suggest showing the masked wave fields (like those in Fig. 1d) rather than just the masks.
[ Technical comments ]
L7-8: “defined”: This would be unnecessary.
L20: pressure → density ? (The latter may be the most directly relevant variable.)
L28: hours → minutes ?
L45-46: The citation of these three references should be placed at the end of the sentence.
L46: “with with”
L48-50: Please rephrase the sentences. For example, “a wave is present at all locations in the data” → “any signal in the data is projected to a wave” ?; “assign low amplitudes”: Please provide the reason (noise?); “which is why …”: I could not understand this logically in the context.
L53: “and as such, a method ...” (comma) ?
L58: stable spatial → spatially stable ?
L94: “large”: Please clarify if this is for the spatial scale or amplitude.
L118: “other levels” commonly stated in the two consecutive sentences seem to indicate different groups of levels: for the former, the levels with similar resolutions and noise magnitudes to 39 km; and the latter, any levels with different characteristics. If this is correct, I suggest avoiding repetition of the same term “other levels” for different objects.
L119: “variables within the neighbourhood method”: This method has not yet been introduced (except being mentioned in the abstract), so discussing some variables used in the method may be premature at this point.
L124: wave properties → spectral properties (as this is for noise)
L142-143: The difference cutoff has been repetitively mentioned here (L142; L143). Please rephrase the sentences.
L154: amplitude → temperature amplitude
L184-185: “but they each hotspot … in Figure 3.”: Please rewrite the sentence.
Fig. 4 caption: “that the axis for vertical wavelength (c)”
L200: data → results ?
L211: break → dissipate (as wave breaking often refers to a special process, not related to the critical level)
L226: “same”: I agree that this result is consistent with Hindley et al. (2020, Fig. 2b). But I suggest rephrase this word, as they presented (net) zonal momentum flux. The same pattern as in Fig. 4b cannot be observed (but inferred) there.
L239: “from 90°N to 90°S”: Please revise this. Waves were not observed around 90°S in boreal winter (Fig. 3a).
L277: and → an
L319 “… is the standard, identifying … remains …”: (1) no conjunction for the two sentences. (2) References may be necessary for the standard.
L353: average → wavenumber (the latter may be more informative)
L356 “… have no extraneous noise” / “or that no noise is …”: Do these two have different meanings ?
Citation: https://doi.org/10.5194/egusphere-2025-455-RC2
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