| 30 Apr 2026
A New Method for Retrieving Momentum Flux Magnitude from Multiple Gravity Wave Signals Using GNSS Radio Occultation Profile Triples
Abstract. Gravity wave (GW) momentum flux (MF) is a key parameter characterizing GW energy transport in the atmosphere, but extracting GW MF from satellite observations remains challenging. Here, we propose a new method for retrieving GW MF magnitude using Global Navigation Satellite System (GNSS) radio occultation (RO) temperature profile triples. Unlike the traditional profile-triple-based method, which only considers the dominant vertical wavelength of the largest-amplitude wave signal, the new method takes into account a set of significant vertical wavelengths determined by an empirical threshold. This threshold is optimized to balance the completeness of MF information and the reliability of GW signals. Experiments are conducted using COSMIC-2 RO dry temperature data. Qualified triples are classified into Type A (triples meeting the criteria of both the new and the traditional methods) and Type B (triples meeting only the new method’s criteria). At most latitudes between 40° S and 40° N, the zonal-mean total MF from Type B triples exceeds that from Type A, with a pronounced peak at around 20° N. The contribution of primary wave signals to the total MF magnitude is significantly lower at the altitude range of 20–25 km than at higher altitudes, likely attributable to frequent wave-breaking processes and the generation of secondary GWs within 20–25 km. Compared with the traditional method, the new method significantly improves the data utilization rate of profile triples and enables a more complete measurement of the total GW MF magnitude which may originate from different sources.
The paper "A New Method for Retrieving Momentum Flux Magnitude from Multiple Gravity Wave Signals Using GNSS Radio Occultation Profile Triples" by Hou et al. introduces a new method for deriving gravity wave (GW) momentum fluxes from triples of COSMIC-2 GNSS radio occultation temperature profiles. The new method is capable of detecting multiple waves that are superimposed on each other. In this way a more complete representation of the GW momentum flux at a given location and a better data usage is achieved than for the traditional approaches that focus on the strongest wave components only.
Overall, the basic idea of the proposed method is a significant improvement over previous work. The paper, however, suffers from major shortcomings and inconsistencies. My main comments are:
(1) The profile triple selection criteria are not sound
(2) Comparisons of GW parameters with previous work are missing; therefore the authors did not notice that the values they derive are unphysical. In particular, GW amplitudes and momentum fluxes are way too high.
(3) It is unclear whether the noise level of the RO data allows to reliably determine multiple waves from profile triples. Therefore the authors should show zonally averaged net momentum fluxes and see whether the distribution matches expectations.
(4) Because only vertical filtering of altitude profiles is applied, temperature perturbations will contain not only GWs but will still be contaminated by global waves. This shortcoming could be acceptable because the paper is just a proof-of-concept. Still, this shortcoming should be mentioned and discussed.
My recommendation for the paper is therefore reject with resubmission encouraged.
A list of more specific comments is given below.
SPECIFIC COMMENTS:
(1) l.17: Please do not call the most dominant waves "primary" because this will cause confusion. One could think that all weaker waves that are detected would be "secondary" and be caused by primary waves by the process of secondary wave generation which is likely not the case. Most likely in the lower stratosphere there is in most cases just a superposition of waves from different sources.
(2) l.19: Delete the speculation about secondary wave generation from the abstract. There is not much evidence for secondary wave generation in this altitude range as most waves in the lower stratosphere are propagating upward as seen in radiosonde observations (e.g., Wang et al., JAS, 2025)
Wang, L., Geller, M. A., and Alexander, M. J.:
Spatial and Temporal Variations of Gravity Wave Parameters. Part I: Intrinsic Frequency, Wavelength, and Vertical Propagation Direction,
J. Atmos. Sci., 62, 125-142.
Usually, generation of secondary GWs is expected to happen in the stratopause and mesopause region (e.g., Chun and Kim, JGR, 2008; Vadas et al., JGR, 2018)
Chun, H.-Y., and Y.-H. Kim (2008),
Secondary waves generated by breaking of convective gravity waves in the mesosphere and their influence in the wave momentum flux,
J. Geophys. Res., 113, D23107, doi:10.1029/2008JD009792.
Vadas, S. L., Zhao, J., Chu, X., & Becker, E. (2018).
The excitation of secondary gravity waves from local body forces: Theory and observation.
Journal of Geophysical Research: Atmospheres, 123, 9296-9325. https://doi.org/10.1029/2017JD027970
There could be another explanation than secondary wave generation for the wave spectrum being more "monochromatic" at altitudes above 25km. This could just be dissipation of parts of the wave spectrum at 20-25km making the wave spectrum more monochromatic without significant secondary wave generation, or it could be an effect of measurement noise.
(3) l.24: Here you write "constituents and water vapor" which is kind of strange because water vapor belongs to the constituents. Please rewrite!
(4) In the introduction you should mention that for GNSS radio occultations there is also a method for deriving GW momentum fluxes based on a "quartet" method that uses tuples of four altitude profiles (quadruples).
Alexander, P., de la Torre, A., & Schmidt, T. (2024).
Global stratospheric properties of gravity waves from 1 year of radio occultations.
Journal of Geophysical Research: Atmospheres, 129, e2023JD040609. https://doi.org/10.1029/2023JD040609
Further, it should be mentioned that if real 3D observations are available there are methods of deriving full wave vectors using 3D volume approaches (e.g., Wright et al., ACP, 2017; Rhode et al., AMT, 2024).
Wright, C. J., Hindley, N. P., Hoffmann, L., Alexander, M. J., and Mitchell, N. J.:
Exploring gravity wave characteristics in 3-D using a novel S-transform technique: AIRS/Aqua measurements over the Southern Andes and Drake Passage,
Atmos. Chem. Phys., 17, 8553-8575, https://doi.org/10.5194/acp-17-8553-2017, 2017.
Rhode, S., Preusse, P., Ungermann, J., Polichtchouk, I., Sato, K., Watanabe, S., Ern, M., Nogai, K., Sinnhuber, B.-M., and Riese, M.:
Global-scale gravity wave analysis methodology for the ESA Earth Explorer 11 candidate CAIRT,
Atmos. Meas. Tech., 17, 5785-5819, https://doi.org/10.5194/amt-17-5785-2024, 2024.
(5) l.73: Is there a special reason for selecting the June-August 2020 period?
(6) Section 3.1, Extraction of Perturbation Temperature:
You should discuss the shortcomings of this method! Just filtering each profile vertically assumes that all vertical structures of the profile having wavelengths in the range 4-13km are gravity waves. This, however, is not the case. There are global wave modes in the same vertical wavelength range which will result in strong biases of the obtained GW distribution.
For example, inertial instabilities usually have vertical wavelengths of around 10km in the stratosphere which is known to bias GW distributions obtained by vertical scale separation (Rapp et al., GRL, 2018; Strube et al., AMT, 2020).
Rapp, M., Doernbrack, A., & Preusse, P. (2018).
Large midlatitude stratospheric temperature variability caused by inertial instability: A potential source of bias for gravity wave climatologies.
Geophysical Research Letters, 45, 10,682-10,690. https://doi.org/10.1029/2018GL079142.
Strube, C., Ern, M., Preusse, P., and Riese, M.:
Removing spurious inertial instability signals from gravity wave temperature perturbations using spectral filtering methods,
Atmos. Meas. Tech., 13, 4927-4945, https://doi.org/10.5194/amt-13-4927-2020, 2020.
Even more importantly, as your work focuses on relatively low latitudes, tropical Kelvin waves are in the same vertical wavelength range as GWs and have considerable temperature amplitudes at 15S-15N, comparable with those of GWs (e.g., Ern et al., ACP, 2008 for a climatology). Kelvin waves have their peak amplitude at the equator which might explain why in your work zonal average momentum fluxes show maximum values close to the equator.
Ern, M., Preusse, P., Krebsbach, M., Mlynczak, M. G., and Russell III, J. M.:
Equatorial wave analysis from SABER and ECMWF temperatures,
Atmos. Chem. Phys., 8, 845-869, https://doi.org/10.5194/acp-8-845-2008, 2008.
(7) l.105: about the spatiotemporal separation criterion:
The 600km miss distance criterion is far too loose! This will lead to undersampling and aliasing of a large fraction of the horizontal wavelength spectrum! Many gravity waves will have shorter horizontal wavelengths and relatively small wave packet sizes. A statistical study by McDonald, JGR, 2012 based on GNSS radio occultations shows that coherence between neighbored altitude profiles gets lost at horizontal separations larger than about 300km for latitudes 30-60deg (his Figure 6). This suggests that the horizontal separation criterion in your work should not exceed 400km (already assuming that at low latitudes GW horizontal wavelengths might be longer than at higher latitudes).
McDonald, A. J. (2012),
Gravity wave occurrence statistics derived from paired COSMIC/FORMOSAT3 observations,
J. Geophys. Res., 117, D15106, doi:10.1029/2011JD016715.
(8) l.108: units in Eq.(1) are missing!
(9) Restrictions for line of sight angle differences should be introduced!
To make sure that the atmosphere in all profiles of a considered tuple is sampled in a similar way, the line of sight direction between all profiles of the tuple should not differ by more than about 10deg (this value was recently used by Alexander et al., JGR, 2024). This will avoid phase shifts between the different profiles of a considered tuple of altitude profiles that are introduced by viewing a considered wave from different angles. These phase shifts will occur particularly for waves of short horizontal wavelengths (see Preusse et al., JGR, 2002; Alexander et al., ESS, 2018; Alexander et al., JGR, 2024).
Preusse, P., A. Doernbrack, S. D. Eckermann, M. Riese, B. Schaeler, J. T. Bacmeister, D. Broutman, and K. U. Grossmann,
Space-based measurements of stratospheric mountain waves by CRISTA, 1. Sensitivity, analysis method, and a case study,
J. Geophys. Res., 107(D23), 8178, doi:10.1029/2001JD000699, 2002.
Alexander P., Schmidt T., & de la Torre, A. (2018).
A method to determine gravity wave net momentum flux, propagation direction, and "real" wavelengths: A GPS radio occultations soundings case study.
Earth and Space Science, 5, 222-230. https://doi.org/10.1002/2017EA000342
Alexander, P., de la Torre, A., & Schmidt, T. (2024).
Global stratospheric properties of gravity waves from 1 year of radio occultations. Journal of Geophysical Research: Atmospheres,
129, e2023JD040609. https://doi.org/10.1029/2023JD040609
(10) l.171-173: You should mention that the long horizontal wavelength criterion could help to exclude remaining contributions caused by global waves, but still it should be clear that the GW distribution will be biased because vertical filtering will not remove all global waves.
(11) l.192, 204 and elsewhere: The use of "primary" will confuse some readers. Better refer to it as "strongest" GW.
(12) Fig.1, Table 1: Please check! The temperature amplitude looks quite large for a GW in the latitude range 40S-40N.
Please note that deviations of up to ~20K would occur in a considered altitude profile when both waves are superimposed!
(13) Fig.2, Table 2: Same as before! Please check!
A 30K GW amplitude is way out of bounds for the lower stratosphere!
(14) Figs. 3, 6, 7, and 8: Momentum flux values are way out of bounds!
For the lower stratosphere values two orders of magnitude lower would be expected! Even singular events should carry much lower momentum fluxes.
(15) The previous comments (12)-(14) show that the paper significantly lacks comparisons of magnitudes of derived GW parameters with previous work!
Magnitudes of GW amplitudes, horizontal wavelengths, and momentum fluxes should be compared with the results obtained by Ern et al., ESSD, 2018 for the paired profile method, with Schmidt et al. (2016) for triples, and Alexander et al. (2024) for quadruples.
It is evident that such comparisons are needed because the authors did not notice that their GW amplitudes and momentum fluxes are unphysical and way too high.
Ern, M., Trinh, Q. T., Preusse, P., Gille, J. C., Mlynczak, M. G., Russell III, J. M., and Riese, M.:
GRACILE: a comprehensive climatology of atmospheric gravity wave parameters based on satellite limb soundings,
Earth Syst. Sci. Data, 10, 857-892, https://doi.org/10.5194/essd-10-857-2018, 2018.
(16) l.510: magnitudes of GW MF generally grow -> magnitudes of GW amplitudes generally grow
(17) l.517 onward: the higher ratios at 30 and 35km could also be an effect of measurement noise, which for GNSS radio occultations becomes relevant above ~30km.
As mentioned before, in the lower stratosphere occurrence of secondary waves should not be a dominant process as most of the observed GWs propagate upward.
And, again, please be more careful with the use of the expressions "primary" and "secondary" GWs.
(18) l.602, 608, 610: for the primary / secondary wave statements see my previous comments.