the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Implementation of a Multi-resolution Analysis Method to Characterize Multi-Scale Wave Structures in Lidar Data
Abstract. This study introduces a processing method based on multi-resolution analysis (MRA) to characterize the multi-scale structures of gravity waves (GWs) with vertical wavelengths less than 13 km in lidar vertical profiles of temperature and wind in the middle atmosphere. The MRA approach is evaluated against conventional techniques, including polynomial fitting, spectral filtering, and nighttime temporal averaging, and applied to a case study of GWs observed on November 20, 2023. Among these methods, MRA demonstrates superior performance by enhancing the signal-to-noise ratio through signal decomposition and selective filtering. This targeted filtering improves the detection and extraction of GW-induced perturbations, particularly for dominant vertical wavelengths around 5 km. In terms of GW potential energy (GWPE), the MRA-based method yields values comparable to those derived from the variance method, except at the stratopause, where it estimates nearly twice the GWPE. However, the variance-based estimate remains within the MRA-derived confidence interval, indicating good agreement. In contrast, the Butterworth low-pass filter produces energy densities an order of magnitude higher than the variance method, suggesting possible overestimation of perturbation amplitudes. Polynomial fitting and nighttime mean methods appear insensitive to small-scale GW structures near the stratopause, where wave dissipation may occur. Beyond energy estimation, the MRA method offers a distinct advantage for analyzing GW propagation and scale interactions due to its multi-scale decomposition capability. It reveals GW features and structures that remain obscured by common techniques, establishing it as a valuable tool for advancing the study of GW dynamics in the middle atmosphere.
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RC1: 'Comment on egusphere-2025-3719', Anonymous Referee #1, 01 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3719/egusphere-2025-3719-RC1-supplement.pdfCitation: https://doi.org/
10.5194/egusphere-2025-3719-RC1 -
RC2: 'Comment on egusphere-2025-3719', Anonymous Referee #2, 10 Sep 2025
Implementation of a Multi-resolution Analysis Method to Characterise Multi-Scale Wave Structures in Lidar Data by Samuel Trémoulu et al. (2025)
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This study presents a multi-resolution analysis (MRA) approach using the 8th-order Daubechies wavelet to analyse gravity waves in lidar data for a single case event. The MRA is compared with traditional methods such as mean background atmospheric temperature, polynomial fitting, Butterworth spectral filtering, and the variance method. The authors demonstrate that MRA outperforms these methods when applied to lidar temperature data. For wind analysis, only MRA is used.
This work introduces a promising tool for gravity wave analysis that could contribute to the understanding of multi-scale atmospheric dynamics. The manuscript is well written; however, it requires additional clarification and explanation of certain choices.
General comments:
- Why are the chosen windows different between methods? It needs some justification.
- It would be useful to see a comparison of the MRA to a conventional wind analysis.
- Section 3.1 Case Study: Several mentions are made of wind, tides, and GWs observed on the day, but the corresponding figures are not shown. Since the paper focuses on the method and the case study, including these figures would help the reader follow the discussion without having to rely solely on the authors’ statements.
- Throughout the article, the same method is called differently, e.g. ‘buttlerworth filter’ and ‘spectral filtering’. Select one way of calling it and use it everywhere.
- There is a misuse of GW and GWPE throughout the entire article. GWPE is defined but then used as GW potential energy. Please change it everywhere, and remove densities after GWPE.
- The summary, conclusions and perspectives need some emphasis on the method comparisons and their weaknesses.
Specific comments:
Figure 4: It could be useful to see a plot with the difference between the temperature and method next to the temperature one.
L007: In an abstract, you should try to avoid the use of acronyms to help readability. It’s okay to use them; however, don’t use an acronym for defining another acronym GW potential energy (GWPE). You are not space-limited, so avoid this practice.
L017-021: Paragraph small, only one citation.
L023: Here the ‘e.g.’ is used. If you are giving an example, only one or two citations are enough. It could be one old and a new one. Instead, 10 are given and not even one is a recent one (2020+). I suggest removing e.g. and adding a later one too.
L024: Duck et al. 2001, the link is broken.
L025: I agree that Lidar observations are capable of inferring long-term trends; however, some of the cited publications are campaigns or techniques, which aren’t studies in long-term trends.
L028-29: Same as before, there are newer studies of GW with Lidar observations.
L085: cal/val is only used twice and in the same sentence. If it is not used later, it is unnecessary to define it.
L150: verticalsinterval
L163/164: You defined MRA in the second sentence but use it in the first sentence, please switch.
L190: eq:3 is the equation of the gravity wave potential energy. Remove density and all the references to it. You have already defined GWPE, so now you can use it.
L200: The reference to the figure is there, but no in-text full explanation of the figure.
Fig2: caption double km.
L205: Again, defining an acronym with an acronym and it should be defined before. Particularly in this case, you don’t need it because it’s the GWPE.
L207: GWE?
Fig. 3: second line: “above” La Réunion, it sounds narrower than actually is. Change to centred over or similar. And the longitude is written with a “,”
Figure 8: red dots? Only one is shown at which I guess is the start.
Figures 7 and 8: Increase label size.
Citation: https://doi.org/10.5194/egusphere-2025-3719-RC2
Data sets
Temperature Lidar Data Alain Hauchecorne https://www-air.larc.nasa.gov/missions/ndacc/data.html?station=la.reunion.maido/ames/lidar/
Wind Lidar Data Sergey Khaykin https://www-air.larc.nasa.gov/missions/ndacc/data.html?station=la.reunion.maido/ames/lidar/
ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate Copernicus Climate Change Service (C3S), ECMWF https://doi.org/10.24381/cds.143582cf
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