| 07 Sep 2026
WAVEGUISE – Wavefield Analysis and Segmentation unraveling an interpretable Set of Wave Packets
Abstract. Atmospheric waves are never perfectly monochromatic and show modulations in amplitude, wavelength, and frequency due to transient background conditions. In observations, they often appear as complex superpositions of multiple interacting wave components. To disentangle this superposition into individual interpretable wave packets and to study their instantaneous spectral properties in an automatic fashion, we introduce a new method: the Wavefield Analysis and Segmentation unraveling an interpretable set of wave packets (WAVEGUISE). Based on the continuous wavelet transform, WAVEGUISE combines watershed segmentation from image processing and density based spatial clustering algorithms to partition the wavelet domain into coherent regions of shared temporal, spatial, and spectral characteristics. We demonstrate the method using three observational data sets of increasing dimensionality: a) a 25-day pressure time series (1-D) from a long-duration super-pressure balloon obtained during the Strateole-2 campaign, b) a 1,400 × 500 km Q-line radiance swath (2-D) from the Atmospheric Waves Experiment (AWE), and c) a OH (3,1) band intensity video sequence (3-D) from the Advanced Mesospheric Temperature Mapper. Applied to these data sets, WAVEGUISE acts as a magnifying glass. The segmentation into a set of dominant and subdominant interpretable wave packets reveals a significantly enhanced level of detail enabling to precisely study dynamical processes such as e.g. wave-wave interaction and to improve wave statistics.
Reichert, R., Pautet, P.-D., and Bramberger, M., "WAVEGUISE – Wavefield Analysis and Segmentation unraveling an interpretable Set of Wave Packets". Theauthors present WAVEGUISE, an algorithm that splits a superposition of atmospheric waves into separate, localised wave packets with instantaneous spectral properties. The authors demonstrate the method on three datasets. The first is a 25-day super-pressure balloon pressure record from Strateole-2 (1-D), which yields 15 packets, interpreted as planetary waves, the diurnal tide and GWs. The second is an AWE OH "Q-line" radiance swath over the central US (2-D), in which a second, weaker ring-like wave field is attributed to convection over Kansas. The third is a 1.5 h AMTM OH image sequence from Río Grande (3-D), which yields five packets with different wavelengths, directions and phase speeds.
The manuscript is not yet convincing, for three main reasons: 1. all three examples are real observations, so there is no way to judge whether the 15, 14 or 5 packets found are correct, spurious or merged. A new decomposition method needs synthetic tests with known packets, noise and overlap, and quantitative skill metrics. 2. The method description is not sufficient to reproduce the results or understand their limits. Key definitions are missing or inconsistent: wavelet normalisation and the white-noise threshold, the features and distance used in DBSCAN, the angular wrapping in 3-D, the reconstruction formula, and how the retained variance is used. The 3-D example also departs substantially from the method described in Sect. 2. 3. the method is described as automatic, but the results depend on manual steps and on parameters that are tuned per dataset without justification. Packets are "sorted manually" (2-D) and "reduced manually" from eight to five (3-D), and the prominence, sMAD factor and ε differ between examples. No sensitivity analysis is given. Some interpretations also go beyond what the method demonstrates, for example wave–wave interaction in the balloon record and source attribution in the AWE swath. The paper does not demonstrate the improved momentum-flux statistics used to motivate it. Therefore, I recommend major revision.
Specific Comments
The introduction cites S-transform, S3D and 2-D Morlet approaches, but the paper never compares WAVEGUISE with them. Please discuss its relation to other multi-component decompositions. These include multiple-peak S-transform analysis (Wright and Gille, 2013), small-volume few-wave decomposition (Lehmann et al., 2012), automatic 2-D Morlet packet extraction (Chen and Chu, 2017) and the method of Berthelemy et al. (2025). Generic multi-component methods also exist: wavelet ridge extraction, synchrosqueezed transforms, and empirical or variational mode decomposition. A quantitative comparison on at least one synthetic case and one observed case, against dominant-mode extraction and one alternative method, would show the added value directly.
The abstract and introduction motivate the method by more complete momentum-flux estimates and better wave statistics (L36–48, L296–299). Neither is demonstrated. The abstract's claims ("magnifying glass", "precisely study dynamical processes such as wave–wave interaction") should be supported, for example by computing packet-resolved momentum flux for the AMTM case, or toned down. Please also add a limitations paragraph covering: crossing instantaneous frequencies, which watershed segmentation will split wrongly; packets closer in spectral space than the wavelet bandwidth; non-wave features such as bores, fronts, cloud edges and instrument artefacts, which will also be segmented; computational cost and memory requirements for the 6-D case.
The code is well documented in the availability statement, but there is no data availability statement for the Strateole-2, AWE and AMTM datasets.
The method is only applied to real observations, so its skill cannot be assessed. I ask the authors to add a validation section using synthetic fields with known packets, for example:
1-D: several packets that overlap in time, including a chirp, two packets whose instantaneous frequencies cross, a packet whose amplitude briefly falls close to zero, and two packets separated in frequency by about one wavelet bandwidth, embedded in white and red noise at several signal-to-noise ratios.
2-D: plane waves plus two concentric ring patterns from different centres with amplitude ratios such as 1:0.2, overlapping in space (directly relevant to the AWE claim).
3-D: two packets with the same wavelength and direction at different locations, and two packets at the same location with different phase speeds.
For each test, please report the number of packets detected versus the number inserted (missed, false and merged packets), errors in amplitude, wavelength, direction and phase speed, and the reconstruction residual, all as a function of noise level and of the main parameters. Without this, the reader cannot judge whether the packets in Figs. 2, 3 and 5 are physical or artefacts of segmentation.
Sect. 2 is the core of the paper but is too brief to reproduce the results or to understand the algorithm's limits. Specific gaps:
Sect. 2.1. The Eqation is unnumbered but later cited as "Eq. 2.1". The wavenumber in the exponent should be kₘ. "m ∈ [0,1]" should be the set {0, 1}, and m = 0 is redundant after mean removal. For multi-dimensional data, please state whether the fit and filter are applied sEqentially along each axis, and whether the order matters.
2. CWT normalisation (Sect. 2.3). Please state the wavelet normalisation explicitly. Interpreting |W| as instantaneous amplitude (L95–96) and the noise scaling in Sect. 2.4 both depend on it. Please give the scale-to-wavelength factor and the angular resolution of the 2-D and 3-D wavelets for the chosen numbers of azimuth and zenith angles. Please define the aspect ratio in the 3-D transform (35.7 in Table A1; units?) and how it couples spatial and temporal scales.
Sect. 2.4.
Please define |W(s)_white| precisely: is it the expected noise amplitude or a confidence level? If it is the mean, then for Gaussian noise (Rayleigh-distributed |W|) about 46 % of pure-noise coefficients exceed it. Please give the false-alarm rate of the chosen threshold.
If the wavelet is amplitude-normalised, white-noise amplitude scales as s^(−D/2) in D dimensions, so the stated 1/√s scaling holds only in 1-D. Please state the scaling used in 2-D and 3-D, including the effect of the aspect ratio.
The per-scale median/sMAD filter removes coefficients close to the median. A coherent wave that fills most of the domain at a given scale raises the median and could be removed as "background". Please discuss this, and state per dataset which stages are applied (Table A1 suggests the sMAD stage is used only in 2-D).
Please explain how the noise levels (0.1 hPa, 0.8 and 80 BI units) were determined. The 0.1 hPa "pressure uncertainty" (L314) is likely an accuracy, not a random-noise level.
Sect. 2.5. Please state explicitly the space in which the watershed runs for each dataset, e.g., (t, s) in 1-D and (x, y, s, θ) in 2-D. Please also state how neighbours are defined across axes with different units and log-spaced scales, and what "connectivity = 1" means. The prominence h is said to be proportional to the noise level, but Table A1 uses 0.1×, 0.25× and 1× the noise level. Please justify these choices.
L125–128 In 2-D, treating θ ∈ [0, π) as periodic is correct. In 3-D the π ambiguity identifies (θ, φ) with (θ + π, π − φ), so independent periodic wrapping of θ and φ joins the wrong neighbours, and all azimuths coincide at φ = 0 and π. Please describe how this is handled.
In Sect. 2.6. Please list the features passed to DBSCAN, their scaling, and the distance metric. Azimuth is circular, so Euclidean distance places 1° and 179° far apart. Please give the units of ε (0.088, 0.123). With minPts = 2 and noise points retained, DBSCAN reduces to single-linkage clustering at threshold ε, which is prone to chaining distinct packets together. Please justify the choice or use a simpler description. Table A1 lists no ε for 3-D: was clustering applied there?
L61–62 says packets are "only treated as separate when they are disconnected in physical space", whereas L142–144 applies this only within a cluster. Please reconcile the two statements.
Section Reconstruction and spectral properties (Sect. 2.7) has two sentences. Please give the inverse formula. A masked set of CWT coefficients is generally not the CWT of any signal, so please discuss amplitude bias and leakage at mask boundaries and the fact that the packets are not orthogonal. Please also explain how instantaneous wavelength, frequency, and direction are obtained (weighted averages of |W| within the segment, or the phase gradient of the reconstruction), and how the 180° ambiguity is resolved for the arrows in Fig. 3c,f.
It is unclear whether this is an input that selects packets (Sect. 3.1: "with 99 % retained variance") or a diagnostic output. As defined, Var(ΣXᵢ)/Var(X) is not a fidelity measure: a reconstruction can match the variance and still differ from the signal, and cross-terms between non-orthogonal packets are ignored. Please use the residual 1 − Var(X − ΣXᵢ)/Var(X), and report the sum of individual packet variances as well. How can the 3-D case reach 100 %?
A per-dataset flowchart or table stating which steps are applied, and with which values, would help greatly.
The abstract (L3–4) describes an automatic method, but the AWE packets are "sorted manually" (L196) and the AMTM packets are "reduced manually" from eight to five (L225). The criteria for these manual decisions are not given, so the results cannot be reproduced. Parameters also vary between examples without stated rules (prominence, sMAD factor, ε, dj, numbers of angles). The authors acknowledge this dependence (L290–294) but do not quantify it. Please:
describe or automate the manual steps;
show how the number of packets and their key properties change with noise level, prominence and ε (e.g., ±50 %) for each example;
give practical rules for choosing the parameters, ideally tied to noise statistics and false-alarm rates.
L174 already shows that a packet splits in two when its amplitude briefly drops below the threshold. This means packet counts, lifetimes and sizes — the quantities the authors propose for statistics (L296–299) — are threshold-dependent.
Taking the 95th percentile over the two spatial dimensions (L218–223) removes spatial information before segmentation. Two packets with the same spectral properties at different places in the field of view (FOV) can then no longer be separated, which is exactly the AWE use case. A packet covering less than about 5 % of the FOV may be suppressed altogether. Please state the smallest detectable areal fraction. Please also explain how spatially localised packets such as WP-II are reconstructed from a spectral–temporal mask.
L221–222 says the percentile reduces the influence of isolated large-amplitude outliers, but a 95th percentile emphasises such outliers once they cover more than 5 % of the FOV.
Sect. 2.4 presents denoising as a standard step, but Appendix A3 says no denoising was applied in 3-D.
The FOV is given as 200 × 160 km (L210), whereas 243 × 213 pixels at 625 m (Table A1) and the axes of Fig. 4 give about 152 × 133 km.
WP-III's period is given as ~1.7 min (L241). Fig. 6b shows ω ≈ 0.045 s⁻¹ for the corresponding series, i.e. ~140 s (2.3 min), which equals the stated minimum temporal scale (2 min 20 s, Table A1). The packet lies at the edge of the analysed scale range and within a factor of two of the 70 s Nyquist period. Please check for edge and aliasing effects, and test the derived parameters against the GW dispersion relation.
The legend of Fig. 6 seems inconsistent with the text. The series with the largest amplitude, λₕ ≈ 25 km, north-westward propagation and c ≈ 30 m s⁻¹ (described as WP-I) is labelled "WP III". The ~10 km eastward series (WP-II in the text) is labelled "WP I", and the short-lived ~100 m s⁻¹ series (WP-III in the text) is labelled "WP II".
A super-pressure balloon samples in a quasi-Lagrangian frame, so the observed periods of planetary waves and tides are Doppler-shifted and are not ground-based periods. The dominant large-scale waves in the tropical lower stratosphere are Kelvin and mixed Rossby–gravity waves (Vial et al., 2001, cited). The attribution to Rossby normal modes (Salby, 1981; Hirota and Hirooka, 1984), which were observed mainly in the extratropical upper stratosphere, needs justification.
The 11-day packet completes only about 2.3 cycles in 25 days. The maximum scale is listed as 25 days (Table A1), which contradicts L88–90 (half the domain).
The text (L168–169, "within the COI and therefore subject to underestimation") uses the opposite convention for the cone of influence (COI) from the Fig. 2 caption ("outside of which coefficients are affected").
Part of the 24 h signal may be the balloon's own diurnal cycle. Please comment.
The suggested wave–wave interactions (L171–173, L177, L272–274) rest on anti-correlated amplitudes of packets that are neighbours in period. A watershed boundary between adjacent spectral regions can shift energy from one segment to the other by construction. Please show with synthetic tests that this anti-correlation is not an artefact, or remove the interpretation.
"Without relying on band-pass filtering" (L185): wavelet-domain masking is an adaptive band-pass filter. Please rephrase.
A single swath has no time information, so propagation direction has a 180° ambiguity. Please state that the arrows in Fig. 3c, f assume propagation away from the presumed source.
The attribution of the second ring-like pattern to Kansas convection is visual. Please fit ring centres objectively (e.g., by back-projecting local wave vectors) with uncertainties. Please also consider propagation time from the convective cells and alternative sources such as secondary waves (Vadas and Azeem, 2021).
Please show all 14 packets (e.g., in the supplement) with their properties and variance fractions, and state the sorting criteria.
Minor Comments
L10: "a OH (3,1) band" → "an OH (3,1) band".
L36–37: Spectra are collapsed mainly to save memory during computation, not disk space. Please rephrase or explain.
L56: "associated with a local peaks" → "associated with local peaks".
L64: Number the equation and write the exponent as i kₘ·x.
L66–67: "m ∈ [0,1]" → "m ∈ {0, 1}".
L71: "least-square fit" → "least-squares fit".
L77: State whether the 10 % Tukey taper applies to each side or in total. Appendix A says "at either boundary". Give the Tukey α parameter.
L86–88: Define the number of scales J and use one notation (dⱼ or dj). Table A1 lists 86, 40 and 17 scales. Please show how these follow from s₀, dj and the maximum scale.
L104: "A defined multiple of the sMAD": give the value here, not only in the appendix.
L151 vs L208: The OH layer height is given as ~86 km and ~87 km.
L163–164: Fig. 2a shows the WAS of the non-denoised series. Please state which WAS (denoised or not) is segmented.
L176–180 vs L272: Sect. 3.1 gives GW periods of 2–12 h, the conclusions give 1–11 h, and Fig. 2 shows packets from 2 ± 1 h to 12 ± 2 h. Please make these consistent.
L181: The dominant-mode reconstruction (21 % of the variance) is "not shown". Please add it to the supplement, since it is the main baseline for the method's added value.
L189–190: Define the AWE "Q-line" radiance, the band and the units. The abstract and the AMTM section refer to the OH(3,1) band, while this section says OH(2,0).
L193–194: Specify which aspect of Vadas and Azeem (2021) the phase-line curvature agrees with.
L196: "table A1" → "Table A1".
L212–217: Fig. 4 shows frames every ~5 min, but the analysis uses 35 s frames. Please state this in the caption.
L226–227: For packets confined to part of the FOV, explain how the amplitude weighting avoids biasing the FOV-mean parameters (Fig. 6) toward noise outside the packet.
L231–232: Make the reasoning explicit: mountain waves have near-zero ground-relative phase speed.
L233–234: The explanation of the amplitude doubling (longer vertical wavelength, less phase averaging) could be tested with the AMTM temperature product.
L240–243: WP-III shows only about three cycles in ~25 min. Please quantify how reliably the CWT determines its period and phase speed.
Fig. 2: Labels overlap and are hard to read. Add a colour bar for the WAS in (a) and an amplitude scale (hPa) for the offset reconstructions in (b). Explain why standard deviations are given only for periods below 12 h.
Fig. 3: The caption describes the panels in the order a, d, b, e, c, f. Please reorder the panels or the caption. Add radiance units and the NEXRAD scan time.
Fig. 6: State the units of ω (rad s⁻¹?). The direction axis (N–W–S–E–N from top) is unconventional; consider degrees. See major comment 4 on the legend.
Table A1: Give units for the aspect ratio, ε and prominence, and explain what "–" means in each row (not applied, or not applicable).
References: Hirota and Hirooka (1984) have no journal. Mixa et al. (2026) has no journal. Ester et al. (1996) needs full proceedings details. Geldenhuys et al. (2022) has no volume. DOIs are missing for most entries.
L278: "wave––wave" → "wave–wave".
L279: "bended phase lines" → "bent phase lines".
L313, L322, L329: "Eq. 2.1" → "Eq. (1)", or whatever number is assigned.
L340: "as it is done in Section 3.3" → "as in Sect. 3.3".
Fig. 6 caption: "FOV-mean parameters amplitudes (a)" → "FOV-mean parameters: amplitudes (a)".