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Intraseasonal Equatorial Kelvin and Rossby Waves in Modern AI-ML Models

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Modern AI weather models reproduce the three-dimensional structure of intraseasonal Kelvin waves, but all four fail on the vertical structure of equatorial Rossby waves, where temperature anomalies point opposite to vertical motion.

desk verdict Useful first multi-model benchmark of intraseasonal wave structure in AI weather models, but the headline Rossby-wave finding is likely contaminated by the kinematically derived vertical velocity. read the letter →

arxiv 2507.07952 v1 pith:CD2QYKFL submitted 2025-07-10 physics.ao-ph

Shrutee Jalan , Jai Sukhatme This is my paper
classification physics.ao-ph
keywords convectivelycoupledequatorialwavesKelvinRossbywavenumber-frequencyspectraAI-MLweathermodelsintraseasonalvariabilitytropicalpredictabilityfree-runningforecasts
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether data-driven weather models, trained only for short-range forecasting, have internalized the basic equatorial wave modes of the tropical atmosphere. The authors run PanguWeather, GraphCast, FourCastNet and Aurora freely for four months, filter the output in wavenumber-frequency space, and composite the structures of intraseasonal Kelvin and Rossby waves. They find that all four models produce Kelvin waves whose horizontal convergence patterns, vertical tilts in temperature, humidity and vertical velocity, and temperature-vertical velocity phase relations closely match reanalysis and observations. For Rossby waves, however, the horizontal gyres come out right while the vertical structure does not: temperature anomalies are systematically inconsistent with the sign of vertical velocity in all four models, even though moisture and vertical velocity anomalies are closer to observed. The result matters because these models are candidates for subseasonal prediction, and a correct representation of convectively coupled waves is thought to underpin tropical predictability.

What carries the argument

The method is a space-time spectral filter and event-compositing pipeline applied to free runs of the four models. Wavenumber-frequency diagrams of symmetric and antisymmetric zonal wind are compared with theoretical dispersion curves for shallow-water equivalent depths of 12, 25 and 50 m to identify Kelvin and Rossby bands; events are selected where zonal wind variance for Kelvin waves, or geopotential height variance for Rossby waves, exceeds one standard deviation above the climatological mean in specified tropical boxes; composites of divergence, horizontal wind, temperature, humidity and pressure velocity are then examined in horizontal maps and vertical cross-sections. This machinery lets the authors isolate the wave signature from chaotic variability and compare each field's structure against reanalysis-based expectations.

What would settle it

Run the same four models in a short-lead configuration, for example 15-day forecasts starting from reanalysis states, filter the Rossby band, and composite temperature and vertical velocity; if temperature anomalies align with vertical velocity in any model at short lead, the claim that all four models fail on Rossby vertical structure would be an artifact of free-run drift rather than a learned deficiency.

Watch

Extended reading notes

Core claim

The paper's central claim is that all four AI-ML models capture the three-dimensional structure of intraseasonal Kelvin waves, including lower-level convergence and upper-level divergence, westward tilt of anomalies with height up to roughly 200 mb and eastward tilt above, and the observed phase relationship between temperature and vertical velocity, while none of them represents the vertical structure of equatorial Rossby waves correctly. In the Rossby composites, the upper-level cyclonic and anticyclonic gyres are present, but the temperature anomaly is of the wrong sign for the sense of vertical motion in all four models, and the divergence field shows an anomalous mid-tropospheric bias and unexpected tilts. The moisture field is much closer to observations, and only GraphCast and FourCastNet show the simultaneous build-up of moisture and deep vertical motion. The authors interpret this as evidence that the models have learned the more divergent Kelvin mode well but have not learned the physical consistency among thermodynamic and dynamical fields required for the more rotational Rossby mode.

Load-bearing premise

The load-bearing premise is that four-month free runs of these forecasting models produce physically realistic intraseasonal variability that can be meaningfully compared with reanalysis; the paper checks red spectra and decorrelation times but does not directly verify that model climatology, variances, or wave activity levels remain stable through the runs.

Editorial extensions

If this is right

  • Free-running AI-ML models can serve as testbeds for intraseasonal tropical variability, because their spectra already show Kelvin and Rossby bands with observed equivalent depths.
  • The Kelvin wave composites, including vertical tilts and phase relationships, provide a benchmark that many traditional GCMs have struggled to reach.
  • Since all four models share the Rossby temperature-vertical velocity sign error, the flaw is likely common to the way these models represent rotational large-scale flow, not specific to one architecture.
  • The diagnostic of wavenumber-frequency filtering plus vertical compositing can be reused to evaluate future AI-ML models, including foundation models, before they are used for subseasonal prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension would be to compute the same Rossby composites over the first month of each free run rather than the full four months; if the temperature sign error disappears, the failure is a drift artifact rather than a learned property.
  • The temperature-vertical velocity inconsistency in the Rossby waves resembles a form of geostrophic or hydrostatic imbalance; if so, adding balance constraints during training or post-processing could improve rotational mode structure.
  • The same composite pipeline could be applied to the MJO or to mixed Rossby-gravity waves once longer free runs with more events become available.
  • The contrast between good moisture and bad temperature in Rossby composites suggests the models may be learning moisture-dynamics coupling but not the thermodynamic energy balance that ties temperature to vertical motion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper examines intraseasonal equatorial Kelvin and Rossby waves in four AI-ML weather models (PanguWeather, GraphCast, FourCastNet, Aurora) through free runs of up to four months. It presents wavenumber-frequency spectra, composite horizontal maps and vertical cross-sections, and Hovmöller diagrams for Kelvin and Rossby waves, comparing them with theory and with reanalysis-based structures from the literature. The authors report that all four models capture the basic Kelvin wave structure including convergence-divergence patterns, vertical tilts, and temperature-vertical velocity phase relations, but that all four models fail to represent the vertical structure of Rossby waves, with temperature anomalies inconsistent with the vertical velocity. The paper is a pure diagnostic study with no parameter fitting and treats the models as black boxes.

Significance. If the main conclusions are robust, this is a useful and timely contribution: it provides one of the first systematic comparisons of intraseasonal equatorial wave structure in modern AI-ML weather models, using multiple models and free runs rather than a single architecture. The Kelvin wave results are encouraging and, if confirmed with appropriate uncertainty quantification, would be a meaningful positive result for the field. The reported Rossby wave temperature-vertical velocity inconsistency is potentially important for the evaluation of physical consistency in data-driven models. The study is self-contained in its use of external benchmarks (shallow-water dispersion curves, reanalysis composites) and does not fit parameters. The authors also deserve credit for transparently describing the kinematic derivation of vertical velocity and for noting that some model differences exist, even if the analysis lacks formal statistical support.

major comments (4)
  1. [Section 2 (Models and Methodology)] The paper's most novel claim—that in all four models Rossby-wave temperature anomalies are inconsistent with the vertical velocity—rests on an omega field whose provenance is not documented. Section 2 states that for models that do not provide pressure velocity, omega is computed kinematically by integrating the continuity equation from the surface with omega_sfc=0, but no section states which models output native omega and which use the derived estimate, nor how the two diagnostics compare. Because the kinematic integral accumulates divergence bias and omits surface-pressure tendency, derived omega can be decorrelated from the model's own temperature field even in an internally consistent model. The abstract's statement 'the temperature anomaly was inconsistent with the nature of the vertical velocity' therefore cannot yet be attributed to a model deficiency. Please report omega provenance per model and add an ERA5 control processed with the identical kinematic omega derivation and identical filtering/compositing, so that the reference comparison is apples-to-apples.
  2. [Section 3 (Wavenumber Frequency Diagrams)] The wavenumber-frequency diagrams and the accompanying 'equivalent depths in accord with observations' claim are based on one run per model, despite the ten four-month runs described in Section 2. With only one realization there is no measure of run-to-run spread, and the qualitative statement that all four models show Kelvin/Rossby bands cannot be separated from sampling variability. Please show at least the run-to-run spread (e.g., mean spectrum with inter-run envelope) or state explicitly why one run is representative.
  3. [Sections 4 and 5 (composites)] The composite comparisons—including the model-difference statements such as weak PanguWeather convergence, GraphCast's upright Kelvin tilt, and FourCastNet's 'cleanest' Rossby humidity—are made without event counts, significance tests, or confidence intervals. The composites may be based on very few events, in which case the visual differences (and even the sign of some anomalies) could be sampling noise. Please include event counts for each model and wave type and add a statistical significance assessment (e.g., bootstrap confidence intervals or field significance on the composites) for the key sign and tilt claims.
  4. [Section 2 (free runs) and Section 6] The entire comparison assumes that four-month free runs of forecast-trained models produce physically realistic intraseasonal variability. The paper provides only indirect evidence—red background spectra and decorrelation timescales—and does not quantify whether model climatology, variances, or wave activity levels drift over the four months, or whether any runs become unstable. If a run drifts to an unrealistic mean state, the composites and even the spectral bands could be artifacts. Please add time series or maps of key variables (e.g., equatorial zonal wind, temperature, precipitation) over the runs, and a comparison of model climatology and variance to ERA5 over the same period.
minor comments (6)
  1. [Acknowledgements] The Acknowledgements section spells 'Aurora' as 'Auroa'; please correct the typo.
  2. [Section 5] The text refers to '200 mbar flow' for the Rossby gyres while the composite maps are labeled 250 mbar; please reconcile the level references.
  3. [References] Several reference entries are malformed or incomplete (e.g., the Guo et al. entry lists 'WM Guo, J Waliser' and the Wheeler and Kiladis entry has broken text); please supply a careful reference cleanup.
  4. [Section 5] The order in which Rossby-wave figures are discussed (Figure 8, then Figure 10, then Figure 9, then Figure 11) is confusing; please renumber or reorder the figures so they appear in the order discussed.
  5. [Section 3] The phrase 'as is observed in from real-world data' appears to contain a typo; please revise to 'as is observed in real-world data.'
  6. [Sections 4 and 5 (Hovmöller diagrams)] The phase speeds estimated from the Hovmöller diagrams are quoted without uncertainty estimates; at minimum, please give the range across runs or state that these are single-composite estimates.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is an external diagnostic evaluation of four black-box AI-ML models against reanalysis and theoretical benchmarks.

full rationale

The paper is a diagnostic evaluation rather than a derivation. It runs four pretrained AI-ML models freely, constructs wavenumber-frequency spectra, filters symmetric and antisymmetric components, and composites model fields around Kelvin and Rossby wave events. No parameter is fitted to any subset of the data and then renamed as a prediction; the theoretical dispersion curves (Matsuno 1966; Wheeler and Kiladis 1999) and reanalysis/observation composites (Straub and Kiladis 2003; Nakamura and Takayabu 2022) are external benchmarks, not outputs of the models or of the authors' own prior work. Citations to the authors' own papers (Suhas and Sukhatme 2020; Suhas et al. 2021; Thakur et al. 2024) appear only as background on shallow-water spectra and Hadley-cell contributions and are not load-bearing for the wave-structure conclusions. The kinematic derivation of pressure velocity for models that do not output it natively (Section 2: 'compute pressure velocity using the kinematic method... integrating the continuity equation from the surface... assuming the pressure velocity at the surface is zero') is a methodological caveat that could affect the Rossby temperature-omega sign comparison, but it is not circular: the derived omega is a deterministic diagnostic based on the model's own divergence field, and the reported inconsistency with temperature is an observed property of the composites, not an input that is reintroduced as an output. No equation in the paper reduces to its own input, and no fitted quantity is presented as an independent prediction. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claims rest entirely on standard equatorial wave theory, standard diagnostic methods, and the fidelity of derived fields and free-running model stability. There are no fitted parameters, ad hoc constants, or invented physical entities.

assumptions (4)
  • standard math Equatorial wave dispersion relations (Matsuno 1966) provide the theoretical curves against which spectral peaks are identified as Kelvin and Rossby waves.
    Used in Section 3 to label spectral activity; the paper does not derive these curves but takes them as established theory.
  • domain assumption The kinematic method for computing pressure velocity from the continuity equation, assuming zero surface pressure velocity, yields accurate enough vertical motion anomalies for composite analysis.
    Section 2 derives omega this way for models that do not output it; errors in divergence or the surface boundary condition could distort the diagnosed vertical tilts and phase relations.
  • domain assumption The four-month free runs of the AI models remain physically realistic and statistically stationary enough to represent intraseasonal variability.
    Section 2 runs each model freely for four months; the paper provides limited checks (red background spectrum, decorrelation timescales) but does not validate model climatology during the runs.
  • domain assumption The event selection criterion (variance exceeding one standard deviation above the climatological mean in specified regions) yields representative composites of the target waves.
    Section 2 defines event selection; the threshold choice is arbitrary and the number of selected events is not reported, so composites may not be statistically robust.

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Cite this review

Pith. "Pith review of Intraseasonal Equatorial Kelvin and Rossby Waves in Modern AI-ML Models." pith.science (2026). https://pith.science/paper/CD2QYKFL

@misc{pith2026250707952,
  author       = {Pith},
  title        = {Pith review of: Intraseasonal Equatorial Kelvin and Rossby Waves in Modern AI-ML Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CD2QYKFL}},
  note         = {Machine review of arXiv:2507.07952}
}
read the original abstract

We examine the structure of large-scale convectively coupled Kelvin and Rossby waves in a suite of modern AI-ML models. In particular, multiple runs of PanguWeather, GraphCast, FourCastNet and Aurora are performed to assess the structure of the aforementioned waves. Wavenumber-frequency diagrams of zonal winds from all models show a clear signature of Rossby and Kelvin waves with equivalent depths that are in accord with observations and reanalysis. Composites of Kelvin waves show correct lower and upper troposphere horizontal convergence patterns, vertical tilts in temperature, humidity and vertical velocity as well as the phase relation between temperature and vertical velocity anomalies. Though, differences between models are notable such as smaller vertical tilts and incorrect surface temperature anomalies in GraphCast and relatively weak convergent flows in PanguWeather. The models had much more difficulty with Rossby waves; while the horizontal gyres were captured, the vertical structure of temperature and divergence was incorrect. Apart from unexpected tilts in various fields, the temperature anomaly was inconsistent with the nature of the vertical velocity in all four models. Curiously, moisture and vertical velocity anomalies were much closer to observations. Further, only two models (GraphCast and FourCastNet) captured the simultaneous generation of deep vertical motion with moisture anomalies. In all, while the representation of these large-scale waves is encouraging, issues with the structure of Rossby waves and especially the inconsistency among fields require further investigation.

Figures

Figures reproduced from arXiv: 2507.07952 by the authors.

Figure 1
Figure 1. Wavenumber-frequency spectra of symmetric component of the 250 mbar zonal winds for [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Wavenumber-frequency spectra of antisymmetric component of the 250 mbar zonal winds [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Kelvin Wave composite in PanguWeather. Horizontal winds (quivers) and divergence [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Kelvin Wave composite in GraphCast. Horizontal winds (quivers) and divergence (colours, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Kelvin Wave composite in FourCastNet. Horizontal winds (quivers) and divergence (colours, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Kelvin Wave composite in Aurora. Horizontal winds (quivers) and divergence (colours, in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Composite Hovm¨oller Diagrams for the Kelvin wave band from day [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Rossby Wave composite in PanguWeather. Horizontal winds (quivers) and divergence [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 10
Figure 10. Figure 10: Rossby Wave composite in FourCastNet. Horizontal winds (quivers) and divergence [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 9
Figure 9. Figure 9: Rossby Wave composite in GraphCast. Horizontal winds (quivers) and divergence (colours, [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 11
Figure 11. Figure 11: Rossby Wave composite in Aurora. Horizontal winds (quivers) and divergence (colours, in [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: Composite Hovm¨oller Diagrams for the Rossby wave band from day [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.