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REVIEW 3 major objections 3 minor 8 cited by

ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read ACE2, a 450-million-parameter learned atmospheric model, can be stepped forward stably for arbitrarily many steps and reproduces atmospheric variability from days to decades, including the response to El Niño and 80-year temperature trends.

desk verdict A serious step forward for learned climate emulators, but the forced-response claim is only established for combined historical forcing, not separable SST and CO2 responses. read the letter →

arxiv 2411.11268 v1 pith:WPOGER2V submitted 2024-11-18 physics.ao-ph cs.LG

Oliver Watt-Meyer , Brian Henn , Jeremy McGibbon , Spencer K. Clark , Anna Kwa , W. Andre Perkins , Elynn Wu , Lucas Harris
show 1 more author
Christopher S. Bretherton
This is my paper · ORCID
classification physics.ao-phcs.LG
keywords machinelearningemulatorclimatevariabilityforcedresponseElNiño-SouthernOscillationtropicalcyclonesMadden-Juliansubseasonal-to-decadalpredictionmassandmoistureconservation
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 tries to establish that a single learned atmospheric model can do what has been reserved for physics-based climate models: run stably for decades while responding to changing sea surface temperature and CO2. If true, a 450-million-parameter emulator could simulate climate variability and forced response at about 1,500 simulated years per wall-clock day, making century-scale ensembles and rare-event studies cheap. ACE2 is autoregressive, runs at 1° resolution with eight vertical layers and 6-hour steps, and is trained separately on the ERA5 reanalysis and on an AMIP-style SHiELD simulation. In 81-year rollouts it reproduces the reference datasets' temperature and moisture trends, the ENSO-driven precipitation pattern, tropical cyclone frequency, the Madden-Julian Oscillation, and sudden stratospheric warmings, while exactly conserving global dry air mass and moisture. The paper states plainly that its sensitivities to separately changing SST and CO2 are not entirely realistic, so the forced-response result is established for the combined historical forcing.

What carries the argument

The central object is ACE2 itself: an autoregressive Spherical Fourier Neural Operator that maps a 6-hourly atmospheric state plus forcing variables (SST, CO2, solar radiation, surface fractions) to the next state, with a physical-corrector module appended as part of the architecture. The corrector enforces exact global dry-air-mass conservation and a closed global moisture budget by adjusting surface pressure and precipitation and deriving the advective moisture tendency as a residual. The other load-bearing mechanisms are the use of CO2 as an input feature, training on two 80-year datasets with historical SST variability, and a checkpoint-selection criterion based on time-mean climate skill rather than short-term loss. Together these let ACE2 roll out for centuries under changing boundary conditions instead of drifting to a fixed climatology.

What would settle it

The decisive test is to generate paired SHiELD simulations with historical SST plus fixed CO2 and fixed SST plus historical CO2, then run ACE2 with the same factorial forcings; if ACE2's separated responses do not match the physics model's, the forced-response claim holds only for the combined historical forcing. The paper's Figure 14 already hints at this, since fixing CO2 removes most near-surface warming.

Watch

Extended reading notes

Core claim

ACE2's central claim is that a model trained only to predict two 6-hour steps ahead can be integrated autoregressively over 81 years and beyond without instability, while tracking the observed atmospheric response to changing boundary conditions. The paper reports that ACE2-ERA5 matches the global-annual mean 2-meter temperature of ERA5 with an $R^2$ of 0.93, that the ENSO-regressed precipitation map is as close to the reference as the reference's own internal variability, and that a 1000-year run under climatological forcing shows no drift in total water path. It generates tropical cyclones, the Madden-Julian Oscillation, and sudden stratospheric warmings as emergent behavior. The authors state the model 'can be stepped forward stably for arbitrarily many steps' and 'accurately reproduces the atmospheric response to El Niño variability and global trends of temperature over the past 80 years.' The same experiments show the separation of CO2 and SST forcing is incomplete: fixing CO2 at its 1940 value removes most near-surface warming and all stratospheric cooling, which is not physically expected.

Load-bearing premise

The load-bearing premise is that the 1940–2020 record, in which sea surface temperature and CO2 rise together, provides enough signal for the model to learn physically correct separate responses to each forcing, a premise the paper's fixed-CO2 test only partially confirms.

Editorial extensions

If this is right

  • Century-scale simulations become cheap enough for large ensembles: ACE2 runs about 1,500 simulated years per wall-clock day on one GPU, so separating forced response from internal variability no longer requires thousands of node-hours.
  • Because ACE2-ERA5 reproduces Madden-Julian Oscillation propagation, tropical cyclone statistics, and polar stratospheric vortex variability, it is a plausible fast platform for subseasonal-to-seasonal predictability studies.
  • The 4-degree version retains most of the 1-degree model's climate skill at a fraction of the cost, which would make paleoclimate and biogeochemistry applications tractable with a learned emulator.
  • The hard dry-air-mass and moisture constraints eliminate the long-term drift seen in the earlier ACE model; a 1000-year simulation forced by climatological 1990–2020 boundary conditions shows no drift in total water path.
  • Weather forecast skill is a separate axis: ACE2-ERA5 sits behind the IFS and GraphCast in medium-range RMSE, so climate fidelity does not automatically buy forecast skill.

Reading between the lines

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

  • Editorial extension: because SST and CO2 rise together in the 1940–2020 training record, the fixed-CO2 experiment suggests the two forcings are entangled in what the model learns; a factorial training set with historical SST at fixed CO2 and vice versa, which the authors note could be generated from SHiELD, is the natural test of whether separable sensitivities are learnable at all.
  • Editorial extension: the model is differentiable and cheap, so it invites use in data assimilation or parameter-estimation loops, where many forward integrations are needed.
  • Editorial extension: the same architecture and conservation constraints could extend to ocean or coupled emulation, since ACE2 itself is atmosphere-only with prescribed SST and sea ice.
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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

3 major / 3 minor

Summary. The paper presents ACE2, a 450M-parameter autoregressive machine learning emulator run at 1-degree resolution and 6-hour steps, trained on either ERA5 or an AMIP-style GFDL SHiELD simulation. It reports stable multi-decadal and millennial rollouts, exact dry-air mass and moisture conservation, realistic ENSO regression patterns, tropical cyclone statistics, MJO propagation, polar stratospheric variability, medium-range weather skill, and roughly 1500 simulated years per wall-clock day. The central claim is that ACE2 accurately captures subseasonal-to-decadal atmospheric variability and forced responses over 1940-2020, while the authors acknowledge that separately varying SST and CO2 produces non-realistic sensitivities.

Significance. If the main claims hold, this is a substantial advance for learned climate emulators: it demonstrates stable long autoregressive simulations under historically varying SST and CO2 forcing, with emergent phenomena such as TCs, MJO, and SSWs, and with enforceable conservation properties. The paper is unusually strong on reproducibility: training targets, code, and trained checkpoints are public, and the 10-year held-out test period, the 1000-year stability check, and the ENSO regression comparisons against reference internal variability provide concrete evidence. The main caveat is that the forced-response claim is broader than what the current evidence supports, because the model's separate SST and CO2 sensitivities are shown in Section 2.4 to be physically questionable.

major comments (3)
  1. [§2.2.1] The fixed-CO2 experiment directly tests the learned separate CO2 sensitivity, and it fails: when CO2 is held at 307 ppm while SST rises, ACE2-SHiELD loses most of the near-surface warming, including high-latitude land amplification that the paper itself (citing Screen et al., 2012) expects to be driven mainly by SST and sea-ice forcing. Because SST and CO2 rise together over 1940-2020, the training data cannot identify which forcing produced the learned trend, so the model's separate sensitivities are not physically grounded. This is load-bearing for the title/abstract claim of "forced responses": the paper establishes an accurate response to the combined historical SST+CO2 forcing, but not an accurate response to the individual forcing agents, which is what scenario interpolation would require. The Discussion in Section 3 acknowledges the limitation, but the framing should be revised, and/or the suggested SHiELD runs with historical SST/fixed CO2 and vice versa should be performed to test whether training-data augmentation fixes the attribution.
  2. [§2.1] The 81-year trend evaluation overlaps substantially with the training data (1940-1995 and 2011-2019) and with the validation/checkpoint-selection period (1996-2000; see Section 4.3). Although ACE2 is trained only on 6-hour transitions, the long-trend R2 values in Figure 1 reflect this overlap and therefore do not by themselves prove out-of-sample generalization of the 80-year trend. The held-out 2001-2010 test period supports the 10-year climate-skill and ENSO-response claims, but it is too short to validate the "past 80 years" trend claim. Please either report trend skill on a fully held-out period (for example, 2001-2010 only) or explicitly restate the trend claim as an in-sample/emergent property of the 6-hourly training objective.
  3. [§4.3] The final model is selected by climate skill over twelve 5-year inference runs spanning 1940-2000, with the q0 channel downweighted by a factor of 10, rather than by held-out test skill. This introduces a mild selection bias into the long-run skill statistics in Figures 1 and 13. The 10-year test period and Figure 20 mitigate the concern, but the paper should quantify how much of the reported 81-year skill is robust across the four training seeds and whether the q0 downweighting changes the qualitative conclusions.
minor comments (3)
  1. [Abstract and §2.4/§3] The phrase "forced responses" should be qualified as "responses to combined historical SST and CO2 forcing" unless the separate-forcing experiments are added, because the paper itself reports non-realistic separate SST and CO2 sensitivities.
  2. [§4.3 (Eq. 6)] The moisture-correction formula appears mis-typed: it should read ⟨E(t) − (TWP(t) − TWP(t−1))/Δt⟩ rather than ⟨E(t) − TWP(t) − TWP(t−1)/Δt⟩.
  3. [Typos] There are several typos: "that ERA5" (Section 2.2.3), "of of" and "variabilty" (Section 2.2.4), and "simmilar" (Appendix A.5).

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: held-out test-period evaluations carry the central claims, and the paper explicitly concedes imperfect separated SST/CO2 sensitivities.

full rationale

ACE2's central claims—81-year global-mean temperature and water-path trends, ENSO-regressed precipitation, MJO, tropical cyclone, and sudden stratospheric warming emergence, 1000-year stability, and exact mass and moisture conservation—do not reduce by construction to the model's fitted inputs or outputs. The model is trained only to predict two 6-hourly steps ahead, and the multi-decadal rollouts are generated autoregressively; no equation in the paper defines the predicted long-term trend as the training target, and the held-out test period (2001-2010, plus 2020) is used for the climate-skill RMSEs and ENSO regression maps, providing independent evidence for the central skill claims. The 81-year trend plots in Figure 1 overlap training and validation data, and the checkpoint-selection metric (Eq. 8) is evaluated over 1940-2000, so the reported 81-year R2 values are mildly in-sample with respect to model selection; this is an evaluation caveat, not a by-construction equivalence. The paper itself flags the most significant limitation: Section 2.4 and Figure 14 show that with CO2 held fixed at 1940 levels, ACE2-SHiELD 'loses much of the trend of near-surface warming, which is not expected,' and the abstract states that 'its sensitivities to separately changing sea surface temperature and carbon dioxide are not entirely realistic.' Thus the separated-forcing claim is explicitly qualified rather than concealed. Self-citations to prior ACE work serve as architecture and baseline references and do not carry a load-bearing uniqueness argument or smuggle in an unverified ansatz. No 'prediction' is a renamed fitted parameter, and no derived quantity equals its input by definition.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper contributes an empirical emulator, not a first-principles derivation. Its skill comes from fitting 450M parameters to 6-hourly data, so the free-parameter ledger is dominated by learned weights and hand-chosen training and selection hyperparameters. The central scientific assumptions are the adequacy of the reference datasets and the sufficiency of short-horizon training for long-horizon climate behavior; both are stated or only partially tested.

free parameters (4)
  • SFNO model parameters (approximately 450M) = learned from training data
    The emulator's dynamics are determined by weights fit to 6-hourly ERA5 and SHiELD transitions; the paper reports no closed-form equations for the learned response.
  • Loss weights for output variables (Table 2) = 0.25 to 10 depending on variable
    Chosen by hand to balance variables and to counteract overfitting and scale differences; they affect which dynamics are prioritized during training.
  • Checkpoint-selection weighting on q0 = 0.1 (downweighted by factor of 10)
    The best model across four training runs was chosen with q0 downweighted in Equation 8 because q0 otherwise dominated the climate-skill metric; disclosed in Section 4.3.
  • Training hyperparameters (embed_dim 384, 8 layers, learning rate 1e-4, etc.) = see Tables 6 and 7
    Selected for ERA5 and reused for SHiELD; no sensitivity analysis is shown for the reported results.
assumptions (5)
  • domain assumption ERA5 and the SHiELD AMIP simulation are adequate references for atmospheric variability and forced response over 1940-2020.
    These datasets are used as training targets and evaluation references; the paper notes ERA5 precipitation and radiation biases and SHiELD circulation biases, so reference errors propagate into the emulator.
  • domain assumption Six-hourly autoregressive training over two time steps is sufficient for the model to learn stable multi-decadal behavior.
    The training objective supervises only two 6-hour steps; stability and climate skill over 81 to 1000 year rollouts are assumed to emerge from this short-horizon objective.
  • ad hoc to paper The historical co-variation of SST and CO2 does not prevent the model from learning physically correct separate sensitivities.
    Section 2.4 shows this axiom is violated: holding CO2 fixed removes most of the near-surface warming. The paper acknowledges the limitation, so the forced-response claim is conditional on this assumption.
  • domain assumption The physical corrector for mass and moisture can be applied before computing the loss without introducing model bias.
    The paper states corrections are applied before the loss, making them part of the architecture, but does not prove they cannot distort learned relationships.
  • standard math Hydrostatic balance justifies replacing the tropical cyclone warm-core thickness criterion with an upper-tropospheric temperature criterion.
    Used in Section 2.2.3 to justify a 0.4 K temperature decrease instead of a 58.8 m2/s2 thickness decrease.

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Cite this review

Pith. "Pith review of ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses." pith.science (2026). https://pith.science/paper/WPOGER2V

@misc{pith2026241111268,
  author       = {Pith},
  title        = {Pith review of: ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WPOGER2V}},
  note         = {Machine review of arXiv:2411.11268}
}
read the original abstract

Existing machine learning models of weather variability are not formulated to enable assessment of their response to varying external boundary conditions such as sea surface temperature and greenhouse gases. Here we present ACE2 (Ai2 Climate Emulator version 2) and its application to reproducing atmospheric variability over the past 80 years on timescales from days to decades. ACE2 is a 450M-parameter autoregressive machine learning emulator, operating with 6-hour temporal resolution, 1{\deg} horizontal resolution and eight vertical layers. It exactly conserves global dry air mass and moisture and can be stepped forward stably for arbitrarily many steps with a throughput of about 1500 simulated years per wall clock day. ACE2 generates emergent phenomena such as tropical cyclones, the Madden Julian Oscillation, and sudden stratospheric warmings. Furthermore, it accurately reproduces the atmospheric response to El Ni\~no variability and global trends of temperature over the past 80 years. However, its sensitivities to separately changing sea surface temperature and carbon dioxide are not entirely realistic.

Figures

Figures reproduced from arXiv: 2411.11268 by the authors.

Figure 1
Figure 1. Global- and annual-mean series for a) 2-meter air temperature and c) total water path over [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. a) - c): Zonal- and time-mean for ACE2 (solid) and its reference datasets (dashed) over test [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Global RMSE between the time-mean of ACE2 and its reference dataset (ERA5 or [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: Maps of regression coefficients of predicted and reference dataset surface precipitation [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Tracks of tropical cyclone-like features over the 2001-2010 period for a) the IBTrACS [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Daily-mean precipitation rate averaged between 10 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Lag correlation of P 20−100day 10◦S−10◦N at all longitudes with P 20−100day 10◦S−10◦N averaged from 80°E to 100°E (e.g. Waliser et al., 2009). P 20−100day 10◦S−10◦N is the surface precipitation rate averaged from 10°S to 10°N, and then filtered with a 20-100 day bandpa…
Figure 8
Figure 8. Figure 8: Annual cycle of zonal-mean u0 (eastward wind vertically integrated from ∼50hPa to top of atmosphere) at (top row) 60◦N and (bottom row) 60◦S for (left column) ERA5 and (right column) ACE2-ERA5. For ERA5, each of the years from 2001-2010 test period are plotted. For ACE…
Figure 9
Figure 9. Figure 9: RMSE of ACE2-ERA5 during 2020, compared to GraphCast and IFS initialized from [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: The global mean total water path for the first and last 100 years of a 1000-year long [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: Single initial condition time-mean biases of [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: Bias of single initial condition ENSO regression coefficient maps of surface precipitation [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: Annual and global mean 2-meter temperature for 81-year inference using 3-member initial [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 14
Figure 14. Figure 14: Global- and annual-mean (a) 2-meter air temperature and (b) level-0 (stratospheric) air [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]
Figure 15
Figure 15. Figure 15: 2-meter air temperature linear trend over 1940-2020 in (a) ACE2-SHiELD and (b) the [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: As in Fig [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]
Figure 17
Figure 17. Figure 17: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p025_17.png]
Figure 18
Figure 18. Figure 18: The (left) minimum sea-level pressure and (right) maximum 10m wind speed within 2 [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]
Figure 19
Figure 19. Figure 19: a) Training and validation loss for ACE2-ERA5 and ACE2-SHiELD, over a 4-member [PITH_FULL_IMAGE:figures/full_fig_p026_19.png]
Figure 20
Figure 20. Figure 20: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p026_20.png]
Figure 21
Figure 21. Figure 21: Timeseries of 6-hourly global mean (a) surface pressure due to dry air only and (b) total [PITH_FULL_IMAGE:figures/full_fig_p027_21.png]
Figure 22
Figure 22. Figure 22: Across the three physical constraint ablation experiments with ACE2-SHiELD (top row) [PITH_FULL_IMAGE:figures/full_fig_p028_22.png]
Figure 23
Figure 23. Figure 23: As in Figure [PITH_FULL_IMAGE:figures/full_fig_p030_23.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.