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REVIEW 3 major objections 5 minor 2 cited by

ACE2-SOM: Coupling an ML atmospheric emulator to a slab ocean and learning the sensitivity of climate to changed CO$_2$

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read ACE2-SOM—a machine-learned atmospheric emulator coupled to a slab ocean—reproduces equilibrium temperature and precipitation change patterns under CO2 doubling, tripling, and quadrupling, including the unseen tripling case.

desk verdict Good, honest pilot showing an ML atmospheric emulator can hit equilibrium CO2 response patterns, but the flagship 3xCO2 result is bracketed interpolation between training climates, not proof of transferable sensitivity. read the letter →

arxiv 2412.04418 v2 pith:QRTJM3T7 submitted 2024-12-05 physics.ao-ph

Spencer K. Clark , Oliver Watt-Meyer , Anna Kwa , Jeremy McGibbon , Brian Henn , W. Andre Perkins , Elynn Wu , Lucas M. Harris
show 1 more author
Christopher S. Bretherton
This is my paper · ORCID
classification physics.ao-ph
keywords machine-learningclimateemulatorslaboceanmodelCO2sensitivityequilibriumresponseautoregressiveprecipitationextremesenergyconservationout-of-samplegeneralization
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

ACE2-SOM—a machine-learned atmospheric emulator coupled to a simplified slab ocean—is trained on equilibrium climates at 1x, 2x, and 4x CO2, then tested at 3x CO2, a concentration it never saw. The paper's central claim is that the emulator accurately reproduces the time-mean spatial patterns of surface temperature and precipitation change with CO2 doubling, tripling, or quadrupling, as well as the vertical profile of warming and changes in extreme precipitation up to the 99.9999th percentile. It also claims that non-equilibrium inference is more fragile: gradual CO2 increase yields correct surface and lower-atmosphere trends but unphysical jumps in the stratosphere, and an abrupt CO2 quadrupling warms the atmosphere too quickly, violating global energy conservation. The result matters because it is the first demonstration that an autoregressive ML emulator can be trained to respond to a substantial greenhouse-gas forcing rather than only to the historical climate.

What carries the argument

The central object is the differentiable coupling of the ACE2 neural atmospheric model to a slab ocean: each 6-hour step the ML model predicts the surface fluxes that make up $F_{\mathrm{net}}$, and the mixed-layer temperature is updated by $\rho_o C_o h\,\partial T_s/\partial t = F_{\mathrm{net}} + Q$, where $Q$ is a prescribed climatological ocean-heat-convergence (Q-flux). This lets the sea surface temperature respond to CO2-driven changes in surface energy fluxes while keeping the whole system trainable by backpropagation. The argument for CO2 sensitivity rides on the model learning to use the prescribed CO2 input to produce radiation and flux responses that match the equilibrium physics-model states it was trained on; the paper's multi-call radiation experiments probe whether those sensitivities are physical, and show that some are not.

What would settle it

Run the trained emulator at a CO2 level between 2x and 4x that was not used in training, for example 2.5x, and compare its equilibrium temperature and precipitation change patterns against a new physics-based reference run at that level; if the pattern errors are comparable to the 3x case, the sensitivity is generalizing, whereas a sharp error spike would indicate interpolation between the quantized training concentrations. A second decisive check is the paper's own radiation multi-call: hold the atmospheric state fixed and vary only CO2; if upward longwave flux at the surface or any shortwave flux changes with CO2, the learned radiative sensitivity is unphysical.

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Extended reading notes

Core claim

On its own terms, the paper establishes that ACE2-SOM, trained on equilibrium output from a 100-km-resolution physics-based model coupled to a slab ocean, can generalize its learned dynamics to a CO2 concentration between the training values. In the out-of-sample 3xCO2 equilibrium, time-mean surface temperature and precipitation biases are small, and the model reproduces the well-known pattern of greenhouse warming—tropical upper-tropospheric maximum, stratospheric cooling, land warming more than ocean—closely. Precipitation extremes up to the 99.9999th percentile of daily rates also match the target model, and the emulator's climate-change-pattern errors are smaller than or comparable to those of a 400-km physics-based baseline at a fraction of the cost. The same skill does not carry over to transitions: with gradually increasing CO2, stratospheric temperature and water content shift abruptly between values correlated with the quantized training CO2 levels, and with abrupt quadrupling, ML-predicted fields relax to the 4x regime faster than the slab ocean, producing a moist static energy budget imbalance and spurious sensitivity of surface and top-of-atmosphere radiative fluxes to CO2.

Load-bearing premise

The equilibrium skill depends on ACE2-SOM's CO2 response being a physically generalizable forcing mechanism rather than an interpolation among the three training CO2 levels; the paper's own evidence of spurious shortwave and upward-longwave flux sensitivities, and of stratospheric values that jump between quantized training levels, shows this assumption can be violated.

Editorial extensions

If this is right

  • If the central claim is correct, equilibrium climate sensitivity experiments—which currently require years of physics-based simulation—could be approximated by a trained ML emulator at roughly 100 times faster simulation speed.
  • The skill extends to precipitation extremes up to the 99.9999th percentile, suggesting the emulator captures not just mean shifts but the distributional response of the hydrological cycle to warming.
  • The out-of-sample 3x result implies the model has learned some generalizable relationship between CO2 forcing and the equilibrium state, rather than simply memorizing the three training climates.
  • The energy-conservation violation in abrupt-CO2 runs shows that autoregressive ML emulators need explicit physical constraints before they can be trusted for transient climate change scenarios.

Reading between the lines

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

  • A natural extension the paper does not pursue is to train on continuously varying CO2 trajectories instead of quantized equilibrium levels; the stratospheric regime shifts suggest this would break the spurious association between CO2 bins and slowly varying fields.
  • The spurious radiative sensitivities point toward a hybrid fix: letting a lightweight, differentiable radiation scheme handle CO2-dependent longwave transfer while the ML model learns the rest of the dynamics.
  • The same equilibrium-training protocol could be extended to other forcing agents—methane, aerosols, or land-use—as long as enough equilibrium reference climates are generated to span the forcing range.
  • One testable consequence of the paper's analysis is that a model trained on only 1x and 4x should fail at 3x if the sensitivity is interpolative; a per-CO2 multi-call diagnostic (net flux versus CO2) could serve as a cheap screening test for physicality.
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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 / 5 minor

Summary. This manuscript couples the Ai2 Climate Emulator version 2 (ACE2) to a slab ocean model, trains the resulting ACE2-SOM on equilibrium SHiELD-SOM output at 1x, 2x, and 4x CO2, and evaluates it in equilibrium (3x CO2) and non-equilibrium (2%/yr gradual increase, abrupt quadrupling) scenarios. The authors report that ACE2-SOM reproduces equilibrium surface temperature and precipitation change patterns, the vertical structure of warming and stratospheric cooling, and extreme precipitation distributions up to the 99.9999th percentile at 3x CO2, with smaller pattern RMSE than a coarse physics-based baseline in most cases. For non-equilibrium scenarios, ACE2-SOM captures global-mean surface temperature and precipitation trends in the gradual-increase case but shows stratospheric regime shifts, too-rapid adjustment under abrupt 4x CO2, violation of the global moist static energy budget, and spurious CO2 sensitivity of radiative fluxes in radiation multi-call experiments. The paper is transparent about these limitations and frames them as motivation for future work.

Significance. If the equilibrium results transfer beyond the specific 3x test, this is a noteworthy proof-of-concept: a learned 6-hourly atmospheric emulator coupled to a slab ocean can emulate the equilibrium climate response to CO2 changes at about 1500 simulated years per day, with public code, processed data, and model checkpoints provided. The paper also includes multiple ensemble members, a noise-floor estimate, and an explicit out-of-sample test, which are strengths. However, the central 'out-of-sample' claim is not yet fully supported, because 3x CO2 is bracketed by the 2x and 4x training concentrations and the paper's own diagnostics in Section 3.2.3 show that the learned CO2 sensitivity is partly unphysical. The honest reporting of non-equilibrium failures is a strength, but it also sharpens the need to determine whether the equilibrium skill reflects interpolation among training climates rather than a generalizable forcing mechanism.

major comments (3)
  1. [Section 3.2.3 and Figure 10; Section 3.2.1] The radiation multi-call experiments show that ACE2-SOM predicts CO2-dependent shortwave fluxes and surface-upward longwave flux that are physically spurious, and that it misses the logarithmic dependence of longwave fluxes on CO2. Section 3.2.1 additionally shows stratospheric fields jumping among values correlated with the quantized training CO2 levels. Because 3x CO2 lies between the 2x and 4x training concentrations, and because the equilibrium test states co-vary with CO2 as in training, the low 3x pattern RMSE is consistent with interpolation among neighboring training climates and does not by itself establish that the learned sensitivity is physically generalizable. I ask the authors to add an exterior-extrapolation equilibrium test (for example 1.5x or 5x CO2, or retraining on 1x/3x/4x and reporting 2x), and to either temper the abstract's 'out-of-sample' wording or qualify it as 'unseen intermediate concentration' until such a test is provided.
  2. [Section 2.2.2 and Section 3.3/Figure 11] The primary equilibrium results in Figures 1-5 are shown for the single best of four random seeds, selected by validation inference. Section 3.3 and Figure 11 reveal non-negligible seed-to-seed spread in the equilibrium climate-change-pattern RMSE for the equilibrium-trained models, but the main text does not quantify this spread for the 3x case or report whether all seeds beat the C24 baseline and remain close to the noise floor. For a central claim about equilibrium skill, the manuscript should report the median and range across seeds for the 3x temperature and precipitation change-pattern RMSE, or present all-seed results in the main text.
  3. [Section 2.2.3 and Section 3.2.2/Figure 9] The paper labels the gradual-increase and abrupt-4x runs as 'out-of-sample,' but the 3x equilibrium run is out-of-sample only in its CO2 value, whereas the non-equilibrium runs are out-of-sample in the combination of CO2 and atmospheric/surface state. This distinction matters because the abrupt-4x run violates global energy conservation (Figure 9) and shows radiative-flux sensitivities that are not physically consistent (Figure 10d). The authors should state explicitly in the abstract and conclusions that the equilibrium skill is not yet evidence of generalizable transient sensitivity, and should reserve 'out-of-sample' for tests that do not lie inside the convex hull of the training forcings or should clearly define the term if they keep the current usage.
minor comments (5)
  1. [Abstract] The sentence 'they violate global energy conservation and exhibit unphysical sensitivities of and surface and top of atmosphere radiative fluxes' contains a typo; it should read 'unphysical sensitivities of surface and top-of-atmosphere radiative fluxes.'
  2. [Figure 3 caption] The caption states 'relative that for C96 SHiELD-SOM'; the phrase should read 'relative to that for C96 SHiELD-SOM.'
  3. [Section 3.1.1] The noise-floor estimate in Equation (4) is described briefly; it would aid reproducibility to state explicitly that the windows are drawn from the same 50-year reference used as the target, and to note any caveat about non-independence between the emulator's internal variability and the reference variability.
  4. [Figure 7 caption] The panels labeled 'air_temperature_0' and 'specific_total_water_0' refer to the top atmospheric layer of ACE2's vertical coordinate; the caption should define the numbering convention for the layer index.
  5. [Table 1] The footnote describing the increasing-CO2 run says 'CO2 increases at a rate of 2% year-1 thereafter up to about 4x CO2 in 2100'; since the run starts in 2030 and rises for 70 years, the compound increase is approximately 3.9x, so 'about 4x' is fine but the arithmetic could be stated explicitly to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: ACE2-SOM is an explicitly fitted emulator whose equilibrium-climate claims are tested against a separately simulated physics-based benchmark, with the 3xCO2 case held out of training and in-sample cases labeled as such.

full rationale

The paper does not present a derivation-from-first-principles; it trains an autoregressive ML emulator on SHiELD-SOM reference output at 1x, 2x, and 4x CO2 and evaluates it on a held-out 3xCO2 equilibrium, a gradual-CO2-increase run, and an abrupt-quadrupling run. The central skill metric is RMSE of ACE2-SOM's equilibrated fields against C96 SHiELD-SOM, a separate physics-based model, so the evaluation is not equivalent to the training objective by construction. Section 2.2.3 explicitly labels 2x and 4x as in-sample and 3x as out-of-sample, so the paper is not renaming fitted reproduction as prediction. The main legitimate concern—that 3x skill may partly reflect interpolation between the bracketing 2x and 4x training climates rather than a physically generalizable CO2 forcing mechanism—is a limitation on external validity, not a circularity; the paper itself reports evidence in Sections 3.2.1 and 3.2.3 (stratospheric regime shifts and spurious radiative sensitivities) that the learned CO2 dependence is not fully physical. Self-citations to Watt-Meyer et al. (2024) for ACE2 architecture and training configuration are methodological and not load-bearing for the new claim, which is evaluated on data generated for this study. No equation-level reduction of the claimed prediction to its inputs was found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim depends on fitted ML weights, a chosen checkpoint, and domain assumptions about the slab ocean and prescribed sea ice. No new physical entities are introduced.

free parameters (3)
  • Neural network weights of ACE2-SOM (SFNO) = Not enumerated; millions of parameters
    Trained on 40 years each of 1x, 2x, and 4x CO2 SHiELD-SOM output; the central emulation skill is a function of these fitted weights.
  • Checkpoint selection among 4 random seeds = Best inline inference skill on 1x/2x/4x validation
    Section 2.2.2: 'we train models with four different random seeds, and focus on results with the model that produced the best inline inference skill.' This choice can inflate reported skill.
  • Training hyperparameters (embedding dimension, vertical levels, epochs) = 384, 8, 30
    Chosen by hand and inherited from ACE2; central results depend on this configuration.
assumptions (5)
  • domain assumption Slab ocean equation (Eq 1) with prescribed Q-flux and mixed layer depth
    Ocean heat transport Q-flux is prescribed from a climatology derived in a separate 1xCO2 run; the paper assumes this Q-flux remains valid across all CO2 levels.
  • domain assumption Prescribed sea ice climatology
    Section 2.1.2: 'we prescribe sea ice based on the same annually repeating observational climatology'; this removes ice-albedo feedback, a known amplifier of CO2 sensitivity.
  • domain assumption SHiELD-SOM reference simulations are treated as ground truth
    All skill metrics are computed relative to C96 SHiELD-SOM; the emulator cannot exceed the fidelity of this target, including its biases.
  • domain assumption The 6-hour autoregressive ML state is sufficient to determine the climate response to CO2
    Sections 3.2.1 and 3.2.3 show this assumption is violated for stratospheric variables and radiative flux sensitivities, undermining generalization to non-equilibrium scenarios.
  • standard math Energy budget equation (Eq 5) from Neelin and Held (1987)
    Used to diagnose energy conservation in the abrupt 4xCO2 test; standard moist static energy budget.

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Cite this review

Pith. "Pith review of ACE2-SOM: Coupling an ML atmospheric emulator to a slab ocean and learning the sensitivity of climate to changed CO$_2$." pith.science (2026). https://pith.science/paper/QRTJM3T7

@misc{pith2026241204418,
  author       = {Pith},
  title        = {Pith review of: ACE2-SOM: Coupling an ML atmospheric emulator to a slab ocean and learning the sensitivity of climate to changed CO$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QRTJM3T7}},
  note         = {Machine review of arXiv:2412.04418}
}
abstract

While autoregressive machine-learning-based emulators have been trained to produce stable and accurate rollouts in the climate of the present-day and recent past, none so far have been trained to emulate the sensitivity of climate to substantial changes in CO$_2$ or other greenhouse gases. As an initial step we couple the Ai2 Climate Emulator version 2 to a slab ocean model (hereafter ACE2-SOM) and train it on output from a collection of equilibrium-climate physics-based reference simulations with varying levels of CO$_2$. We test it in equilibrium and non-equilibrium climate scenarios with CO$_2$ concentrations seen and unseen in training. ACE2-SOM performs well in equilibrium-climate inference with both in-sample and out-of-sample CO$_2$ concentrations, accurately reproducing the emergent time-mean spatial patterns of surface temperature and precipitation change with CO$_2$ doubling, tripling, or quadrupling. In addition, the vertical profile of atmospheric warming and change in extreme precipitation rates up to the 99.9999th percentile closely agree with the reference model. Non-equilibrium-climate inference is more challenging. With CO$_2$ increasing gradually at a rate of 2% year$^{-1}$, ACE2-SOM can accurately emulate the global annual mean trends of surface and lower-to-middle atmosphere fields but produces unphysical jumps in stratospheric fields. With an abrupt quadrupling of CO$_2$, ML-controlled fields transition unrealistically quickly to the 4xCO$_2$ regime. In doing so they violate global energy conservation and exhibit unphysical sensitivities of and surface and top of atmosphere radiative fluxes to instantaneous changes in CO$_2$. Future emulator development needed to address these issues should improve its generalizability to diverse climate change scenarios.

Figures

Figures reproduced from arXiv: 2412.04418 by the authors.

Figure 1
Figure 1. Time series of daily and global mean surface temperature (a) and precipitation (b) with 3xCO2 in each ensemble member of C96 SHiELD-SOM (black) and ACE2-SOM (blue). Time and ensemble mean bias in surface temperature (c) and precipitation (d) in ACE2-SOM relative to C96 SHiELD-SOM, and the same for C24 SHiELD-SOM relative to C96 SHiELD￾SOM in (e) and (f). Note that ACE2-SOM bias maps are plotted at 1◦ resolution, whi… view at source ↗
Figure 2
Figure 2. 4 ◦ root mean square error of the time and ensemble mean for all variables predicted by ACE2-SOM (blue), compared to that for C24 SHiELD-SOM (orange) and a noise floor esti￾mate (gray). Error bars represent ± 2 standard deviations of the noise floor. The uncertainty is assumed to be similar for ACE2-SOM and C24 SHiELD-SOM, so we use the same error bars, though the logarithmic scale of the y-axis makes the size of th… view at source ↗
Figure 3
Figure 3. Time and ensemble mean difference in surface temperature between the 3xCO2 climate and 1xCO2 climate in C96 SHiELD-SOM (a), ACE2-SOM (c), and C24 SHiELD-SOM (e). Panels (d) and (f) show the error in emulating this change pattern for ACE2-SOM and C24 SHiELD-SOM, respectively. Panel (b) shows the global 4◦ RMSE of the climate change pat￾tern for all the perturbed climates for ACE2-SOM and C24 SHiELD-SOM relative that … view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: As for [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: As for [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Histograms of daily-mean precipitation rate in C96 SHiELD-SOM (black), ACE2- SOM (blue), and C24 SHiELD-SOM (orange) in the 1xCO2 (thin lines) and 3xCO2 (thick lines) equilibrium climates. C96 SHiELD-SOM and ACE2-SOM data has been regridded to 4◦ resolu￾tion for a fair…
Figure 7
Figure 7. Figure 7: Time evolution of global annual mean surface temperature (a), stratospheric tem￾perature (b), precipitation rate (c), and stratospheric specific total water (d) in C96 SHiELD￾SOM (black), ACE2-SOM (blue), and C24 SHiELD-SOM (orange). The vertical dashed lines at years …
Figure 8
Figure 8. Figure 8: Time evolution of global monthly mean temperature at the fourth vertical level, numbered from top of atmosphere to bottom (a), ocean monthly mean surface temperature (b), and global monthly mean specific total water at the fourth vertical level (c) in a simulations whe…
Figure 9
Figure 9. Figure 9: 6-hourly global mean column-integrated moist static energy tendency (a) and net energy flux into the atmosphere (b) in the first two months of an inference run with abruptly quadrupled CO2 with C96 SHiELD-SOM (black), ACE2-SOM (blue), and C24 SHiELD-SOM (orange). –19– …
Figure 10
Figure 10. Figure 10: One-year mean difference between radiative flux components predicted with CO2 perturbed by a varying scale factor and those predicted with 1xCO2. Regions with gray shading correspond to CO2 concentrations that are outside the range seen during training. 1.74xCO2 and 2…
Figure 11
Figure 11. Figure 11: Global 4◦ root mean square error of the time and ensemble mean climate change pattern of surface temperature (a) and precipitation (b) with C24 SHiELD-SOM (orange), ACE2-SOM trained only on equilibrium climate data (blue), and ACE2-SOM trained only on output from the …
Figure 12
Figure 12. Figure 12: Global annual mean time series of surface temperature (a) and (d), stratospheric temperature (b) and (e), and stratospheric specific total water (c) and (f) in equilibrium-climate￾trained models (top row) and increasing-CO2-trained models (bottom row). The target C96 …

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