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arxiv: 2606.07928 · v1 · pith:NZMD7XQ6new · submitted 2026-06-06 · ⚛️ physics.ao-ph

Disentangling the effects of sea surface temperature and CO₂ in global machine learned weather-climate emulators

Spencer K. Clark , Troy Arcomano , James P. C. Duncan , Brian Henn , Anna Kwa , Jeremy McGibbon , W. Andre Perkins , Elynn Wu
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Lucas M. Harris Oliver Watt-Meyer Christopher S. Bretherton
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Pith reviewed 2026-06-27 19:12 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords climate emulatormachine learningsea surface temperatureCO2 forcingrandom-CO2 simulationsenergy conservationweather-climate modelingAMIP
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The pith

Training climate emulators on data where sea surface temperature and CO2 vary independently enables accurate simulation of previously inaccessible scenarios like AMIP +4 K and abrupt 4xCO2.

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

Prior machine-learned climate emulators failed outside narrow ranges because their training data tied sea surface temperature and CO2 together, preventing the models from learning the distinct influence of each. The paper demonstrates that adding reference simulations in which those two drivers change independently, balanced with standard AMIP and equilibrium runs plus an energy conservation constraint, produces an emulator that works across both familiar and new forcing cases. A reader would care because this removes a key barrier to using fast emulators for exploring climate responses that full physics models cannot reach quickly. The approach keeps the model interpretable by enforcing conservation while inheriting the reference model's biases.

Core claim

Trained on a balance of AMIP, equilibrium-climate, and random-CO2 data where SST and CO2 vary independently, together with a total energy conservation constraint, the resulting model accurately emulates its reference model not only in the scenarios where earlier versions succeeded but also in AMIP +4 K and slab-ocean-coupled abrupt 4xCO2 cases where they produced unphysical behavior.

What carries the argument

Random-CO2 reference simulations in which sea surface temperature and CO2 are prescribed to vary independently, breaking their correlation in prior training datasets.

If this is right

  • The emulator reproduces reference-model output in AMIP +4 K scenarios.
  • The emulator reproduces reference-model output under slab-ocean-coupled abrupt 4xCO2 forcing.
  • The model is more data-efficient than predecessors while maintaining accuracy in standard AMIP and equilibrium-climate regimes.
  • Enforcing total energy conservation improves interpretability of the emulator's response to separate SST and CO2 changes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same independent-variation training strategy could be tested on other pairs of correlated climate drivers such as aerosol loading and temperature.
  • Extending the method to include interactive ocean or land components would test whether the disentangling benefit survives when more Earth-system feedbacks are active.
  • The energy-conservation constraint might be combined with additional physical constraints to further reduce drift in long integrations.

Load-bearing premise

Prescribing SST and CO2 to vary independently in the random-CO2 simulations is enough to overcome the correlation problem and let the model learn their separate effects.

What would settle it

Running the new emulator on AMIP +4 K or abrupt 4xCO2 forcing and observing the same unphysical behavior seen in earlier models would show the central claim does not hold.

Figures

Figures reproduced from arXiv: 2606.07928 by Anna Kwa, Brian Henn, Christopher S. Bretherton, Elynn Wu, James P. C. Duncan, Jeremy McGibbon, Lucas M. Harris, Oliver Watt-Meyer, Spencer K. Clark, Troy Arcomano, W. Andre Perkins.

Figure 1
Figure 1. Figure 1: Time-varying uniform sea surface temperature perturbation (a) and CO2 concen￾tration logarithmically centered about 1x (b), 2x (c), and 4x (d) the year-1997 CO2 concentration in each ensemble member of the random-CO2 simulations. step fine-tuning, we use a randomly selected number of steps per batch between 1 and 20 following the distribution in Perkins et al. (2026), optimizing on only the last predicted … view at source ↗
Figure 2
Figure 2. Figure 2: Global annual mean time series of 2 m temperature (a) and total water path (b) in an ensemble of simulations with SHiELD, ACE2-SHiELD, and ACE2S-SHiELD+ between 1980 and 2020. The gray shaded region indicates the region of the dataset held out from train￾ing of ACE2S-SHiELD+, though note it was included in training ACE2-SHiELD. Bias maps of 2012-2020-mean 2 m temperature and precipitation rate for ACE2-SHi… view at source ↗
Figure 3
Figure 3. Figure 3: Global daily mean time series of surface temperature (a) and precipitation rate (b) in a five-member ensemble of 10-year SOM-coupled simulations with SHiELD (black) and ACE2S-SHiELD+ in a 3xCO2 equilibrium climate. Bias maps of time and ensemble mean surface temperature and precipitation rate for ACE2-SOM (c)-(d) and ACE2S-SHiELD+ (e)-(f). –11– [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Global annual mean time series of surface temperature (a), stratospheric tem￾perature (b), precipitation rate (c), and stratospheric specific total water (d) in a two-member ensemble of 70-year SOM-coupled 2pctCO2 simulations with SHiELD, ACE2-SOM, and ACE2S￾SHiELD+. 3.1.3 2pctCO2 inference ACE2S-SHiELD+ also exhibits comparable skill to ACE2-SOM in SOM-coupled inference with CO2 increasing at a rate of 2 … view at source ↗
Figure 5
Figure 5. Figure 5: AMIP inference initialized in 1979 with fixed CO2 (solid lines): global annual mean 2 m temperature (a) and stratospheric temperature (b) in SHiELD, ACE2-SHiELD, ACE2S￾SHiELD+no-RC, and ACE2S-SHiELD+. To give a sense for the impact of holding the CO2 constant on each of these fields, the dashed black line shows their evolution in SHiELD in a traditional AMIP simulation with time-varying CO2. spite this, it… view at source ↗
Figure 6
Figure 6. Figure 6: 2012 through 2020 mean difference in 2 m temperature between an AMIP +4 K simulation and an AMIP simulation with SHiELD (a), ACE2-SHiELD (b), ACE2S￾SHiELD+no-RC (c), and ACE2S-SHiELD+ (d). Panels (e)-(g) show the response pattern error relative to the target SHiELD. –14– [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: CO2 forcing (a), global mean stratospheric temperature (b), and global mean 2 m temperature (c) in mostly held-out random-CO2 inference centered about 4xCO2 in SHiELD, ACE2-SOM, ACE2S-SHiELD+no-RC, and ACE2S-SHiELD+. Periods where the CO2 forcing was fully held out from training or validation are shaded in gray. Note we have inverted the y-axis in panel (a) to highlight the expected inverse relationship be… view at source ↗
Figure 8
Figure 8. Figure 8: Global, daily, and ensemble mean time series of lowest level temperature (a), mid-tropospheric temperature (b), stratospheric temperature (c), precipitation rate (d), latent heat flux (e), and total water path (f) in SOM-coupled abrupt 4xCO2 simulations (solid lines) with SHiELD, ACE2-SOM, ACE2S-SHiELD+no-RC-no-EC, ACE2S-SHiELD+no-RC, ACE2S￾SHiELD+no-EC, and ACE2S-SHiELD+. The dashed black line in each pan… view at source ↗
Figure 9
Figure 9. Figure 9: Time-and-ensemble-mean response to abrupt 4xCO2 of latent heat flux over the initial 7 days of SOM-coupled simulation with SHiELD (a), ACE2-SOM (b), ACE2S￾SHiELD+no-RC (c), and ACE2S-SHiELD+ (d). Panels (e)-(g) show the corresponding pattern errors of the ML models relative to SHiELD. –18– [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: As in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: As in [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Regional-mean evolution of various fields in a single 10-year SOM-coupled abrupt 4xCO2 inference simulation with SHiELD, ACE2-SOM, ACE2S-SHiELD+no-RC, and ACE2S￾SHiELD+. Panels (a) and (b) show the ocean- and land-mean surface temperature, respectively; panel (c) shows the global mean uppermost model layer temperature; and panel (d) shows the global mean upward longwave radiative flux at the top of the at… view at source ↗
read the original abstract

While previous versions of the Ai2 Climate Emulator (ACE) have been trained with CO$_2$ as a forcing, they are only accurate within a narrow range of scenarios, for example climate over the last 80 years forced by observed sea surface temperature (SST), sea ice, and CO$_2$ (AMIP), or equilibrium or near-equilibrium climates with CO$_2$ concentrations ranging from 1x to 4x that of the present day. Attempting to simulate climate forced by AMIP SST perturbed by +4 K or the response to an abrupt quadrupling of CO$_2$, results in unphysical behavior. We attribute this to these models being trained on datasets where the SST and CO$_2$ are correlated, limiting their ability to accurately learn their separate effects. In this study we introduce a new class of "random-CO$_2$" reference simulations where the SST and CO$_2$ are prescribed to vary independently. Trained on a balance of AMIP, equilibrium-climate, and random-CO$_2$ data, and including a total energy conservation constraint for improved interpretability, we present a more data-efficient model that not only accurately emulates its reference model in scenarios in which previous models excelled, but also scenarios like AMIP +4 K and slab-ocean-coupled abrupt 4xCO$_2$ where they did not. Limitations are that it has simplified or prescribed representations of other Earth system components like the ocean, land, and sea ice; does not expose other known climate drivers as forcings; and relies solely on physics-based model output for training data, inheriting the biases relative to observations thereof. Each of these represent opportunities for future work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that previous ACE emulators fail in out-of-distribution scenarios (AMIP +4 K, abrupt 4xCO2) because training data had correlated SST and CO2; it introduces random-CO2 reference simulations where SST and CO2 are prescribed independently, trains a balanced mixture of AMIP, equilibrium, and random-CO2 data, adds a total energy conservation constraint, and reports improved emulation accuracy and physical consistency in the previously failing regimes.

Significance. If the quantitative results hold and the disentanglement is demonstrated, the work would address a recognized limitation in ML climate emulators—the inability to generalize when forcings are decorrelated—while adding a physically motivated constraint. The data-generation strategy and energy constraint are concrete, reproducible contributions that could be adopted by other emulator efforts.

major comments (2)
  1. [Abstract / §3] Abstract and §3 (training data and model description): the central claim that independent prescription of SST and CO2 in the random-CO2 runs is sufficient to let the network learn their separate effects rests on an untested assumption. The emulator receives joint atmospheric states as input; without an explicit architectural separation (e.g., separate forcing channels) or auxiliary loss (e.g., counterfactual or attribution terms), the network could still learn only joint mappings. The energy constraint improves conservation but does not isolate the two forcings. This is load-bearing for the generalization results in AMIP+4 K and abrupt 4xCO2.
  2. [Results] Results section (quantitative validation): the abstract states improved performance but supplies no error metrics, skill scores, or uncertainty ranges for the new scenarios. Without these numbers (and comparison to the prior ACE versions on the same test cases), it is impossible to judge whether the claimed improvement is statistically meaningful or merely qualitative.
minor comments (2)
  1. [Abstract] The limitations paragraph is appropriately candid; it could be expanded with a short discussion of how the simplified ocean/land/sea-ice representations might still induce biases even after the SST/CO2 disentanglement step.
  2. [Methods] Notation for the energy constraint should be defined explicitly (e.g., which fluxes are included in the total energy residual) so that readers can reproduce the loss term.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of our methodology and presentation. We address each major comment below and will revise the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract / §3] Abstract and §3 (training data and model description): the central claim that independent prescription of SST and CO2 in the random-CO2 runs is sufficient to let the network learn their separate effects rests on an untested assumption. The emulator receives joint atmospheric states as input; without an explicit architectural separation (e.g., separate forcing channels) or auxiliary loss (e.g., counterfactual or attribution terms), the network could still learn only joint mappings. The energy constraint improves conservation but does not isolate the two forcings. This is load-bearing for the generalization results in AMIP+4 K and abrupt 4xCO2.

    Authors: We agree that our method does not include explicit architectural separation or auxiliary losses to enforce disentanglement, and that the energy constraint addresses conservation rather than isolation of forcings. The approach instead relies on exposing the model to training data with independently varying SST and CO2 via the random-CO2 simulations, which breaks the correlations present in standard datasets. The improved performance in decoupled scenarios provides empirical support, but we acknowledge this remains a data-driven assumption rather than a mechanistically proven separation. We will revise §3 to explicitly discuss this assumption, its limitations, and implications for generalization. We will also add a brief ablation comparing performance with and without the random-CO2 data to better quantify its role. revision: partial

  2. Referee: [Results] Results section (quantitative validation): the abstract states improved performance but supplies no error metrics, skill scores, or uncertainty ranges for the new scenarios. Without these numbers (and comparison to the prior ACE versions on the same test cases), it is impossible to judge whether the claimed improvement is statistically meaningful or merely qualitative.

    Authors: The results section of the manuscript includes quantitative validation and comparisons to prior ACE versions, but we accept that the abstract lacks specific metrics. We will revise the abstract to report key error metrics (such as RMSE for temperature, humidity, and wind fields), skill scores, and uncertainty ranges for the AMIP+4 K and abrupt 4xCO2 scenarios, with explicit side-by-side comparisons to previous ACE emulators on the same test cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity; improvements rely on new independent data and constraint

full rationale

The paper's central claim rests on generating new 'random-CO2' reference simulations where SST and CO2 vary independently (explicitly stated in the abstract), training a neural network emulator on a balanced mix of these plus AMIP and equilibrium data, and adding a total energy conservation constraint. Performance gains on AMIP+4K and abrupt 4xCO2 scenarios are presented as empirical outcomes of this expanded training distribution and constraint, not as quantities derived by construction from fitted parameters or prior self-citations. No equations or steps reduce the claimed disentanglement to a renaming, self-definition, or load-bearing self-citation chain. The architecture receives joint states but the separation is attributed to the data design itself, which is externally generated and falsifiable. This is a standard data-driven ML setup with no load-bearing circular reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on abstract; the central claim rests on the assumption that independent variation in training data disentangles effects, plus the domain assumption that energy conservation aids interpretability. No specific numerical free parameters or invented entities are detailed.

axioms (2)
  • domain assumption SST and CO2 correlation in training data limits ability to learn separate effects
    Invoked to explain prior model failures (abstract).
  • domain assumption Total energy conservation constraint improves interpretability
    Added to the model as stated in abstract.

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discussion (0)

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Reference graph

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