Disentangling the effects of sea surface temperature and CO$_2$ in global machine learned weather-climate emulators

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.

• The paper demonstrates that including decoupled SST and CO₂ training data enables robust separation of their respective impacts in machine-learned climate emulators.
• The novel stochastic architecture, enhanced with physical constraints and energy conservation, achieves accurate replication of both instantaneous and equilibrium climate responses.
• The approach underscores the importance of diverse training data for reliable extrapolation to policy-relevant and extreme forcing scenarios.

Disentangling SST and CO$_2$ Effects in Machine-Learned Global Climate Emulators

Introduction

This paper addresses a critical limitation in current ML-based atmospheric emulators: poor generalization to climate scenarios where key forcings—sea surface temperature (SST) and atmospheric CO$_2$ concentration—are independently perturbed, a regime often encountered in idealized and policy-relevant climate experiments. Previous instantiations of the Ai2 Climate Emulator (ACE) demonstrated good performance within the narrow support of their training distributions, where SST and CO$_2$ are highly correlated, but produced unphysical or erroneous results when these forcings are decoupled. The presented work introduces new reference datasets and a stochastic model architecture to robustly separate and emulate the respective climate responses to changes in SST and CO$_2$, with explicit attention to energy conservation and data efficiency.

Methodology

The study leverages the SHIELD atmospheric GCM at coarse resolution as the emulation target, consistent with prior ACE work. Three categories of reference simulations are utilized:

• AMIP (Atmospheric Model Intercomparison Project): Periods with observed SST, sea ice, and transient CO$_2$ concentration.
• SOM-coupled: Equilibrium, transient, and abruptly forced runs with a slab-ocean model, sampling a range of CO$_2$ levels (1x–4x present).
• Ramped-SST-random-CO$_2$: Novel reference simulations wherein ensemble members are forced with dynamically and independently evolving SST and CO$_2$—thereby breaking their climatological correlation.

Models are trained in two principal configurations: with and without inclusion of the random-CO$_2$ datasets. Additionally, ablations are performed on the use of a global energy conservation corrector. The ML architecture evolves from previous deterministic spherical Fourier neural operators (SFNO) to a stochastic variant akin to ACE2S with increased model capacity (embedding dimension), probabilistic loss (CRPS/energy score), and physical constraints (flux positivity, global and column moisture/dry air conservation).

Numerical Results

Standard Scenarios (Correlated SST and CO$_2$)

In conventional regimes where SST and CO$_2$0 remain correlated—as in historical AMIP or equilibrium slab-ocean experiments—the model trained with random-CO$_2$1 data ("ACE2S-SHIELD$_2$2") achieves performance comparable to baseline ACE2-SHIELD and ACE2-SOM. This includes:

• R$_2$3 of 0.81–0.93 for annual global-mean 2m temperature, competitive with baselines.
• Ensemble spread and precipitation statistics consistent with the target model.
• Minor increases in pattern RMSE over sea-ice regions, likely attributed to limited training in these boundary regimes.
• Long-term stability in coupled equilibrated climates, with one out of four 1000-year runs exhibiting an upper-stratospheric shift, attributed primarily to model stochasticity.

Out-of-Distribution Forcings (Uncorrelated SST and CO$_2$4)

The core advancement is in scenarios characterized by strong SST–CO$_2$5 decorrelation:

• AMIP with Fixed CO$_2$6: Baseline ACE2-SHIELD underestimates the surface warming response when CO$_2$7 is held fixed and SST is allowed to evolve, while ACE2S-SHIELD$_2$8 accurately distinguishes the correct roles of each forcing on surface and stratospheric temperatures.
• AMIP +4K (Uniform SST Increase): ACE2S-SHIELD$_2$9 recovers the physically expected near-uniform surface warming ($_2$04.4 K global mean, RMSE $_2$1 0.3 K) and correct radiative and hydrological responses, outperforming ablated models and previous literature where land surface cooling was spuriously predicted under these circumstances.
• Ramped-SST-random-CO$_2$2: In instances with highly variable, independently sampled CO$_2$3 and SST paths, only models exposed to this decorrelated domain during training emulate the correct instantaneous and equilibrated responses in the troposphere and stratosphere, both in trend and response timescale.
• Abrupt 4xCO$_2$4 (SOM-Coupled): Models without random-CO$_2$5 training demonstrate nonphysical, step-like temperature adjustments or an unrealistically fast precipitation and hydrological cycle response due to misattribution of forcing sources. ACE2S-SHIELD$_2$6 not only reproduces the correct radiative, thermodynamic, and moisture responses but also accurately captures the timescales and spatial patterns of adjustment over both short (90-day) and long (10-year) horizons.

Role of Energetic Constraints

Inclusion of a global energy conservation corrector improves interpretability and attenuates some pathologies when random-CO$_2$7 data is not present, but is not, by itself, sufficient to guarantee physical generalization to held-out or extreme forcing scenarios. Once randomly sampled CO$_2$8 states are included in the training regime, the stochastic model recovers energy-conserving, robust behavior, and the benefit of the explicit energy corrector becomes marginal for the considered metrics.

Implications and Future Directions

This study demonstrates that data-driven atmospheric emulators can accurately and stably generalize to a much wider manifold of climate forcing scenarios if their training data properly samples the space of independently evolving boundary conditions and drivers. The results underscore the paramount importance of training data diversity—not just for i.i.d. interpolation, but for robust extrapolation to out-of-distribution or policy-relevant future scenarios.

The approach delineates a scalable path toward unified, data-driven general circulation emulation frameworks that remain accurate under non-equilibrium and idealized forcing regimes—scenarios central to physical attribution, feedback evaluation, and impact assessment experiments. However, important limitations remain:

• Component limitations: The current architecture employs highly simplified or prescribed representations of ocean, land, and ice, restricting its application to fully coupled, interactive Earth system modeling.
• Limited forcing exposure: Only CO$_2$9 is considered; future models must address more complex, multi-forcing scenarios (e.g., aerosols, CH$_2$0, N$_2$1O) with similar decorrelation and data generation strategies.
• Dependence on GCM “perfect model” assumption: Transfer to observation-trained models faces additional generalization and bias correction challenges.

Potential extensions include integration into coupled emulators (e.g., “SamudrACE”) and hybrid physics-ML frameworks to further improve extrapolative skill, especially where explicit constraints (e.g., conservation laws) can be more tightly integrated with learned representations.

Conclusion

By supplementing ML-based atmospheric emulator training with simulations spanning uncorrelated SST and CO$_2$2 evolution, the presented methodology yields a stochastic neural surrogate that robustly separates and emulates the climate impacts of major external forcings. This addresses previously identified generalization failures in ML-based climate models, facilitating their application to a more comprehensive set of idealized and future climate scenarios while maintaining computational and data efficiency. The findings reinforce the essential interplay between training data design and physical emulator reliability, setting clear research directions towards robust, multi-forcing, coupled-system emulation.