ACE2S: Advanced AI Climate Emulator

• ACE2S is a neural operator-based emulator that models global atmospheric dynamics with autoregressive techniques and strict physical constraints.
• It extends its predecessor with a 450M-parameter architecture operating on a 1°×1° grid, accurately conserving dry-air mass, moisture, and energy.
• Its efficiency enables diverse applications including ensemble forecasting, climate sensitivity experiments, and coupling with ocean models for long-term simulations.

Ai2 Climate Emulator version 2, usually abbreviated ACE2, is an autoregressive machine-learning emulator of the global atmosphere designed to bridge weather and climate timescales. In its canonical formulation, ACE2 operates with 6-hour temporal resolution on a $1^\circ \times 1^\circ$ global grid with eight vertical layers, exactly conserves global dry air mass and moisture, and can be integrated stably for arbitrarily many steps; later ACE2S designations are used for closely related ACE2 configurations trained on reanalysis, on physics-based climate-model output, and in stochastic variants for ensemble generation and downscaling (Watt-Meyer et al., 2024, Rucker et al., 31 Oct 2025, Perkins et al., 20 Dec 2025). Across these papers, the framework is used for subseasonal variability, decadal forced responses, equilibrium and transient $\mathrm{CO}_2$ perturbation experiments, slab-ocean and full-depth ocean coupling, Green’s-function calculations, and kilometer-scale precipitation emulation (Clark et al., 2024, Antonio et al., 30 Mar 2026, Wu et al., 13 May 2025).

1. Nomenclature and model lineage

ACE2S is best understood as a designation applied to several ACE2-based configurations rather than a single immutable model checkpoint. The underlying lineage begins with ACE, a 200M-parameter autoregressive emulator of FV3GFS that was formulated for long-term stable climate prediction and shown to remain stable for 100 years while requiring nearly $100\times$ less wall-clock time and being $100\times$ more energy efficient than its reference model (Watt-Meyer et al., 2023). ACE2 expands that program to a 450M-parameter emulator with explicit boundary-condition inputs such as sea surface temperature and $\mathrm{CO}_2$, exact conservation of global dry-air mass and moisture, and stable rollouts on timescales from days to millennia (Watt-Meyer et al., 2024).

In the later literature, the same core system appears under several ACE2S labels. “Benchmarking atmospheric circulation variability in an AI emulator, ACE2, and a hybrid model, NeuralGCM” refers to the fully data-driven ACE2-ERA5 emulator as “ACE2S” (Baxter et al., 6 Oct 2025). “Benchmarking Regional Thermodynamic Trends in an AI emulator, ACE2, and a hybrid model, NeuralGCM” expands the name as “AI2 Climate Emulator 2 – Satellite era” (Rucker et al., 31 Oct 2025). “HiRO-ACE” uses “ACE2S” for a stochastic variant of deterministic ACE2 (Perkins et al., 20 Dec 2025). The 2026 forcing-disentanglement study presents a new ACE2S trained jointly on AMIP, equilibrium slab-ocean, and “random-$\mathrm{CO}_2$” simulations (Clark et al., 6 Jun 2026).

Configuration	Training source	Distinguishing feature
ACE (Watt-Meyer et al., 2023)	FV3GFS climatological-SST simulations	200M-parameter predecessor
ACE2 (Watt-Meyer et al., 2024)	ERA5 or AMIP-style SHiELD	450M parameters; exact dry-air mass and moisture conservation
ACE2-SOM (Clark et al., 2024)	SHiELD-SOM at $1\times$, $2\times$, $4\times$ $\mathrm{CO}_2$	Slab-ocean coupling for climate sensitivity
ACE2-NEMO (Antonio et al., 30 Mar 2026)	Pretrained ACE2 coupled to NEMO	Multi-decadal integrations with a full-depth dynamical ocean
ACE2S-SHiELD$\mathrm{CO}_2$0 (Clark et al., 6 Jun 2026)	AMIP, equilibrium slab-ocean, and random-$\mathrm{CO}_2$1 data	Separate learning of SST and $\mathrm{CO}_2$2 effects
HiRO-ACE ACE2S (Perkins et al., 20 Dec 2025)	ERA5 pretraining, X-SHiELD fine-tuning	Stochastic coarse-grid emulator for 3 km downscaling

This multiplicity of usages is substantive rather than terminological. Some ACE2S instances are deterministic atmosphere-only emulators, some are stochastic ensemble generators, and some are components inside coupled or cascaded Earth-system frameworks.

2. Neural-operator formulation and state evolution

The architectural core of ACE2S is the Spherical Fourier Neural Operator (SFNO). In ACE2, the state update is written as

$\mathrm{CO}_2$3

where $\mathrm{CO}_2$4 denotes the atmospheric state and $\mathrm{CO}_2$5 the forcing vector at time $\mathrm{CO}_2$6 (Watt-Meyer et al., 2024). In the coupled ACE2-NEMO formulation, the same step is written as

$\mathrm{CO}_2$7

with $\mathrm{CO}_2$8 containing prescribed boundary forcings such as $\mathrm{CO}_2$9, incoming solar radiation, and SST or sea-ice information (Antonio et al., 30 Mar 2026). The HiRO-ACE stochastic variant introduces explicit randomness,

$100\times$0

with $100\times$1, so that repeated rollouts define an ensemble rather than a single trajectory (Perkins et al., 20 Dec 2025).

Across published ACE2S configurations, the common numerical setting is a $100\times$2 global grid, eight vertical levels, and a 6-hour time step (Watt-Meyer et al., 2024, Rucker et al., 31 Oct 2025). ACE2 uses an SFNO backbone in an encoder–core–decoder arrangement with a 384-dimensional latent field and eight successive spectral update layers (Watt-Meyer et al., 2024). ACE2-SOM also uses embedding dimension 384, but specifies $100\times$3 successive SFNO blocks with spherical harmonic transform, learned global Fourier filtering in spectral space, inverse transform, and a local MLP (Clark et al., 2024). The newer forcing-disentanglement ACE2S uses a stochastic SFNO architecture with variable embedding dimension 512 (Clark et al., 6 Jun 2026).

Input and output definitions vary with the training target, but the recurrent pattern is the same. ACE2-ERA5 and related ACE2S models ingest three-dimensional temperature, humidity, and winds together with surface or near-surface state variables and boundary forcings such as SST, sea-ice concentration, top-of-atmosphere shortwave flux, and global mean $100\times$4 (Watt-Meyer et al., 2024, Rucker et al., 31 Oct 2025). Diagnostic outputs typically include precipitation and radiative and turbulent fluxes. In ACE2-SOM, the emulator outputs 6-hour tendency increments of the prognostic fields plus surface fluxes $100\times$5 (Clark et al., 2024). In ACE2-NEMO, momentum fluxes, evaporation, and some ice-point fluxes are instead recalculated through bulk formulae (Antonio et al., 30 Mar 2026).

A central architectural claim of ACE2 is that the formulation permits evaluation of physical laws such as conservation of mass and moisture (Watt-Meyer et al., 2023). Later ACE2 papers strengthen this by moving from approximate budget skill to hard enforcement inside the forward pass (Watt-Meyer et al., 2024).

3. Training datasets, forcing representation, and physical constraints

ACE2S training protocols are strongly conditioned by the intended forcing regime. Reanalysis-based ACE2 is trained on ERA5 from 1940–1995, 2011–2019, and 2021–2022, with validation on 1996–2000 and testing on 2001–2010 plus 2020 for weather skill (Watt-Meyer et al., 2024). AMIP-style physics-model variants are trained on output from GFDL SHiELD or DOE EAMv3, regridded to $100\times$6 and vertically coarsened to eight levels (Watt-Meyer et al., 2024, Wu et al., 13 May 2025). ACE2-SOM is trained jointly on equilibrium-climate SHiELD-SOM simulations at $100\times$7, $100\times$8, and $100\times$9 preindustrial $100\times$0, using five-member ensembles and 50 post-spin-up years per level (Clark et al., 2024). The stochastic HiRO-ACE emulator is first pretrained on ERA5 and then fine-tuned on ten years of coarsened X-SHiELD storm-resolving output (Perkins et al., 20 Dec 2025).

Boundary-condition treatment is explicit. ACE2 injects SST as a two-dimensional snapshot-level input field and broadcasts global mean $100\times$1 as a constant-in-space channel, along with solar forcing, surface fractions, and topography (Watt-Meyer et al., 2024). This design allows historical forcing experiments but does not guarantee that SST and $100\times$2 effects will be disentangled. That limitation became a central issue in later work. The 2026 forcing study argues that earlier ACE versions were trained in regimes where SST and $100\times$3 varied “in lock-step,” so the emulator learned only their joint effect (Clark et al., 6 Jun 2026). Its remedy is a new class of random-$100\times$4 reference simulations in which SST and $100\times$5 vary independently: SST follows a warming ramp, while $100\times$6 is updated every 30 days by draws of the form

$100\times$7

around central levels $100\times$8 (Clark et al., 6 Jun 2026).

Physical constraints are one of the most distinctive elements of the ACE2 line. In ACE2, dry-air pressure is defined as

$100\times$9

and the model enforces exact global conservation of dry-air mass and column moisture at each 6-hour step through a physical-corrector module (Watt-Meyer et al., 2024). ACE2-SOM enforces dry-air mass and column-integrated moisture conservation exactly within machine precision via Lagrange multipliers in the loss (Clark et al., 2024). The newer ACE2S further adds a total-energy conservation constraint during fine-tuning, requiring the global vertically integrated energy tendency to equal the net energy input plus a constant “unaccounted heating” $\mathrm{CO}_2$0, and applies a globally uniform $\mathrm{CO}_2$1 correction so that the balance holds exactly (Clark et al., 6 Jun 2026). This extension is important because earlier ACE2 variants did not conserve total energy, a deficiency that became visible in abrupt-forcing experiments (Watt-Meyer et al., 2024, Clark et al., 2024).

Loss formulations also vary by objective. Deterministic ACE2 uses MSE-based objectives over multiple outputs and autoregressive steps (Watt-Meyer et al., 2024). ACE2-SOM uses

$\mathrm{CO}_2$2

with $\mathrm{CO}_2$3 enforcing exact conservation (Clark et al., 2024). The stochastic ACE2S in the forcing-disentanglement study is trained with a weighted mixture of Continuous Ranked Probability Score and Energy Score, while HiRO-ACE uses an “almost fair” CRPS plus a spectral Energy Score to preserve grid-scale variability and sharp probabilistic ensembles (Clark et al., 6 Jun 2026, Perkins et al., 20 Dec 2025).

4. Skill in atmospheric variability and forced historical trends

ACE2’s central empirical result is that a fully data-driven neural operator can remain stable while reproducing a broad range of emergent atmospheric phenomena. The base ACE model was shown to be stable for 100 years and to outperform a coarser FV3GFS baseline on over 90% of 44 tracked variables, with 41/44 outputs having lower time-mean RMSE (Watt-Meyer et al., 2023). ACE2 extends this to an 81-year historical setting and a 1000-year climatological-forcing integration, showing no drift in global mean total water path or surface pressure and throughput of about 1500 simulated years per wall-clock day on a single NVIDIA H100 GPU (Watt-Meyer et al., 2024).

On weather-to-decadal timescales, ACE2 reproduces phenomena usually used as qualitative stress tests for climate emulators. ACE2-ERA5 captures basin-by-basin tropical cyclone frequency within $\mathrm{CO}_2$4, minimum sea-level pressures and 10 m wind speeds closely matching ERA5; it exhibits Madden–Julian Oscillation propagation nearly identical in phase speed and amplitude to ERA5; and it reproduces the seasonal cycle, interannual spread, and sudden stratospheric warming events in its top layer zonal winds (Watt-Meyer et al., 2024). Historical climate-scale skill is quantified by $\mathrm{CO}_2$5–0.97 for global and annual mean 2 m temperature and total water path over 1940–2020 (Watt-Meyer et al., 2024).

More formal dynamical benchmarking reveals both strengths and limits. In atmospheric circulation diagnostics, ACE2S reproduces the MJO ridge between zonal wavenumbers $\mathrm{CO}_2$6–5, the Kelvin-wave ridge up to $\mathrm{CO}_2$7, and extratropical eddy–mean-flow spectra aligned with critical levels, while underestimating absolute eddy-momentum-flux amplitude by $\mathrm{CO}_2$8–30% (Baxter et al., 6 Oct 2025). At the same time, it fails to sustain a regular quasi-biennial oscillation with the observed $\mathrm{CO}_2$9-month timescale and does not exhibit a coherent $\mathrm{CO}_2$0-day spectral peak in the propagating Southern Annular Mode (Baxter et al., 6 Oct 2025). The diagnosed causes in that paper are the 6-hour loss emphasizing fast dynamics, coarse vertical resolution with only one stratospheric layer near 50 hPa, and implicit loss weighting that de-emphasizes stratospheric wind signals (Baxter et al., 6 Oct 2025).

Regional thermodynamic-trend benchmarks give a mixed but technically specific picture. For Arctic Amplification at 850 hPa over $\mathrm{CO}_2$1–$\mathrm{CO}_2$2, ACE2S produces a 1981–2014 trend of $\mathrm{CO}_2$3 versus $\mathrm{CO}_2$4 in ERA5, with RMSE $\mathrm{CO}_2$5, correlation $\mathrm{CO}_2$6, and bias $\mathrm{CO}_2$7 (Rucker et al., 31 Oct 2025). In midlatitude vertical temperature trends over $\mathrm{CO}_2$8–$\mathrm{CO}_2$9, ACE2S achieves trend error $1\times$0 at all eight levels and average profile RMSE $1\times$1, outperforming both NeuralGCM and an AMIP ensemble (Rucker et al., 31 Oct 2025). It also matches the tropical upper-tropospheric warming trend at 250 hPa exactly, with $1\times$2 and trend error $1\times$3 (Rucker et al., 31 Oct 2025). However, ACE2S underestimates heat-extreme trends in the U.S. Southwest and does not capture the full magnitude of drying trends in arid regions, although it generally performs better than the physics-based models compared in that study (Rucker et al., 31 Oct 2025).

A further limitation appears when ACE2 is evaluated outside the center of its training climatology. In a boreal-winter assessment over 1996–2010, ACE2 shows a global mean cold bias of about $1\times$4, with the largest biases over North America, Northern Europe, and western Russia; its climatology for 1996–2010 most closely matches ERA5 from 1976–1990 on average, and over the Eastern U.S. the best-matching span is 1966–1980 (Landsberg et al., 26 Sep 2025). That result is consistent with the broader concern that historical-data training alone does not guarantee faithful extrapolation to warmer climates.

5. Sensitivity to SST and $1\times$5, equilibrium climate, and coupled extensions

The relation between ACE2S and climate forcing is the central scientific issue in the post-2024 literature. ACE2 was explicitly designed to accept varying SST and $1\times$6 inputs, and it accurately reproduces El Niño precipitation and outgoing-longwave-radiation anomaly regressions, with precipitation-regression RMSE $1\times$7 (Watt-Meyer et al., 2024). Yet the same paper shows that in fixed-$1\times$8 experiments, while SST trends continue, ACE2 loses nearly all surface warming and stratospheric cooling trends, demonstrating that the emulator had not disentangled SST and $1\times$9 effects perfectly (Watt-Meyer et al., 2024).

ACE2-SOM was the first direct attempt to teach an ACE2-based emulator equilibrium climate sensitivity to altered $2\times$0. It couples the atmospheric emulator to a differentiable slab ocean with mixed-layer energy balance

$2\times$1

where $2\times$2 (Clark et al., 2024). In equilibrium-climate inference, including out-of-sample $2\times$3, ACE2-SOM produces unbiased, stable 10-year rollouts of surface temperature and precipitation, spatial biases below $2\times$4 in $2\times$5 and $2\times$6 in precipitation, and time-mean RMSE reductions of 54–96% across all 20 predicted fields relative to a baseline C24 SHiELD-SOM (Clark et al., 2024). It also matches extreme precipitation changes up to the 99.9999th percentile within sampling uncertainty (Clark et al., 2024).

The same paper identifies a sharp distinction between equilibrium and transient skill. Under a gradual $2\times$7 $2\times$8 ramp, ACE2-SOM tracks global $2\times$9 and precipitation with $4\times$0 and biases $4\times$1, but exhibits unphysical stratospheric “regime shifts” when crossing training-seen $4\times$2 levels (Clark et al., 2024). Under abrupt $4\times$3, atmospheric prognostic fields jump within 1–2 months directly to their $4\times$4 equilibrium values, violating the moist-static-energy budget and producing spurious dependencies of radiative fluxes on instantaneous $4\times$5 (Clark et al., 2024). These failures motivated the later random-$4\times$6 training strategy.

The forcing-disentanglement ACE2S addresses exactly those pathologies. Trained on a balance of AMIP, equilibrium-climate, and random-$4\times$7 data, and including a global total-energy conservation constraint, it reproduces held-out AMIP, equilibrium, and transient responses that older ACE2 variants handled poorly (Clark et al., 6 Jun 2026). In AMIP $4\times$84 K SST at fixed $4\times$9, it attains spatial-response RMSE of $\mathrm{CO}_2$0 temperature $\mathrm{CO}_2$1 relative to SHiELD and captures the correct land–ocean warming contrast (Clark et al., 6 Jun 2026). In slab-ocean-coupled abrupt $\mathrm{CO}_2$2, the version trained with random-$\mathrm{CO}_2$3 data matches SHiELD’s multi-week response timescales in temperature, latent-heat flux, total water path, and TOA radiative fluxes, and reduces 7-day latent-heat-flux and SWTOA-flux pattern errors by more than 60% compared with ACE2-SOM (Clark et al., 6 Jun 2026).

ACE2 has also been extended beyond slab-ocean coupling. ACE2-NEMO interactively couples the emulator to the NEMO full-depth dynamical ocean through OASIS3-MCT with a 6-hour coupling interval, in what is described as the first multi-decadal integrations of a machine-learned atmosphere interacting with a full-depth dynamical ocean (Antonio et al., 30 Mar 2026). The coupled system is stable for 70 years and produces realistic fast-timescale air–sea coupling in the tropical Pacific, but its Niño3.4 spectrum is nearly red noise with very muted ENSO peaks, associated with a Bjerknes-feedback slope $\mathrm{CO}_2$4 that is $\mathrm{CO}_2$5–50% weaker than EC-Earth3P and ERA5 (Antonio et al., 30 Mar 2026). In historical forcing experiments, ACE2-NEMO tracks EC-Earth3P and reanalysis through about 1980, then flattens because net downward shortwave radiation declines too quickly, cooling SST by $\mathrm{CO}_2$6–1 K over 1980–2010 (Antonio et al., 30 Mar 2026).

Green’s-function studies provide an additional forcing-sensitivity test. When ACE2 is trained on EAMv3 and evaluated under the GFMIP SST-patch protocol, its full-ocean sensitivity map $\mathrm{CO}_2$7 is qualitatively similar to EAMv3, with map-wide spatial pattern correlation 0.53, but significant regional discrepancies remain, especially in the northeast tropical Pacific (Wu et al., 13 May 2025). Reanalysis-trained ACE2-ERA5 similarly reproduces the physically expected pattern of TOA radiative feedbacks to local SST anomalies, but likely underestimates the magnitude of the radiative response to historical warming (Loon et al., 15 Feb 2025). These Green’s-function results are notable because they test causal response structure rather than only free-running climatology.

6. Computational profile, applications, and unresolved problems

A defining characteristic of ACE2S is its efficiency. The original ACE required about 1 s per simulated day on one A100 GPU, compared with about 77 s per day for FV3GFS on 96 CPU cores (Watt-Meyer et al., 2023). ACE2 increases throughput to approximately 1500 simulated years per wall-clock day on one NVIDIA H100-80GB, with energy cost about 11 Wh per simulated year; relative to GFDL SHiELD at C96, this corresponds to about $\mathrm{CO}_2$8 greater speed and about $\mathrm{CO}_2$9 greater energy efficiency (Watt-Meyer et al., 2024). ACE2-SOM reports the same order of advantage over its physics-based target (Clark et al., 2024). For Green’s-function calculations, the full ACE2 GFMIP-like suite on EAMv3 was completed in 2.3 wall-days on one A100 GPU, versus 8.15 million core-hours and about 331 wall-days for the physics model (Wu et al., 13 May 2025).

This efficiency has enabled a widening range of applications. ACE2 has been used for long historical integrations, ENSO-regression analysis, tropical-cyclone diagnostics, SST Green’s functions, slab-ocean climate-sensitivity studies, and interactive coupling to a dynamical ocean (Watt-Meyer et al., 2024, Wu et al., 13 May 2025, Clark et al., 2024, Antonio et al., 30 Mar 2026). In HiRO-ACE, a stochastic ACE2S provides coarse $\mathrm{CO}_2$00 atmospheric fields that feed a diffusion-based downscaling model trained on 3 km X-SHiELD output. The resulting two-stage system reproduces the distribution of extreme precipitation rates through the 99.99th percentile, keeps time-mean precipitation biases below 10% almost everywhere, and can generate decades of 6-hourly high-resolution regional precipitation within a single day using one H100 GPU (Perkins et al., 20 Dec 2025).

The open problems are correspondingly specific. Earlier ACE2 variants learned unrealistic instantaneous radiative sensitivities to $\mathrm{CO}_2$01, violated global energy conservation under abrupt forcing, and quantized upper-level state variables when trained only on a few discrete $\mathrm{CO}_2$02 levels (Clark et al., 2024). Reanalysis-trained ACE2S captures many weather and subseasonal metrics but misses low-frequency stratospheric modes such as the QBO and the propagating SAM (Baxter et al., 6 Oct 2025). Regional trend studies show persistent weaknesses in heat extremes and land-atmosphere drying, plausibly linked to the absence of an explicit land-surface model and to the rarity of extreme events in the training distribution (Rucker et al., 31 Oct 2025). Coupled ACE2-NEMO indicates that learning fast air–sea coupling is not sufficient to recover realistic low-frequency tropical variability or cloud-mediated shortwave feedbacks (Antonio et al., 30 Mar 2026). The forcing-disentanglement paper adds that current ACE2S versions still rely on simplified or prescribed ocean, land, and sea-ice representations, omit aerosols and other greenhouse gases, and inherit biases from the physics-based reference model used for training (Clark et al., 6 Jun 2026).

Taken together, these results position ACE2S as a technically distinctive class of neural climate emulator: global, autoregressive, spectrally nonlocal, physically constrained in mass and moisture and in some versions total energy, computationally cheap enough for very large ensembles, and already capable of reproducing many climate-relevant emergent behaviors. The principal research frontier is no longer mere rollout stability, but faithful representation of forced response operators, slow feedbacks, and out-of-distribution climate sensitivities.