---
title: 'ACE2S: Advanced AI Climate Emulator'
url: https://www.emergentmind.com/topics/ai2-climate-emulator-ace2s
type: topic
---

# ACE2S: Advanced AI Climate Emulator

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 [2411.11268; 2511.00274; 2512.18224]. 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 [2412.04418; 2603.28704; 2505.08742].

## 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 [2310.02074]. 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 [2411.11268].

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” [2510.04466]. “Benchmarking Regional Thermodynamic Trends in an AI emulator, ACE2, and a hybrid model, NeuralGCM” expands the name as “AI2 Climate Emulator 2 – Satellite era” [2511.00274]. “HiRO-ACE” uses “ACE2S” for a stochastic variant of deterministic ACE2 [2512.18224]. The 2026 forcing-disentanglement study presents a new ACE2S trained jointly on AMIP, equilibrium slab-ocean, and “random-\(\mathrm{CO}_2\)” simulations [2606.07928].

| Configuration | Training source | Distinguishing feature |
|---|---|---|
| ACE [2310.02074] | FV3GFS climatological-SST simulations | 200M-parameter predecessor |
| ACE2 [2411.11268] | ERA5 or AMIP-style SHiELD | 450M parameters; exact dry-air mass and moisture conservation |
| ACE2-SOM [2412.04418] | SHiELD-SOM at \(1\times\), \(2\times\), \(4\times\) \(\mathrm{CO}_2\) | Slab-ocean coupling for climate sensitivity |
| ACE2-NEMO [2603.28704] | Pretrained ACE2 coupled to NEMO | Multi-decadal integrations with a full-depth dynamical ocean |
| ACE2S-SHiELD\(^+\) [2606.07928] | AMIP, equilibrium slab-ocean, and random-\(\mathrm{CO}_2\) data | Separate learning of SST and \(\mathrm{CO}_2\) effects |
| HiRO-ACE ACE2S [2512.18224] | 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
\[
x_{t+1} \;=\;\mathcal{F}_\theta\bigl(x_t,\;f_t\bigr)\;+\;\epsilon_t,
\]
where \(x_t\) denotes the atmospheric state and \(f_t\) the forcing vector at time \(t\) [2411.11268]. In the coupled ACE2-NEMO formulation, the same step is written as
\[
x_{t+1}=x_t\;+\;\Delta x(x_t,b_t;\theta),
\]
with \(b_t\) containing prescribed boundary forcings such as \(\mathrm{CO}_2\), incoming solar radiation, and SST or sea-ice information [2603.28704]. The HiRO-ACE stochastic variant introduces explicit randomness,
\[
X_t = f_\theta(X_{t-1}, Z_t),
\]
with \(Z_t \sim \mathcal{N}(0, I_{64})\), so that repeated rollouts define an ensemble rather than a single trajectory [2512.18224].

Across published ACE2S configurations, the common numerical setting is a \(1^\circ \times 1^\circ\) global grid, eight vertical levels, and a 6-hour time step [2411.11268; 2511.00274]. ACE2 uses an SFNO backbone in an encoder–core–decoder arrangement with a 384-dimensional latent field and eight successive spectral update layers [2411.11268]. ACE2-SOM also uses embedding dimension 384, but specifies \(L=6\) successive SFNO blocks with spherical harmonic transform, learned global Fourier filtering in spectral space, inverse transform, and a local MLP [2412.04418]. The newer forcing-disentanglement ACE2S uses a stochastic SFNO architecture with variable embedding dimension 512 [2606.07928].

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 \(\mathrm{CO}_2\) [2411.11268; 2511.00274]. 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 \((R_{lw\downarrow}, R_{lw\uparrow}, R_{sw\downarrow}, R_{sw\uparrow}, SH, LH)\) [2412.04418]. In ACE2-NEMO, momentum fluxes, evaporation, and some ice-point fluxes are instead recalculated through bulk formulae [2603.28704].

A central architectural claim of ACE2 is that the formulation permits evaluation of physical laws such as conservation of mass and moisture [2310.02074]. Later ACE2 papers strengthen this by moving from approximate budget skill to hard enforcement inside the forward pass [2411.11268].

## 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 [2411.11268]. AMIP-style physics-model variants are trained on output from GFDL SHiELD or DOE EAMv3, regridded to \(1^\circ\) and vertically coarsened to eight levels [2411.11268; 2505.08742]. ACE2-SOM is trained jointly on equilibrium-climate SHiELD-SOM simulations at \(1\times\), \(2\times\), and \(4\times\) preindustrial \(\mathrm{CO}_2\), using five-member ensembles and 50 post-spin-up years per level [2412.04418]. The stochastic HiRO-ACE emulator is first pretrained on ERA5 and then fine-tuned on ten years of coarsened X-SHiELD storm-resolving output [2512.18224].

Boundary-condition treatment is explicit. ACE2 injects SST as a two-dimensional snapshot-level input field and broadcasts global mean \(\mathrm{CO}_2\) as a constant-in-space channel, along with solar forcing, surface fractions, and topography [2411.11268]. This design allows historical forcing experiments but does not guarantee that SST and \(\mathrm{CO}_2\) 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 \(\mathrm{CO}_2\) varied “in lock-step,” so the emulator learned only their joint effect [2606.07928]. Its remedy is a new class of random-\(\mathrm{CO}_2\) reference simulations in which SST and \(\mathrm{CO}_2\) vary independently: SST follows a warming ramp, while \(\mathrm{CO}_2\) is updated every 30 days by draws of the form
\[
X(t) = 2^{n(t)}\,X_0,\qquad n(t)\sim \mathrm{Uniform}(-2,2),
\]
around central levels \(X_0 \in \{1\times,2\times,4\times\,\mathrm{CO}_2\}\) [2606.07928].

Physical constraints are one of the most distinctive elements of the ACE2 line. In ACE2, dry-air pressure is defined as
\[
p_s^{\rm dry}(t)\;=\;p_s(t)\;-\;g\,\mathrm{TWP}(t),
\]
and the model enforces exact global conservation of dry-air mass and column moisture at each 6-hour step through a physical-corrector module [2411.11268]. ACE2-SOM enforces dry-air mass and column-integrated moisture conservation exactly within machine precision via Lagrange multipliers in the loss [2412.04418]. 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” \(H_0\), and applies a globally uniform \(\delta T\) correction so that the balance holds exactly [2606.07928]. This extension is important because earlier ACE2 variants did not conserve total energy, a deficiency that became visible in abrupt-forcing experiments [2411.11268; 2412.04418].

Loss formulations also vary by objective. Deterministic ACE2 uses MSE-based objectives over multiple outputs and autoregressive steps [2411.11268]. ACE2-SOM uses
\[
L_{\rm total}=L_{\rm MSE}+L_{\rm cons},
\]
with \(L_{\rm cons}\) enforcing exact conservation [2412.04418]. 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 [2606.07928; 2512.18224].

## 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 [2310.02074]. 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 [2411.11268].

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 \(\pm 10\%\), 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 [2411.11268]. Historical climate-scale skill is quantified by \(R^2 \approx 0.93\)–0.97 for global and annual mean 2 m temperature and total water path over 1940–2020 [2411.11268].

More formal dynamical benchmarking reveals both strengths and limits. In atmospheric circulation diagnostics, ACE2S reproduces the MJO ridge between zonal wavenumbers \(k=2\)–5, the Kelvin-wave ridge up to \(f\sim0.4\,\mathrm{d}^{-1}\), and extratropical eddy–mean-flow spectra aligned with critical levels, while underestimating absolute eddy-momentum-flux amplitude by \(\sim 20\)–30% [2510.04466]. At the same time, it fails to sustain a regular quasi-biennial oscillation with the observed \(\sim 28\)-month timescale and does not exhibit a coherent \(\sim 150\)-day spectral peak in the propagating Southern Annular Mode [2510.04466]. 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 [2510.04466].

Regional thermodynamic-trend benchmarks give a mixed but technically specific picture. For Arctic Amplification at 850 hPa over \(60^\circ\)–\(90^\circ\mathrm{N}\), ACE2S produces a 1981–2014 trend of \(0.28\,\mathrm{K\,dec}^{-1}\) versus \(0.30\,\mathrm{K\,dec}^{-1}\) in ERA5, with RMSE \(0.02\,\mathrm{K\,dec}^{-1}\), correlation \(r=0.92\), and bias \(-0.02\,\mathrm{K\,dec}^{-1}\) [2511.00274]. In midlatitude vertical temperature trends over \(20^\circ\)–\(60^\circ\mathrm{N}\), ACE2S achieves trend error \(<0.02\,\mathrm{K\,dec}^{-1}\) at all eight levels and average profile RMSE \(0.015\,\mathrm{K\,dec}^{-1}\), outperforming both NeuralGCM and an AMIP ensemble [2511.00274]. It also matches the tropical upper-tropospheric warming trend at 250 hPa exactly, with \(0.13\,\mathrm{K\,dec}^{-1}\) and trend error \(0.00\) [2511.00274]. 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 [2511.00274].

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 \(-0.35\,\mathrm{K}\), 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 [2509.22359]. 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 \(\mathrm{CO}_2\), 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 \(\mathrm{CO}_2\) inputs, and it accurately reproduces El Niño precipitation and outgoing-longwave-radiation anomaly regressions, with precipitation-regression RMSE \(\approx 0.46\,\mathrm{mm\,day}^{-1}\,\mathrm{K}^{-1}\) [2411.11268]. Yet the same paper shows that in fixed-\(\mathrm{CO}_2\) experiments, while SST trends continue, ACE2 loses nearly all surface warming and stratospheric cooling trends, demonstrating that the emulator had not disentangled SST and \(\mathrm{CO}_2\) effects perfectly [2411.11268].

ACE2-SOM was the first direct attempt to teach an ACE2-based emulator equilibrium climate sensitivity to altered \(\mathrm{CO}_2\). It couples the atmospheric emulator to a differentiable slab ocean with mixed-layer energy balance
\[
\rho_o C_o\,h\,\frac{\partial T_s}{\partial t} = F_{\rm net} + Q,
\]
where \(F_{\rm net}=R^{lw}_\downarrow-R^{lw}_\uparrow+R^{sw}_\downarrow-R^{sw}_\uparrow-SH-LH\) [2412.04418]. In equilibrium-climate inference, including out-of-sample \(3\times\mathrm{CO}_2\), ACE2-SOM produces unbiased, stable 10-year rollouts of surface temperature and precipitation, spatial biases below \(0.2\,\mathrm{K}\) in \(T_s\) and \(0.1\,\mathrm{mm\,day}^{-1}\) in precipitation, and time-mean RMSE reductions of 54–96% across all 20 predicted fields relative to a baseline C24 SHiELD-SOM [2412.04418]. It also matches extreme precipitation changes up to the 99.9999th percentile within sampling uncertainty [2412.04418].

The same paper identifies a sharp distinction between equilibrium and transient skill. Under a gradual \(2\%\ \mathrm{yr}^{-1}\) \(\mathrm{CO}_2\) ramp, ACE2-SOM tracks global \(T_s\) and precipitation with \(R^2 \ge 0.98\) and biases \(<0.1\,\mathrm{K}\), but exhibits unphysical stratospheric “regime shifts” when crossing training-seen \(\mathrm{CO}_2\) levels [2412.04418]. Under abrupt \(4\times\mathrm{CO}_2\), atmospheric prognostic fields jump within 1–2 months directly to their \(4\times\mathrm{CO}_2\) equilibrium values, violating the moist-static-energy budget and producing spurious dependencies of radiative fluxes on instantaneous \(\mathrm{CO}_2\) [2412.04418]. These failures motivated the later random-\(\mathrm{CO}_2\) training strategy.

The forcing-disentanglement ACE2S addresses exactly those pathologies. Trained on a balance of AMIP, equilibrium-climate, and random-\(\mathrm{CO}_2\) data, and including a global total-energy conservation constraint, it reproduces held-out AMIP, equilibrium, and transient responses that older ACE2 variants handled poorly [2606.07928]. In AMIP \(+\)4 K SST at fixed \(\mathrm{CO}_2\), it attains spatial-response RMSE of \(2\ \mathrm{m}\) temperature \(\simeq 0.22\,\mathrm{K}\) relative to SHiELD and captures the correct land–ocean warming contrast [2606.07928]. In slab-ocean-coupled abrupt \(4\times\mathrm{CO}_2\), the version trained with random-\(\mathrm{CO}_2\) 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 [2606.07928].

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 [2603.28704]. 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 \(\alpha\) that is \(\sim 30\)–50% weaker than EC-Earth3P and ERA5 [2603.28704]. 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 \(\sim 0.5\)–1 K over 1980–2010 [2603.28704].

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 \(d\overline N/dSST\) is qualitatively similar to EAMv3, with map-wide spatial pattern correlation 0.53, but significant regional discrepancies remain, especially in the northeast tropical Pacific [2505.08742]. 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 [2502.10893]. 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 [2310.02074]. 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 \(100\times\) greater speed and about \(700\times\) greater energy efficiency [2411.11268]. ACE2-SOM reports the same order of advantage over its physics-based target [2412.04418]. 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 [2505.08742].

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 [2411.11268; 2505.08742; 2412.04418; 2603.28704]. In HiRO-ACE, a stochastic ACE2S provides coarse \(100\,\mathrm{km}\) 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 [2512.18224].

The open problems are correspondingly specific. Earlier ACE2 variants learned unrealistic instantaneous radiative sensitivities to \(\mathrm{CO}_2\), violated global energy conservation under abrupt forcing, and quantized upper-level state variables when trained only on a few discrete \(\mathrm{CO}_2\) levels [2412.04418]. Reanalysis-trained ACE2S captures many weather and subseasonal metrics but misses low-frequency stratospheric modes such as the QBO and the propagating SAM [2510.04466]. 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 [2511.00274]. 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 [2603.28704]. 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 [2606.07928].

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.

Source: https://www.emergentmind.com/topics/ai2-climate-emulator-ace2s