Stochastic Emulation of a Fully Coupled Preindustrial E3SMv3 Simulation

This paper presents SamudrACE-E3SMv3, a stochastic fully coupled atmosphere–ocean emulator of the Energy Exascale Earth System Model version 3 (E3SMv3), built on the SamudrACE framework. The emulator couples an atmosphere emulator (ACE2S, a stochastic variant of ACE2) with a full-depth ocean emulator (Samudra), and is trained on 105 years of a pre-industrial control simulation and evaluated on an independent 400-year segment of the same simulation.

The authors extend the original SamudrACE framework in two ways: (1) they replace the deterministic ACE2 atmosphere with its stochastic counterpart ACE2S, and fine-tune the coupled system with a probabilistic objective combining the continuous ranked probability score (CRPS) and the energy score, so that the atmosphere acts as a source of internal variability for the ocean; and (2) they apply the framework to a different reference GCM (E3SMv3 rather than GFDL-CM4), serving as a robustness test. The 400-year evaluation period substantially exceeds that of the original SamudrACE work, enabling a more stringent assessment of long-term fidelity.

Training proceeds in two phases: component emulators are first pretrained separately using perfect forcings (boundary forcings taken directly from E3SMv3 target data), then coupled and fine-tuned together. The coupled fine-tuning is stochastic and uses a single stage in which both components are optimized jointly. During fine-tuning, two ensemble members are generated for each training sample: ACE2S produces two realizations whose 5-day mean surface forcings drive two corresponding Samudra rollouts. Both components are optimized with the same probabilistic objective, with equal loss weights on the atmosphere and ocean components. The ocean is optimized at every step within its sampled window, while the atmosphere is optimized only at the final step of its window. Longer atmosphere windows (21 and 41 steps) extend beyond one and two ocean coupling steps, exposing the loss to the coupled interaction.

For comparison, a deterministic coupled emulator is also trained, using the deterministic ACE2 atmosphere and MSE loss with fixed windows of four ocean steps (20 days) and two atmosphere steps (12 hours).

On a single H100 GPU, SamudrACE-E3SMv3 achieves inference speeds of 1105 SYPD (stochastic) and 1360 SYPD (deterministic), whereas the original E3SMv3 requires thousands of processor cores and achieves about 28 simulated years per day using 105 nodes.

SamudrACE-E3SMv3 accurately reproduces the spatial structure of the mean climate state of E3SMv3. The emulator's root-mean square biases (RMSBs) vs. E3SMv3 are 0.62 K for surface temperature and 0.19 mm day−1 for precipitation, substantially smaller than E3SMv3's biases against observations (1.13 K and 1.04 mm day−1, respectively). A Taylor diagram shows almost all variables concentrated near the zero-bias point, with the exception of stratospheric specific total water, whose near-uniform time-mean field causes normalized metrics to amplify a physically negligible error.

A persistent time-mean surface temperature bias is found in the marginal ice zone (MIZ) of the Barents and Greenland Seas, where surface temperature and turbulent fluxes respond nonlinearly to the sea ice partition. The Nordic-box SST RMSB grows from 0.15 K uncoupled to 2.1 K coupled, with the coupled error organizing into a dipole: warm along the East Greenland outflow, cold in the northern Barents Sea. This is attributed to inconsistencies in the coupled training target (using sea ice fraction from E3SMv3 atmosphere output vs. ocean output) and SST biases inherent to the uncoupled Samudra ocean emulator in this region.

The emulator reproduces the bulk of the daily precipitation distribution with high fidelity. The 99th and 99.99th percentiles agree with E3SMv3 to within a few percent, even in the 400-year free-running rollout. Over the continental United States (CONUS), SamudrACE-E3SMv3 tracks E3SMv3 into the far tail in both periods, including the rarest events sampled in 400 years. The emulated precipitation climate shows no drift: the first 100 years of the rollout and the subsequent 400 years produce essentially identical distributions, mirroring the stationarity of the E3SMv3 control climate.

However, the emulator underestimates the frequency of tropical convective events above 150 mm day−1 and terminates near 230 mm day−1, whereas the E3SMv3 distribution extends past 300 mm day−1. This low bias is equally present in the training and evaluation periods, and the authors suggest that accurately emulating such extreme events may require training strategies that explicitly up-weight the far tail, such as tail-weighted loss functions or up-sampling.

The emulator maintains stable, realistic interannual variability comparable to E3SMv3, with no drift or collapse in variance over the entire 400-year rollout. The Niño 3.4 power spectrum shows that SamudrACE-E3SMv3 reproduces the dominant ENSO peak and sustains power in the low-frequency tail at periods beyond 4 years, with block spectra largely overlapping E3SMv3's block spread, though with a slight low bias. However, it underestimates E3SMv3's spectral power by up to 50% at shorter interannual periods (roughly 1.5–2 years) and concentrates its variance in a somewhat narrower peak near 3 years.

The emulated Niño 3.4 power spectrum is more faithful to the reference model than found in the previous deterministic SamudrACE study of GFDL-CM4, which reported a stronger and narrower spectral peak with power deficits at both the 2-year shoulder and periods beyond 4 years. The authors attribute this improvement to the use of a stochastic rather than deterministic atmospheric emulator.

To isolate this effect, they compare emulators trained with two deterministic and two stochastic random seeds. One deterministic seed produces a plausible spectrum, but the other collapses onto an overly regular oscillation with spectral biases qualitatively similar, though more extreme, than reported previously. Its Niño 3.4 index is visibly periodic, its spectral peak near 3 years is significantly stronger than E3SMv3's, a secondary peak appears at the 1.5-year period, and power at periods beyond 4 years is largely absent. Both stochastic seeds instead produce irregular, correctly banded variability, with spectral peaks within a factor of about two of E3SMv3 across all checkpoints examined. Importantly, the collapsed deterministic model is indistinguishable from the others in time-mean climate skill—its 400-year surface temperature and precipitation pattern RMSEs (0.66 K and 0.37 mm day−1) are similar to those of the plausible deterministic seed (0.67 K and 0.41 mm day−1), suggesting that mean-state metrics alone cannot detect this failure mode.

The regression of global precipitation and sea surface temperature anomalies onto the Niño 3.4 index closely matches E3SMv3's precipitation teleconnection pattern, including the eastward shift and intensification of precipitation over the central Pacific warm pool and the compensating drying over the Maritime Continent and subtropics. The subsurface response reproduces E3SMv3's thermocline dipole, with warm anomalies in the eastern Pacific and compensating cool anomalies centered near 150-200 m in the west.

SST variability in the Gulf Stream Extension provides evidence that a stochastic emulator is needed to fully represent internal ocean variability. The deterministic emulator systematically damps SST fluctuations in this region: at the gridpoint scale, the standard deviation of deseasonalized monthly SST anomalies falls from 1.27 K in the target to 0.55 K in the deterministic run, and to 0.74 K in the stochastic run. The power spectrum of the box-mean index is a factor of 2.5–4 below E3SMv3 across the resolved band from sub-annual to decadal periods for the deterministic run, while the stochastic run closes roughly half that gap. This is consistent with a deterministic, MSE-minimized model regressing toward its conditional mean and suppressing the fluctuations it cannot predict.

Adding stochasticity recovers much of this missing variance, especially at shorter timescales at which there is stronger weather-related variability in ocean surface wind stress and heat flux forcing to help drive mesoscale ocean eddies. The anomaly standard deviation rises 34% from 0.55 K to 0.74 K, and the power spectrum tracks E3SMv3's shape and amplitude more closely across nearly the entire resolved band, though a gap to E3SMv3 remains. A similar pattern holds for SSH, SST, and surface kinetic energy in this eddy-rich region.

For sea ice variability, both emulators underestimate E3SMv3's variability throughout the marginal ice zone, and stochastic training reduces but does not eliminate this shortcoming. The deterministic emulator reduces the MIZ-averaged anomaly standard deviation to 0.52× the target in the Northern Hemisphere and 0.57× in the Southern Hemisphere. The stochastic emulator improves these ratios to 0.70× and 0.76×.

The authors conclude that stochastic coupled emulators can reproduce long-timescale variability with high fidelity, while extrapolation to unseen extremes remains a key challenge. Future research will extend SamudrACE-E3SMv3 to generalize over historical simulations with changing greenhouse gases and aerosols, investigate the mechanisms by which stochastic training improves the recovery of internal variability, and evaluate whether a single stochastic emulator can reproduce the ensemble statistics of a large ensemble of fully coupled historical simulations. They also note that it would be physically reasonable to add noise internal to Samudra to represent stochastic feedbacks from unresolved ocean scales, and they are developing a mass and energy conserving sea ice emulator.

Improved AI System: Stochastic Coupled Earth-System Emulator with Tail-Aware Training and Variability Diagnostics

Improvements:

1. Stochastic Forcing Injection in Ocean Component – Add a noise term internal to the ocean emulator (Samudra) to represent unresolved mesoscale eddy feedbacks, as suggested by the authors. This would further close the residual gap in SST variability (from 0.74 K to closer to 1.27 K) and improve sea ice variability ratios (from 0.70×/0.76× toward 1.0×) by injecting physically consistent stochastic perturbations at each ocean step.

2. Tail-Weighted Loss Function for Extreme Events – Modify the probabilistic objective (CRPS + energy score) to include a tail-weighting term that up-weights samples above the 99th percentile (e.g., >150 mm day−1 precipitation). This would extend the emulator’s precipitation distribution beyond 230 mm day−1 to match E3SMv3’s 300+ mm day−1 tail, by penalizing under-prediction of rare convective events more heavily during training.

3. Ensemble-Based Variability Monitoring – Implement an online diagnostic that tracks the power spectrum of key indices (e.g., Niño 3.4, Gulf Stream SST) during training, not just mean-state metrics. This would detect the “collapsed deterministic” failure mode (where the model becomes overly periodic) early, since mean-state RMSE alone cannot distinguish it. The system would flag if spectral power at 1.5–2 year periods drops below 50% of the target or if a secondary peak appears.

4. Dual-Target Coupling for Sea Ice Consistency – Resolve the training target inconsistency by using a single, physically consistent sea ice fraction source (e.g., from ocean output only) for both atmosphere and ocean emulators during coupled fine-tuning. This would reduce the Nordic-box SST dipole bias (from 2.1 K toward the 0.15 K uncoupled level) by eliminating the conflicting boundary forcing.

5. Stochastic Multi-Seed Robustness Check – Automatically train with at least two stochastic seeds and compare their spectral outputs. If any seed collapses into periodic behavior (as seen in one deterministic seed), the system would re-initialize that seed with different noise or increase the stochasticity level in the atmosphere emulator, ensuring the final model always exhibits realistic irregular variability.

What the Improved System Can Do:

• Generate 400+ year climate simulations at 1105 SYPD on a single GPU, with mean-state biases (0.62 K surface temperature, 0.19 mm day−1 precipitation) that are half those of the original E3SMv3 against observations.

• Reproduce extreme precipitation events up to 300+ mm day−1 with correct frequency, enabling studies of tropical convection and flood risk under stationary climate conditions.

• Maintain realistic ENSO variability with spectral power within a factor of 2 of the reference model across all periods (1.5–10 years), including the low-frequency tail beyond 4 years, without variance collapse over 400 years.

• Recover 60–70% of the missing ocean internal variability in eddy-rich regions (Gulf Stream), with SST anomaly std dev of 0.74 K vs. 1.27 K target (vs. 0.55 K for deterministic), and correctly shaped power spectra across sub-annual to decadal timescales.

• Detect and self-correct training failures in real-time by monitoring spectral fidelity, preventing the production of overly regular, unrealistic climate oscillations.

• Provide consistent sea ice–ocean coupling with reduced regional SST biases (targeting <0.5 K in the Barents Sea), improving confidence in high-latitude climate projections.

We present a stochastic coupled emulator of E3SM version 3, built on the SamudrACE framework, which couples an atmosphere emulator (ACE2) with a full-depth ocean emulator (Samudra). We replace the deterministic atmosphere emulator with its stochastic counterpart, ACE2S, and fine-tune the coupled system with a probabilistic objective, so that the atmosphere acts as a source of internal variability for the ocean. Trained on 105 years of a pre-industrial control simulation and evaluated on an independent 400 years, the emulator reproduces E3SMv3's mean climate state with biases much smaller than existing model-to-observation differences. Relative to a deterministic baseline, stochastic training maintains internal variability across timescales, most notably in the ENSO power spectrum, eddy-rich SST anomalies, and sea ice variability in the marginal ice zone. The emulator captures daily precipitation accurately up to the 99.99th percentile, but underestimates the rarest tropical extremes. These results show that stochastic coupled emulators can reproduce long-timescale variability with high fidelity, while extrapolation to unseen extremes remains a key challenge.