HClimRep-Ocean: A Global Ocean Emulator on an Unstructured Mesh

1 Introduction

• Ocean emulation matters for marine services and climate predictability because the ocean is the coupled system’s slow component and primary memory, with predictability extending beyond the atmosphere’s roughly two-week deterministic horizon.Its eddies are roughly an order of magnitude smaller than atmospheric counterparts, alongside complex coastlines, straits, and seasonal ice.Source: §1 · p. 2
• Existing ocean ML systems span reanalysis-trained short- to medium-range forecasts, climate-timescale emulators, and surface-only models; the cited systems operate on regular grids or derived graphs rather than a global model’s native mesh.The introduction places this work among broader ML forecasting advances, including GraphCast, GenCast, and AIFS [3].Source: §1 · pp. 2–3
• Regular latitude–longitude grids can under-resolve constrained, active ocean regions, while regridding native model fields discards adaptive resolution and can introduce projection artifacts and conservation errors.The cited examples include coastlines, straits, shelf seas, marginal ice zones, and western boundary currents.Source: §1 · p. 3
• HClimRep-Ocean runs directly on FESOM2’s native unstructured mesh and receives atmospheric input only at initialization, isolating predictability carried by the ocean state.The authors anticipate reduced predictive power for atmospherically driven surface fields without later forcing.Source: §1 · p. 3
• The reanalysis-trained variant achieves the lowest RMSD against GLORYS across most OceanBench variables, depths, and lead times; a 180-day rollout remains bounded but is only a qualitative stability check.Only one 180-day rollout was available, so it does not establish forecast skill at that range.Source: §1 · p. 3

2.1 Training

• Training data come from simulated AWI-CM3 v3.1.3 data, whose ocean component is FESOM2 on the CORE2 mesh, nominally 1° with roughly 20–25 km refinement in the tropics and high latitudes.The mesh has approximately 126,858 surface nodes and 244,659 triangle elements. The architecture extends without modification to FESOM2 D3 (∼3 km in western boundary currents) and NG5 (∼5 km globally).Source: §2.1 · p. 4
• The emulator predicts temperature and salinity at 20 depths to 450 m, sea-surface height, sea-surface salinity and temperature at nodes, and horizontal velocity on elements.The atmosphere influences the training ocean fields, but the emulator receives no atmospheric input after initialization.Source: §2.1 · p. 4
• Nine atmospheric fields from the same coupled trajectory are supplied at initialization, spanning wind, near-surface temperature and dewpoint, precipitation, radiation, and sea-level pressure.These channels represent pathways through which the atmosphere acts on the upper ocean and sea-surface height.Source: §2.1 · p. 4
• Training uses daily snapshots from 209 model years, with the final year held out; the validation year is climatologically ordinary and control-run drift is negligible relative to reported errors.There are 329 daily validation initializations; the reported drift projections over 180 days are ≤1.5 mK, ≤0.3 m psu, and ≤0.2 mm.Source: §2.1 · pp. 4–5
• The OceanBench variant uses the same forcing-free architecture, pretrained on EERIE and fine-tuned on GLORYS12; its ocean fields are remapped to a regular 1/4° grid, while ERA5 remains on its native N320 grid.This variant differs from the main model in training data and input grid.Source: §2.1 · p. 5

2.2 Model Architecture

• Three streams encode surface-node, element, and atmospheric inputs; local attention combines streams within cells, global attention integrates neighborhood information, and forecasting advances latent states through temporal windows.Read-out heads form fixed-size per-cell representations, and projection heads decode latent states to target coordinates.Source: §2.2 · pp. 5–6, Figure 1 · p. 6

3 Verification methodology

• Quantitative skill uses 329 daily initializations of the held-out year, each forecast for 30 days; one 180-day integration from a single initial condition is reserved for stability assessment.The 15- and 30-day scores are summarized in Table 2.Source: §3 · pp. 6–7, Table 2 · p. 8
• The well-posed verification target is the parent model’s trajectory, separating emulator fidelity from the parent model’s departure from the real ocean; the reanalysis-trained variant’s OceanBench evaluation is complementary.The emulator is a surrogate for AWI-CM3/FESOM2, so this evaluation does not itself test real-ocean accuracy.Source: §3 · p. 7
• References are persistence and day-of-year climatology, plus damped-anomaly persistence, the MSE-optimal linear combination of persistence and climatology.The damped baseline represents the expected relaxation toward climatology when atmospheric weather noise is set to zero; its in-sample-tuned e-folding times are 30 days for temperature and salinity and 15 days for sea-surface height and currents.Source: §3 · p. 7
• Spatial statistics are weighted by true mesh areas and include RMSE, anomaly correlation, normalized standard deviation, and skill scores; temporal variability is assessed with area-weighted power spectra.The verification also stratifies by zonal bands, six active regions, and depth profiles to 450 m.Source: §3 · pp. 7–8

4.1 Global skill versus lead time

• For surface fields, the emulator beats damped persistence for currents, loses for temperature and salinity, and is nearly tied for sea-surface height.At 15 days, temperature error is 0.613 °C versus 0.532 °C for damped persistence, while sea-surface height errors are 0.0454 versus 0.0457 m; current improvements are 18% at 2.5 m and 48% at 95 m. Without atmospheric forcing after initialization, tracer anomalies decay toward climatology, whereas learned dynamics carry current forecasts; the emulator also produces spatially coherent ocean states.Source: §4.1 · pp. 9–10

4.2 Vertical structure

• At 450 m, temperature is not improved over persistence and salinity is worse than climatology, while velocity remains the best-predicted field at depth.Deep temperature has a persistence skill score of −0.65 at 15 days; at 450 m, salinity skill against persistence is −4.7. At 95 m, velocity component-mean anomaly correlation is 0.87 at 15 days and 0.76 at 30 days. Mean temperature and salinity profiles drift by at most 0.05 °C and 0.02 psu over 30 days, though a cold bias reaches −0.061 °C near 150 m at 30 days.Source: §4.1 · p. 10, §4.2 · pp. 11, 14

4.3 Dependence on initialization season

• Surface temperature error rises by factors of 1.9 in the Northern Hemisphere and 1.8 in the Southern Hemisphere from local winter to summer starts, while autumn yields the greatest gain over persistence.The same seasonal pattern occurs in opposite calendar seasons across hemispheres; sea-surface height error instead peaks in local winter. Seasonal errors reflect changing mixed-layer depth and atmospheric forcing, so single-season verification can misstate error by nearly a factor of two.Source: §4.3 · pp. 14–15

4.4 Variability and spectra

• At periods shorter than a week, the emulator retains 53% of surface-temperature power, 50% of surface-salinity power, 33% of sea-surface-height power, and 18% of surface-velocity power.At 15 days, it reproduces 104% of reference surface-temperature variance and 94% of salinity variance, but only 74% of sea-surface-height variance and 67% of surface eddy kinetic energy; eddy-energy retention is 18% in the Gulf Stream extension and 21% in the Antarctic Circumpolar Current. Tracer variance is redistributed toward slower, larger scales, while dynamic fields lose variance most strongly in mesoscale regions.Source: §4.4 · p. 16

4.5 Predictability horizon and long-rollout behaviour

• In a single 180-day rollout, forecast error exceeds climatology after 16 days for sea-surface height, 37 for salinity, 46 for surface temperature, and 70 for surface currents, then saturates rather than diverging.The mean state is preserved, but day-180 eddy kinetic energy is 54% of reference at the surface versus 83% at 107 m; the rollout is qualitative because only one initial condition was integrated. Tracer and sea-surface-height anomaly amplitudes later overshoot, while surface currents remain at 0.78 of reference.Source: §4.5 · p. 19
• With robust median-absolute-deviation spreads, surface-temperature overshoot is 1.04 rather than 1.28, while the current deficit deepens to 0.53 rather than 0.78.The tracer overshoot is carried by a minority of points, whereas the current deficit is a property of the field as a whole.Source: §4.5 · p. 20

Comparison to GLORYS reanalysis

• For other surface variables, HClimRep has the lowest RMSD at every evaluated lead, including 0.11–0.13 m s−1 for currents and 0.06 m for sea-surface height.Sea-surface salinity RMSD is 0.41 PSU at day 1 and 0.39 PSU at day 10, roughly 20–40 % below the next-best system.Source: §5 · p. 21, Table 4 · p. 21
• At day 10, SST RMSD is 0.64 °C for HClimRep versus 0.61 °C for WenHai and 0.66 °C for GLO12.The authors attribute the small forcing-free-design gap to the inability to track atmospherically driven SST variability; HClimRep's RMSD is lower than GLO12's at longer leads.Source: §5 · pp. 20–21, Table 4 · p. 21
• HClimRep achieves the lowest RMSD across most variable–depth–lead-time combinations; sea-surface temperature is the sole variable where a forced system scores lower.The authors interpret the pattern as a trade-off: modest surface-temperature penalty but consistent advantages in dynamical fields and subsurface thermohaline structure.Source: §5 · pp. 21–22

Subsurface fields

• At depths from 50 to 500 m, HClimRep has the lowest temperature RMSD among challengers at every lead, and the lowest salinity RMSD from the surface through 500 m.Subsurface current RMSD is also lowest or tied-lowest at 50 m and 100 m.Source: §5 · p. 21

Derived diagnostics

• HClimRep has the smallest Lagrangian trajectory deviation at every lead, while GLO12 is clearly superior for mixed-layer-depth RMSD.At day 9, trajectory deviation is 67.5 km for HClimRep versus 83.0 km for GLO12; mixed-layer-depth RMSD is approximately 49–51 m for HClimRep versus 32–36 m for GLO12.Source: §5 · pp. 21–22

Comparison to in-situ observations

• Against in-situ observations, HClimRep is within ∼0.05 °C of GLO12 for surface SST and has the lowest or tied-lowest near-surface current RMSD.Its sea-level anomaly RMSD against altimetry is 0.06–0.07 m, comparable to the other systems.Source: §5 · p. 22

6.1 The unstructured mesh

• The graph architecture handles CORE2 connectivity natively, produces spatially smooth fields across mesh transitions, and supports native-mesh spectra without regridding artifacts.The discussion reports no discontinuities or degradation at resolution transitions.Source: §6.1 · p. 22
• CORE2 results do not demonstrate an advantage over a regular grid of comparable mean resolution, but finer FESOM2 meshes offer substantially greater local resolution with fewer vertices than uniform grids.The architecture can target D3 and NG5 meshes without modification, requiring retraining on their higher-resolution output.Source: §6.1 · pp. 22–23

6.2 Comparison to other ocean ML systems

• Published-system comparisons are qualitative because training data, verification targets, protocols, lead times, and variables differ; OceanBench supplies a shared protocol only for the reanalysis-trained variant.That variant bridges the target gap by training on GLORYS12 and evaluating under a shared protocol.Source: §6.2 · pp. 23–24
• HClimRep’s SST RMSD against GLORYS reanalysis is 0.57–0.64 °C over days 1–10, competitive but not best-in-class; its subsurface temperature, salinity, current, SSH, and Lagrangian scores are lowest reported.Source: §6.2 · p. 23

6.3 Limitations

• Forcing-free rollout prevents the emulator from reproducing the ocean's response to atmospheric variability after initialization, contributing to spectral damping and the SST gap against forced systems.Reintroducing prescribed atmospheric forcing is identified as the most direct way to address the surface freezing.Source: §6.3 · p. 24, §6.4 · p. 24
• Training uses one AWI-CM3 realization under fixed greenhouse-gas forcing, so the emulator inherits parent-model biases and the FESOM2-trained variant has not been evaluated against observations.The OceanBench reanalysis retraining addresses this limitation only partly.Source: §6.3 · p. 24
• The prognostic state covers only 20 levels in the upper ~450 m, leaving deep-ocean processes unconstrained, and the single deterministic forecast cannot represent uncertainty or full flow variance.Deeper levels are straightforward in principle but increase graph size and training cost.Source: §6.3 · p. 24

6.4 Paths to improvement

• Suggested extensions include step-wise atmospheric forcing, probabilistic formulations, variance-aware losses, rollout training, and eddy-resolving targets.D3 (~3 km in western boundary currents) and NG5 (~5 km globally) are identified as future training targets with more spatial detail.Source: §6.4 · p. 24

• A reanalysis-trained variant achieves the lowest RMSD against GLORYS across the majority of variables, depths, and lead times in OceanBench against five other systems.The paper presents HClimRep-Ocean as the first ML ocean emulator to run directly on a global ocean model's native unstructured mesh.Source: §7 · p. 24
• With forcing removed, currents retain skill at all lead times, while SST and SSS decay toward damped-anomaly persistence within roughly two weeks; subsurface temperature and salinity RMSD are lower than other systems from 50 to 500 m.The authors interpret this pattern as indicating where ocean predictability resides when atmospheric forcing is removed.Source: §7 · p. 25
• The authors identify reintroducing atmospheric forcing as the most direct route to closing the SST gap, with probabilistic formulations and eddy-resolving data as complementary next steps.They describe the native-mesh foundation as scalable for these extensions.Source: §7 · p. 25

• At 15 days, retained eddy energy is 0.64 in the tropical Pacific versus 0.17–0.25 in western boundary currents and the Southern Ocean; at 107 m, those regions retain 0.62–0.85.Regional skill tracks retained mesoscale energy, and global scores understate deficits in eddy-active regions.Source: A Regional analysis · p. 25
• In the tropical Pacific all fields beat persistence (+0.20 to +0.51), while surface currents beat it in every region (+0.17 to +0.51); salinity is negative elsewhere, worst in the Agulhas (−1.36) and Southern Ocean (−0.67).Table 7 reports regional skill means and standard deviations across 329 held-out initializations.Source: A Regional analysis · p. 25, Table 7 · p. 26
• Gulf Stream surface-temperature skill is +0.17 ± 0.32, negative for roughly a third of initializations, compared with +0.46 ± 0.09 in the tropical Pacific, where it is positive for essentially all.The best-forecast regions are also the most consistent across initializations.Source: A Regional analysis · p. 26
• Across initializations, skill distributions are asymmetric: Agulhas salinity is negative in every initialization, while tropical Pacific fields are positive in 94–100%.The figure describes distributions over 329 held-out initializations at a 15-day horizon.Source: Figure 10 · p. 26

• The 1.138×10^9-parameter model uses AdamW, gradient clipping, and a three-phase learning-rate schedule, with peak rates of 5×10^-5 for pre-training and 10^-5 for fine-tuning.Training uses bfloat16 mixed precision and bfloat16 attention.Source: §B.2 · p. 27
• Training is distributed across eight NVIDIA A100 GPUs, with one sample per GPU and a global batch of eight forecast rollouts per optimizer step.The setup combines DDP and FSDP across two nodes.Source: §B.2 · pp. 27–28
• The physical-space objective combines mean-squared error with a dynamic loss that renormalizes each channel by its running error scale, preventing temperature and salinity from dominating smaller velocity and sea-level channels.Both prognostic streams have unit weight; the diagnostic atmospheric stream contributes no loss.Source: §B.2 · p. 28

B.3 Training protocol

• The three-stage protocol progresses from masked-token pre-training to 15-step forecast fine-tuning and final refinement of the global aggregation engine.Fine-tuning freezes the encoder blocks and stream embeddings; the final stage leaves 268.5 M parameters trainable for 1408 optimiser steps.Source: §B.3 · p. 28
• Daily AWI-CM3 FESOM2 fields from 2000–2208 form the training data, while the following year is held out for forecast initialisations.Each mini-epoch draws 2048 training samples, or 4096 during pre-training.Source: §B.3 · p. 28
• Validation uses 64 samples per mini-epoch from the held-out year, and training does not use exponential moving averages of the weights.Source: §B.3 · pp. 28–29