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Neptune: An AI model for Global Ocean Subseasonal Prediction

Davide Donno, Italo Epicoco, Massimo Cafaro, Gabriele Accarino, Mohammad M. Amirian, Viviana Acquaviva, Paola Nassisi, Doroteaciro Iovino, Annalisa Bracco, Simona Masina, Pierre Gentine

arXiv:2609.08606v1physics.ao-phcs.AI

TL;DR

Reliable S2S forecasting requires ocean representation, while conventional OGCMs are computationally expensive and difficult to develop. Neptune uses CNNs and SFNOs with prescribed atmospheric forcing to emulate global ocean and sea-ice states, reproducing oceanic evolution for up to 60 days and supporting high-resolution S2S emulation.

  • Problem

    Reliable S2S forecasting requires representing ocean dynamics, but traditional OGCMs are computationally expensive and difficult to develop and improve.

  • Method

    Neptune combines CNNs and SFNOs with prescribed daily atmospheric forcing to emulate global ocean and sea-ice variables at 1° and 0.25° resolution.

  • Results

    Neptune reproduces the spatio-temporal evolution of oceanic fields up to 60 days and remains stable over long timescales across statistical, physical-coherence, and climate-index evaluations.

  • Takeaways & Limitations

    Neptune provides evidence that end-to-end data-driven ocean emulators can support next-generation S2S forecasting at high spatio-temporal resolution.

  • Takeaways & Limitations

    Performance decreases in highly dynamic regions, while long-lead forecasts show smoothing of EKE and challenges resolving high-frequency mesoscale variability.

Abstract

from arXiv · show

Subseasonal-to-seasonal (S2S) forecasting is societally critical, supporting decision-making in sectors ranging from water and agricultural management to disaster risk reduction, energy planning, and insurance. Achieving reliable predictions at these timescales requires representing the ocean and its dynamics, but traditional physics-based Ocean General Circulation Models (OGCMs), are computationally expensive and difficult to develop and improve because of the code complexity. In this work, we propose Neptune, an end-to-end data-driven framework for global ocean and sea-ice components emulation tailored for S2S timescales, up to 60 days. Neptune combines Convolutional Neural Networks (CNNs) and Spherical Fourier Neural Operators (SFNOs) to effectively capture local features and global cross-scale interactions, thereby obtaining a coherent representation of the ocean state. Forced by prescribed daily atmospheric fields, Neptune emulates ocean state variables, from temperature and salinity, to zonal and meridional currents, from sea surface height to sea ice thickness and concentration, with daily outputs at the ocean surface and through the water column. Specifically, we propose two variants of Neptune, Neptune-1 and Neptune-025, capable of emulating the ocean state at 1° and 0.25° resolution, respectively. Evaluated against a suite of metrics, including statistics (RMSE, CRPS and ACC), physical coherency (Ocean Heat Content, Eddy Kinetic Energy and Ice Brier Score) and climate indices (ENSO and Z20 metric, IOD), Neptune successfully reproduces the spatio-temporal evolution of the oceanic fields up to 60 days, and is stable over long timescales. Neptune provides compelling evidence that end-to-end data-driven ocean emulators can become a powerful component of next-generation S2S forecasting systems, emulating ocean state at high spatio-temporal resolution.

1 Introduction and State of the art

Reliable S2S forecasting depends on representing ocean dynamics, yet ocean data-driven modeling remains challenging because of complex boundaries, sparse observations, and multiscale behavior. Neptune addresses this gap with a CNN–SFNO framework for global ocean and sea-ice emulation at daily resolution for up to 60 days.

  • Motivation: S2S forecasts provide actionable weeks-to-months lead times for preparing for heatwaves, droughts, floods, and marine extremes.They support decisions in agriculture, fishery management, disaster risk reduction, energy planning, and insurance.
  • Motivation: Ocean dynamics are essential to reliable S2S prediction because the ocean stores and redistributes heat, freshwater, and other climate-relevant properties over longer timescales than the atmosphere.
  • Research gap: Data-driven ocean modeling is harder than atmospheric modeling because complex coastlines, basin boundaries, and sparse observations limit the representation of ocean dynamics.
  • Research gap: Existing data-driven ocean models span coarse global forecasting, high-resolution regional modeling, and decadal prediction, but global ocean emulators remain limited in resolution and scope.The cited global ocean emulators work at a coarse 1° × 1° spatial resolution.
  • Contribution: Neptune combines CNNs and SFNOs to emulate global ocean and sea-ice states with prescribed atmospheric forcing, daily outputs, and forecasts up to 60 days.The framework includes ocean variables such as temperature, salinity, currents, sea-surface height, and mixed-layer depth, plus sea-ice concentration and thickness; Neptune-1 uses 1° resolution and Neptune-025 is fine-tuned to 0.25° resolution.

2 Materials and Methods

Neptune is trained and evaluated as a data-driven emulator of global ocean and sea-ice states using reanalysis data, atmospheric forcing, residual forecasting, and a hybrid convolutional-SFNO architecture. Its design combines local and global representations while supporting physical-coherency evaluation.

  • Datasets: ORAS5 supplies daily global ocean and sea-ice data from 1993–2022 at 0.25° × 0.25° resolution for Neptune’s training and evaluation.Selected variables include temperature, salinity, zonal and meridional velocities, mixed-layer thickness, sea-ice thickness, and sea-ice concentration.
  • Datasets: ERA5 atmospheric forcing provides daily 2 m temperature, 2 m dewpoint, 10 m wind components, and mean sea-level pressure.These variables represent atmospheric influences on heat, moisture, and momentum exchange with the ocean.
  • Forecast formulation: Neptune approximates ocean evolution by predicting two consecutive residual states from current and previous ocean states plus atmospheric forcing.Residuals are defined as differences between consecutive ocean states, and two-step prediction supports reconstruction of steady ocean dynamics.
  • Architecture: The encoder-decoder architecture combines convolutional blocks for local multiscale patterns with SFNO blocks for global spectral relationships.Inputs are projected into a 256-dimensional latent space, while spherical processing avoids projection distortions and supports long-range spatial correlations.
  • Architecture: Day-of-year and Gaussian noise are injected through conditional layer normalization to represent seasonality and generate ensemble forecasts.The decoder reconstructs residual fields that are projected back into the original physical space.
  • Evaluation metrics: Physical coherency is assessed with Ocean Heat Content, Eddy Kinetic Energy, and an Ice Brier Score for sea-ice concentration.OHC integrates temperature over the upper 300 m, EKE evaluates transient-flow variability, and IBS evaluates probabilistic ice prediction using a 15% threshold.

3 Results

Neptune’s evaluation uses 60-day forecasts initialized daily during the 2019–2021 test period. Results are organized around statistical accuracy, physical coherency, climate indices, and the higher-resolution Neptune-025 variant.

  • Evaluation design: 2019–2021 test-set forecasts are initialized daily and evaluated at each lead time through 60 days.Each initial condition produces a 60-day forecast trajectory for benchmarking.
  • Evaluation design: Statistical evaluation uses RMSE, CRPS, and ACC, while physical-coherency evaluation uses OHC, EKE, and IBS.These metrics assess forecast error, probabilistic skill, anomaly correlation, ocean heat structure, dynamical variability, and sea-ice prediction.
  • Evaluation design: Oceanic-index evaluation examines ENSO, the Z20 metric, and the Indian Ocean Dipole across the 60-day forecast horizon.The analysis targets both the occurrence and intensity of these climate-related signals.
  • Evaluation design: Climatology-based metrics use daily climatology derived from the 1993–2016 training period to avoid test-period leakage.The training-derived climatology provides a consistent evaluation baseline.

3.1 Statistical Evaluation

Neptune generally outperforms climatology across statistical metrics and maintains coherent ocean-state predictions through 60 days, although skill declines for some highly variable fields and regions at longer leads.

  • Root Mean Squared Error: Neptune’s RMSE is lower than climatology for most variables, with errors decreasing asymptotically and approaching climatology by 60 days without drift.The exception is uo and vo velocities, MLD, and SIT, for which Neptune does not consistently improve on climatology.
  • Root Mean Squared Error: Neptune coherently models selected ocean-state variables across lead times, including in regions with high mesoscale variability.Figure 2b reports low RMSE for each selected variable, despite modeling challenges in regions such as the Gulf Stream and Kuroshio.
  • Root Mean Squared Error: MLD and horizontal-current skill degrades near 60 days, with errors increasing in regions of strong variability and for velocities beyond 40–50 days.The MLD degradation is attributed to coarse upper-ocean vertical resolution, while velocity errors reflect difficulty tracking highly variable patterns.
  • Continuous Ranked Probability Score: Neptune’s CRPS is better than climatology for most variables up to 30 days, then declines slightly toward the 60-day limit.Higher CRPS occurs in highly chaotic regions, including western boundary currents and the Antarctic Circumpolar Current.
  • Anomaly Correlation Coefficient: Neptune preserves skillful ACC across ocean fields and lead times, with temperature ACC above 0.75 through 30 days and above 0.5 after 60 days.Temperature has the highest ACC across depths, while currents, MLD, and SIT show weaker or faster-declining correlation skills.

3.2 Physical Coherency

Neptune reproduces physically coherent ocean and sea-ice behavior across 60-day forecasts, preserving large-scale thermal, energetic, and ice structures while smoothing some extremes and regional details.

  • Ocean Heat Content: The lowest OHC Pearson correlation is 0.988 at 60 days, while total OHC remains exceptionally stable across forecasts.Neptune nearly reproduces OHC seasonality, although spatial biases emerge in highly variable regions.
  • Ocean Heat Content: Eastward-propagating OHC anomalies remain coherent across the equatorial Pacific after 60 days, indicating stable autoregressive behavior.The model captures propagation from the western boundary toward the South American coast, but progressively under-represents extreme values.
  • Eddy Kinetic Energy: Spatial EKE distributions remain remarkably stable over 60 days, and Neptune models major energetic regions including the Kuroshio and Gulf Stream.Velocity-field smoothing causes decreases in localized EKE and affects spectral detail.
  • Ice Brier Score: Up to 30 days, both poles remain spatially faithful in Ice Brier Score, while Arctic errors degrade more than Antarctic errors by 60 days.Antarctic errors remain concentrated near ice-edge dynamics, whereas Arctic errors spread toward the central pack.

3.3 Oceanic Indices

Neptune reproduces major oceanic climate indices through 60-day forecasts, retaining ENSO and IOD structure while showing lower predictability for wind-sensitive eastern-Pacific thermocline variability.

  • Evaluation scope: The evaluation targets ENSO, its associated Z20 metric, and IOD as crucial indices for S2S ocean forecasting.These indices assess whether Neptune captures relevant climate variability beyond individual ocean fields.
  • ENSO: Neptune accurately reproduces ENSO’s large-scale characteristics, spatial symmetry, and timing, with thermic amplitude damping after 60 days.The model learned the Niño-Niña sequence in the 2019–2021 test set.
  • Z20: Z20 correlation declines from 0.89 to 0.77 in the western box and from 0.63 to 0.34 in the eastern box between t+10 and t+60.The western basin is deeper and slower, whereas the eastern basin is shallower and more wind-forced, producing stronger amplitude damping.
  • IOD: IOD spatial correlation declines from 0.99 at t+10 to 0.89 at t+60 while preserving the dipole’s morphology and polarity.The architecture combines local and global convolutions to represent regional IOD patterns.

3.4 Evaluation on Neptune-025

Neptune-025 preserves coherent ocean and sea-ice behavior at 0.25° resolution, although fine-tuning leaves some regional biases and slightly lower performance than Neptune-1.

  • Surface skill: At t+60, Neptune-025 surface RMSE is slightly higher than after pre-training and is concentrated mainly in energetic regions.Its spatial error distribution is similar to Neptune-1.
  • Ocean Heat Content: Neptune-025 faithfully represents OHC spatial patterns over 60 days but develops a cool equatorial bias and slight average-OHC decline.The reported error remains negligible relative to the variable’s scale.
  • Eddy Kinetic Energy: After 60 days, Neptune-025 slightly overestimates Antarctic Circumpolar Current energy and underestimates equatorial energy.High-frequency spectral details are also slightly under-represented, likely because of MAE-loss smoothing.
  • Sea ice: Neptune-025 retains similar sea-ice skills, with higher IBS error at the North Pole and more slowly increasing South Pole RMSE at t+60.The hemispheric asymmetry matches the coarser-resolution version.
  • Overall assessment: Neptune-025 remains an effective eddy-resolving emulator despite slightly lower performance than Neptune-1 on some metrics.The authors identify additional fine-tuning or larger model capacity as possible ways to improve small-scale ocean dynamics.

4 Discussion

Neptune combines CNNs and SFNOs to emulate global ocean and sea-ice states, with Neptune-025 extending the framework to eddy-resolving resolution. Evaluations show strong large-scale physical coherence and climate-index skill, while fine-scale variability remains a limitation.

  • Model design: CNN and SFNO components capture local features, global interactions, and multiscale ocean dynamics in Neptune-1 and Neptune-025.The framework combines convolutional layers with spherical operators to represent interactions across spatial scales.
  • Model design: Neptune-025 adapts the Neptune-1 framework to high-resolution data with small fine-tuning effort and forecasts ocean and sea-ice states for up to 60 days.It uses prescribed atmospheric forcing and is described as an eddy-resolving emulator.
  • Statistical evaluation: RMSE, CRPS, and ACC evaluations confirm skillful ocean-state prediction, including low temperature RMSE and preserved ACC across long lead times.Neptune-025 preserves similar RMSE skills, while Neptune-1 maintains coherent large-scale morphology over longer leads.
  • Physical coherence: Both variants reproduce the spatio-temporal evolution of Ocean Heat Content, but Neptune-025 shows a slight progressive decline in total OHC over the forecast horizon.The paper associates this decline with limited fine-tuning epochs or the network’s 13M-parameter size.
  • Physical coherence: Neptune preserves EKE distributions and power spectra above 10^3 km wavelengths but has lower skill for fine-scale, high-frequency mesoscale variability.The loss of fine-scale EKE information is attributed to input resolution and the deterministic loss function.
  • Physical coherence: Both emulators maintain large-scale sea-ice pattern coherence, especially near the South Pole, while Ice Brier Scores degrade faster near dynamic coastlines at 60 days.The reported degradation is strongest in highly dynamic coastal regions.
  • Climate indices: Neptune-1 reproduces ENSO and IOD indices with high temporal and spatial correlations after 60 days, alongside skill in the Z20 metric.These results are presented as evidence of captured large-scale atmosphere–ocean coupling and interannual variability.

5 Conclusion

The paper presents Neptune as a CNN–SFNO architecture for global ocean forecasting at S2S timescales. It reports fast, high-resolution emulation with strong large-scale skill, while identifying remaining limitations in spherical processing, dynamic regions, and fine-scale variability.

  • Contribution: Neptune combines CNNs and SFNOs to forecast the global ocean and sea-ice state at subseasonal-to-seasonal timescales.The architecture uses spherical operators for global interactions and convolutional components for local dynamics.
  • Contribution: Neptune offers a faster alternative to computationally expensive physics-based models and is suitable for ensemble forecasting at high spatial and temporal resolution.The paper contrasts its computational profile and resolution with other data-driven ocean emulators.
  • Limitations: The encoder and decoder remain defined on a rectangular grid although the SFNO is structured on a sphere.Future work proposes spherical local convolutions to improve architectural coherence.
  • Limitations: Performance decreases in highly dynamic regions, and long-lead EKE smoothing indicates unresolved high-frequency mesoscale variability.The paper proposes larger models, improved training strategies, and advanced probabilistic methods as future directions.
  • Future directions: Neptune reproduces large-scale ocean dynamics but remains challenged by high-frequency mesoscale variability and depends primarily on the ORAS5 reanalysis dataset.The conclusion suggests adding other reanalyses and simulation data and developing a coupled atmosphere–ocean emulator.

A Appendix

The appendix provides additional results for the Neptune global ocean model.

  • Appendix: The appendix contains additional results for the Neptune global ocean model.

A.3 Oceanic Indices

The appendix reports spatial error diagnostics for Neptune across ocean variables, sea-ice fields, lead times, and energetic regions. It includes RMSE, CRPS, ACC, and power spectral density views for evaluating forecast skill and spatial scales.

  • RMSE diagnostics: Salinity, eastward and northward velocity, sea surface height, and mixed layer depth are evaluated with spatial RMSE from t+10 to t+60 days.
  • RMSE diagnostics: Sea-ice concentration and thickness receive separate spatial RMSE evaluations over both the North Pole and South Pole across t+10 to t+60 days.
  • CRPS diagnostics: A CRPS scorecard and variable-specific spatial CRPS figures report probabilistic forecast errors across lead times from t+10 to t+60 days.The scorecard represents lower CRPS values in white and higher values in blue.
  • CRPS diagnostics: Mixed layer depth and polar sea-ice concentration and thickness are also assessed with spatial CRPS over the same forecast-lead range.
  • ACC diagnostics: Spatial ACC diagnostics cover temperature, salinity, both velocity components, sea surface height, mixed layer depth, and polar sea-ice fields from t+10 to t+60 days.
  • ACC diagnostics: Polar sea-ice concentration and thickness are separately evaluated with ACC diagnostics for the North Pole and South Pole.
  • Spectral diagnostics: Power spectral density plots compare ground truth with forecasts across wavelengths in five energetic regions: Kuroshio, Gulf Stream, Brazil-Malvinas Confluence, Antarctic Circumpolar Current, and Agulhas.Wavelength represents spatial scale on the x-axis, while PSD is shown on the y-axis.
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