Data-driven ensemble prediction of the global ocean

Qiusheng Huang; Xiaohui Zhong; Anboyu Guo; Ziyi Peng; Lei Chen; Hao Li

physics.ao-phMar 20, 2026

Data-driven ensemble prediction of the global ocean

Authors: Qiusheng Huang, Xiaohui Zhong, Anboyu Guo, Ziyi Peng, Lei Chen, Hao Li

Organizations: Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, China. · Shanghai Innovation Institute, Shanghai, China. · Shanghai Academy of Artificial Intelligence for Science, Shanghai, China. · FuXi Intelligent Computing Technology Co., Ltd., Shanghai, China. ·

Abstract

Data-driven models have advanced deterministic ocean forecasting, but extending machine learning to probabilistic global ocean prediction remains an open challenge. Here we introduce FuXi-ONS, the first machine-learning ensemble forecasting system for the global ocean, providing 5-day forecasts on a global 1° grid up to 365 days for sea-surface temperature, sea-surface height, subsurface temperature, salinity and ocean currents. Rather than relying on repeated integration of computationally expensive numerical models, FuXi-ONS learns physically structured perturbations and incorporates an atmospheric encoding module to stabilize long-range forecasts. Evaluated against GLORYS12 reanalysis, FuXi-ONS improves both ensemble-mean skill and probabilistic forecast quality relative to deterministic and noise-perturbed baselines, and shows competitive performance against established seasonal forecast references for SST and Niño3.4 variability, while running orders of magnitude faster than conventional ensemble systems. These results provide a strong example of machine learning advancing a core problem in ocean science, and establish a practical path toward efficient probabilistic ocean forecasting and climate risk assessment.

Figures & tables

Figure 1: Depth-averaged forecast skill Comparison of FuXi-ONS with baselines over all lead times. Forecast performance over the 2021–2023 test period for salinity (S), temperature (ST), zonal current (SU), meridional current (SV), and sea surface height (SSH) as a function of lead time up to 360 days. Rows show the continuous ranked probability score (CRPS), spread-skill ratio (SSR), root mean square error (RMSE), and anomaly correlation coefficient (ACC). CRPS and SSR are reported only for the two ensemble methods, FuXi-ONS and FuXi-Aim-Perlin. RMSE and ACC further include the deterministic baseline FuXi-Aim and persistence. Lower values indicate better performance for CRPS and RMSE, whereas higher values indicate better performance for SSR and ACC. FuXi-ONS consistently provides the best overall probabilistic performance and the strongest deterministic performance of the ensemble mean across most variables and lead times.

Figure 2: Depth-dependent normalized improvement of FuXi-ONS as a function of forecast lead time. Columns correspond to salinity (S), temperature (ST), zonal current (SU), and meridional current (SV). Rows show the relative changes in CRPS, SSR, RMSE, and ACC, respectively, across forecast lead times and depth levels. For CRPS and SSR, the normalized improvement is computed relative to FuXi-Aim-Perlin; for RMSE and ACC, it is computed relative to FuXi-Aim.

Figure 3: Niño3.4 forecasts for the 2021-02 initialization. Niño3.4 index forecasts from GLORY, NMME, IRI-D, IRI-ALL, and FuXi-ONS as a function of lead season. IRI-D uses only dynamical models, whereas IRI-ALL combines dynamical and statistical models. FuXi-ONS w1–w6 denote forecasts initialized every 5 days within the month, specifically 1 February, 6 February, 11 February, 16 February, 21 February, and 26 February 2021, and the FuXi-ONS mean denotes the average over these six forecasts. The horizontal axis is expressed in overlapping 3-month seasons, where each value is the mean over the labeled season, for example FMA denotes the average of February, March, and April.

Figure 4: Comparison of FuXi-ONS with NMME for sea-surface temperature forecasting. RMSE, ACC, CRPS, and SSR of monthly SST forecasts as a function of lead time. The blue solid line denotes FuXi-ONS, and the red line with circle markers denotes NMME. All metrics are averaged over forecasts initialized in 2021.

Figure 5: Architecture of the FuXi-ONS ensemble forecasting framework . (a) Structured-noise generation module. Given the current ocean state $X_{t}$ , the model predicts state-dependent perturbation statistics and samples spatially correlated noise through an SPDE-based Matérn formulation, yielding the structured perturbation field $N_{t}^{(m)}$ . (b) Forecast module. The initial atmospheric state $A_{\mathrm{init}}$ and auxiliary input $C$ are encoded into latent conditioning features $F_{\mathrm{air}}$ and $F_{c}$ . The perturbed ocean state $X_{t}+N_{t}^{(m)}$ is then mapped to the next-step forecast $\hat{X}_{t+1}^{(m)}$ . Multiple ensemble members are generated by resampling $N_{t}^{(m)}$ at each forecast step.

Probabilistic Forecasting

Probabilistic forecasting predicts distributions or events with quantified uncertainty to support reliable decisions under uncertainty.

See all 230 papers

Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting
May 14, 2026Daniel Holmberg, Joel Oskarsson, Erik Wikingsson +2Graph Neural Networks Uncertainty Quantification
University of Helsinki · ETH AI Center · Linköping University
Neptune: An AI model for Global Ocean Subseasonal Prediction
Sep 8, 2026Davide Donno, Italo Epicoco, Massimo Cafaro +8Neural Surrogate Modeling Climate Modeling
Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, Italy · CMCC Foundation - Euro-Mediterranean Center on Climate Change, Italy · Department of Earth and Environmental Engineering, Columbia University, New York, NY, USA +2
FuXiWeather2: Learning accurate atmospheric state estimation for operational global weather forecasting
Mar 16, 2026Xiaoze Xu, Xiuyu Sun, Songling Zhu +5Weather Forecasting Data Assimilation
Shanghai Academy of Artificial Intelligence for Science, Shanghai, & 200232, China. · Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai & 200433, China. · FuXi Intelligent Computing Technology Co., Ltd., Shanghai & 200233, China.

May 14, 2026J/K move · Enter open · S save

Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting

Daniel Holmberg, Joel Oskarsson, Erik Wikingsson, Fredrik Lindsten+1

University of Helsinki · ETH AI Center · Linköping University

Graph Neural Networks Uncertainty Quantification Probabilistic Forecasting Spatiotemporal Forecasting

Open paper AskPDF arXiv

Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass. We apply Njord globally at 0.25° resolution and regionally to the Baltic Sea at 2 km resolution. To scale to these large ocean grids we introduce K-means cluster meshes that adapt to irregular sea surface geometry. Experiments demonstrate strong performance on both domains compared to deterministic machine learning baselines, while also providing uncertainty estimates from the sampled ensemble forecasts. On the global OceanBench benchmark, Njord achieves the lowest errors on average across upper-ocean variables when evaluated against real-world observations, with the largest improvements in surface temperature prediction.

Abstract

Probabilistic Forecasting

Explore similar work

Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting

Neptune: An AI model for Global Ocean Subseasonal Prediction

FuXiWeather2: Learning accurate atmospheric state estimation for operational global weather forecasting