Sampling sea state using a diffusion model

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.

Explicit onshore tsunami inundation forecasting can improve public risk awareness, but deterministically predicted inundation boundaries under highly uncertain conditions, such as near-field tsunamis generated by megathrust earthquakes, may falsely imply safety outside the boundaries. Consequently, current warnings primarily target coastal tsunami height, not onshore inundation. Although machine learning enables instant inundation predictions, they remain deterministic, lacking uncertainty quantification. Here, we develop a probabilistic ensemble model based on a conditional diffusion model (a type of generative AI) that reconciles accuracy with calibration. Validated with the 2011 Tohoku-oki earthquake data, our model faithfully tracks the postearthquake uncertainty decreasing over time while accurately predicting inundation depth and extent. Our framework shows that generative AI can shift tsunami forecasting from determinism to probabilism, providing a foundation for next-generation early warning.

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.