Calibration of a neural network ocean closure for improved mean state and variability

Subgrid parametrizations of vertical mixing in ocean models depend on free coefficients that cannot be measured directly and must be calibrated against high-fidelity references such as large-eddy simulations (LES). Existing approaches return point estimates and leave the associated uncertainty unquantified, a limitation when the inverse problem is ill-posed or when distinct parameter configurations fit the data comparably well. Simulation-based inference (SBI) addresses exactly this: given a prior and access to the simulator, it approximates the full posterior over parameters without requiring a tractable likelihood, at a cost set by the number of simulator evaluations. We apply it to tunax, a JAX-based single-column ocean model, to calibrate the coefficients of its $k$--$\varepsilon$ closure. A blockwise PCA summary statistic compresses the simulator output along the depth axis while preserving its forcing--horizon--variable structure, making inference tractable at modest budgets. We compare neural posterior estimation and its sequential variants against a recent training-free approach built on a tabular foundation model. The latter recovers informative posteriors from a few hundred simulator calls, outperforming the trained estimators at every budget considered.

Ocean general circulation models (OGCMs) are essential to climate science but computationally expensive, limiting ensemble size and forcing scenarios. Neural emulators promise orders-of-magnitude speedups, yet existing ocean emulators have not combined fine spatial resolution with multi-year autoregressive rollouts. Samudra, the first autoregressive neural ocean emulator to produce multi-decade global rollouts, is limited to $1^\circ$ resolution and exhibits two long-horizon failure modes: variance collapse, the loss of temporal variability, and imprinting artifacts, in which velocity patterns leak into deep-ocean fields. We present Samudra 2, which introduces a wider U-Net backbone with modified ConvNeXt-style blocks and a reduced block-internal expansion factor, together with a dynamic loss that reweights output channels according to their prediction errors, strengthening gradients for slow-evolving deep-ocean fields. At $1^\circ$, Samudra 2 increases upper-ocean global-mean temperature $R^2$ from 0.56 to 0.87 and reduces deep-ocean temperature error by roughly sevenfold. The same architecture scales to $1/2^\circ$ and $1/4^\circ$ over approximately 8-year autoregressive rollouts, recovering mesoscale eddies and sharp western boundary currents. Running on a single GPU, Samudra 2 enables larger ensembles for sea-level projections, ocean heat uptake, and climate variability studies. All artifacts are publicly available: project page, code, checkpoints, documentation.

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.