High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data. Here, we present a generative state-space model and an optimization framework that enable learning directly from sparse and noisy observations. The model is essentially a hidden Markov model with a continuous state space, where oceanic physical quantities are treated as hidden states and measurements as observations, enabling a unified representation of ocean fields and observational data. Both the initial-state and state-transition modules are implemented as neural networks to capture the complexity and temporal evolution of ocean states, while the emission module is formulated as a masked Gaussian distribution. To train the model from sparse observations, we derive an optimization framework based on the expectation-maximization (EM) algorithm. The framework alternately reconstructs high-fidelity ocean fields via Langevin dynamics and optimizes deep neural networks to capture temporal evolution. Theoretical analysis shows that the framework maximizes the likelihood of observations under the generative model. For efficiency, we assume that ocean-state evolution follows a stationary, ergodic, and Markovian stochastic process and adopt only length-two state sequences during optimization. Experiments on CMIP6 simulation data and FY-3D satellite data demonstrate high-fidelity reconstruction and accurate prediction, showing that sparse observations can directly improve the model's representation of ocean-state dynamics. This work offers a scalable pathway for next-generation Earth system models to learn directly from sparse, incomplete real-world observations.

Despite comprising over 70% of its surface, the world's oceans are critically underobserved compared to the land surface or the atmosphere. Understanding the global ocean requires jointly observing its surface and subsurface structure, yet no standardized, high-resolution dataset couples satellite surface fields to co-located in situ depth profiles in an AI-ready format. Existing resources either consist of model-reconstructed gridded products rather than observations, cover only a single variable or basin, or operate at resolutions too coarse for mesoscale dynamics. We introduce OceanDepths, the first open, global, regridded AI-ready dataset that pairs satellite-derived sea surface temperature (SST), sea surface salinity (SSS), and sea surface height (SSH) L4 products with co-located EN4 subsurface temperature and salinity profiles, complemented by matched GLORYS12 ocean reanalysis data to support comparisons or multi-stage learning. The dataset spans 2000-2024 at 0.1 degrees x 0.1 degrees spatial resolution and at weekly temporal resolution, covering the entire globe's sea surface and with over 9.5 million paired profiles interpolated to 50 standardized depth levels. We provide a configurable system to split the globe in equally sized spatial patches. The 4D multivariate structure, high resolution, long temporal extent, and extreme sparsity of subsurface observations (approximately 0.01% per depth level) make OceanDepths a challenging testbed for novel AI methods. We demonstrate subsurface state reconstruction as an example task with simple baseline models, but also envision OceanDepths to support the development of observation-based forecast methods and other related tasks. Available at: https://huggingface.co/datasets/ESA-philab/OceanDepths.

The reconstruction of ocean subsurface temperature (OST) using satellite remote sensing data holds significant scientific value for advancing the understanding of ocean dynamics and climate variability. However, the scarcity of subsurface observations, combined with the high degree of nonlinearity and spatiotemporal heterogeneity in subsurface processes, poses substantial challenges to the accuracy and generalization capability of traditional reconstruction methods. To address these limitations, this study proposes an adaptive framework that could capture both vertical structural dependencies and temporal variation patterns of OST via spatio-temporal clustering. By incorporating this framework with various deep learning models, e.g., dual-path convolutional neural networks (DP-CNN), Attention U-Net, and Vision Transformer (ViT), the OST field can be accurately reconstructed at a global scale only using surface observations, i.e., sea surface temperature (SST), sea surface salinity (SSS), sea surface height (SSH), and sea surface wind (SSW). Experimental results demonstrate that multiple deep learning methods using the proposed framework largely outperform their original counterparts, yielding improvements in RMSE ranging from 12.4% to 27.2%. This study provides a reliable solution for subsurface temperature reconstruction, offering important implications for meteorological modeling and climate change assessment.