Typically, numerical simulations of the ocean, weather, and climate are coarse, and observations are sparse and gappy. Recently, generative diffusion models have emerged as state-of-the-art tools for image generation and shown promise in various high-dimensional inverse problems. In this work, we apply and benchmark generative diffusion modeling approaches to super-resolution and inference from coarse, sparse, and gappy observations. We apply both guided approaches that minimally adapt a pre-trained unconditional diffusion model and conditional approaches that require training with paired high-resolution and coarse-resolution or observational data. We first show applications to idealized 2D quasi-gesotrophic turbulence on the beta-plane in two dynamical regimes, the eddy regime and the jet regime. Next, we show extensions to inference of surface oceanic flows in the Gulf of Mexico from gappy, noisy observations. Our comprehensive skill metrics include norms of the reconstructed fields, turbulence statistical quantities, quantification of the super-resolved probabilistic ensembles and their errors, and validation of the generated posterior distributions. We also study the sensitivity to tuning parameters such as guidance strength. Our results highlight the trade-offs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment in oceanographic and geophysical inverse problems.

We report the preliminary results of the international MASTR (Mini-Adaptive Sampling Test-Run) Experiment under the UGOS (Understanding the Gulf Ocean Systems) Program. The experiment utilized cutting-edge ocean observing technologies, including autonomous platforms, moorings, aircraft, and high-frequency radar, to collect near–real-time temperature, salinity, and velocity observations in the southeastern Gulf of America and Yucatan Channel. These observations provided critical insights into the complex dynamics of the Loop Current (LC) and its associated eddies, which influence regional circulation and operational predictability. Six ocean buoyancy gliders were deployed in the western Yucatan Strait near Mahahual, México. Four gliders were deployed from January to April 2024; and two, from July to November 2023. The high-frequency radar system near Cancun, México, operational throughout the experiment, observed surface velocity patterns and extreme weather events, including Hurricane Idalia (August 26 to September 2). Radar data captured the spatial and temporal position of the Yucatan Current speed core and revealed the LC system’s evolution from a retracted state. Observations exposed the complexity of the LC system, influenced by topographic, tidal, geostrophic, ageostrophic, and wind forcing. Nearly 3,900 temperature and salinity profiles were collected, significantly improving LC and hurricane intensity forecasts. Integrating near–real-time observations into federal and industry models enhanced forecast accuracy. This experiment underscores the value of adaptive sampling in advancing regional circulation understanding and operational forecasting. Findings will inform the 2025 Grand Adaptive Sampling Experiment, support cost-effective observing systems, and improve offshore risk management and hurricane predictions.