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Abstract Circulation in the Gulf of Mexico is dominated by the Loop Current and associated mesoscale eddies. These mesoscale eddies pose a safety risk to offshore energy production and potential dispersal of large-scale pollutants like oil. We use a data-driven, physics-informed, and numerically consistent deep learning–based ocean emulator called OceanNet to generate a 120-day forecast of the sea surface height (SSH) in the eastern Gulf of Mexico. OceanNet uses a new dataset of high-resolution data assimilative ocean reanalysis (1993–2022) as input. This model is trained using years 1993–2018 and evaluated on four eddies during years 2019–21. For comparison, we use a state-of-the-art numerical ocean model to generate a dynamical model prediction initialized every 5 days from 27 April 2019 to 1 April 2020 (during eddies Sverdrup and Thor) using persistent forcing and boundary conditions. The dynamical model takes seven wall-clock days to run, whereas OceanNet runs in minutes. Edges of Loop Current eddies (LCEs) pose the most potent risk to offshore energy operations and pollutant dispersal due to strong water velocities. Therefore, most of the analysis focuses on edge accuracy, quantified by the modified Hausdorff distance. The edge of the LCEs is defined by the 17-cm sea surface height contour, which generally coincides with the strongest water velocity. The OceanNet prediction outperforms both persistence and the dynamical model prediction. Overall, this new ocean emulator provides a promising new approach to generate seasonal forecasts of LCEs and generates large model ensembles efficiently to quantify forecast uncertainty that is long needed by scientists and decision-makers for offshore operations. Significance StatementCirculation in the Gulf of Mexico (GoM) is dominated by the energetic Loop Current and associated mesoscale eddies (typically 150–400 km in diameter). As these eddies propagate westward through the Gulf, they pose a safety risk to offshore energy production and potential large-scale pollutant dispersal. We used ocean model output (1993–2022) to train a data-driven ocean emulator called OceanNet that generates a seasonal (up to 120 day) prediction of sea surface height (SSH) in the eastern GoM. For comparison, a simple dynamical model prediction is also evaluated. OceanNet’s performance is assessed with a focus on edge accuracy, the most potent risk to offshore energy operations and pollutant dispersal. Overall, OceanNet performs well for a seasonal forecast and shows great potential for further development. 

Abstract. Many meteorological and oceanographic processes throughout the eastern US and western Atlantic Ocean, such as storm tracks and shelf water transport, are influenced by the position and warm sea surface temperature of the Gulf Stream (GS) – the region's western boundary current. Due to highly nonlinear processes associated with the GS, predicting its meanders and frontal position has been a long-standing challenge within the numerical modeling community. Although the weather and climate modeling communities have begun to turn to data-driven machine learning frameworks to overcome analogous challenges, there has been less exploration of such models in oceanography. Using a new dataset from a high-resolution data-assimilative ocean reanalysis (1993–2022) for the northwestern Atlantic Ocean, OceanNet (a neural-operator-based digital twin for regional oceans) was trained to predict the GS's frontal position over subseasonal to seasonal timescales. Here, we present the architecture of OceanNet and the advantages it holds over other machine learning frameworks explored during development. We also demonstrate that predictions of the GS meander are physically reasonable over at least a 60 d period and remain stable for longer. OceanNet can generate a 120 d forecast of the GS meander within seconds, offering significant computational efficiency. 

Abstract While data-driven approaches demonstrate great potential in atmospheric modeling and weather forecasting, ocean modeling poses distinct challenges due to complex bathymetry, land, vertical structure, and flow non-linearity. This study introduces OceanNet, a principled neural operator-based digital twin for regional sea-suface height emulation. OceanNet uses a Fourier neural operator and predictor-evaluate-corrector integration scheme to mitigate autoregressive error growth and enhance stability over extended time scales. A spectral regularizer counteracts spectral bias at smaller scales. OceanNet is applied to the northwest Atlantic Ocean western boundary current (the Gulf Stream), focusing on the task of seasonal prediction for Loop Current eddies and the Gulf Stream meander. Trained using historical sea surface height (SSH) data, OceanNet demonstrates competitive forecast skill compared to a state-of-the-art dynamical ocean model forecast, reducing computation by 500,000 times. These accomplishments demonstrate initial steps for physics-inspired deep neural operators as cost-effective alternatives to high-resolution numerical ocean models. 

Abstract. Many meteorological and oceanographic processes throughout the eastern United States and western Atlantic Ocean, such as storm tracks and shelf water transport, are influenced by the position and warm sea surface temperature of the Gulf Stream (GS)- the region's western boundary current. Due to highly nonlinear processes associated with the GS, predicting its meanders and frontal position have been long-standing challenges within the numerical modeling community. While the weather and climate modeling communities have begun to turn to data-driven machine learning frameworks to overcome analogous challenges, there has been less exploration of such models in oceanography. Using a new dataset from a high-resolution data-assimilative ocean reanalysis (1993–2022) for the Northwest Atlantic Ocean, OceanNet (a neural operator-based digital twin for regional oceans) was trained to identify and track the GS’s frontal position over subseasonal-to-seasonal timescales. Here we present the architecture of OceanNet and the advantages it holds over other machine learning frameworks explored during development while demonstrating predictions of the Gulf Stream Meander are physically reasonable over at least a 60-day period and remain stable for longer. 

Abstract Transfer learning (TL), which enables neural networks (NNs) to generalize out-of-distribution via targeted re-training, is becoming a powerful tool in scientific machine learning (ML) applications such as weather/climate prediction and turbulence modeling. Effective TL requires knowing (1) how to re-train NNs? and (2) what physics are learned during TL? Here, we present novel analyses and a framework addressing (1)–(2) for a broad range of multi-scale, nonlinear, dynamical systems. Our approach combines spectral (e.g. Fourier) analyses of such systems with spectral analyses of convolutional NNs, revealing physical connections between the systems and what the NN learns (a combination of low-, high-, band-pass filters and Gabor filters). Integrating these analyses, we introduce a general framework that identifies the best re-training procedure for a given problem based on physics and NN theory. As test case, we explain the physics of TL in subgrid-scale modeling of several setups of 2D turbulence. Furthermore, these analyses show that in these cases, the shallowest convolution layers are the best to re-train, which is consistent with our physics-guided framework but is against the common wisdom guiding TL in the ML literature. Our work provides a new avenue for optimal and explainable TL, and a step toward fully explainable NNs, for wide-ranging applications in science and engineering, such as climate change modeling. 

Abstract Recent years have seen a surge in interest in building deep learning-based fully data-driven models for weather prediction. Such deep learning models, if trained on observations can mitigate certain biases in current state-of-the-art weather models, some of which stem from inaccurate representation of subgrid-scale processes. However, these data-driven models, being over-parameterized, require a lot of training data which may not be available from reanalysis (observational data) products. Moreover, an accurate, noise-free, initial condition to start forecasting with a data-driven weather model is not available in realistic scenarios. Finally, deterministic data-driven forecasting models suffer from issues with long-term stability and unphysical climate drift, which makes these data-driven models unsuitable for computing climate statistics. Given these challenges, previous studies have tried to pre-train deep learning-based weather forecasting models on a large amount of imperfect long-term climate model simulations and then re-train them on available observational data. In this article, we propose a convolutional variational autoencoder (VAE)-based stochastic data-driven model that is pre-trained on an imperfect climate model simulation from a two-layer quasi-geostrophic flow and re-trained, using transfer learning, on a small number of noisy observations from a perfect simulation. This re-trained model then performs stochastic forecasting with a noisy initial condition sampled from the perfect simulation. We show that our ensemble-based stochastic data-driven model outperforms a baseline deterministic encoder–decoder-based convolutional model in terms of short-term skills, while remaining stable for long-term climate simulations yielding accurate climatology. 

Abstract There is growing interest in discovering interpretable, closed‐form equations for subgrid‐scale (SGS) closures/parameterizations of complex processes in Earth systems. Here, we apply a common equation‐discovery technique with expansive libraries to learn closures from filtered direct numerical simulations of 2D turbulence and Rayleigh‐Bénard convection (RBC). Across common filters (e.g., Gaussian, box), we robustly discover closures of the same form for momentum and heat fluxes. These closures depend on nonlinear combinations of gradients of filtered variables, with constants that are independent of the fluid/flow properties and only depend on filter type/size. We show that these closures are the nonlinear gradient model (NGM), which is derivable analytically using Taylor‐series. Indeed, we suggest that with common (physics‐free) equation‐discovery algorithms, for many common systems/physics, discovered closures are consistent with the leading term of the Taylor‐series (except when cutoff filters are used). Like previous studies, we find that large‐eddy simulations with NGM closures are unstable, despite significant similarities between the true and NGM‐predicted fluxes (correlations >0.95). We identify two shortcomings as reasons for these instabilities: in 2D, NGM produces zero kinetic energy transfer between resolved and subgrid scales, lacking both diffusion and backscattering. In RBC, potential energy backscattering is poorly predicted. Moreover, we show that SGS fluxes diagnosed from data, presumed the “truth” for discovery, depend on filtering procedures and are not unique. Accordingly, to learn accurate, stable closures in future work, we propose several ideas around using physics‐informed libraries, loss functions, and metrics. These findings are relevant to closure modeling of any multi‐scale system.