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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 We present a lightweight, easy‐to‐train, low‐resolution, fully data‐driven climate emulator, LUCIE, that can be trained on as low as 2 years of 6‐hourly ERA5 data. Unlike most state‐of‐the‐art AI weather models, LUCIE remains stable and physically consistent for 100 years of autoregressive simulation with 100 ensemble members. Long‐term mean climatology from LUCIE's simulation of temperature, wind, precipitation, and humidity matches that of ERA5 data, along with the variability. We further demonstrate how well extreme weather events and their return periods can be estimated from a large ensemble of long‐term simulations. We further discuss an improved training strategy with a hard‐constrained first‐order integrator to suppress autoregressive error growth, a novel spectral regularization strategy to better capture fine‐scale dynamics, and finally an optimization algorithm that enables data‐limited (as low as 2 years of 6‐hourly data) training of the emulator without losing stability and physical consistency. Finally, we provide a scaling experiment to compare the long‐term bias of LUCIE with respect to the number of training samples. Importantly, LUCIE is an easy to use model that can be trained in just 2.4 hr on a single A‐100 GPU, allowing for multiple experiments that can explore important scientific questions that could be answered with large ensembles of long‐term simulations, for example, the impact of different variables on the simulation, dynamic response to external forcing, and estimation of extreme weather events, amongst others. 

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 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. 

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 Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO₂). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs. 

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.