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According to the National Academies, a week long forecast of velocity, vertical structure, and duration of the Loop Current (LC) and its eddies at a given location is a critical step toward understanding their effects on the gulf ecosystems as well as toward anticipating and mitigating the outcomes of anthropogenic and natural disasters in the Gulf of Mexico (GoM). However, creating such a forecast has remained a challenging problem since LC behavior is dominated by dynamic processes across multiple time and spatial scales not resolved at once by conventional numerical models. In this paper, building on the foundation of spatiotemporal predictive learning in video prediction, we develop a physics informed deep learning based prediction model called—Physics-informed Tensor-train ConvLSTM (PITT-ConvLSTM)—for forecasting 3D geo-spatiotemporal sequences. Specifically, we propose (1) a novel 4D higher-order recurrent neural network with empirical orthogonal function analysis to capture the hidden uncorrelated patterns of each hierarchy, (2) a convolutional tensor-train decomposition to capture higher-order space-time correlations, and (3) a mechanism that incorporates prior physics from domain experts by informing the learning in latent space. The advantage of our proposed approach is clear: constrained by the law of physics, the prediction model simultaneously learns good representations for frame dependencies (both short-term and long-term high-level dependency) and inter-hierarchical relations within each time frame. Experiments on geo-spatiotemporal data collected from the GoM demonstrate that the PITT-ConvLSTM model can successfully forecast the volumetric velocity of the LC and its eddies for a period greater than 1 week. 

Despite the large efforts made by the ocean modeling community, such as the GODAE (Global Ocean Data Assimilation Experiment), which started in 1997 and was renamed as OceanPredict in 2019, the prediction of ocean currents has remained a challenge until the present day—particularly in ocean regions that are characterized by rapid changes in their circulation due to changes in atmospheric forcing or due to the release of available potential energy through the development of instabilities. Ocean numerical models’ useful forecast window is no longer than two days over a given area with the best initialization possible. Predictions quickly diverge from the observational field throughout the water and become unreliable, despite the fact that they can simulate the observed dynamics through other variables such as temperature, salinity and sea surface height. Numerical methods such as harmonic analysis are used to predict both short- and long-term tidal currents with significant accuracy. However, they are limited to the areas where the tide was measured. In this study, a new approach to ocean current prediction based on deep learning is proposed. This method is evaluated on the measured energetic currents of the Gulf of Mexico circulation dominated by the Loop Current (LC) at multiple spatial and temporal scales. The approach taken herein consists of dividing the velocity tensor into planes perpendicular to each of the three Cartesian coordinate system directions. A Long Short-Term Memory Recurrent Neural Network, which is best suited to handling long-term dependencies in the data, was thus used to predict the evolution of the velocity field in each plane, along each of the three directions. The predicted tensors, made of the planes perpendicular to each Cartesian direction, revealed that the model’s prediction skills were best for the flow field in the planes perpendicular to the direction of prediction. Furthermore, the fusion of all three predicted tensors significantly increased the overall skills of the flow prediction over the individual model’s predictions. The useful forecast period of this new model was greater than 4 days with a root mean square error less than 0.05 cm·s−1 and a correlation coefficient of 0.6.