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The ocean circulation is modulated by meandering currents and eddies. Forecasting their evolution is a key target of operational models, but their forecast skill remains limited. We propose a machine learning approach that improves the output of an ocean circulation model by learning and predicting its systematic biases. This method can be applied a priori to any region, and is tested in the Gulf of Mexico, where the Loop Current (LC) and the large anticyclonic eddies that detach from it are major forecasting targets. The LC dynamics are recurrent and lie on a low‐dimensional dynamical attractor. Building upon the information gained analyzing this low dimensional attractor, we improve the representation of sea surface anomalies in model outputs through information from satellite altimeter data using a Sequence‐to‐Sequence model, which is a special class of Recurrent Neural Network. Building upon the HYCOM‐NCODA analysis system, we deliver a correction to the forecast at the observation resolution. For at least 15 days the proposed method learns to forecast the systematic bias in the HYCOM‐NCODA, outperforming persistence, and improving the forecast. This data‐driven approach is fast and can be implemented as an added step to any dynamical hindcasting or forecasting model. It offers an interesting avenue for further developing hybrid modeling tools. In these tools, fundamental physical conservations are preserved through the integration of partial differential equations which obey them. In addition, the method highlights specific deficiencies of the hindcast system that deserve further investigation in the future.

 

The Gulf of Mexico is a very productive and economically important system where riverine runoff acts as a linkage between the continental shelf and the open ocean, providing nutrients in addition to freshwater. This work investigates the three-dimensional transport and pathway structure of this river runoff offshore the continental shelf using ensembles of numerical simulations with different configurations regarding grid resolution (mesoscale resolving and submesoscale permitting) and river setup using suites of 5-months long integrations covering nearly 3 years. The riverine forcing is applied only at the surface over an area around the river mouth, a strategy often adopted in numerical studies, or as a meridional flux with a vertical extension. The simulated flow captures the southward offshore transport of river runoff driven by its interaction with the largest mesoscale circulations in the basin, the Loop Current and Loop Current eddies. This pathway is strong and well-document during summer but also active and relevant in winter, despite a less obvious surface signature. The most intense transport occurs primarily at the peripheries of the Loop Current and the detached eddies, and the freshwater is subducted as deep as 600 m around the mesoscale anticyclonic eddies. Submesoscale motions strengthen slightly the spread of freshwater plumes in summer but their contribution is negligible, if not negative, in winter. Differences in the freshwater distribution and transport volume among runs are small and generally less than 10% among ensembles, with overall slightly higher volume of freshwater transported off-shore and at depth in submesoscale permitting runs that include a velocity flux in their riverine input representation. 

Submesoscale circulations influence momentum, buoyancy and transport of biological tracers and pollutants within the upper turbulent layer. How much and how far into the water column this influence extends remain open questions in most of the global ocean. This work evaluates the behavior of neutrally buoyant particles advected in simulations of the northern Gulf of Mexico by analyzing the trajectories of Lagrangian particles released multiple times at the ocean surface and below the mixed layer. The relative role of meso- and submesoscale dynamics is quantified by comparing results in submesoscale permitting and mesoscale resolving simulations. Submesoscale circulations are responsible for greater vertical transport across fixed depth ranges and also across the mixed layer, both into it and away from it, in all seasons. The significance of the submesoscale-induced transport, however, is far greater in winter. In this season, a kernel density estimation and a detailed vertical mixing analysis are performed. It is found that in the large mesoscale Loop Current eddy, upwelling into the mixed layer is the major contributor to the vertical fluxes, despite its clockwise circulation. This is opposite to the behavior simulated in the mesoscale resolving case. In the “submesoscale soup,” away from the large mesoscale structures such as the Loop Current and its detached eddies, upwelling into the mixed layer is distributed more uniformly than downwelling motions from the surface across the base of the mixed layer. Maps of vertical diffusivity indicate that there is an order of magnitude difference among simulations. In the submesoscale permitting case values are distributed around 10 –3 m 2 s –1 in the upper water column in winter, in agreement with recent indirect estimates off the Chilean coast. Diffusivities are greater in the eastern portion of the Gulf, where the submesoscale circulations are more intense due to sustained density gradients supplied by the warmer and saltier Loop Current. 

The diurnal cycling of submesoscale circulations in vorticity, divergence, and strain is investigated using drifter data collected as part of the Lagrangian Submesoscale Experiment (LASER) experiment, which took place in the northern Gulf of Mexico during winter 2016, and ROMS simulations at different resolutions and degree of realism. The first observational evidence of a submesoscale diurnal cycle is presented. The cycling is detected in the LASER data during periods of weak winds, whereas the signal is obscured during strong wind events. Results from ROMS in the most realistic setup and in sensitivity runs with idealized wind patterns demonstrate that wind bursts disrupt the submesoscale diurnal cycle, independently of the time of day at which they happen. The observed and simulated submesoscale diurnal cycle supports the existence of a shift of approximately 1–3 h between the occurrence of divergence and vorticity maxima, broadly in agreement with theoretical predictions. The amplitude of the modeled signal, on the other hand, always underestimates the observed one, suggesting that even a horizontal resolution of 500 m is insufficient to capture the strength of the observed variability in submesoscale circulations. The paper also presents an evaluation of how well the diurnal cycle can be detected as function of the number of Lagrangian particles. If more than 2000 particle triplets are considered, the diurnal cycle is well captured, but for a number of triplets comparable to that of the LASER analysis, the reconstructed diurnal cycling displays high levels of noise both in the model and in the observations.