Estimating Vertical Ocean Velocity from Horizontal Currents: Linear and Depth-Conditional Neural-Network Approaches on a High-Resolution Regional Ocean Model

Abstract

The vertical component of the ocean velocity, w, is several orders of magnitude smaller than the horizontal components u and v, yet it controls vertical tracer transport, upwelling, and mixed-layer ventilation. Because w is extremely difficult to measure directly and is normally obtained only diagnostically from the continuity equation, predicting it from the horizontal velocity field is a problem of both practical and physical interest. We address this problem with two data-driven methods, a physically-motivated linear baseline and a convolutional neural network conditioned on depth through Feature-wise Linear Modulation (FiLM). Both methods are applied to a high-resolution regional simulation of the Coastal and Regional Ocean Community model over the Western Mediterranean, using a sub-region of the south-west Mediterranean Sea as a training region and two independent, out-of-sample regions for validation: the Alboran Sea, with a distinct dynamical regime driven by Atlantic inflow through the Strait of Gibraltar, and a transition region between Almería and Cartagena, between the Alboran Sea and the open western Mediterranean. Once the FiLM network is regularized enough to avoid overfitting to a single training domain, we find that its comparison with the physically interpretable linear baseline is domain- and depth-dependent rather than uniform: near the reference depth, essentially all of the achievable out-of-sample performance on both validation domains is already captured by the linear model, but at the deepest levels tested the FiLM network outperforms the linear baseline on the transition domain, whereas on Alboran it does not.