A generalized stochastic formulation of the Ekman-Stokes model with statistical analyses

To describe the upper ocean Ekman boundary layer, a novel stochastic model is formulated to better capture the interplay between random components associated to numerically unresolved physical process induced by wind, waves, and currents. Accounting for the uncertainty of unresolved velocity fluctuations, resulting Ekman velocities display increased variability, higher kinetic energy, and more frequent extreme events than in an Ekman-Stokes model with time-correlated additive Gaussian forcing. Near the surface, stronger correlations and skewed probability distributions are also revealed. Sensitivity analyses highlight impacts of transient winds and surface waves, which deepen circulation and increase the dispersion of realizations in a balanced way according to errors representations. Energy and transport are maximized when the mean directions of wind velocity and surface waves coincide. This model offers a new approach to describing upper ocean dynamics, providing improved insights for anticipating vertical fluxes and enhancing predictive capabilities.