A Generalized Stochastic Formulation of the Ekman–Stokes Model with Statistical Analyses

Abstract To describe the upper-ocean Ekman boundary layer, a novel stochastic model is formulated to better capture the interplay between random components associated with the 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 error 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. Significance Statement The upper-ocean boundary layer plays a critical role in regulating air–sea interactions, vertical mixing, and climate variability. Many existing boundary layer models employ deterministic turbulence closures that do not account for the inherently random nature of unresolved small-scale processes. This study presents a novel stochastic framework that explicitly incorporates the random effects of wind forcing, surface waves, and turbulent transport, while maintaining key physical balances. The results demonstrate enhanced variability and a higher frequency of extreme events, emphasizing the relevance of stochasticity in upper-ocean dynamics. This approach provides a physically consistent representation of boundary layer processes, with potential benefits for improving ocean modeling and forecasting of an ensemble of realizations at coarse resolution.