We developed a hierarchy of idealized deterministic–stochastic models to simulate sea surface currents in the Gulf of Trieste. They include tide- and wind-driven sea surface current components, resolving the slowly varying part of the flow, and a stochastic signal, representing the fast-varying small-scale dynamics. The comparison with high-frequency radar observations shows that the non-Gaussian stochastic model captures key dynamics and mimics the observed fat-tailed probability distribution.