Comparing an idealized deterministic-stochastic model (SUP model, version 1) of the tide- and wind-driven sea surface currents in the Gulf of Trieste to high-frequency radar observations

In the Gulf of Trieste, the sea surface currents were observed by high-frequency radar for almost 2 years (2021-2022) at a temporal resolution of 30 min. We developed a hierarchy of idealized models to simulate the observed sea surface currents, combining a deterministic and a stochastic approach, in order to reproduce the externally forced motion and the internal variability, which is characterized by fat-tailed statistics. The deterministic signal includes tidal and Ekman forcing and resolves the slowly varying part of the flow, while the stochastic signal represents the fast-varying small-scale dynamics, characterized by Gaussian or fat-tailed statistics, depending on the statistic used. This is done using Langevin equations and modified Langevin equations with a gamma-distributed variance parameter. The models were adapted to resolve the dynamics under nine tidal and wind forcing protocols in order to best fit the observed forced motion and internal variability probability density function (PDF). The stochastic signal requires 2 stochastic degrees of freedom when the average tidal forcing is adopted, while it needs 1/2 stochastic degree of freedom when the complete tidal forcing is used. Despite its idealization, the deterministic-stochastic model with stochastic fat-tailed statistics captures the essential dynamics and permits mimicking the observed PDF. Moreover, a fluctuation response relation is valid when the stochastic signal is perturbed, showing that the response to an external perturbation can be obtained by considering the fluctuations of the unperturbed system.