A stochastic model is derived from wind stress and bottom pressure gauge data to examine the response of the Antarctic Circumpolar Current (ACC) transport to wind stress forcing. A general method is used to estimate the drift and diffusion coefficients of a continuous stationary Markovian system. As a first approximation, the response of the ACC to wind stress forcing can be described by a multivariate Ornstein-Uhlenbeck process: Gaussian red noise wind stress drives the evolution of the ACC transport, which is damped by a linear drag term. The model indicates that about 30(±10)% of ACC variability is directly driven by the wind stress. This stochastic model can serve as a null hypothesis for studies of wind driven ACC variability. A more accurate stochastic description of the wind stress over the Southern Ocean requires a multiplicative noise component. The variability of the wind stress increases approximately linearly with increasing wind stress values. A multiplicative stochastic process generates a power-law distribution rather than a Gaussian distribution. A simple stochastic model shows that non-Gaussian forcing could have a significant impact on the velocity (or transport) probability density functions (PDFs) of the wind-driven circulation. The net oceanic damping determines whether the distribution of the oceanic flow is Gaussian (small damping) or resembles the distribution of the atmospheric forcing (large damping).
Sura, Philip, and Sarah T. Gille. 2003. "Interpreting wind-driven Southern Ocean variability in a stochastic framework." Journal of Marine Research 61, (3). https://elischolar.library.yale.edu/journal_of_marine_research/12