Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.