Bayesian inference of ocean diffusivity from Lagrangian trajectory data

A Bayesian approach is developed for the inference of an eddy-diffusivity field
from Lagrangian trajectory data. The motion of Lagrangian particles is modelled
by a stochastic differential equation associated with the advection-diffusion equation. An inference scheme is constructed for the unknown parameters that appear in this equation, namely the mean velocity, velocity gradient, and diffusivity tensor. The scheme provides a posterior probability distribution for these parameters, which is sampled using the Metropolis-Hastings algorithm. The approach is applied first to a simple periodic flow, for which the results are compared with the prediction from homogenisation theory, and then to trajectories in a three-layer quasigeostrophic double-gyre simulation. The statistics of the inferred diffusivity tensor are examined for varying sampling interval and compared with a standard diagnostic of ocean diffusivity. The Bayesian approach proves capable of estimating spatially-variable anisotropic diffusivity fields from a relatively modest amount of data while providing a measure of the uncertainty of the estimates.