Bayesian inference of ocean diffusivity from Lagrangian trajectory data

Abstract

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.