Efficient Bayesian inference for globally defined ocean transport and diffusivity fields

Eddy diffusion is commonly used to characterise subgrid-scale mixing of tracer quantities. Inferring eddy diffusivity from oceanic observations however remains challenging. Existing Lagrangian approaches typically rely on an a priori mean-eddy decomposition, followed by spatially and temporally averaging certain eddy quantities. This leads to two potential issues 1) the definition of the mean components in the Lagrangian quantities is often unclear and 2) Lagrangian particles rarely stay within a geographical area throughout the considered time span, leading to ambiguity in the spatial attribution of the estimated diffusivity.

A novel Bayesian approach is developed to surmount these challenges. Using only time-series of Lagrangian trajectories, the Bayesian approach infers simultaneously global fields of mean flow and symmetric positive-definite tensor diffusivity for a stochastic differential equation. This avoids the ambiguity in the mean-eddy decomposition and does not require the particles to remain spatially localised. Probabilistic estimates and uncertainty quantification of quantities of interest are established by sampling the resulting posterior distribution using Markov chain Monte Carlo methods. We overcome the computational challenge of the evaluation of the full posterior, which involves an exceedingly large number of numerical solutions of the advection-diffusion equation, by coarse-graining the information gathered from the trajectory data. The Bayesian approach proves capable of estimating the mean flow and diffusivity with a modest amount of data from a three-layer quasigeostrophic double-gyre model.