Maddison, James

Vanneste, Jacques

Ying, Yik Keung

2021-08-05T12:08:06Z

2021-08-05T12:08:06Z

2020-11-30

Eddy diffusion is commonly used to characterise subgrid-scale mixing of tracer quantities in geophysical fluid simulations. Limited by data availability, estimating eddy diffusivity from observational data remains challenging. This thesis describes a novel Bayesian framework to infer ocean transports and diffusivity fields from Lagrangian trajectories data. Modelling the Lagrangian trajectories by a stochastic differential equation whose transition density is given by the advection--diffusion equation, this framework produces a posterior probability distribution for the parameters defining the transport and diffusivity fields, enabling uncertainty quantification. In this thesis, Lagrangian trajectories from a three-layer quasigeostrophic double-gyre configuration are used to test the inference schemes. The double-gyre is a classic idealisation of large-scale ocean circulation. Mesoscale eddies are continuously produced and dissipated, leading to a complicated time-dependent flow which can plausibly be coarse-grained as diffusion and suitably used to validate the new inference schemes. Different approaches are implemented based on the Bayesian framework. In a local approach, the ocean domain is divided into an array of cells. Cell-wise defined linear velocity and constant diffusivity fields are inferred using the displacement data of Lagrangian particles originating from the cell. This approach proves capable of estimating the diffusivity in areas with a slow flow such that particles remain in the neighbourhood of their originating cell, but it fails to account for the particle trajectories straddling multiple cells in the considered time interval. An approach to correct the inference for particles straddling two cells is devised using large deviation theory, assuming the dominance of advective transport over diffusive transport. This approach successfully infers piecewise constant velocity and diffusivity using synthesised trajectories, especially in the limit of increasing dominance of advection. A global approach is then developed to infer velocity and diffusivity fields defined on the entire domain. This resolves the locality restriction on the trajectory data in the local approach. A naïve implementation of the global inference, however, involves an exceedingly large number of solutions to the advection--diffusion equation. A data coarse-graining approach is applied to overcome the computational challenge. The impact of the data coarse-graining procedures is quantified in the limit of large data. The global approach is applied to the double-gyre simulation data, using a finite volume method for the solution of advection--diffusion equation. The results demonstrate that the global approach enables a robust inference of the mean flow and diffusivity fields at varying sampling interval

https://hdl.handle.net/1842/37868

http://dx.doi.org/10.7488/era/1143

en

The University of Edinburgh

Ying, Y. K., Maddison, J. R., Vanneste, J., 2019. Bayesian inference of ocean diffusivity from Lagrangian trajectory data. Ocean Modelling 140, 101401

climate prediction models

mesoscale eddies

Bayesian framework

eddy diffusivity

synthetic trajectory data

Bayesian inference for ocean transport and diffusivity fields from Lagrangian trajectory data

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy