Stochastic modelling and inference of ocean transport

Abstract

Inference of ocean dynamical properties from observations requires a suite of sta- tistical tools. In this thesis we assemble and develop a selection of useful methods for oceanographic inference problems. Our work is centred around the modelling of ocean transport. We consider Lagrangian observations, including those obtained from surface drifters. We adopt a Bayesian approach which offers a coherent frame- work for diagnosing and predicting ocean transport and enables principled uncer- tainty quantification. We also emphasise the role of stochastic models.

We begin with the problem of comparing stochastic models on the basis of ob- servations. We apply Bayesian model comparison to classical stochastic differential equation models of turbulent dispersion given trajectory data generated by simula- tion of particles in an idealised forced–dissipative model of two-dimensional turbu- lence. We discuss how model preference is quantifiably sensitive to the timescale on which the models are applied. The method is widely applicable and accounts for uncertainty in model parameters.

We then consider purely data-driven models for particle dynamics. In particular we build a probabilistic neural network model of the single-particle transition density given observations from the Global Drifter Program. The transition density model can be used either to emulate surface transport, by modelling trajectories as a discrete- time Markov process, or to estimate spatially-varying dynamical statistics including diffusivity. As is standard for probabilistic neural networks we train our model to maximise the likelihood of data. The model outperforms existing stochastic models, as assessed by skill scores for probabilistic forecasts, and is better able to deal with non-uniform data than standard methods.

A weakness of our transition density model is that, since it is trained by maximum likelihood rather than Bayesian inference, its predictions come without uncertainty quantification. This is especially concerning in regions where little data is available and point estimates of statistics such as diffusivity cannot be trusted. With this mo- tivation we discuss state-of-the-art methods in approximate Bayesian inference and their effectiveness in building Bayesian neural networks. We highlight deficiencies in current methods and identify the key challenges in providing uncertainty quan- tification with neural network models. We illustrate these issues both in a simple one-dimensional problem and in a Bayesian version of our transition density model.