Lagrangian Coherent Data Assimilation for chaotic geophysical systems

Abstract

This thesis develops a new method for estimating geophysical parameters based on Lagrangian Coherent Data Assimilation (LaCoDA), a nascent eld combining data assimilation and Lagrangian coherent structure techniques. Lagrangian coherent structure theory deals with characterising and extracting uid structures which have a dominant impact on the transport of key ow properties (Balasuriya et. al., Physica D, 2018:31-51). Data assimilation (DA) is a methodology for combining information from observational data with that from a mathematical model to make predictions about dynamical systems (Lahoz & Schneider, Front. Environ. Sci., Springer-Verlag, 2014). Lagrangian Coherent Data Assimilation attempts to combine these two areas to devise data assimilation schemes which exploit information from Lagrangian coherent structures to improve data assimilation in chaotic systems (Maclean et. al. Physica D, 2017:36-45). The LaCoDA technique developed here combines the data assimilation algorithm known as Approximate Bayesian Computation (ABC) with a Lagrangian coherent structure method, the Finite Time Lyaponov Exponent (FTLE). The new method, denoted FTLE-ABC, is tested on estimating the parameter from the Rossby wave model, a mathematical model which simulates an important type of atmospheric ow. FTLE-ABC is shown to outperform the benchmark methods, a standard particle lter and a standard ABC scheme, for particular regimes of the true value of , the chaoticity of the ow and the time step used in the DA scheme. In particular, the estimated chaotic timescale is found to impact FTLE-ABC's performance, with the algorithm often performing better in parameter regimes for which the chaotic timescale is fairly constant with .