Lagrangian Coherent Data Assimilation for chaotic geophysical systems
Date
2021
Authors
Crocker, Rose Joy
Editors
Advisors
Balasuriya, Sanjeeva
Mitchell, Lewis
Maclean, John
Mitchell, Lewis
Maclean, John
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
Statement of Responsibility
Conference Name
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 .
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2021
Provenance
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