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https://hdl.handle.net/2440/132625
Type: | Thesis |
Title: | Lagrangian Coherent Data Assimilation for chaotic geophysical systems |
Author: | Crocker, Rose Joy |
Issue Date: | 2021 |
School/Discipline: | School of Mathematical Sciences |
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 . |
Advisor: | Balasuriya, Sanjeeva Mitchell, Lewis Maclean, John |
Dissertation Note: | Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2021 |
Keywords: | geophysical systems Parameter Estimation particle filters Approximate Bayesian Computation Finite Time Lyapunov Exponent Rossby wave flow data assimilation dynamical systems chaos |
Provenance: | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals |
Appears in Collections: | Research Theses |
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Crocker2021_MPhil.pdf | 9.5 MB | Adobe PDF | View/Open |
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