McDougall, Damon (2012) Assimilating Eulerian and Lagrangian data to quantify flow uncertainty in testbed oceanography models. PhD thesis, University of Warwick.

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Abstract

Data assimilation is the act of merging observed data into a mathematical model.
This act enables scientists from a wide range of disciplines to make predictions. For
example, predictions of ocean circulations are needed to provide hurricane disaster
maps. Alternatively, using ocean current predictions to adequately manage oil spills
has significant practical applications. Predictions are uncertain and this uncertainty
is encoded into a posterior probability distribution. This thesis aims to explore two
overarching aspects of data assimilation, both of which address the influence of the
mathematical model on the posterior distribution.
The first aspect we study is model error. Error is always present in mathematical
models. Therefore, characterising posterior flow information as function of model
error is paramount in understanding the practical implications of predictions. In
a model describing advective transport, we make observations of the underlying
flow at fixed locations. We characterise the mean of the posterior distribution as a
function of the error in the advection velocity parameter. When the error is zero,
the model is perfect and we reconstruct the true underlying flow. Partial recovery of
the true underlying flow occurs when the error is rational, the denominator of which
dictates the number of Fourier modes present in the reconstruction. An irrational
error leads to retrieval only of the spatial mean of the flow.
The second aspect we study is the control of ocean drifters. Commonplace in
oceanography is the collection of ocean drifter positions. Ocean drifters are devices
that sit on the surface of the ocean and move with the flow, transmitting their
position via GPS to stations on land. Using drifter data, it is possible to obtain a
posterior on the underlying flow. This problem, however, is highly underdetermined.
Through controlling an ocean drifter, we attempt to improve our knowledge of the
underlying flow. We do this by instructing the drifter to explore parts of the flow
currently uncharted, thereby obtaining fresh observations. The efficacy of a control
is determined by its e↵ect on the variance of the posterior distribution. A smaller
variance is interpreted as a better understanding of the flow. We show a systematic
reduction in variance can be achieved by utilising controls that allow the drifter to
navigate new or ‘interesting’ flow structures, a good example of which are eddies.

Item Type:	Thesis (PhD)
Subjects:	G Geography. Anthropology. Recreation > GC Oceanography Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Eulerian graph theory, Lagrangian functions, Oceanography -- Mathematical models, Unsteady flow (Fluid dynamics)
Official Date:	August 2012
Dates:	Date Event August 2012 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jones, C. K. R. T. (Christopher K. R. T.); Stuart, A. M.
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC); Natural Environment Research Council (Great Britain) (NERC)
Extent:	viii,141 leaves : illustrations.
Language:	eng

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