Lagrangian data assimilation is the process of estimating a velocity flow field, given observations of the locations of passive drifters whose trajectories are determined by the flow. This problem often poses difficulties for traditional data assimilation algorithms, as it involves variables which may be high-dimensional and highly nonlinear. This thesis discusses the design and implementation of a hybrid particle - ensemble Kalman filter for Lagrangian data assimilation, which avoids the disadvantages of each filter individually while exploiting their strengths. This filter applies the ensemble Kalman filter (EnKF) update to the potentially high-dimensional flow state, and the particle filter (PF) to the highly nonlinear drifter state. As a proof of concept, this filter is tested on the linear shallow water equations, for which the flow field can be parameterized to a low-dimensional variable. Results show that the hybrid filter outperforms the EnKF in highly non-Gaussian situations, and in particular when the time between observations is long, both by better capturing the Bayesian posterior distribution and by better tracking the truth. The hybrid filter and the EnKF are then applied to the nonlinear shallow water equations, to compare their results with different drifter deployment strategies. Results suggest that the velocity field is better estimated when the drifters target energetic regions of the flow, both inside and outside vortices; on the other hand, the height field is best approximated when the drifters are spread evenly across the domain. Finally, we investigate the general application of particle filters to high-dimensional nonlinear systems, and find that the so-called "optimal proposal" implementation can afford greater performance than the standard proposal implementation.
Slivinski, Laura C.,
"Lagrangian Data Assimilation and its Applications to Geophysical Fluid Flows"
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.