Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model Mid-year Progress Report

The process of assimilating data into geophysical models is of great practical importance. Classical approaches to this problem have considered the data from an Eulerian perspective, where the measurements of interest are ow velocities through xed instruments. An alternative approach considers the data from a Lagrangian perspective, where the position of particles are tracked instead of the underlying ow eld. The Lagrangian perspective also permits the application of tools from dynamical systems theory to the study of ows. However, very simple ow elds may lead to highly nonlinear particle trajectories. Thus, special care must be paid to the data assimilation methods applied. This project will apply Lagrangian data assimilation to a model point-vortex system using three assimilation schemes: the extended Kalman lter, the ensemble Kalman lter, and the particle lter. The eectiveness of these schemes at tracking the hidden state of the ow will be quantied. The project will also consider opportunities for observing system design (the optimization of observing systems through knowledge of the underlying dynamics of the observed system) by applying a methodology for detecting manifolds within the structure of the ow.