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P3: Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model
Author: David Darmon , Advisor: Kayo Ide (AOSC,CSCAMM,IPST)
Problem Statement Presentation
Project Proposal
Abstract
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 flow velocities through fixed instruments. An alternative approach considers the data from a Lagrangian perspective, where the position of particles are tracked instead of the underlying flow field. The Lagrangian perspective also permits the application of tools from dynamical systems theory to the study of flows. However, very simple flow fields 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 filter, the ensemble Kalman filter, and the particle filter. The effectiveness of these schemes at tracking the hidden state of the flow will be quantified. 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 flow.
MidYear Progress Report and
Presentation
Final Presentation ,
Final Report
