Tuesday, April 27 2021
9:00am - 11:00am
PhD Thesis Presentation
Topological Groups and Ensemble Transform Kalman Filter

One variant of the ensemble Kalman filter (EnKF) is the ensemble transform Kalman filter (ETKF). The main advantage of the ETKF is that it creates an ensemble with the desired statistics by a deterministic transformation without the need to use random perturbations of the data. The ensemble mean and covariance of the ETKF were proved to converge to those of the Kalman Filter (KF) in the large ensemble limit; however, nothing seems to be known about the probability distribution of the ensemble members themselves, other than that it is clearly not Gaussian. The ensemble Kalman filter (EnKF) was proposed as a linear solver in variational data assimilation, in which solving a large nonlinear least squares problem is needed. The method converges to deterministic iterations for the nonlinear least squares problem, but the result requires control of the ensemble members. For my thesis, I propose to investigate the probability distribution of the ensemble members, which may lead to study asymptotic convergence of the ensemble members. A characterization of the probability distribution of the ensemble members may allow identifying bounds on their spread. As a proof of concept, extending the notion of exchangeability of ensembles, I show that the group of orthogonal matrices acts transitively on the set of ensembles and use the theory of invariant probability measures along with tools from group theory to gain insight into probability distributions of the ensemble members in the ETKF and application to foundations of the ETKF use in variational data assimilation.
Speaker:Basma Tumi
Location:See Zoom link from email

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