UCLA Department of Atmospheric and Oceanic Sciences

AOS 271 Seminars

ABSTRACT: We consider evolution problems for which the initial conditions are not known precisely and some solution components are observed subject to measurement errors. The solution to this problem is provided by the celebrated Kalman filter in case the system is linear and all errors and the initial conditions are normally distributed. Various extensions to nonlinear differential equations have been proposed in the past. One of the currently most popular approaches is provided by the ensemble Kalman filter technique (EnKF) which is now widely being used, for example, in meteorology. In joint work with Bergemann and Gottwald, we have proposed a continuous Kalman update formulation which I will present in my talk. Independent of the particular update formulation, a number of additional questions need to be addressed. Most of these questions relate to small ensemble sizes and poor approximations to the ensemble covariance matrix as well as infrequent assimilation steps. I will describe regularization techniques, such a ensemble inflation, localization and temporal mollification, to overcome current EnKF limitations in the context a continuous ensemble Kalman update formulations.