Robust Ensemble Kalman Filters and Localization for Multiple State Variables

Abstract

Ensemble Kalman filters (EnKF) is a statistical technique used to estimate the state of a nonlinear spatio-temporal dynamical system. This dissertation consists of three parts. First, we develop a methodology to make EnKF robust, based on the employment of robust statistics. This methodology is necessary, since current EnKF algorithms tend to be sensitive to gross observation errors caused by technical or human errors during the data collection process, resulting in large biases or error variances. Second, we discuss the localization in the EnKF algorithms for simultaneous estimation of multiple state variables. The localization of the background-error covariance has proven to be an efficient method in reducing the sampling errors and compensating with the underestimation of the background error covariance terms. For a system of multiple state variables, the localization should be carefully applied in order to guarantee positive-definiteness of the matrices of the filtered background-error covariances. Rigorous localization methods for the case of multiple state variables, however, have rarely been considered in the literature. We introduce a number of localization filters that ensure that the background-error covariance matrix is positive-definite. Lastly, we extend the proposed robust method to both linear and nonlinear dynamical systems of multiple state variables.