Abstract
We provide an introduction into the use and estimation of the uncertainty in state estimation by classical and ensemble data assimilation methods. In particular, we discuss how uncertainty is represented in state-of-the-art data assimilation methods. Then, we discuss the modification of Gaussian uncertainty distributions by nonlinear state propagation and how this is taken into account by methods such as 3D-VAR, 4D-VAR, the ensemble Kalman filter (EnKF or SQR-Filter), modern particle filters (such as the LPF or LAPF), and Gaussian mixture filters (such as the LMCPF). Simple examples demonstrate the phenomena and several numerical results for Lorenz 63 and 96 are given.
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