A Comparison of Two Variants of Localized Particle Filter

Ensemble Kalman filters (EnKF) as a popular alternative of variational data assimilation schemes have been widely applied in research and operations. EnKF is under the assumption of the Gaussian distribution for both the prior state and the observation errors. In contrast, the particle filter (PF) estimates the posterior probability without relying on such assumptions.

The challenge of PF is the collapse of particle weights (i.e. “filter degeneracy”) due to the limited number of particles. This issue has prevented PF from being implemented in high dimensional systems. Two promising variants of PF have been proposed to alleviate the filter degeneracy. Both localize the impact of observations and maintain only partial moments of the Bayesian update of particles. One is a serial/sequential, local PF (SLPF). The other is a local nonlinear ensemble transform filter (LNETF) where parallel updates are performed within local patches. SLPF maintains the full moments of PF at locations close to observations and preserve prior particles away from observations,, but only maintain variance in the grey zone. . LNETF maintains the first two moments of PF within the local patches. Both have implemented other supplementary approaches to enhance the filter stability, e.g. inflation of observational error.

In this study, SLPF and LNETF were systematically compared in both the Lorenz96 and the Lorenz2005 models. LNETF was found more sensitive to the selection of parameters than LPF through a test in the training period. The optimal localization radius for SLPF and LNETF are similar and gradually increase (decrease) with more particles used (smaller observation error variance). The comparison of the two methods for both the Gaussian and non-Gaussian observational errors was performed also. Finally, some implications of the results on the localization of PF will be discussed.