A localized weighted ensemble Kalman filter for high-dimensional systems

Abstract

To avoid filter collapse, a new localized weighted ensemble Kalman filter (LWEnKF) is presented. This filter is a nonlinear non-Gaussian filter that combines some of the advantages of the particle filter (PF) and of the ensemble Kalman filter (EnKF). Additionally, the new method can overcome filter degeneracy in high-dimensional system applications. Based on the weighted ensemble Kalman filter (WEnKF), we extend the scalar weight of each particle to a vector and limit the influence of distant observations through a localization function. According to the results of experiments using the Lorenz ‘96 model with 40 variables, the LWEnKF with only 10 particles can prevent filter degeneracy. In addition, tests of the new filter are also performed using a two-layer quasi-geostrophic model to demonstrate the feasibility of using the new method in high-dimensional numerical weather prediction models. Comparisons among the LWEnKF, the local particle filter (LPF) and the localized perturbed observation EnKF (LEnKF) reveal that the proposed method can combine the advantages of the latter two in certain aspects, even providing better performance in some situations. This characteristic of the LWEnKF indicates its potential for data assimilation of different types of observations. Moreover, the new filter is compared to the block-local ensemble Kalman particle filter (LEnKPF). Experiments showed that the LWEnKF has an obvious advantage over the LEnKPF when the number of particles is small, which indicates its potential for realistic applications limited by computing resources.