A Weighted Modulated Ensemble-Based Particle Kalman Filter for Nonlinear Systems

This study proposes a hybrid data assimilation method called the weighted modulated ensemble-based particle Kalman filter (WMPKF), which combines the analysis procedures of the particle filter (PF) and the gain ensemble transform Kalman filter (GETKF). During the analysis step, WMPKF first expands the background ensemble using the modulation product ensemble expansion method employed by GETKF for model space covariance localization. To enhance assimilation performance for nonlinear systems, the posterior state in WMPKF is then estimated based on the analysis mean obtained from PF and the update term (comprising the Kalman gain and innovation) computed by GETKF using the PF-weighted modulated (expanded) background ensemble members. Finally, the original (unexpanded) analysis ensemble members are generated by adding the analysis ensemble perturbations obtained from GETKF using the PF-weighted modulated background ensemble members to the estimated analysis state. Through this analysis ensemble generation process, WMPKF can avoid the resampling step that is typically used in PFs. Cycling data assimilation experiments with the 40-variable Lorenz-96 model show that GETKF and WMPKF, which employ model space covariance localization based on the modulated ensemble, achieve higher assimilation accuracy than the local ensemble transform Kalman filter (LETKF), the localized particle filter (LPF), and the local iterative particle-ensemble Kalman filter (IPF-EnKF), which use observation space covariance localization, when assimilating nonlinear and nonlocal satellite-like observations. Furthermore, the cycling experiments demonstrate that WMPKF, which executes the hybrid analysis based on both PF and GETKF, can assimilate nonlinear satellite-like observations more effectively than GETKF that assumes the linearity of observation operators.