Ensemble-based Filtering and Smoothing Methods for the Sequential Data Assimilation with Highly Nonlinear Observation System

Sequential data assimilation which is methodology and concept used mainly in the meteorology and oceanography, aims at accommodating physical variables of simulation models to observation data. The Ensemble Kalman Filter (EnKF) was invented and is used in sequential data assimilation. This procedure is based on the second order statistics and it cannot deal with these systems directly if observed data are nonlinear transformation of states. This problem is resolved by extending the state vector, but this cannot reflect ensemble states completely. On the other hand, it is well known that the Particle Filter (PF), which is developed in statistical field, can deal with higher order statistics and nonlinear transformed states without extension. Both of them are ensemble-based filtering methods and can be extended to fixed lag smoother (the EnKS and the Particle Smoother(PS)). This research demonstrates that the PF and the PS are superior to the EnKF and the EnKS in assimilating nonlinear observation by numerical experiments.