Two-Stage Filtering for Joint State-Parameter Estimation

Abstract This paper presents an approach for the simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters, has been investigated in many previous studies and some success with this technique has been reported in the case where model parameters are additive. However, many geophysical or climate models contain nonadditive parameters such as those arising from physical parameterization of subgrid-scale processes, in which case the state augmentation technique may become ineffective. This is due to the fact that the inference of parameters from partially observed states based on the cross covariance between states and parameters is inadequate if states and parameters are not linearly correlated. In this paper, the authors propose a two-stage filtering technique that runs particle filtering (PF) to estimate parameters while updating the state estimate using an ensemble Kalman filter (EnKF). These two “subfilters” interact recursively based on the point estimates computed at each stage. The applicability of the proposed method is demonstrated using the Lorenz-96 system, where the forcing is parameterized and the amplitude and phase of the forcing are to be estimated jointly with the state. The proposed method is shown to be capable of estimating these model parameters with a high accuracy as well as reducing uncertainty while the state augmentation technique fails.