A practical scheme of the sigma‐point Kalman filter for high‐dimensional systems

While applying a sigma‐point Kalman filter (SPKF) to a high‐dimensional system such as the oceanic general circulation model (OGCM), a major challenge is to reduce its heavy burden of storage memory and costly computation. In this study, we propose a new scheme for SPKF to address these issues. First, a reduced rank SPKF was introduced on the high‐dimensional model state space using the truncated single value decomposition (TSVD) method (T‐SPKF). Second, the relationship of SVDs between the model state space and a low‐dimensional ensemble space is used to construct sigma points on the ensemble space (ET‐SPKF). As such, this new scheme greatly reduces the demand of memory storage and computational cost and makes the SPKF method applicable to high‐dimensional systems. Two numerical models are used to test and validate the ET‐SPKF algorithm. The first model is the 40‐variable Lorenz model, which has been a test bed of new assimilation algorithms. The second model is a realistic OGCM for the assimilation of actual observations, including Argo and in situ observations over the Pacific Ocean. The experiments show that ET‐SPKF is computationally feasible for high‐dimensional systems and capable of precise analyses. In particular, for realistic oceanic assimilations, the ET‐SPKF algorithm can significantly improve oceanic analysis and improve ENSO prediction. A comparison between the ET‐SPKF algorithm and EnKF (ensemble Kalman filter) is also tribally conducted using the OGCM and actual observations.