A local sigma-point unscented Kalman filter for geophysical data assimilation

Abstract

The prior covariance calculated in the Reduced-rank Sigma-Point Kalman filter (RSPKF) data assimilation method can be suboptimal as a result of finite number of sigma points, effects of sampling error, process error, and other factors. In this study, we analyse the performance of RSPKF by applying a localization scheme that combines local analysis and global generation of sigma points. The analysis at each model grid for the entire domain are updated using only the observations local to the analysis grid. The localization enables a high rank approximation of the background error covariance in a local subspace of greatly lower dimension than the global domain using a small number of sigma points. The global-analysis vector is constructed combining the local analyses at all model grid points. The global analysis-covariance matrix is generated in the ensemble subspace and the global sigma points are constructed following the RSPKF algorithm. Numerical experiments of our method utilized the Lorenz-96 model. The performance of the localization scheme is assessed in the presence of varying parameters such as the number of sigma points (k), inflation factor (ϕ), localization radius (d) and the number of model variables (Nx). When the localization is implemented, the number of sigma points required to achieve the minimum RMSE is significantly reduced compared to a case where no localization is used, for three different cases of model variables (Nx). We also show that the approximate number of sigma points used to obtain optimal estimate is independent of the state dimension Nx of the model. This further highlights the importance of localization in RSPKF, making it a potential candidate for data assimilation in oceanic or atmospheric General Circulation Models (GCMs).