Guocan Wu

By Guocan Wu and Xiaogu Zheng

The estimation accuracy of ensemble forecast errors is crucial to the assimilation results for all ensemble-based schemes. The ensemble Kalman filter (EnKF) is a widely used scheme in land surface data assimilation, without using the adjoint of a dynamical model. In EnKF, the forecast error covariance matrix is estimated as the sampling covariance matrix of the ensemble forecast states. However, past researches on EnKF have found that it can generally lead to an underestimate of the forecast error covariance matrix, due to the limited ensemble size, as well as the poor initial perturbations and model error. This can eventually result in filter divergence. Therefore, using inflation to further adjust the forecast error covariance matrix becomes increasingly important. In this chapter, a new structure of the forecast error covariance matrix is proposed to mitigate the problems with limited ensemble size and model error. An adaptive procedure equipped with a second-order least squares method is applied to estimate the inflation factors of forecast and observational error covariance matrices. The proposed method is tested on the well-known atmosphere-like Lorenz-96 model with spatially correlated observational systems. The experiment results show that the new structure of the forecast error covariance matrix and the adaptive estimation procedure lead to improvement of the analysis states.

Part of the book: Kalman Filters