Hongze Leng, academy of ocean science and engeneering
An improved ensemble variational data assimilation method
Abstract: This work investigates the performance of an ensemble transform Kalman filter in the form of variational data assimilation method with a flow-dependent background error covariance, which is called Four-Dimensional Ensemble Transform Local Kalman Filtering (4DETLKF). Unlike most hybrid schemes, a combination of static and flow-dependent covariance is not needed. A limited ensemble size may lead to the underestimation of the ensemble covariance, however, by introducing localization into the ensemble anomalies, the rank of the square root of the error covariance matrix is significantly increased, and the spurious correlations in the error covariance matrix can be reduced. The ensemble mean is updated by minimizing a cost function with an extended control variable, and the analysis increment is calculated in an extended space with much more dimensions than that spanned by forecast ensemble perturbations. The analysis ensemble perturbations are then obtained by an ETKF-based scheme. To investigate the performance of the 4DETLKF, it is applied to a dynamic Lorenz96 system and compared with the stochastic Ensemble Kalman filter (the EnKF) and the Ensemble Kalman Smoother (the EnKS). The results show that this method can perform better than the others in the cases of relatively small ensemble sizes and relatively long correlation scale lengths. Furthermore, the true trajectory can be followed by only 5 ensemble members very well even in the condition of 1000 dimensions.