A review of the deterministic ensemble Kalman filtering methods and related techniques

The present paper aims to provide a brief review on several deterministic ensemble Kalman filtering (EnKF) methods and the related practical techniques to prevent filter divergence. Since Evensen (1994), several formulations of EnKF have been proposed, and Whitaker and Hamill (2002) suggested that a deterministic method, a.k.a. an ensemble square root filter (EnSRF, Andrews 1968), is expected to outperform the classical perturbed observation methods (e.g., Houtekamer and Mitchell 1998) especially in a limited ensemble size, which is usually the case in realistic atmospheric models. There are several EnSRFs proposed for atmospheric data assimilation, including an ensemble transform Kalman filter (ETKF) by Bishop et al. (2001), an ensemble adjustment Kalman filter (EAKF) by Anderson (2001), an EnSRF by Whitaker and Hamill (2002), all of which are effective when observational data are assimilated serially, and a local ensemble Kalman filter (LEKF) by Ott et al. (2002; 2004), where observations are assimilated simultaneously in a local patch. As Tippett et al. (2003) indicated, ensemble formulations in the deterministic method are not theoretically unique, and it is not clear if there is a unique preferable choice in the various possible implementations. In addition, there are several practical techniques to avoid filter divergence such as localization of the forecast error correlations, hybrid combinations with three-dimensional variational (3DVAR) method, a double ensemble method, covariance inflation, and random noise addition to analysis ensemble.