A new localization implementation scheme for ensemble data assimilation of non-local observations

Localization technique is commonly used in ensemble data assimilation of small-size ensemble members. It effectively eliminates the spurious correlations of the background and increases the rank of the system. However, one disadvantage in current localization schemes is that it is difficult to implement the assimilation of non-local observations. In this paper, we test a new localized implementation scheme that can directly assimilate non-local observations without pinpointing them. A classical local support correlation function matrix is first sampled by a set of local correlation function ensemble members (the size is M). Then, the dynamical ensemble (the size is N) is combined with the local correlation function ensemble to form an N × M ensemble by multiplying each dynamical member with each local correlation function member using the Schur product. The covariance matrix constructed by the N×M members is proved to approximate the Schur product of the local support correlation matrix and the dynamical covariance matrix. This scheme is verified through assimilating both local and non-local observations with a linear advection model and an intermediate coupled model. The analysis results show that this scheme is feasible and effective in providing reasonable and high-quality analysis fields with a relatively small dynamical ensemble size.