Since the ensemble covariance is rank deficient (there are many more state variables, typically millions, than the ensemble members, typically less than a hundred), it has large terms for pairs of points that are spatially distant. Since in reality the values of physical fields at distant locations are not that much correlated, the covariance matrix is tapered off artificially based on the distance, which gives rise to localized EnKF algorithms. These methods modify the covariance matrix used in the computations and, consequently, the posterior ensemble is no longer made only of linear combinations of the prior ensemble.