The error covariance formulation in the maximum likelihood ensemble filter (MLEF) suggests a close connection with Lyapunov (linear regime) and bred vectors (nonlinear regime). The issue of error covariance localization is addressed in relation to the localization property of Lyapunov vectors, and the related roughening interface theory. Results with assimilation of simulated observations, using a global shallow-water model, will be presented. In particular, the impact of dynamic localization on the number of assimilated observations will be examined.