arXiv:2507.23199v3 Announce Type: replace Abstract: We consider filtering problems with partial observations of nonlinear dynamical systems, where accurate state estimation relies on information transfer from observed to unobserved components. Although the ensemble Kalman filter (EnKF) is widely used in this setting, rigorous error estimates remain limited because the information transfer mechanism induces non-symmetric matrix structures that are difficult to analyze. Existing analyses often avoid this difficulty by restricting the covariance or inflation to the observed subspace, which suppresses the observed-unobserved coupling. In this study, we establish uniform-in-time error bounds for the EnKF applied to the partially observed Lorenz 96 model, a prototypical chaotic dynamical system, both with and without the covariance projection. Numerical experiments are consistent with the theoretical findings and show how the covariance projection affects the observed--unobserved information flow and resulting accuracy under comparatively sparse observations.