  Concurrent observation technologies have made high-precision real-time data
available in large quantities. Data assimilation (DA) is concerned with how to
combine this data with physical models to produce accurate predictions. For
spatial-temporal models, the Ensemble Kalman Filter with proper localization
techniques is considered to be a state-of-the-art DA methodology. This article
proposes and investigates a localized Ensemble Kalman Bucy Filter (l-EnKBF) for
nonlinear models with short-range interactions. We derive dimension-independent
and component-wise error bounds and show the long time path-wise error only has
logarithmic dependence on the time range. The theoretical results are verified
through some simple numerical tests.
