Ensemble Kalman filtering with colored observation noise

The Kalman filter (KF) is derived under the assumption of time-independent (white) observation noise. Although this assumption can be reasonable in many ocean and atmospheric applications, the recent increase in sensors coverage such as the launching of new constellations of satellites with global spatio-temporal coverage will provide high density of oceanic and atmospheric observations that are expected to have time-dependent (colored) error statistics. In this situation, the KF update has been shown to generally provide overconfident probability estimates, which may degrade the filter performance. Different KF-based schemes accounting for time-correlated observation noise were proposed for small systems by modeling the colored noise as a first-order autoregressive model driven by white Gaussian noise. This work introduces new ensemble Kalman filters (EnKFs) that account for colored observational noises for efficient data assimilation into large-scale oceanic and atmospheric applications. More specifically, we follow the standard and the one-step-ahead smoothing formulations of the Bayesian filtering problem with colored observational noise, modeled as an autoregressive model, to derive two (deterministic) EnKFs. We demonstrate the relevance of the colored observational noise-aware EnKFs and analyze their performances through extensive numerical experiments conducted with the Lorenz-96 model.