Ensemble Kalman filtering with coloured 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 sensor coverage, such as the launching of new constellations of satellites with global spatio-temporal coverage, will provide high density of oceanic and atmospheric observations which are expected to have time-dependent (coloured) 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 modelling the coloured noise as a first-order autoregressive model driven by white Gaussian noise. This work introduces new ensemble Kalman filters (EnKFs) which account for coloured 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 coloured observational noise, modelled as an autoregressive model, to derive two (deterministic) EnKFs. We demonstrate the relevance of the coloured observational noise-aware EnKFs and analyze their performances through extensive numerical experiments conducted with the Lorenz-96 model.

Ensemble Kalman Filter Lorenz-96 model One-step-ahead Smoothing time-correlated observational noise