It has long been speculated that a Kalman filter for numerical weather prediction (NWP) models would provide significant improvements in
both the analyses (i.e., the initial conditions for the model) and forecasts.
While a naive implementation of the Kalman filter is impossible with present computers, work over the last decade suggests that a Monte-Carlo approach, in which the required covariances are estimated from an ensemble of forecasts, may be both feasible and effective. This approach is usually known as the ensemble Kalman filter (EnKF). Surprisingly, the EnKF appears to
work with ensembles of a few 10's of members even for systems, such as in NWP, with dimension of 10^7 or more. I will discuss possible reasons for
this surprising performance, along with other topics in ensemble filtering, including sampling error, non-Gaussian effects, and error in the forecast model.
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