Ensemble Kalman filtering

TLDR

The study demonstrates how the EnKF relates to the Kalman filter, quantifies imbalance in initial conditions and model‑error magnitude, and aims to guide further EnKF improvements. The operational EnKF uses a small ensemble, counteracts under‑estimation of spread, localizes covariances, and tests the filter’s assumptions while quantifying imbalance and model error. Implementation of the EnKF at the Canadian Meteorological Centre shows it can be used operationally, but severe localization induces imbalance that limits time interpolation and model‑error parametrization. © 2005 Royal Meteorological Society.

Abstract

Abstract An ensemble Kalman filter (EnKF) has been implemented at the Canadian Meteorological Centre to provide an ensemble of initial conditions for the medium‐range ensemble prediction system. This demonstrates that the EnKF can be used for operational atmospheric data assimilation. We show how the EnKF relates to the Kalman filter. In particular, to make the ensemble approximation feasible, we have to use a fairly small ensemble with many less members than either the number of model coordinates, or the number of independent observations, or the (unknown) dimension of the dynamical system. To nevertheless obtain good results, we must (i) counter the tendency of the ensemble spread to underestimate the true error, and (ii) localize the ensemble covariances. The localization is severe and leads to imbalance in the initial conditions. The operational EnKF is used to investigate to what extent our system respects the underlying hypotheses of both the Kalman filter and its ensemble approximation. In particular, we quantify the imbalance in the initial conditions and the magnitude of the model‐error component. The occurrence of imbalance constrains the ways in which time interpolation can be performed and in which parametrized model error can be added. With this study we hope to obtain and provide guidance for further improvements to the EnKF. Copyright © 2005 Royal Meteorological Society