  The iterative ensemble Kalman filter (IEnKF) in a deterministic framework was
introduced in Sakov et al. (2012) to extend the ensemble Kalman filter (EnKF)
and improve its performance in mildly up to strongly nonlinear cases.
  However, the IEnKF assumes that the model is perfect. This assumption
simplified the update of the system at a time different from the observation
time, which made it natural to apply the IEnKF for smoothing. In this study, we
generalise the IEnKF to the case of imperfect model with additive model error.
  The new method called IEnKF-Q conducts a Gauss-Newton minimisation in
ensemble space. It combines the propagated analysed ensemble anomalies from the
previous cycle and model noise ensemble anomalies into a single ensemble of
anomalies, and by doing so takes an algebraic form similar to that of the
IEnKF. The performance of the IEnKF-Q is tested in a number of experiments with
the Lorenz-96 model, which show that the method consistently outperforms both
the EnKF and the IEnKF naively modified to accommodate additive model noise.
