Asynchronous data assimilation with the EnKF in presence of additive model error

The term ‘asynchronous data assimilation’ (ADA) refers to modifications of sequential data assimilation methods that take into consideration the observation time. In Sakov et al. [Tellus A, 62, 24–29 (2010)], a simple rule has been formulated for the ADA with the ensemble Kalman filter (EnKF). To assimilate scattered in time observations, one needs to calculate ensemble forecast observations using the forecast ensemble at observation time. Using then these ensemble observations in the EnKF update matches the optimal analysis in the linear perfect model case. In this note, we generalise this rule for the case of additive model error