An Ensemble Kalman Filter with Four-Dimensional Incremental Analysis Update to data assimilation
To take into account the propagation of the analysis increment during an assimilation window, a four-dimensional IAU (4DIAU) update for the EnKF is proposed. It constructs time-varying analysis increments by applying all observations in an assimilation window to state variables at different times during the assimilation window. It then gradually applies these time-varying analysis increments through the assimilation window by use of IAU. The EnKF with 4DIAU (EnKF-4DIAU) reduces imbalances in the analysis and better retains the time-varying information in the analysis increments compared to the EnKF with 3DIAU (EnKF-3DIAU). The EnKF-4DIAU is tested in a dry two-layer primitive equation model and the NCEP Global Forecast System (GFS). Results from the two models show that the EnKF-4DIAU produces lower error than the EnKF without IAU and the EnKF-3DIAU.