A Four-Dimensional Incremental Analysis Update for the Ensemble Kalman Filter

Abstract

Abstract The analysis produced by the ensemble Kalman filter (EnKF) may be dynamically inconsistent and contain unbalanced gravity waves that are absent in the real atmosphere. These imbalances can be exacerbated by covariance localization and inflation. One strategy to combat the imbalance in the analyses is the incremental analysis update (IAU), which uses the dynamic model to distribute the analyses increments over a time window. The IAU has been widely used in atmospheric and oceanic applications. However, the analysis increment that is gradually introduced during a model integration is often computed once and assumed to be constant for an assimilation window, which can be seen as a three-dimensional IAU (3DIAU). Thus, the propagation of the analysis increment in the assimilation window is neglected, yet this propagation may be important, especially for moving weather systems. To take into account the propagation of the analysis increment during an assimilation window, a four-dimensional IAU (4DIAU) used with the EnKF is presented. 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. Results from a dry two-layer primitive equation model and the NCEP GFS show that EnKF with 4DIAU (EnKF-4DIAU) and 3DIAU (EnKF-3DIAU) reduce imbalances in the analysis compared to EnKF without initialization (EnKF-RAW). EnKF-4DIAU retains the time-varying information in the analysis increments better than EnKF-3DIAU, and produces better analysis and forecast than either EnKF-RAW or EnKF-3DIAU.