Coupling ensemble Kalman filter with four-dimensional variational data assimilation

This study examines the performance of coupling deterministic four-dimensional variational assimilation (4DVAR) to ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by ensemble-based filters while taking advantage of the relative insensitivity of 4DVAR to rank deficient background error covariance information. The deterministic analysis produced by 4DVAR provides an estimate of the minimum error variance state about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach have been demonstrated in an idealized model with simulated observations. It is found that the E4DVAR may outperform both 4DVAR and EnKF under both perfect- and imperfect-model scenarios with comparable computational costs.