On the Equivalence Between Suboptimal 4D-Var and EnKF

Two families of methods are widely used in data assimilation: the four dimensional variational (4D-Var) approach, and the ensemble Kalman filter (EnKF) approach. The two families have been developed largely through parallel research efforts, and each method has its advantages and disadvantages. It is of interest to combine the two approaches and develop hybrid data assimilation algorithms. This paper investigates the theoretical equivalence between the suboptimal 4D-Var method (where only a small number of optimization iterations are performed) and the practical EnKF method (where only a small number of ensemble members are used) in a linear Gaussian setting. The analysis motivates a new hybrid algorithm: the optimization directions obtained from a short window 4D-Var run are used to construct the EnKF initial ensemble. Numerical results show that the proposed hybrid ensemble filter method performs better than the regular EnKF method for both linear and nonlinear test problems.