4-D-Var or ensemble Kalman filter?

We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4-D-Var. For infrequent observations, when ensemble perturbations grow non-linearly and become non-Gaussian, 4-D-Var attains lower errors than EnKF. If the model is imperfect, the 4-D-Var with long windows requires weak constraint. Similar results are obtained with a quasi-geostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3-D-Var and guidance on model error and 'observation localization'. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4-D-Var, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.