Discussion on ‘4D-Var or EnKF?’

The development of data assimilation techniques for numerical weather prediction has been very successful ever since the early 1950s until now, starting with simple two-dimensional and univariate spatial interpolation techniques like the successive corrections (SC, Bergthorsson and Döös, 1955) ending up with the four-dimensional variational data assimilation (4D-Var, Rabier et al., 2000) and ensemble Kalman filter (EnKF, Evensen, 1994) techniques of today. Looking a bit closer into the steps of this development, one may see a gradual and continuous development. Already SC schemes were based on the idea of data assimilation, that is, they treated the deviations between observations and a model background field in the spatial interpolation process. SC schemes were generally optimized on statistics of observation minus background data, and included also multivariate relationships. With the introduction of Optimum Interpolation (OI, Eliassen, 1954; Gandin, 1963), both of these aspects of data assimilation were handled more rigorously. An important next step was the generalization of OI to three spatial dimensions (Lorenc, 1981), and after that the step to three-dimensional variational data assimilation (3D-Var, Parrish and Derber, 1992) was not big. Adding the time-development of the assimilation increments over the data assimilation window, we arrive at 4D-Var. The idea of gradual development should in my opinion be applied in the ongoing discussion on 4D-Var and EnKF. Both methods try to address non-linearities and the errors of the day through an implicit (4D-Var) or an explicit (EnKF) description of flow-dependent forecast error structures. On one hand, 4DVar in its present strong constraint formulation form is limited to development of flow-dependency over a rather short data assimilation window. On the other hand, EnKF applies a more general flow-dependency from an ensemble of assimilation background states, but is limited due to the small number of ensemble members, which makes great care in the utilization of the derived error covariance structures necessary. In contrast, 4D-Var applies very robust covariance structures, derived as long-term averages, at the start of the assimilation window. Taking these two fundamental and complimentary characteristics of 4D-Var and EnKF