Ensemble Kalman Filter: Current Status and Potential

In this chapter we give an introduction to different types of Ensemble Kalman filter, describe the Local Ensemble Transform Kalman Filter (LETKF) as a representative prototype of these methods, and several examples of how advanced properties and applications that have been developed and explored for 4D-Var (four-dimensional variational assimilation) can be adapted to the LETKF without requiring an adjoint model. Although the Ensemble Kalman filter is less mature than 4D-Var, its simplicity and its competitive performance with respect to 4D-Var suggest that it may become the method of choice. The mathematical foundation of data assimilation is reviewed by Nichols (chapter Mathematical Concepts of Data Assimilation). Ide et al. (1997) concisely summarized the sequential and variational approaches in a paper introducing a widely used notation that we follow here, with bold low-case letters and bold capitals representing vectors and matrices, respectively. Non-linear operators are, however, represented in bold Kunster script (as in other chapters in this book). Since variational methods (chapter Variational Assimilation, Talagrand) and sequential methods basically solve the same problem (Lorenc 1986; Fisher et al. 2005) but make different approximations in order to become computationally feasible for large atmospheric and oceanic problems, it is particularly interesting to compare them whenever possible. In this chapter we briefly review the most developed advanced sequential method, the Ensemble Kalman filter (EnKF) and several widely used formulations (Section 2). In Section 3 we compare the EnKF with the corresponding most advanced variational approach, 4D-Var (see chapter Variational Assimilation, Talagrand). Because 4D-Var has a longer history (e.g. Talagrand and Courtier 1987; Courtier and Talagrand 1990; Thépaut and Courtier 1991), and has been implemented in many operational centers (e.g. Rabier et al. 2000), there are many innovative ideas that have been developed and explored in the context of 4D-Var, whereas the EnKF is a newer and less mature approach. We therefore present in Section 3 examples of how specific approaches explored in the context of 4D-Var can be simply adapted to the EnKF. These include the 4D-Var smoothing property that leads to a faster spin-up, the outer loop that increases the analysis accuracy in the presence of non-linear observation operators, the adjoint sensitivity of the forecasts to the observations, the use of lower resolution analysis grids, and the treatment of model errors. Section 4 is a summary and discussion.