A strategy for operational implementation of 4D‐Var, using an incremental approach

Abstract An order of magnitude reduction in the cost of four‐dimensional variational assimilation (4D‐Var) is required before operational implementation is possible. Preconditioning is considered and, although it offers a significant reduction in cost, it seems that it is unlikely to provide a reduction as large as an order of magnitude. An approximation to 4D‐Var, namely the incremental approach, is then considered and is shown to produce the same result at the end of the assimilation window as an extended Kalman filter in which no approximations are made in the assimilating model but in which instead a simplified evolution of the forecast error is introduced. This approach provides the flexibility for a cost—benefit trade‐off of 4D‐Var to be made.