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

SUMMARY An order of magnitude reduction in the cost of fourdimensional variational assimilation (4D-Var) is required before operational implementation is possible. Reconditioning is considered and, although it offers a signi6cant 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 simplitied evolution of the forecast error is introduced. This approach provides the flexibility for a cost-benefit trade-off of 4D-Var to be made. The development of variational four-dimensional assimilation (4D-Var) from the stage of being a theoretical possibility to being a practical reality is progressing at a rapid pace. The first results of four-dimensional variational assimilation using real observations were provided by Thbpaut et al. (1993b) using an adiabatic primitive-equation model at truncations "21 and T42. More recently Andersson ef al. (1994) used 4D-Var with a T63 model to assimilate remotely-sensed data such as infrared and microwave TOVS radiance measurements, while Thdpaut et d. (1993a) used 4D-Var with the same model to assimilate normalized radar backscatter cross-section measurements from the ERS-1 scatterometer.

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