A reformulation of the background error covariance in the ECMWF global data assimilation system

The background error covariance plays an important role in modern data assimilation andanalysis systems by determining the distribution of the information in the data in space andbetween variables. A new formulation has been developed for use in the ECMWF system. Thenon-separable structure functions depend on the horizontal and vertical scales and a generalizedlinear balance operator to imply multivariate structure functions. The balance operator isincorporated into the definition of the analysis variables to ensure good preconditioning of theproblem. The formulation and structure of the background error covariance are presented, andthe implications for the analysis increments are examined. This reformulation became the operational ECMWF formulation in 3D-Var in May 1997 and in 4D-Var in November 1997.