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 assi milation and analysis systems by determining the distribution of the inform ation in the data in space and between variables. A new formulation has bee n developed for use in the ECMWF system. The non-separable structure functi ons depend on the horizontal and vertical scales and a generalized linear b alance operator to imply multivariate structure functions. The balance oper ator is incorporated into the definition of the analysis variables to ensur e good preconditioning of the problem. The formulation and structure of the background error covariance are presented, and the implications for the an alysis increments are examined. This reformulation became the operational E CMWF formulation in 3D-Var in May 1997 and in 4D-Var in November 1997.