Often, the assimilation of new radar and satellite data has little or even negative impact on the model analysis from current 3D- and 4D-Var systems.These shortcomings can be traced, to a large extent, to the over-simplified and unrealistic background and observation error covariances that are in use. One knows, in particular, that the background error covariance matrix provides the main vehicle by which information from the observation increments is propagated to those grid points and model variables that are not directly used to formulate the observation operator. Analysis increments from current data assimilation systems are often dominated by nearly isotropic structures that reflect poorly the mass and thermal gradients of the model background state. Under the assumption that the background error covariances can be modeled as the product of the error variances with error correlation functions, the task is mainly that of improving the specification of the latter.

The Eta 3D-Var analysis system uses a variable transform that justifies the neglect of cross correlations of the background errors, and applies the isotropic assumption to the auto-correlation functions. The use of the pseudo-relative humidity as the transformed moisture variable leads to some desirable anisotropy in the increments of the specific humidity. We propose to improve the Eta 3D-Var analysis system by relaxing the isotropic assumption for the moisture variable in the transformed space. While retaining the simplicity inherent to the isotropic model, we introduce an exponential factor defined in terms of the model background state and parameterized correlation lengths. The "look-up" tables for the correlation lengths are derived from error statistics obtained with the NMC method. Results from applying this approach will be presented, and a discussion on the extension of the method to the other analysis variables will be offered. The necessary adjustments of the recursive filter used to convolve the observation increments with the background error covariance matrix will also be discussed. Finally, some thoughts on the use of ensemble forecasting to determine the appropriate filtering directions will also be offered.