The Kalman filter is a data assimilation scheme which, unlike currently operational methods such as optimal interpolation (01), makes systematic use of forecast model dynamics in order to accurately determine the evolution of the forecast error covariance matrix. Previous studies with a simple one-dimensional model indicated that the Kalman filter, if applied operationally, would yield analyzed and subsequent forecast fields superior, to those resulting from 01. These studies did not address the enormous computational burden that the Kalman filter would appear to pose if applied in an operational setting, to an actual numerical weather prediction (NWP) model. In this report we introduce a number of techniques which, taken together, reduce dramatically the computational complexity of the Kalman filter. The new filter algorithm gains its efficiency, in part, by taking explicit advantage of the fact that forecast errors are significantly correlated only over rather small distances. It also utilizes fully the vector-processing capabilities of the CYBER 205 computer. Part of the overall method is an analysis algorithm which processes observations one at a time, i.e., it loops on observations rather than analysis grid points, thereby eliminating both the necessity of matrix inversions and the necessity of restarting the entire analysis to accommodate late-arriving observations. This analysis algorithm would be useful in OI schemes as well as in the Kalman filter. We apply the Kalman filter to a two-dimensional shallow-water channel model. Numerical experiments demonstrate, first of all, that the filter is indeed computationally feasible in two dimensions. The results show also that actual forecast error correlations, which are computed exactly by the Kalman filter differ markedly from the rather simple, homogeneous, correlations prescribed currently in the NMC OI analysis system. The experiments suggest a number of improvements to our computational approach, which should render the Kalman filter practical for operational data assimilation into fully three-dimensional NWP models.

"Practical predictability refers to the application of some of the techniques, used in the investigation of the classical predictability problem by Lorenz, Leith, and Smagorinsky, to the assessment of the operational performance of weather prediction models. The results produced may provide useful adjuncts to or extensions of NMC's standard diagnostic and verification programs"--Introduction.

"This note describes a procedure exactly equivalent to normal mode initialization which does not require explicit mention of normal modes. Mode space equations are replaced by simple differential equations which relate geostrophic and ageostrophic components of the model initial state"--Introduction.