Simplification of the Kalman filter for meteorological data assimilation

We propose a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance, which is the central and most expensive aspect of the Kalman filter algorithm. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. These experiments are designed to isolate the effect of simplifying the evolution of the forecast error covariance. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.