OPTIMAL APPROXIMATION OF KALMAN FILTERING WITH TEMPORALLY LOCAL 4D-VAR IN OPERATIONAL WEATHER FORECASTING

The adoption of the Extended Kalman Filter (EKF) for data assimilation in operational weather forecasting would provide estimates of prediction error covariance and make it possible to take model error into account in the assimilation process. Unfortunately, full-blown Kalman filtering is not feasible even on the fastest parallel supercomputers. We propose a novel approximation to EKF, called the Variational Kalman Filter, or VKF. In VKF, a low rank approximation to the prediction error covariance matrix is generated by a very short, temporally local four dimensional variational assimilation cycle, at a low computational cost. VKF provides a locally optimal approximation to the error covariance matrix and also allows model error to be incorporated in the assimilation process. Initial numerical tests with VKF applied to an advection-reaction-dispersion equation are reported.