Suboptimal Schemes for Atmospheric Data Assimilation Based on the Kalman Filter

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. In order to employ a methodology for exact comparison among these schemes we maintain a linear environment, choosing a beta--plane shallow water model linearized about a constant zonal flow for the testbed dynamics. Our results show that constructing dynamically-balanced forecast error covariances, rather than using conventional geostrophically-balanced ones, is essential for successful performance of any SOS. A posteriori initialization of SOSs to comp...