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 di erent algorithms based on simpli cation of the standard Kalman lter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optimal for linear problems with known statistics. The SOS's considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simpli ed 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 ow 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 SOS's to compensate for model/ data imbalance sometimes results in poor performance. Instead, properly constructed dynamically{balanced forecast error covariances eliminate the need for initialization. When the SOS's studied here make use of dynamically{balanced forecast error covariances, the di erence among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically{balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact. -2