Tracking Atmospheric Instabilities with the Kalman Filter. Part II: Two-Layer Results

Abstract

Abstract Sequential data assimilation schemes approaching true optimality for sizable atmospheric models are becoming a reality. The behavior of the Kalman filter (KF) under difficult conditions needs therefore to be understood. In this two-part paper the authors implemented a KF for a two-dimensional shallow-water model with one or two layers. The model is linearized about a basic flow that depends on latitude; this permits the one-layer (1-L) case to be barotropically unstable. Constant vertical shear in the two-layer (2-L) case induces baroclinic instability. The stable and unstable 1-L cases were studied in Part I. In the unstable case, even a very small number of observations can keep the forecast and analysis errors from the exponential growth induced by the flow's instability. In Part II, the authors now consider the 2-L, baroclinically stable and unstable cases. Simple experiments show that both cases are, quite similar to their barotropic counterparts. Once again, the KF is shown to keep the esti...