TRACKING ATMOSPHERIC INSTABILITIES WITH THE KALMAN FILTER .2. 2-LAYERRESULTS

Sequential data assimilation schemes approaching true optimality for s izable atmospheric models are becoming a reality. The behavior of the Kalman filter (KF) under difficult conditions needs therefore to be un derstood. In this two-part paper the authors implemented a KF for a tw o-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 (I-L) case to be barotropically unstable. Constant verti cal shear in the two-layer(2-L) case induces baroclinic instability. T he stable and unstable 1-L cases were studied in Part I. In the unstab le case. even a very small number of observations can keep the forecas t and analysis errors from the exponential growth induced by the Bowls instability. In Part II, the authors now consider the 2-L, baroclinic ally stable and unstable casts. Simple experiments show that both case s are quite similar to their barotropic counterparts. Once again, the KF is shown to keep the estimated flow's error bars bounded, even when a small number of observations-taken with realistic frequency-is util ized.