Error growth and Kalman filtering within an idealized baroclinic flow

The dynamics of covariances within a baroclinic flow are presented, as obtained by an explicit computation of the forecast error covariance matrix. This is possible since the numerical model is a low-dimensional, semi-geostrophic, uniform potential vorticity model. In addition, idealized observations and observation errors are assimilated with a Kalman filter. This allows for designing a large set of idealized observation system simulations (IOSS) where the impact of extra measurements in data sparse areas is studied. The results show that maximal error growth is concentrated along the large-scale frontal strips. When baroclinic interactions are switched off, error growth is enhanced in the upstream parts of the system, and damped in the downstream regions. This shows that barotropic growth alone significantly departs from the mixed barotropic-baroclinic case, so that the baroclinic effects cannot be neglected. The IOSS indicate that a permanent data supply produces a significant damping of error growth, because the data are injected continuously in time. The sensitivity studies show that the positions of the pseudo-observations must be in the vicinity of the frontal structures, and that both the surface front and the tropopause jet have to be sampled. When a widespread, non-permanent observation network is considered, objective targeting strategies are worked out, and their impact on the 2-day forecast error field is studied. The striking feature is the strong dependency of the forecast error on the initial error covariance. II is found that the errors are decreased efficiently by targeted pseudo-observations only if dynamically reshaped correlations are specified, instead of the conventional isotropic ones.