Error growth and Kalman filtering within an idealized baroclinic flow

Abstract

The dynamics of covariances within a baroclinic flow are presented, as obtained by an explicitcomputation of the forecast error covariance matrix. This is possible since the numerical modelis a low-dimensional, semi-geostrophic, uniform potential vorticity model. In addition, idealizedobservations and observation errors are assimilated with a Kalman filter. This allows for designinga large set of idealized observation system simulations (IOSS) where the impact of extrameasurements in data sparse areas is studied. The results show that maximal error growth isconcentrated 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 downstreamregions. 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 thata permanent data supply produces a significant damping of error growth, because the data areinjected continuously in time. The sensitivity studies show that the positions of the pseudoobservationsmust be in the vicinity of the frontal structures, and that both the surface frontand the tropopause jet have to be sampled. When a widespread, non-permanent observationnetwork is considered, objective targeting strategies are worked out, and their impact on the2-day forecast error field is studied. The striking feature is the strong dependency of the forecasterror on the initial error covariance. It is found that the errors are decreased efficiently bytargeted pseudo-observations only if dynamically reshaped correlations are specified, insteadof the conventional isotropic ones.