Short-range evolution of small perturbations in a barotropic model

The short-range evolution of small initial errors is numerically investigated with an f-plane shallow-water model. It is shown that this evolution can be approximated by a linearized model for meteorologically realistic situations, and for ranges of up to about 48 hours. The results are consistent with a description of the slow manifold as an attracting set along which the dynamics of the flow is dominated by an instability process. As a consequence of the relatively large time scale for the meteorologically significant components of the flow, the linear model valid for short periods can befurther simplified to a constant coefficient model describing only the evolution of the large-scale components of the error. The possible implicationsof this result for the improvement of assimilation procedures are briefly discussed.