Small error dynamics and the predictability of atmospheric flows

In this paper, linear small-error theory is applied to the study of weather predictability. A simple baroclinic shear model and a barotropic channel model with a localized jet are used as examples. It is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. Unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.