From the dynamical systems point of view, the behavior of the Earth's atmosphere is extremely high dimensional (e.g., a realistic atmospheric model based on a modal expansion would necessarily include many modes). In spite of the atmosphere's high dimensionality, it is demonstrated that, in a suitable sense, the local finite-time atmospheric dynamics is often low dimensional.

A statistic, the BV-dimension, that measures the effective local finite-time dimensionality of a atmosphere is discussed. A large experimental ensemble of forecasts is produced using the T62 horizontal resolution version of the operational global model of the National Centers for Environmental Prediction (NCEP). The statistic is applied to this large ensemble to characterize the dimensionality of the local finite-time dynamics. Regions identified by the low BV-dimension are shown to be associated with the breakdown of numerical forecasts due to chaos. These regions have a well defined three-dimensional structure and they have a lifetime on the order of one week. The development and propagation of such regions will be shown.

Results are compared from ensembles with increasing numbers of members to indicate the necessary number required to characterize dynamical instabilities due to chaos in the extratropics. The implications of these results to data assimilation and improved weather forecasting will be discussed.