In this paper, the spatio-temporally changing nature of predictability is studied in a reduced resolution version of the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Uncertain initial conditions (analyses) are obtained by assimilating noisy simulated observations of the hypothetical "true" state and observations of the real atmosphere with the Local Ensemble Transform Kalman Filter (LETKF) data assimilation system of the University of Maryland. This data assimilation system also provides initial conditions for an ensemble of forecasts. Predictability of atmospheric predictability is assessed by investigating the dependence of the performance of the ensemble forecast system on the atmospheric flow in capturing the forecast uncertainties. We show that the larger the forecast error, the more certain that the ensemble can fully capture the space in which forecast errors evolve. We explain this behavior using the E-dimension, a diagnostic that was developed at the University of Maryland.