This paper explores the relationship between NWP model forecast multiscale second-moment statistics and ensemble spread. The relationship between the spread of two ensembles with different forecast models is derived, and shown to be a function of the ratio of the different energy spectra (a spectral response). More (less) spectral amplitude in a forecast model leads to more (less) ensemble spread. A simple statistical model is used to illustrate the instantaneous effect on ensemble spread when ensemble dispersion comes exclusively from amplitude dispersion among the members. This relationship suggests a method for calibrating ensembles to account for NWP models with insufficient spatial variance. NWP model dynamics introduce a time-dependent and complex spectral response that can be empirically estimated by comparing the categorical forecasts from two models. The extent to which knowledge of the spectral response of two models can calibrate the respective ensemble spread is explored by comparing spectra and dispersion curves computed from ensembles with three different atmospheric models.

Results show that when differences in two models produce ensembles that differ primarily in amplitude dispersion, time-dependent spectral responses of categorical forecasts can explain those differences. But when model changes produce ensembles that differ significantly in phase dispersion, the differences in ensemble behavior cannot be explained by the spectral response. These relationships lead to a method to calibrate ensembles generated with models that contain less spatial variance than the atmosphere, and to predict the effect of model changes on ensemble performance. They may also lead to a method for correcting the typically under-dispersive ensembles observed with limited-area mesoscale models.