A three-dimensional multivariate modal analysis of atmospheric predictability with application to the ECMWF ensemble

The method relies on the decomposition of the global three-dimensional wind and geopotential fields onto the normal-mode functions. The ensemble properties are quantified in terms of the 50-member ensemble spread associated with the balanced and inertio-gravity (IG) modes for forecast ranges every 12 h up to 7 days.

Ensemble reliability is defined for the balanced and IG modes comparing the ensemble spread with the control analysis in each scale. Modal analysis shows that initial uncertainties in the ECMWF ENS are largest in the tropical large-scale modes and their spatial distribution is similar to the distribution of the short-range forecast errors. Initially the ensemble spread grows most in the smallest scales and in the synoptic range of the IG modes but the overall growth is dominated by the increase of spread in balanced modes in synoptic and planetary scales in the midlatitudes.