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

A new methodology for the analysis of ensemble prediction systems (ENSs) is presented and applied to one month (December 2014) of ECMWF operational ensemble forecasts. 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 hours 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 largescale 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. During the forecasts, the distribution of spread in the balanced and IG modes grows towards the climatological spread distribution characteristic of the analyses. In 2-day forecast range, the global IG spread reaches 60% of its asymptotic value while the same percentage of the global balanced spread is reached after 5 days of forecasts. An under-dispersiveness of the system is suggested to be associated with the lack of tropical variability, primarily the Kelvin waves.