Balance properties of the short-range forecast errors in the ECMWF 4D-Var ensemble

In this paper the normal-mode function framework is applied to the representation of time-averaged structure of short-term forecast error variances in the 20-member ensemble based on the 4D-Var assimilation system of ECMWF. The applied methodology provides an attractive way to measure the balance by splitting forecast error variances into parts projecting on the balanced and inertio-gravity (IG) circulations; the approach is particularly suitable for the Tropics, where IG circulation dominates on all scales. A little over 50% of the global forecast error variance at short range is balanced. The component of the variance associated with eastward IG modes dominates over the westward IG modes on all zonal scales but the difference gets larger as the zonal wave number increases. There is a major difference in the vertical variance distribution between the balanced and IG modes. A large part of the balanced variance projects on to the barotropic structure in the troposphere, while the IG variances are found in vertical modes that have equatorially trapped horizontal structures corresponding to equivalent depths between a few tens and few hundred metres. The variance growth between 3 h and 12 h range is substantially different in the balanced, eastward and westward IG modes. The balanced variance growth dominates whereas the variance growth in the westerly IG modes is small. In the eastward IG modes, the variance growth is most significant in the large-scale equatorial Kelvin mode.