The ECMWF implementation of three-dimensional variational assimilation (3D-Var). II: Structure functions

Abstract

Structure functions for the 3D-Var assimilation scheme of the European Centre for Medium-Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time. Results compare satisfactorily with those reported in the existing literature. Non-separability of the correlation functions is a pervasive feature. Accounting for non-separability in 3D-Var is necessary to reproduce geostrophic characteristics of the statistics, such as the increase of length-scale with height for the horizontal correlation of the mass variable, sharper vertical correlations for wind than for mass and shorter horizontal length-scales for temperature than for mass. In our non-separable 3D-Var, the vertical correlations vary with total wave-number and the horizontal correlation functions vary with vertical level.