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

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.