THE ECMWF IMPLEMENTATION OF 3-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 statisti cs of the differences between two forecasts valid at the same time. Re sults compare satisfactorily with those reported in the existing liter ature. Non-separability of the correlation functions is a pervasive fe ature. Accounting for non-separability in 3D-Var is necessary to repro duce geostrophic characteristics of the statistics, such as the increa se of length-scale with height for the horizontal correlation of the m ass variable, sharper vertical correlations for wind than for mass and shorter horizontal length-scales for temperature than for mass. In ou r non-separable 3D-Var, the vertical correlations vary with total wave -number and the horizontal correlation functions vary with vertical le vel.