The multi-variate design between the analysis variables of mass and wind is a challenge. Since the variables are defined in physical space it is not easy to apply the linear balance operator, which involves the inverse of the Laplacian. Yet, the relation between the mass field and the stream function is at least linear, so that a statistical relations between the two is possible and can be latitude dependent.
The choice of analysis variables, application of fat-tailed error spectra, and definition and estimation of the scales of the structure functions are discussed. Scores of anomaly correlation and tropical vector wind error of global data assimilation results are compared between using this experimental 3D Var and the operational Spectral Statistical-Interpolation in NCEP.