An observational map analysis scheme is described, whereby the vector field derived from discrete observations of wind and geopotential may be partitioned into its geostrophic, nondivergent and divergent parts without the need to solve Poisson-type equations relating streamfunction and velocity potential fields to estimated divergence and vorticity data. The method is based on a multivariate statistical interpolation formulation, which assumes a generalized random field model for scalar streamfunction and velocity potential variables, and a linear correlation between streamfunction and geopotential fluctuations. A similar formulation can also be used for wind field analysis based only on vector wind data. Sample analyses using synoptic upper-air observations over North America illustrate some properties of the method. It is shown, for example, that the estimated partitioning of the large-scale wind field into nondivergent and divergent parts is sensitive to the relative magnitudes of streamfunction and velocity potential variance implied by the random field model, but that the analysis is generally insensitive to external boundary conditions which are also an implicit property of the prescribed field model. The use of an estimated value of the divergent wind variance fraction, based on a simple iterative analysis method, appears to yield more realistic fields of kinematic divergence and vorticity than those obtained assuming equal contributions from divergent and rotational influences.
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M. A. Pedder (1989) studied this question.