On the influence of map analysis formulation in the estimation of wind field derivatives

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Many wind field analysis formulations which have been described in the meteorological literature do not take into account the cross-coherence of the sampled component variables. As a result, such formulations can produce spurious amplification or damping of derived vorticity and divergence. This effect is examined with particular reference to a linear weighting scheme in which an optimal vector component weighting is derived from a homogeneous and isotropic correlation model for streamfunction and velocity potential variables. It is demonstrated theoretically and in sample analyses that unless the contributions to total vector variance from divergent and solenoidal effects are equal, then estimated fields of both vorticity and divergence derived as linear functions of component data are adversely affected by the exclusion of cross-component weighting. The same effect is shown to occur when empirical distance-weighting or surface-fitting formulations are used, and is particularly serious when such methods are used to estimate divergence from scattered observations sampling a predominantly solenoidal field. It is concluded that univariate methods for analysis of atmospheric winds cannot in general produce unbiased estimates of wind field derivatives unless the scale of spatial sampling is much less than the characteristic spatial scale of velocity variation.