Correlation Functions for Wind and Geopotential on Isobaric Surfaces

The fact that the geostrophic wind equations describe a large fraction of the relation between wind and geopotential and that the atmosphere approximates horizontal homogeneity and is nearly isotropic leads to two differential equations relating the correlation coefficients for geopotential with those for longitudinal and transverse wind components. Consequently, empirical formulas for any one of these correlation coefficients cannot be reasonably considered without reference to both the others. A family of three such related correlation coefficients must simultaneously fit observed correlations for all three quantities concerned. Several such self-consistent sets of correlation coefficients are compared with the data.