On approximations to geopotential and wind-field correlation structures

The purpose of this note is to show that a correlation structure model which is rigorously derived from simple stochastic assumptions for geopotential anomalies, automatically satisfies the essential properties of correlation representations as they are used in multivariate optimal interpolation and diagnostic studies. The parameters of the illustrations are derived from observed covariances, with location-specific local-time-average values defining the anomalies of the covariance (correlation) computations. For this reference field, it is shown that the two-dimensional model in (Δφ, Δλ) arguments reproduces pronounced anisotropy in correlation structure of height and geostrophic-wind field anomalies. Comparisons are made with model-implicit isotropic correlation arrays which are similar to those computed directly from observed statistical arrays and(similarly) fail to provide accurate representation of true ensemble field relationships.