The effect of horizontal gradients of height-field forecast error variances upon OI forecast error statistics

In the formulation of statistical relationships among forecast errors in the optimal interpolation (OI) analysis system at NMC, it is currently assumed that horizontal gradients of the height-field forecast error standard deviation, [sigma]z are negligible. This homogeneity assumption is reasonable only in areas of uniform data density and quality. The dominant feature on the maps of [sigma]z actually produced by the OI system is in fact the rapid change of [sigma]z near boundaries between data-dense and data-sparse regions. In this note we rederive the statistical relationships among forecast errors, without assuming that the [sigma]z field is homogeneous. The resulting forecast error statistics are compared with the conventional ones, using realistic [sigma]z fields. The comparison shows that the wind-field forecast error standard deviations are increased over the entire globe, and by as much as about 30% in some regions. The wind-height and wind-wind forecast error correlations are changed even more dramatically. For example, the correlation between height and zonal wind forecast errors at a point is 0.0 if [sigma]z is constant there, but becomes as large as about °0.6 at points where [sigma]z is changing rapidly. More generally, the wind-height and wind-wind forecast error correlations lose the homogeneity and isotropy properties they possess in conventional OI formulations, in a manner reflecting the variability of data density and quality encountered over the globe. Stephen E. Cohn and Lauren L. Morone. "October 1984." "This is an unreviewed manuscript, primarily intended for informal exchange of information among NMC staff members." System requirements: Adobe Acrobat Reader. Includes bibliographical references (page 26). 1984 NWS (National Weather Service) NCEP (National Centers for Environmental Prediction) Library Public Domain 2285