Tropospheric Geopotential and Velocity Variances over the Arctic

As an elaboration of recent studies by BUELL (1954, 1957) and JENKINSON  (1956), the relation between the standard deviation of contour height and the vector standard deviation of geostrophic wind velocity is formulated, both for point values (variations in time) and for chart values (variations in space). The relation between wind and contour variances for a simple schematic contour pattern is examined, from the point of view of both space and time statistics.

The relationship between the space variance of contour height (S²) and the space variance of the geostrophic wind (σ²) was evaluated over the Arctic (north of about 60° N) at the 500-mb level. A high degree of correlation was found to exist between these two quantities, although the form of the relationship (σ² proportional to S) did not agree with the results of previous studies (BUELL, JENKINSON, loc.cit.) of time variances. However, a reanalysis of such data for northern latitudes yielded results virtually identical with those of the present study.

In both cases, the standard error of estimate was too large to enable one to calculate accurately the wind variance from the height variance for synoptic purposes, but the relationships do allow climatological estimates (seasonal, etc.) to be made of the mean kinetic energy and of the size and amplitude of the dominant wave systems.