The relation between standard deviation of contour height and standard vector deviation of wind

Abstract

AbstractA formula is derived, believed to be valid for all places outside the tropics and at all levels between the top of the friction layer and about 300 mb, expressing standard vector deviation of wind as a constant multiplied by the product of the standard deviation of contour height and the cosecant of latitude.The formula may be written σ = 0.064 s cosec where a is the standard vector deviation of wind in kt, s is the standard deviation of contour height in ft and ϕ is the latitude.A similar relationship is derived for levels between 300 mb and 100 mb. We may write σ = κw cosec ϕ where κ has the same value at all places but decreases uniformly with height from 0.064 at 300 mb to 0.033 at 100 mb.World seasonal maps of the standard vector deviation of wind immediately above the friction layer have been prepared from corresponding maps of the standard deviation of surface pressure; and seasonal maps of standard vector deviation of wind at 500 mb over part of the North Atlantic were prepared from maps of standard deviation of contour height computed directly from daily values.