Application of a Diagnostic Richardson Number Tendency to a Case Study of Clear Air Turbulence

Abstract

An index for the development of clear air turbulence on a synoptic scale is derived using the time rate of change of the Richardson number following the air motion, the so-called diagnostic Ri tendency. The method used in calculing the Ri tendency is a modified version of Roach's derivation, which in application had several undesirable features. The modification consisted in treating separately the effects of the change of stability and of the vertical wind shear, and expressing the change of the vertical wind shear by substitution from the thermal wind equation and then using the well-known frontogenetical function. The time rate of change of Ri was better expressed as the time to reduce Ri to the critical value, assumed to be unity since bulk layers were used. This index was tested on Hardy et al.'s case study of CAT observed at Wallops Island at 1700 GMT 19 February 1970 at the 750-mb level. Considering advection effects, it was found that the 800-mb level results presented have indicated that the Ri tendency reasonably predicted the lowering of Ri to near the critical value in an upper level frontal zone prior to its passage at Wallops Island. The change of the wind shear was found to be the predominate term in reducing Ri, being about four times the change of the stability in the region of interest.