Filamentation Time Diagnosis of Thinning Troughs and Cutoff Lows

This paper analyzes synoptic-scale trough-thinning processes using a filamentation time diagnostic. The filamentation time diagnostic is derived from the potential vorticity equation expressed in spherical coordinates in the horizontal plane and the isentropic coordinate in the vertical direction. The diagnostic is an accurate measure of stirring processes under the condition of ‘‘slowly varying velocity gradients.’’ Troughthinning processes are analyzed for one tropical example and two midlatitude examples. The results indicate that the filamentation time for the tropical trough-thinning event is generally longer than those for the midlatitude trough events. In addition to the effects of stretching and shearing deformation, the filamentation time diagnostic contains the effects of divergence. For the calculation of filamentation time on isentropic surfaces in spherical coordinates, it is acceptable to ignore the curvature effects in the tropics; however, in both the midlatitudes and the tropics, isentropic divergence effects should be retained for improved accuracy. Combining an analysis of cross potential vorticity contour flows on isentropic surfaces with the filamentation time analysis gives a more complete description of the dynamics. The results show that the filamentation time diagnostic can serve as a useful aid in the analysis and prediction of trough thinning and cutoff-low formation.