Scaling of
Simplified Vorticity Equation at Various Levels of Troposphere




Upper Troposphere 
Negligible 



Middle Troposphere 


Zero 

Surface 

Negligible 


Green shading = Terms that
are large
Case 1: Upper Troposphere
(1)
Horizontal
Divergence is ÒdiagnosedÓ or Òassociated withÓ or ÒcoincidentÓ with areas of
positive (cyclonic) vorticity advection (and vice versa). This is because, for example, air
parcels streaming from trough axis to ridge axis experience, typically, great
horizontal divergence. This
divergence is so great that by the time they reach the ridge axis, their
vorticity has been reduced to the value that originally was at the ridge axis.
Please
note that equation (1) does NOT
mean that vorticity advection ÒcausesÓ divergence or that divergence causes
vorticity advection. Equation (1)
expresses an association that appears on weather maps.
Case 2: Middle Troposphere
Horizontal
divergence is minimal or zero in the middle troposphere. Thus,
(2a)
states that air parcels conserve their absolute vorticity (in the restrictive
circumstance of no horizontal divergence). The is called ÒConservation of
Absolute VorticityÓ.
Equation
(2b) states that the local changes in vorticity observed at a location would be
due simply to the advection of vorticity by the wind. Essentially the vorticity pattern
translates with the trough and ridge pattern responsible for it.
Case 3: Lower Troposphere
Since
lower tropospheric patterns tend to be nearly concentric circles or ellipses,
vorticty advection is minimal or zero (vorticity contours are parallel to
height contours or isobars).
(3)
Equation
(3) states that all the local changes in vorticity will be due to convergence
or divergence. This normally
occurs by cross contour flow relative to the closed systems found on, say, sea
level weather maps.