Geography Reference
In-Depth Information
(move westward against the mean flow).
3
Waves of intermediate wavelength may
be quasi-stationary or move eastward much slower than the mean geostrophic wind
speed. Since positive maxima in relative vorticity are associated with cyclonic dis-
turbances, regions of positive vorticity advection, which can be estimated easily
from upper level maps, are commonly used as aids in forecasting synoptic-scale
weather disturbances.
Vorticity advection does not alone determine the evolution of meteorological
systems. A change in the vertical shear of the horizontal wind associated with
differential (i.e., height dependent) vorticity advection will drive an ageostrophic
vertical circulation, which adiabatically adjusts the horizontal temperature gra-
dient to maintain thermal wind balance. The convergence and divergence fields
associated with this vertical circulation will not only modify the effects of vortic-
ity advection at upper levels, but will force changes in the vorticity distribution in
the lower troposphere where advection may be very weak.
In an analogous manner, thermal advection, which is often strong near the sur-
face, does not merely force changes in the temperature in the lower troposphere.
Rather, it will induce a vertical circulation, which through its associated divergence
and convergence patterns will alter the vorticity fields both near the surface and
aloft so that thermal wind balance is maintained.
The vertical circulation induced by quasi-geostrophic differential vorticity advec-
tion and thermal advection is generally an order of magnitude larger than that
induced by boundary layer pumping (5.38). Thus, it is reasonable to neglect bound-
ary layer effects to a first approximation in quasi-geostrophic theory.
6.3
QUASI-GEOSTROPHIC PREDICTION
Although, as explained above, the ageostrophic vertical motion plays an essential
role in the maintenance of thermal wind balance as the flow evolves, the evolution
of the geostrophic circulation can actually be determined without explicitly deter-
mining the distribution of ω. Defining the geopotential tendency χ
∂/∂t , and
recalling that the order of partial differentiation may be reversed, the geostrophic
vorticity equation (6.19) can be expressed as
≡
1
f
0
∇
f
1
f
0
∇
∂ω
∂p
2
χ
2
=−
V
g
·∇
+
+
f
0
(6.21)
3
Observed long waves tend to remain stationary rather than to retrogress. This is believed to be a result
of processes such as modification of the Rossby phase speed by potential vorticity gradients associated
with the mean flow, nonlinear interactions with transient short waves, forcing due to topographic
influences, and diabatic heating contrasts associated with land-sea differences, as was mentioned
previously in Section 6.1.
