Geography Reference
In-Depth Information
followed by substituting from (3.37) to yield
p
s
∂p
s
∂t
≈−
(
∇·
V
) dp
(3.44)
0
0 and have
neglected advection by the ageostrophic surface velocity in accord with the scaling
arguments in Section 3.5.1.
According to (3.44), the surface pressure tendency at a given point is determined
by the total convergence of mass into the vertical column of atmosphere above
that point. This result is a direct consequence of the hydrostatic assumption, which
implies that the pressure at a point is determined solely by the weight of the column
of air above that point. Temperature changes in the air column will affect the heights
of upper level pressure surfaces, but not the surface pressure.
Although, as stated earlier, the tendency equation might appear to have potential
as a forecasting aid, its utility is severely limited due to the fact that, as discussed in
Section 3.5.1,
Here we have assumed that the surface is horizontal so that w
s
=
V
is difficult to compute accurately from observations because it
depends on the ageostrophic wind field. In addition, there is a strong tendency for
vertical compensation. Thus, when there is convergence in the lower troposphere
there is divergence aloft, and vice versa. The net integrated convergence or diver-
gence is then a small residual in the vertical integral of a poorly determined quantity.
Nevertheless, (3.44) does have qualitative value as an aid in understanding the
origin of surface pressure changes, and the relationship of such changes to the hori-
zontal divergence. This can be illustrated by considering (as one possible example)
the development of a thermal cyclone. We suppose that a heat source generates
a local warm anomaly in the midtroposphere (Fig. 3.11a). Then according to the
hypsometric equation (3.34), the heights of the upper level pressure surfaces are
raised above the warm anomaly, resulting in a horizontal pressure gradient force
∇·
Fig. 3.11
Adjustment of surface pressure to a midtropospheric heat source. Dashed lines indicate
isobars. (a) Initial height increase at upper level pressure surface. (b) Surface response to
upper level divergence.
