Geography Reference
In-Depth Information
at the upper levels, which drives a divergent upper level wind. By (3.44) this upper
level divergence will initially cause the surface pressure to decrease, thus generat-
ing a surface low below the warm anomaly (Fig. 3.11b). The horizontal pressure
gradient associated with the surface low then drives a low-level convergence and
vertical circulation, which tends to compensate the upper level divergence. The
degree of compensation between upper divergence and lower convergence will
determine whether the surface pressure continues to fall, remains steady, or rises.
The thermally driven circulation of the above example is by no means the only
type of circulation possible (e.g., cold core cyclones are important synoptic-scale
features). However, it does provide insight into how dynamical processes at upper
levels are communicated to the surface and how the surface and upper troposphere
are dynamically connected through the divergent circulation. This subject is con-
sidered in detail in Chapter 6.
Equation (3.44) is a lower boundary condition that determines the evolution
of pressure at constant height. If the isobaric coordinate system of dynamical
equations (3.2), (3.5), (3.6), and (3.27) is used as the set of governing equations,
the lower boundary condition should be expressed in terms of the evolution of
geopotential (or geopotential height) at constant pressure. Such an expression can
be obtained simply by expanding D/Dt in isobaric coordinates
∂
∂t
=−
ω
∂
∂p
V
a
·∇
−
and substituting from (3.27) and (3.43) to get
p
s
∂
s
∂t
RT
s
p
s
≈−
(
∇·
V
) dp
(3.45)
0
where we have again neglected advection by the ageostrophic wind.
In practice the boundary condition (3.45) is difficult to use because it should
be applied at pressure p
s
, which is itself changing in time and space. In simple
models it is usual to assume that p
s
is constant (usually 1000 hPa) and to let
ω
0atp
s,
For modern forecast models, an alternative coordinate system is
generally employed in which the lower boundary is always a coordinate surface.
This approach is described in Section 10.3.1.
=
PROBLEMS
3.1.
An aircraft flying a heading of 60
◦
(i.e., 60˚ to the east of north) at air speed
200ms
−
1
moves relative to the ground due east (90˚) at 225 m s
−
1
. If the
plane is flying at constant pressure, what is its rate of change in altitude (in
