Geography Reference
In-Depth Information
order 1000 km. There is a special class of planetary scale motions for which the
divergence term in the vorticity equation is important even outside of regions of
active precipitation (see Section 11.4). For such motions the pressure field cannot
be diagnosed from a balance relationship. Rather, the pressure distribution must
be predicted from the primitive equation form of the dynamics equations.
For precipitating synoptic-scale systems in the tropics, the above scaling con-
siderations require considerable modification. Precipitation rates in such systems
are typically of order 2 cm d
−
1
. This implies condensation of m
w
=
20 kg water
for an atmospheric column of 1 m
2
cross section. Because the latent heat of con-
10
6
Jkg
−
1
, this precipitation rate implies an addition of
heat energy to the atmospheric column of
densation is L
c
≈
2.5
×
10
7
Jm
-2
d
-1
m
w
L
c
∼
5
×
If this heat is distributed uniformly over the entire atmospheric column of mass
p
0
/g
10
4
kg m
−
2
, then the average heating rate per unit mass of air is
J/c
p
≈
L
c
m
w
/c
p
(p
0
/g)
∼
≈
5Kd
−
1
In reality the condensation heating due to deep convective clouds is not distributed
evenly over the entire vertical column, but is a maximum between 300 and 400
hPa, where the heating rate can be as high as 10 K d
−
1
. In this case the approx-
imate thermodynamic energy equation (11.10) implies that the vertical motion
on the synoptic scale in precipitating systems must have a magnitude of order
W
3cms
−
1
in order that the adiabatic cooling can balance the condensation
heating in the 300-400-hPa layer. Therefore, the average vertical motion in precip-
itating disturbances in the tropics is an order of magnitude larger than the vertical
motion outside the disturbances. As a result the flow in these disturbances has
a relatively large divergent component so that the barotropic vorticity equation
(11.14) is no longer a reasonable approximation, and the full primitive equations
must be used to analyze the flow.
∼
11.3
CONDENSATION HEATING
The manner in which the atmosphere is heated by condensation of water vapor
depends crucially on the nature of the condensation process. In particular, it is
necessary to differentiate between latent heat release through large-scale verti-
cal motion (i.e., synoptic-scale forced uplift) and the latent heat release due to
deep cumulus convection. The former process, which is generally associated with
midlatitude synoptic systems, can be incorporated easily into the thermodynamic
energy equation in terms of the synoptic-scale field variables. The large-scale
heating field resulting from the cooperative action of many cumulonimbus cells,
