Geoscience Reference
In-Depth Information
(
ρ
v
udA
)
1
(
ρ
v
udA
)
2
x
1
x
2
x
Figure 9.3 Zonal moisture transport through an elemental
volume.
where
z
TOP
is the height of the top of the atmospheric column, essentially the
height of the tropopause.
The value of
W
will change when there is a net source or sink of water vapor:
dW
=
Σ
(
sources inks
−
).
(9.5)
dt
Sources include evaporation from the surface and from liquid water suspended
in or falling through the column,
E
, and moisture convergence into the column
by the atmospheric circulation. Sinks of water vapor are precipitation,
P
, and
moisture divergence by the circulation.
Consider moisture convergence in the
x
-direction for the elemental volume
drawn in
Figure 9.3
. The rate at which water mass is carried into the volume
by the zonal flow
at x
1
through an area
dA
perpendicular to the wind vector is
(
V
r , which has units of
kg
H
2
/s. Similarly, the rate at which water is trans-
ported out of the volume is
(
udA
)
V
r . Using Eq. 9.2, the rate of water vapor
mass accumulation in the volume due to zonal transport is
udA
)
(
ρ
qu
)
−
(
ρ
qu
)
dA
,
(9.6)
7
A
1
2
and the rate of water vapor mass accumulation per unit volume associated
with the zonal flow is
(
ρ
qu
)
−
(
ρ
qu dA
)
(
ρ
qu
)
−
(
ρ
qu dA
)
7
A
7
A
2
(
ρ
qu
)
1
2
2
1
.
=−
−
(9.7)
"
2
x
dV
dAxx
(
−
)
2
1
Note that if
(
r
2 2
< 0, and water vapor is converg-
ing in the volume. Generalizing to three dimensions, the rate of water vapor
mass accumulation in the volume is
qu
r >
(
qu
r , then
(
)
)
qu
)/
x
2
(
ρ
qu
)
2
(
ρ
q
v
)
2
(
ρ
q
w
)
v
−
−
−
/
−
d
$
(
ρ
qv
).
(9.8)
2
x
2
y
2
z
The term on the right-hand side of (Eq. 9.8) is called the
water vapor moisture
flux convergence
.
Combining Eqs. (9.4), (9.5), and (9.8), we obtain the equation for the atmo-
spheric column water vapor balance:
