Geoscience Reference
In-Depth Information
for the left hand side of Equation (16.41) to be negligible in comparison with the
right hand side. Such conditions apply in the atmospheric boundary layer (ABL).
Consequently in the ABL the continuity equation for mass of air can be simplified
to become:
∂∂∂
++ =
∂∂ ∂
uvw
xy
0
(16.42)
z
This equation can be re-written in the vector format as:
∇=
.
v
0
(16.43)
Conservation of atmospheric moisture
The time rate of change of the total moisture concentration at a particular point in
the atmosphere is equal to the sum of two terms. The first is the transfer of mois-
ture to that point by molecular transport. This is equivalent to the transfer of a
component of momentum by molecular transfer described earlier and is repre-
sented by including an analogous term in the continuity equation for moisture.
The second contribution is from a source/sink term,
S
q
total
, that corresponds to the
possible creation or destruction of water molecules by chemical means.
Consequently, the continuity equation for moisture takes the form:
total
total
total
total
∂
q
∂
q
∂
q
∂
q
+
u
+
v
+
w
t
x
y
z
∂
∂
∂
∂
(16.44)
total
S
⎛
2
total
2
total
2
total
⎞
∂
q
∂
q
∂
q
q
=υ
+
+
+
⎜
⎟
q
∂
x
2
∂
y
2
∂
z
2
r
⎝
⎠
a
which equation can be written more concisely in vector format as:
total
S
∂
q
total
q
total
2
total
+∇
vq
.
=υ∇
q
+
(16.45)
q
∂
t
r
a
This equation for total moisture might be split into two separate equations which
describe the conservation of water vapor and the conservation of liquid/solid
water (such as cloud droplets) in the atmosphere separately, thus:
S
⎛
2
2
2
⎞
E
∂
q
∂
q
∂
q
∂
q
∂
q
∂
q
∂
q
q
u
v w
++
v
(16.46)
+++ =υ
++
⎜
⎟
q
∂
t
∂
x
∂
y
∂
z
∂
x
2
∂
y
2
∂
z
rr
2
⎝
⎠
a
a
l
S
l
l
l
l
⎛
2
l
2
l
2
l
⎞
E
∂
q
∂
q
∂
q
∂
q
∂
q
∂
q
∂
q
q
u
v
w
+
v
(16.47)
+
+
+
= υ
+
+
−
⎜
⎟
q
∂
t
∂
x
∂
y
∂
z
∂
x
2
∂
y
2
∂
z
rr
2
⎝
⎠
a
a
