Geoscience Reference
In-Depth Information
Thus, if a sample of moist air has a total pressure,
P
, the contribution to that
pressure given by the water vapor molecules it contains,
e
, called the
vapor pressure
of the moist air, is given by:
e RT
=
r
(2.6)
vv
where
r
v
is the (variable) density of the water vapor in the moist air mixture and
R
v
is the gas constant for water vapor. Similarly, if we treat the remainder of the moist
air as being one gas, the contribution to the total pressure of this dry air compo-
nent of the moist air gas mixture is (
P
-
e
), given by:
(
)
(
)
Pe
−=
rr
RT
(2.7)
a
v
d
where
r
a
is the density of the moist air mixture and
R
d
is the gas constant of the dry
air. Like the mixing ratio and specific humidity, the vapor pressure of the air is a
measure of the amount of water vapor present in a sample of moist air and it is
frequently used as such in this text.
The different measures of atmospheric water vapor content are of course inter-
related. Because (
R
d
/
R
v
)
0.62, the relationship between the specific humidity and
vapor pressure of the air can be shown to have the form:
=
(
)
eR R
r
r
0.62
0.38
e
d
v
v
q
==
=
−
(2.8)
(
)
P
e
⎡
⎤
Pe RR
−−
⎣
1
a
⎦
d
v
with
q
in kg kg
−1
. However, because
e
is usually much less than
P
it is often accept-
able to assume that, to an accuracy of a few percent:
0.622
e
qr
==
(2.9)
P
Virtual temperature
Combining Equations (2.6) and (2.7) gives:
⎡
⎤
⎛
R
⎞
r
(
)
P
R T
R T
R T
v
v
=−
rr r r
+
=
1
+ −
1
⎢
⎥
(2.10)
⎜
⎟
a
v
d
v
v
a
d
R
r
⎝
⎠
⎢
⎥
⎣
⎦
d
a
This equation can be re-written as:
P RT
=
r
(2.11)
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