Geoscience Reference
In-Depth Information
80
8
Fig. 2.1 The saturation vapor
pressure
e
∗
of water
(in hPa, left-hand
ordinate scale), and its
derivative
de
∗
/
dT
(in
hPa K
−
1
, right-hand
ordinate scale), both
as functions of
temperature.
70
7
60
6
hPa
50
5
e*
hPa K
−
1
40
4
30
3
20
2
de*/dT
10
1
0
0
0
−
10
10
20
30
40
Temperature (
C)
°
vapor is
log
e
i
=−
9
.
09718(
T
0
/
T
−
1)
−
3
.
56654 log(
T
0
/
T
)
(2.13)
+
0
.
876793 (1
−
T
/
T
0
)
+
log
e
io
where
T
0
is the ice-point temperature 273.16 K, and
e
i0
the saturation vapor pressure at
the ice-point temperature, i.e. 6.1071 hPa. Lowe (1977), who has also compared other
currently used expressions for the saturation vapor pressure, has presented polynomials for
e
∗
,
de
∗
/
dT
,
e
i
,
and
de
i
/
dT
, which are quite accurate and suitable for rapid computation.
For computational speed these polynomials should be used in nested form; for
e
∗
the
representation takes the form
e
∗
=
a
0
+
T
(
a
1
+
T
(
a
2
+
T
(
a
3
+
T
(
a
4
+
T
(
a
5
+
Ta
6
)))))
(2.14)
where the polynomial coefficients are as follows when
T
is in K,
a
0
=
6984
.
505 294
,
a
1
=−
188
.
903 931 0
,
a
2
=
2
.
133 357 675
,
a
3
=−
1
.
288 580 973
×
10
−
2
,
a
4
=
4
.
393 587 233
×
10
−
5
,
a
5
=−
8
.
023 923 082
×
10
−
8
and
a
6
=
6
.
136 820 929
×
10
−
11
,
.
2.2
HYDROSTATICS AND ATMOSPHERIC STABILITY
The first law of thermodynamics states that the heat added to a system equals the sum
of the change in internal energy and the work done by the system on its surroundings. If
these quantities are taken per unit mass and in differential form, this is for partly saturated
air
dh
=
du
+
pd
α
(2.15)
α
=
ρ
−
1
is the specific volume,
where
is the density of the air, and (in this Section 2.2
only)
u
represents the internal energy. The equation of state (2.7), which on account
ρ
