Geoscience Reference
In-Depth Information
Table 4.1 Values of
(
γ
/
Δ
)
at 1000 mb (
γ
is defined by Equation (4.19)
and
Δ
can be obtained from Table 2.4)
Air temperature
T
a
(
◦
C)
γ/
(
)
−
20
5.864
−
10
2.829
0
1.456
5
1.067
10
0.7934
15
0.5967
20
0.4549
25
0.3505
30
0.2731
35
0.2149
40
0.1707
is commonly referred to as the psychrometric constant; at 20
◦
C and
p
=
1013.25 hPa it
0.67 hPa K
−
1
. Note that the
is
difference is replaced by that of
T
,since they are
often practically the same in the surface layer. The crucial step in Penman's analysis is
the assumption
e
s
−
γ
=
θ
e
a
T
a
=
(4.20)
T
s
−
where
=
(
de
∗
/
dT
) is the slope of the saturation water vapor pressure curve
e
∗
=
e
∗
(
T
)
at the air temperature
T
a
(see Figure 2.1);
e
a
e
∗
(
T
a
) is the corresponding saturation
=
vapor pressure and
e
s
e
∗
(
T
s
) is the vapor pressure at the temperature of the surface,
as indicated by the subscript. Since
e
s
for a wet surface is the value at saturation, the
Bowen ratio(4.18) is thus, approximately
=
1
(
e
a
−
γ
e
a
)
Bo
=
−
(4.21)
(
e
s
−
e
a
)
In this expression
depends only on temperature and
γ
depends on both temperature
and pressure. Values of (
1000 hPa are presented
in Table 4.1 and Figure 4.2; they were obtained by means of (4.19) and values of
γ/
) for different temperatures at
p
=
and
L
e
listed in Table 2.4. Substitution of (4.21) into (4.16) produces
e
a
−
E
1
E
γ
γ
e
a
Q
ne
=
+
−
(4.22)
e
s
−
e
a
In the second term on the right of Equation (4.22), a bulk-transfer equation can be used,
such as (4.7), to replace the unknown
E
e
a
)byawind function
f
e
(
u
r
). Thus (4.22)
yields the desired result, the Penman (1948) equation in its usual form
/
(
e
s
−
+
γ
γ
+
γ
E
=
Q
ne
+
E
A
(4.23)