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)
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