Geoscience Reference
In-Depth Information
1.5
γ
/
Δ
1
Δ
/(
Δ
+
γ
)
0.5
0
0
10
20
30
40
Temperature (
°
C)
Fig. 4.2
Temperature dependence of (
γ/
Δ
) and
Δ
/
(
Δ+
γ
) at 1000 hPa;
γ
is defined by Equation (4.18)
de
∗
/
and
Δ=
dT
is shown in Figure 2.1, and can be obtained from Equation (2.12) or from Table 2.4.
where
E
A
, a drying power of the air, is defined by
f
e
(
u
r
)(
e
a
−
E
A
=
e
a
)
(4.24)
The ratio
) is illustrated inFigure 4.2 for a pressure of 1000 hPa. Note that in
Penman's (1948) original derivation it was assumed that
Q
ne
=
/
(
+
γ
L
e
and that all the
other terms in Equation (4.14) are negligible. As mentioned, from the practical point of
view, the main feature of this result is that it requires measurements of mean specific
humidity, wind speed and temperature at one level only. This isadirect consequence
of the approximation introduced in(4.20). For this reason, Penman's equation is useful
when measurements at more than one level, needed for profile methods or standard
energy budget methods, are unavailable or impractical.
Equation (4.23) has been widely used, but there isstill no generally accepted way
to formulate
f
e
(
u
r
), the wind function in
E
A
. Its definition in(4.24) suggests that any
suitable mass transfer coefficient can be used for this purpose (see Section 4.2.2). Penman
(1948) originally proposed an equation of the Stelling-type (4.5) as follows
R
n
/
f
e
(
u
2
)
=
0.26 (1
+
0.54
u
2
)
(4.25)
where
u
2
is the mean wind speed at 2 m above the surface inms
−
1
, and the constants
require that
E
A
in Equation (4.24) is inmmd
−
1
and the vapor pressure is inhPa. There
are indications that Equation (4.25) yields reasonable results for natural terrainwith
small to moderate roughness (see Thom and Oliver, 1977); on the basis of experimental
observations, it has also been suggested (Doorenbos and Pruitt, 1975) that for irrigated
crops, the constant 0.54 should be replaced by 0.86. In calculations of long-term mean
