Geoscience Reference
In-Depth Information
2
E
pa
/E
po
1.5
1
0.5
E/E
po
0
0
0.2
0.4
0.6
0.8
1
Moisture index, E/E
pa
Fig. 4.8
Sketch illustrating the complementary relationship between the actual evaporation
E
and the
apparent potential evaporation
E
pa
, for varying conditions of moisture availability, as expressed by
their ratio
E
/
E
pa
. Both
E and E
pa
are normalized with the true potential evaporation
E
po
.
not at all in the first term on the right-hand side. Substitution of (4.23) and (4.31) into
(4.45) yields the practical result
+
γ
γ
+
γ
E
=
(2
α
e
−
1)
Q
ne
−
E
A
(4.48)
As before, there are several ways of estimating
E
A
, the drying power of the air. It can
simply be estimated in terms of the vapor pressure deficit by means of Equation (4.24)
with Penman's wind function (4.25). It can also be estimated in terms of the specific
humidity deficit of the air by means of the mass transfer coefficient Ce defined in Equation
(4.3). In this case the actual evaporation isgiven by
+
γ
γ
+
γ
(
q
2
−
E
=
(2
α
e
−
1)
Q
ne
−
Ce
u
1
ρ
q
2
)
(4.49)
The main advantage of (4.48), (4.49) and other equations like them based on the com-
plementary approach, is that they do not require any information related to soilmoisture,
canopy resistance, or other measures of aridity, because they rely on meteorological
parameters only. The mainlimitation is that, while the idea underlying (4.45) issimple
and plausible, it was not arrived at inarigorous theoretical or experimental way. Equa-
tions like (4.48) and (4.49) have been applied in a number of studies inwidely different
climates. The approach appears to perform best under conditions with relatively mild
advection. However, under strongly advective conditions with large saturation humid-
ity deficits, it seems that the validity of the assumptions on which it is based become
questionable. Sugita
et al
. (2001) concluded that (4.45) is only approximately valid in
most cases; Hobbins
et al
. (2001) showed how the basic approach can be improved
by calibration of the parameters
α
e
and
E
A
(or Ce) in Equation (4.49). Although the
