Geoscience Reference
In-Depth Information
Fig. 4.4
Illustration of the commonly assumed
relationship between the moisture
availability factor
β
e
and the water
content status
w
of the land surface
complex. In practical applications this
can be used with both apparent and
actual potential evaporation.
β
e
1
w
0
w
c
w
0
1955; Budyko, 1974, p. 335; Manabe, 1969; Carson, 1982). The values of
w
c
must be determined by calibration; for a surface soil layer with an assumed thickness of
about 1 m,
w
0
and
w
0
is generally taken to be of the order of 10-20 cm of water. The reduction
factor
, such as
the accumulated actual evaporation minus precipitation (Priestley and Taylor, 1972),
the local near-surface soilmoisture content (see Davies and Allen, 1973; Crago and
Brutsaert, 1992; Chen and Brutsaert, 1995), the soilmoisture deficit (Grindley, 1970)
and the antecedent precipitation index (Choudhury and Blanchard, 1983; Mawdsley and
Ali, 1985; Owe
et al
., 1989), again through calibration of the model with available data.
In some implementations of the same idea, the actual evaporation
E
is expressed in
terms of the equilibrium evaporation
E
e
, by combining Equation (4.33) with (4.31), as
follows
β
e
can also be related to some other surface moisture indices beside
w
E
=
(
β
e
α
e
)
E
e
(4.35)
inwhich
E
e
can be determined by means of (4.30). For instance, Figure 4.5 shows the
results of Davies and Allen (1973) expressed as the product (
β
e
α
e
) versus volumetric
water content of the upper 5 cm of the soil. Although a nonlinear function is fitted to
the data, it issimilar to Equation (4.34). With data measured over prairie terrain itwas
found by Chen and Brutsaert (1995) that, with
θ
10
as the volumetricmoisture content in
the upper 10 cm of the soil profile, the relationship between
E
and
E
e
can be described
by the following linear function
(
β
e
α
e
)
=
1
.
26(
θ
10
−
0
.
05)
/
0
.
22
(4.36)
in the range 0
26 for higher moisture contents; how-
ever, it was also observed that the relationship could be improved markedly by
making (
.
05
≤
θ
10
≤
0
.
27, and (
β
e
α
e
)
=
1
.
β
e
α
e
) not only dependent on soilmoisture content but also on the density of the
grassy vegetation cover, as expressed by the leaf area index
La
and the green vegetation
fraction.
