Geoscience Reference
In-Depth Information
Equation (4.39) is in the form of the Penman-Monteith equation (see, however, Monteith,
1973; 1981; Thom, 1975)
Numerous experiments have been conducted to determine resistance values for different
types of vegetation. This has been mostly done in the context of expressions related to
Equation (4.39). A few examples are beans (Black
et al
., 1970), sugar beets (Brown and
Rosenberg, 1977), tropical rainforest (Dolman
et al
., 1991), eucalyptus forest (Dunin and
Greenwood, 1986), pine forest (Gash and Stewart, 1975; Lindroth, 1985), maize (Mascart
et al
., 1991), barley (Monteith
et al
., 1965), sorghum (Szeicz
et al
., 1973), and fir forest
(Tan and Black, 1976). In addition, many attempts have been made to relate resistance
parameters with such factors as Bowen ratio, soilmoisture suction in the root zone, soil
moisture deficit, humidity deficit in the air, solar radiation, temperature, leaf area index
and others (see VanBavel, 1967; Szeicz and Long, 1969; Federer, 1977; Garratt, 1978;
Lindroth, 1985; Stewart, 1988; Gash
et al
. 1989). The relationships developed so far are
mainly statistical, so that they are vegetation and site dependent. Therefore, the resistance
formulation is probably not yet sufficiently general to be practical for predictive purposes,
but it has been useful as a diagnostic index in certainsimulation studies (for example, to
calculate missing data).
As a note of caution, in previous studies the resistance formulation has not always been
used with consistent definitions for Ce (or
r
av
) and
r
s
(Thom, 1972; Brutsaert, 1982, p. 111).
For instance, the drag coefficient Cd (or the related so-called aerodynamic conductance)
is often used instead of Ce, as required in the rigorous derivation of Equation (4.23) with
(4.24) and (4.27). This drag coefficient is defined in(2.37). Because it is not likely that
above vegetation
z
0
=
z
0v
, nor that
m
=
v
(or
h
), Cd is rarely equal to Ce. As a result
of this inappropriate use of Cd (instead of Ce), it is not clear how the turbulence aspects
of the transport, normally embodied in Ce, can be partitioned or separated from the strictly
vegetational and/or soilmoisture aspects of the transport supposedly embodied in
r
s
. This
has undoubtedly contributed to the difficulty in deriving general relationships for both Ce
and
r
s
on the basisof(4.39).
Although the resistance formulation with
r
s
may appear conceptually quite different
from Equation (4.33) with the reduction factor
β
e
, both approaches are, in fact, practically
the same. Indeed, (4.38) is equivalent with (4.33) (inwhich (4.3) is used to represent
E
p
for
a wet surface) and a reduction factor
β
e
=
(1
+
r
s
Ce
u
1
)
−
1
(4.40)
Similarly, (4.39) is the same as (4.33) with (4.23) and a reduction factor
β
e
=
[1
+
r
s
Ce
u
1
γ/
(
+
γ
)]
−
1
(4.41)
and as (4.33) with (4.31) and a reduction factor
β
e
=
α
−
1
e
[1
+
γ
Ce
u
1
ρ
(
q
2
−
q
2
)
/
Q
ne
][1
+
r
s
Ce
u
1
γ/
(
+
γ
)]
−
1
(4.42)
In practical applications of Equations (4.38) and (4.39) a knowledge of the parameters Ce
and
r
s
is essential. The physical nature of Ce is well understood and based on sound turbu-
lence theory. But the conceptual significance of the resistance concept remains problematic,
inspite of the many studies devoted to it.
