Geoscience Reference
In-Depth Information
Then
H
E
=
H
−
C
=
(B3.1.3)
1
+
ˇ
where
ˇ
=
C/E
is known as the Bowen ratio. Experimental evidence suggests that the Bowen
ratio will often have a fairly constant value for a surface, at least for clear sky conditions without
soil water limitations on evapotranspiration (Brutsaert and Sugito, 1992; Nichols and Cuenca,
1993; Crago and Brutsaert, 1996).
The sensible heat flux is a function of the temperature gradient in the air above the vegetation
canopy, whereas the latent heat flux is a function of the humidity or vapour pressure gradient
above the canopy. Both are also dependent on factors such as the roughness of the canopy and
wind speed (expressed as an aerodynamic resistance to transport). Rough canopies and higher
wind speeds (low values of aerodynamic resistance) result in much more efficient mixing of
the air and faster rates of transport. The transport equations are generally assumed to be of the
form:
1
r
a,H
a
c
p
(
T
o
−
T
z
)
C
=
(B3.1.4)
where
r
a,H
is the aerodynamic resistance to transport of heat,
a
is the density of the air,
c
p
is the
specific heat capacity of the air,
T
o
is the temperature of the surface and
T
z
is the temperature
of the air at some reference height
z
.The
big leaf
assumption here becomes apparent in the use
of the surface temperature,
T
o
, which must represent some effective value for all the different
surfaces of the canopy as a whole.
For the latent heat flux, the equivalent transport equation is
1
r
a,V
a
c
p
E
=
(
e
o
−
e
z
)
(B3.1.5)
where
r
a,V
is the aerodynamic resistance to the transport of vapour,
e
o
is the vapour pressure at
the effective canopy surface,
e
z
is the vapour pressure at the reference height
z
and
is called
the psychrometric constant (
66 PaK
−1
). The problem with these equations so far is that the
temperature and vapour pressure at the surface are not easily measured. To make the system
of equations solvable, John Monteith came up with the idea of using an additional conceptual
expression for the transport of vapour (Monteith, 1965) from the interior of the stomata of the
leaf surfaces to the free air, as
=
1
r
c
a
c
p
E
=
(
e
s
(
T
o
)
−
e
o
)
(B3.1.6)
where
r
c
is an effective stomatal resistance for the canopy as a whole, generally known as the
canopy resistance, and
e
s
(
T
o
) is the saturated vapour pressure at the surface temperature
T
o
.
Combining these expressions allows the unknown vapour pressure at the conceptual
big leaf
surface to be eliminated such that
1
r
a,V
+
r
c
a
c
p
E
=
(
e
s
(
T
o
)
−
e
z
)
(B3.1.7)
There is still the problem of estimating
e
s
(
T
o
)
. This is done by assuming that
e
s
(
T
o
)
can be
approximated by the expression
e
s
(
T
z
)
+
e
{
T
o
−
T
z
}
where
e
represents the slope of the sat-
uration vapour pressure versus temperature curve. The original form of the Penman-Monteith
equation uses this linear interpolation of the saturation vapour pressure curve. Milly (1991)
has suggested that a higher order approximation will produce more accurate predictions.
