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d) What happens with
L
v
E
if the temperature increases (at given relative humidity)
e) Under which conditions is it possible that
L
v
E
is larger than the available energy
input (
Q*
-
G
)?
7.2.2 Penman-Monteith Derivation
Monteith (
1965
) and Rijtema (
1965
) independently proposed how to extend the Pen-
man method to vegetated surfaces, resulting in what is nowadays called the Penman-
Monteith method.
To make the link from a wet surface to a vegetated surface, the concept of the 'big
leaf' is introduced. The vegetation is simpliied to one single leaf, with one idealized
stomatal cavity (see
Figure 7.2
, and compare to
Section 6.4
in
Chapter 6
). All water
vapour is assumed to originate from the stomata, and hence the Penman-Monteith
methods aims to describe the process of transpiration, not evaporation. Furthermore,
the method is - strictly speaking - limited to surfaces that are fully covered by vege-
tation: a mixture of vegetation and bare soil (sparse vegetation) cannot be dealt with,
as this would involve two different pathways for water vapour (from the soil and
from the plants) and two different surface temperatures. Shuttleworth and Wallace
(
1985
) provide an example of how the Penman-Monteith method could be extended
to deal with evapotranspiration from sparse canopies: both transpiration and soil
evaporation.
Nevertheless, the water vapour lux described by the Penman-Monteith method is
here referred to as evapotranspiration (hence including both transpiration and evapo-
ration from soil and intercepted water). Where appropriate, it is indicated which com-
ponent of evapotranspiration is described with the Penman-Monteith equation.
As compared to the wet surface discussed in
Section 7.2.1
, the transport path for
heat has not changed: transport takes place from a surface with temperature
T
s
to the
atmosphere with temperature
T
a
at a certain height. But water vapour does not orig-
inate at the surface of the leaf, but from within the stomatal cavity. This leads to two
important assumptions:
•
The air within the stomatal cavity is saturated with water vapour, at the surface temperature
T
s
, that is,
eeT
= ( . This appears to be a sound assumption, even under conditions of
considerable water stress (Ball,
1987
).
The transport from within the leaf to the surface of the leaf experiences a separate
s
sat
s
•
resistance, the canopy resistance
2
r
c
. This resistance acts in series with the aerodynamic
resistance
r
a
. Although the introduction of a canopy resistance is both mathematically
simple and conceptually appealing (it looks like a stomatal resistance; see
Figure 7.2
), it
shifts the complexity of the determination of evapotranspiration largely toward the spec-
iication of the canopy resistance (see
Section 7.2.3
).
2
The canopy resistance is also frequently called 'surface resistance', and indicated as
r
s
. But to prevent confusion
with the stomatal resistance, we use the term canopy resistance and symbol
r
c
here.
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