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the boundary layer can develop (larger leaves have thicker boundary layers). The
boundary-layer resistance can be approximated as (Gates,
1980
)
5
:
r
=
k
f
(6.42)
b,h
f
u
f
where
u
f
is the wind speed outside the laminar boundary layer,
f
is the length of the
leaf in the direction of the air low and
k
f
is of the order of 180 s
1/2
m
-1
. Thus, a small
value of
r
b,h
, and consequently strong coupling between leaf temperature and air tem-
perature, occurs at high wind speeds and for small leaves.
Question 6.9:
Consider an individual leaf in air with a temperature of 20 ºC. The leaf is
exposed to a net radiation of 400 W m
-2
, transpires an amount of water equivalent 10
-4
kg m
-2
s
-1
and has a boundary-layer resistance of 40 s m
-1
.
a) Determine the leaf temperature (assume an air density of 1.20 kg m
-3
and
c
p
= 1013
J kg
-1
K
-1
).
b) The plant is under water stress, partly closes its stomata, leading to a reduction of the
transpiration to 0.3∙10
-4
kg m
-2
s
-1
. Again determine the leaf temperature.
c) The same conditions apply as for question (a), but owing to a reduced wind speed
the boundary-layer resistance has increased to 80 s m
-1
. Determine the leaf temper-
ature.
Question 6.10:
In
Figure 6.24
the luxes of sensible heat, latent heat and CO
2
are shown
at two levels, one within the canopy and one above. Explain for each of the quantities
the difference in lux between the two levels.
6.6.5 Dew
Whereas during day time vegetation converts liquid water to water vapour, during
night time the reverse may happen: water vapour condensates on the canopy surface.
This happens if the temperature of the surface falls below the dew point of the air in
and above the canopy. For dew to occur two things are needed: a sink of energy and
a source of water vapour.
A sink of energy is needed because the latent energy released on condensation
needs to be removed from the canopy. For condensation to occur, the other terms in
the (simpliied) surface energy balance need to act as a net sink (
Q*- H - G < 0
). This
5
The boundary-layer thickness
δ
can be approximated as
δ
=
f
u
/ where
ν
is the kinematic viscosity of air
(order of 1.5·10
-5
m
2
s
-1
). Assuming a linear temperature proile in the boundary layer, the heat lux is
H
f
ν
D
/
. It also
shows that the boundary-layer resistance depends on the transported scalar because the molecular diffusivities for
heat, water vapour and CO
2
are different (
D
T
= 2.13·10
-5
m
2
s
-1
,
D
v
= 2.42·10
-5
m
2
s
-1
and
D
c
= 1.47·10
-5
m
2
s
-1
at
20 °C; Gates,
1980
).
=−
(
ρ
c
D
T
−
T
)
/
δ
u
, where
D
T
is the molecular diffusivity for heat. This deines
r
b,h
as
p
Ta
leaf
f
f
T
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