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stomata close. The right-hand side of (
6.28
) is an alternative way to denote this linear
relationship by deining the slope
a
d
, which yields
D
0
= (
f
max
-
f
min
)/
a
d
.
Γ
(equivalent
to
q
cc
) and
a
d
are plant-speciic parameters. Usually, a distinction is made between C
3
and C
4
plants. The slope
a
d
is steeper for C
4
plants than for C
3
plants: C
4
plants react
more strongly to dry air.
Combination of Eqs. (
6.26
) and (
6.28
) yields a model for the stomatal conductance
that incorporates both the correlation to net assimilation and the response to transpi-
ration:
1
aA
gg
=+
1
n
(6.29)
s,c
0,c
ρ
( )
D
q
− +
Γ
1
a
e
ce
2
D
0
and
a
=−
(
1
f
) /(
1
− −
f
)
1
min max
(this expression for
a
2
is
slightly different from the one given by Ronda et al., 2001). This shows that indeed
the stomatal conductance decreases as the vapour pressure deicit increases.
Equation (
6.29
) can be simpliied further by noting that the transpiration rate
where
a
=−
−
1
(
f
max
)
2
1
(
)
T
=
1.
g
ρ
qT q
(
)
−
and neglecting
g
0
, resulting in (Leuning,
1995
):
s,c
sat
e
e
a
a
g
=
( )
−
1
A
2
T
(6.30)
s,c
n
ρ
q
Γ
ρ
a
D
ce
30
R
D
Rp
(
)
=
where we used
qT q
()−
=
3
aD
. Thus, stomatal conductance increases
sat
e
e
e
e
with an increasing assimilation rate (note that
A
n
> 0 for net uptake) and decreases
with increasing transpiration. This expression can be rewritten to obtain the water use
eficiency (WUE) at the leaf level:
v
A
T
1
16
1
a
( )
+
WUE
==
n
q
Γ
2
(6.31)
ce
.
a
a
DD
13
e
0
Clearly, a high vapour pressure deicit is detrimental for the WUE. Furthermore, an
increase in the external CO
2
concentration will increase the WUE. Finally, WUE will
differ between C
3
and C
4
plants through the CO
2
compensation point and the dif-
ference in sensitivity to vapour pressure deicit. The concept of WUE is sometimes
employed to explain optimal stomatal responses: how do plants obtain the maximum
assimilation while losing as little water as possible (e.g., Farquhar and Sharkey,
1982
;
Zhang and Nobel,
1996
)?
The preceding analysis (in particular Eq. (
6.29
)) shows how the stomatal
conductance is related to a number of variables related to the photosynthesis process
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