Geoscience Reference
In-Depth Information
Jacobs (
1994
,
1996
) and Calvet et al. (
1998
). Here we discuss mainly the
A
-
g
s
model
as presented by Ronda et al. (
2001
), which is largely based on Jacobs (
1994
).
The starting point is the expression for the stomatal conductance developed in
Chapter 6
, Eq. (
6.29
). However, this expression is valid only for high light intensi-
ties, as at low light intensities the ratio of internal to external CO
2
concentration is no
longer constant (Jacobs,
1994
). If Eq. (
6.29
) would be applied in low light conditions,
A
g
would be less than
R
d
, then
A
n
would be negative, and the computed conductance
would be negative as well. Therefore, Ronda et al. (
2001
) pragmatically replaced
A
n
by
A
g
to obtain the correct behaviour
3
:
aA
1
1
g
gg
=+
(9.29)
s,c
0,c
ρ
( )
D
q
− +
Γ
1
a
e
ce
2
D
0
where
a
1
and
a
2
are given in
Section 6.4.3
. Recall that the variables with subscript 'e'
(external) are deined just outside the stomata, not at some reference level above the
vegetation.
Apart from the plant-speciic parameters, this model for stomatal conductance
model needs to be complemented with a model for
A
g
. For this, use is made of a more
or less mechanistic model for the gross assimilation rate
A
g
(i.e., net assimilation plus
dark respiration:
A
n
+
R
d
). This model is based on a quantiication of the two limiting
factors for assimilation: supply of CO
2
and supply of PAR (Jacobs et al.,
1996
; see
also
Chapter 6
). If neither of the factors is limiting, the maximum net assimilation (or
maximum primary production)
A
n,max
is attained (the plateau in
Figure 6.13a
and
b
).
For the CO
2
-limited case at low
q
ci
the net assimilation is given by
Ag
ρ
( Γ
where
g
m
is the mesophyll conductance.
g
m
determines the initial slope in
Figure 6.13a
.
For higher internal CO
2
concentrations the actual net assimilation rate
A
n
is related
to
q
ci
through the following interpolation between CO
2
-limited and CO
2
-unlimited
conditions (note that it is the net assimilation, not the gross assimilation that is limited
by CO
2
supply):
=
q
−
n
m
ci
ρ
gq
A
(
−
Γ
)
AA
=
1
− −
exp
(
m i
(9.30)
n,c
n,max
n,max
where the extra subscript 'c' indicates that
A
n,c
is the CO
2
-limited net assimilation (in
the literature often denoted as
A
m
)
For the light-limited case at low light intensities, the net assimilation is lin-
early related to the absorbed PAR:
AI
=
PAR
−
R
, where is the initial light use
n
d
3
Jacobs (
1994
) uses an interpolation between the situation at high-light conditions where
A
n
can be used, and low-
light conditions where
A
g
should be used to prevent a negative
g
s
. Furthermore, he subtracts the CO
2
transport
through the cuticula (with conductance
g
0,c
) from the assimilation rate, thus eliminating
g
0,c
from Eq. (
9.29
).
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