J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 235
Soybean datasets, respectively. For the sake of clarity, only three classes of root-zone soil moisture were rep-
resented in Figs. 1 and 2: dry, intermediate, and wet. As the distribution of soil moisture conditions differed
from one experiment to the other, the classes’ bound- aries are not the same. While the classical decrease of
g
′ s
in response to increasing D
′ s
is observed for both datasets, marked differences appear in the relative
position of dry, intermediate, and wet points. In partic- ular, there is a clear dependence of g
′ s
on the soil mois- ture class in Fig. 2 Soybean, while the results from
MUREX show a more complex behaviour Fig. 1. These features are analysed in this paper in terms of
stomatal response to soil water stress Section 5.
4. Model calibration in unstressed conditions
In order to assess the inter- and intra-specific vari- ability of the parameterisations of stomatal conduc-
tance, both A–g
s
and T
s
-based Jarvis approaches were applied to the unstressed datasets. In many of the anal-
ysed leaf-air exchange measurements, the response of g
s
to D
s
is clearly non-linear, and the formulation of the A–g
s
model is very efficient to simulate the non-linearity, provided appropriate values of g
∗ m
and D
∗ max
are used Jacobs et al., 1996; Calvet et al., 1998. 4.1. Interspecific variability
The unstressed values of g
∗ m
and D
∗ max
displayed in Tables 2–4, were obtained using an optimisation
technique consisting in minimising the RMS error between the simulated and the measured g
s
, for differ- ent values of D
s
. The optimal values of g
∗ m
and D
∗ max
were produced by an iterative, quasi-Newton algo- rithm. The same method was applied to the MUREX
micrometeorological data Calvet et al., 1999, after computing estimates of g
′ s
and D
′ s
at the canopy level from observations of LAI, flux, air humidity and
temperature, and surface temperature. The soybean field data of Olioso et al. 1996 were not employed
to estimate unstressed parameters since most of the data were acquired during stressed conditions. The
unstressed parameters r
∗ smin
and α
∗ H
of the Jarvis ap- proach were obtained by using the same optimisation
procedure, and are also presented in Tables 2–4. Ta- bles 2–4 show that either g
∗ m
and D
∗ max
or r
∗ smin
and α
∗ H
, are extremely variable from one species to another.
As far as the A–g
s
approach is concerned, C
4
plants present the highest values of g
∗ m
, and woody plants the lowest values, while C
3
herbaceous plants occupy an intermediate position. Fig. 3 presents plots of the
natural logarithm of g
∗ m
and D
∗ max
in unstressed con- ditions. While the pooled 63 studies do not present a
particular correlation between lng
∗ m
and lnD
∗ max
, linear relationships are observed after separating C
3
from C
4
plants, and herbaceous from woody plants. The logarithmic equation lng
∗ m
= a − b lnD
∗ max
is statistically significant for C
4
plants and C
3
herba- ceous species only see Fig. 1, with values of a as
5.323 and 2.381, respectively, and values of b as 0.8929 and 0.6103, respectively with D
∗ max
in g kg
− 1
and g
∗ m
in mm s
− 1
. This result, obtained using the A–g
s
model, is also valid using the Jarvis approach not shown. Considering the natural logarithm of
r
∗ smin
− 1
and α
∗ H
− 1
, the equation ln1000r
∗ smin
= a −b ln1α
∗ H
is statistically significant for the pooled C
4
plants and C
3
herbaceous species, with values of a and b as 4.135 and 0.5086, respectively with α
∗ H
in g kg
− 1
, and r
∗ smin
in s m
− 1
. 4.2. Intraspecific variability
Interestingly, these parameters’ difference may oc- cur within the same plant species, also, suggesting that
either the cultivar or the growing conditions may con- tribute to determine g
∗ m
and D
∗ max
. Table 5 summarises the results obtained for maize, rice, tobacco, bean,
and sunflower. From the corresponding growing con- ditions listed in Table 5, the magnitude of D
∗ max
seems to be correlated with the size of the pot in which the
plant was grown: generally, the lowest value of D
∗ max
obtained for a given plant species, corresponds to the smallest pots, that is, the lower potential extension of
the roots. Concerning rice, it seems that another effect is at stake since the air-humidity growing conditions
themselves may influence g
∗ m
on the long term Ta- ble 5: for the same conditions of soil substrate, plants
grown under humid air present a higher value of g
∗ m
, while D
∗ max
does not change.
5. The effect of soil water stress
In several existing Jarvis-type approaches, a stress function depending on soil water content is applied to
236 J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247
Fig. 3. The natural logarithm of unstressed mesophyll conductance g
∗ m
vs. the natural logarithm of the unstressed maximum leaf-to-air saturation deficit D
∗ max
. Each point results from the optimisation of the A–g
s
model Jacobs et al., 1996 according to leaf or field estimates of stomatal conductance as a function of leaf-to-air, or canopy-to-air saturation deficit, respectively. The pooled 63 studies are shown and
comprise C
4
plants Table 4, herbaceous C
3
plants Table 2, and woody C
3
plants Table 3. The C
4
and herbaceous C
3
regression lines dashed and solid, respectively are plotted. Two outliers are excluded from the C
3
correlation: Nicotiana glauca Farquhar et al., 1980, and Lycopersicon esculentum Jolliet and Bailey, 1992.
the value of g
s
. For example, in Noilhan and Planton 1989, the stress function is the extractable soil water
content defined as θ =
w − w
wilt
w
fc
− w
wilt
, 9
where w is the soil volumetric moisture in the root- zone, and w
fc
and w
wilt
are the root-zone moisture
Table 5 Intraspecific variability of the obtained mesophyll conductance at 25
◦
C g
∗ m25
, and the maximum leaf-to-air saturation deficit D
∗ max
a
Plant Reference
D
∗ max
g kg
− 1
g
∗ m25
mm s
− 1
Leaf temperature
◦
C Growing conditions
Maize Dai et al. 1992
29.0 16.12
30 3.5 l pot
Maize Farquhar et al. 1989
166.4 9.14
30 45 l pot
Rice Morison and Gifford 1983
42.4 1.00
25 3 l pot
Rice Kawamitsu et al. 1993
60.8 0.99
30 16 l pot, 85 RH
Rice Kawamitsu et al. 1993
59.8 0.58
30 16 l pot, 35 RH
Rice El-Sharkawy et al. 1984
334.5 0.20
30–35 25 l pot, submerged
Tobacco Dai et al. 1992
42.7 1.11
30 3.5 l pot
Tobacco Farquhar et al. 1980
105.0 0.07
28 6 l pot
Common bean El-Sharkawy et al. 1984
178.2 0.25
30–35 25 l pot
Common bean Comstock and Ehleringer 1993
217.4 0.92
30 15 l pot
Sunflower Hall et al. 1976
123.9 1.29
30–35 6 l pot
Sunflower Turner et al. 1984
273.0 0.29
30 25–35 l pot
a
The related growing conditions, as well as the imposed leaf temperature during gas exchange measurements are indicated. The pot volume is expressed in units of litres 1 l=10
− 3
m
3
, and RH stands for relative air humidity.
content at field capacity and wilting point, respec- tively. In Eq. 2, r
∗ smin
is replaced by its stressed value r
smin
= r
∗ smin
θ . In ISBA–A–g
s
, the same stress function is applied to g
∗ m
assuming that D
∗ max
has a constant value comprised between 30 and 60 g kg
− 1
Jacobs et al., 1996; Calvet et al., 1998: in Eqs. A.1, A.3, and A.6, g
∗ m
is replaced by g
m
= θ g
∗ m
. In this kind of model, the effect of soil water stress has to be
J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 237
applied to the parameters of photosynthesis in order to obtain consistent values of both net assimilation and
stomatal conductance because g
s
is estimated from the value of A
n
in Eq. A.5. In this study there is no a priori fixed or assumed form of the stress func-
tion contrary to Noilhan and Planton, 1989; Calvet et al., 1998. Instead, an empirical response is searched
for from the basic data. The stressed parameters of the model obtained by optimisation may be consid-
ered as characteristic values of the plant in different conditions of drought. The θ value is considered as a
variable, not as a stress function, and is employed a posteriori to describe the evolution of the stressed pa-
rameters. In order to investigate the soil water stress effect through both A–g
s
and Jarvis approaches, val- ues of the stressed parameters g
m
and D
max
or r
smin
and α
H
, were derived from five studies either physio- logical or micrometeorological concerning C
3
-plants and comprising drought episodes, by using the same
optimisation method as for the unstressed plants. 5.1. The stressed parameters of the A–g
s
model Figs. 4 and 5 present the results obtained using
the A–g
s
model. For each study, the corresponding
Fig. 4. The response to soil water stress of plants following an offensive strategy, using the A–g
s
model. The mesophyll conductance g
m
is given as a function of the maximum leaf-to-air saturation deficit D
max
, in stressed and unstressed conditions. Values of g
m
and D
max
were obtained by optimising the A–g
s
model for several classes of decreasing extractable soil water content θ or soil water potential ψ, according to sunflower — Turner et al., 1984, 1985, hazel tree — Farquhar et al., 1980 leaf or MUREX — Calvet et al., 1999 field
estimates of stomatal conductance as a function of leaf-to-air, or canopy-to-air saturation deficit, respectively.
drought-driven trajectories in the g
m
–D
max
space is indicated according to the extractable soil moisture or
to the soil water potential. The stress responses are noticeably different among the studied plant species.
However, two prevailing behaviours are observed: 1 sunflower, hazel tree, and the MUREX fallow Fig. 4
undergo a decrease in g
m
and an increase in D
max
dur- ing the first stage of soil water depletion; then D
max
decreases rapidly at fairly constant values of g
m
ex- cept for sunflower, the g
m
of which ends up decreas- ing when the soil becomes very dry; 2 conversely,
the cowpea and soybean crops Fig. 5 present an in- crease in g
m
and a decrease in D
max
for moderate soil desiccation, and a decrease in g
m
over a small range of D
max
for more pronounced soil dryness. It is in- teresting to note that for both strategies, the g
m
–D
max
response to the first stage of water stress is almost parallel to the C
3
-line of Fig. 3 see Section 6.1. 5.2. The stressed parameters of the T
s
-based Jarvis approach
Figs. 6 and 7 present the results obtained using the T
s
-based Jarvis approach. In this case, the model pa- rameters r
smin
and α
H
are displayed separately as
238 J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247
Fig. 5. The response to soil water stress of plants following a defensive strategy, using the A–g
s
model. The mesophyll conductance g
m
is given as a function of the maximum leaf-to-air saturation deficit D
max
, in stressed and unstressed conditions. Values of g
m
and D
max
were obtained by optimising the A–g
s
model for several classes of decreasing extractable soil water content θ according to Cowpea — Hall and Schulze, 1980 leaf or Soybean — Olioso et al., 1996 field estimates of stomatal conductance as a function of leaf-to-air, or
canopy-to-air saturation deficit, respectively.
a function of θ because no simple relationship could be found between either r
smin
and α
H
or r
− 1
smin
and α
− 1
H
. However, the main conclusions obtained with the A–g
s
parameters concerning the stomatal sensitivity to D
s
represented here by the parameter α
H
are con- firmed. Sunflower, hazel tree, and the MUREX fallow
Fig. 6 show lower values of α
H
for intermediate soil moisture, while the opposite behaviour is observed for
cowpea and soybean Fig. 7.
Fig. 6. The response to soil water stress of plants following an offensive strategy, using the T
s
-based Jarvis approach. The leaf sensitivity to leaf-to-air saturation deficit α
H
, left, and the minimum stomatal resistance r
smin
, right are plotted vs. the extractable soil moisture θ Eq. 9. In the case of hazel tree, soil water potential values ψ were converted to θ values by using the arbitrary function
θ = |ψ |
− b
− | ψ
min
|
− b
|ψ
max
|
− b
− | ψ
min
|
− b
, with b=3.5, ψ
min
=− 20 bar, and ψ
max
=− 13 bar.
5.3. The stressed parameters of the T
a
-based Jarvis approach
The results obtained using the T
a
-based Jarvis ap- proach not shown show that the general trend of the
r
smin
and α
H
response to soil moisture is the same as in Figs. 6 and 7. However, the evolution of the stom-
atal sensitivity to D
s
is more complex than the rela- tively smooth adaptation observed with the T
s
-based
J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 239
Fig. 7. The response to soil water stress of plants following a defensive strategy, using the T
s
-based Jarvis approach. The leaf sensitivity to leaf-to-air saturation deficit α
H
, left, and the minimum stomatal resistance r
smin
, right are plotted vs. the extractable soil moisture θ Eq. 9.
Jarvis approach in Figs. 6 and 7. This result indicates that using T
a
as a factor of the stomatal aperture is not fundamentally different from using T
s
, but that T
s
seems to be a better descriptor of the temperature de- pendence of the g
s
parameters.
6. A parameterisation of soil water stress based on the A