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Contents lists available at ScienceDirect
Agricultural and Forest Meteorology
journal homepage: www.elsevier.com/locate/agrformet
Soil water stress and coupled photosynthesis–conductance models: Bridging the
gap between conflicting reports on the relative roles of stomatal, mesophyll
conductance and biochemical limitations to photosynthesis
Trevor Keenan a,*, Santi Sabate a,b, Carlos Gracia a,b
a
b
CREAF, Autonomous University of Barcelona (UAB), 08193 Barcelona, Spain
Department of Ecology, University of Barcelona (UB), 08007 Barcelona, Spain
A R T I C L E I N F O
A B S T R A C T
Article history:
Received 28 September 2009
Received in revised form 4 December 2009
Accepted 9 January 2010
Various plant responses to water stress have been reported, but conflicting reports as to which limiting
process is the most important and ecophysiologicaly relevant during water stressed periods make it
difficult to confidently model terrestrial CO2 and water flux responses. It has become increasingly
accepted that mesophyll conductance could play a role in regulating photosynthesis during periods of
water stress. We adapt the Farquhar-BB-type canopy photosynthesis–conductance model coupling to
incorporate mesophyll conductance, embed it in an ecophysiological forest model and use it to simulate
the effects of seasonal soil water stress on canopy CO2 and water fluxes at a Mediterranean Quercus ilex
forest. Tests of various hypotheses regarding the relative roles of stomatal conductance limitations (SCL),
mesophyll conductance limitations (MCL) and biochemical limitations (BL) confirmed that during water
stressed periods, applying only BL allows for the accurate simulation of CO2 and water fluxes. Neither SCL
nor MCL alone could accurately reproduce the observed CO2 and water fluxes. However, a combination of
both MCL and SCL was successful at reproducing water stress induced reductions in CO2 and water fluxes,
suggesting that mesophyll conductance could bridge the gap between conflicting reports on the
processes behind responses to water stress in the field.
ß 2010 Elsevier B.V. All rights reserved.
Keywords:
Terrestrial modelling
Photosynthesis model
Drought stress
Mesophyll conductance
Mediterranean climate
1. Introduction
Process-based models that incorporate the relevant ecosystem
processes to successfully simulate the sensitivity of ecosystem
functioning to drought stress at all relevant time scales are
indispensable tools. Such models of natural vegetation can assess
the influence of stresses on the photosynthetic capacity of plants
(Centritto et al., 2003; Loreto et al., 2003; Loreto & Centritto, 2008)
and predict the effects of climate change on photosynthesis
(Rogers & Humphries, 2000), thus helping to assess the vulnerability of ecosystems. Moreover, they are the only available tool for
scaling carbon assimilation up from the leaf to whole plant and/or
ecosystem (Harley & Baldocchi, 1995; Niinemets & Anten, 2009).
Previous modelling studies, however, have highlighted the lack of
model skill, at site, regional and global scales, to successfully
reproduce the effects of seasonal stress due to low soil water
availability, in particular in Mediterranean ecosystems (Morales
et al., 2005; Jung et al., 2007).
* Corresponding author at: CREAF, Edfici C, Universidad Autonoma de Barcelona,
08193 Bellaterra, Spain. Tel.: +34 93 581 2915; fax: +34 93 581 4151.
E-mail address: [email protected] (T. Keenan).
Projections of climate change (IPCC, 2007) suggest that higher
temperatures, and increased potential evapotranspiration, as well
as changes in seasonal precipitation patterns, will aggravate the
seasonal drought stress characteristic to Mediterranean ecosystems (Giorgi et al., 2004; Giorgi, 2006; Beniston et al., 2007). Soil
water availability is already the main limiting factor to global plant
photosynthesis (Nemani et al., 2003), in particular in arid or semiarid ecosystems within Mediterranean climate regions (Boyer,
1982). An increase in anomaly events such as the 2003 European
drought could also increase the amount of stress experienced in
many non-Mediterranean forest ecosystems in Europe. However,
despite recent advances (e.g., Grassi & Magnani, 2005), the effect of
soil water stress on photosynthesis, and the vulnerability of
Mediterranean vegetation to climate change, will not be fully
understood until we untangle the ecophysiological responses and
the main limitations imposed by water stress on leaf photosynthesis (Loreto & Centritto, 2008).
Many different approaches have been developed over the last
two decades to simulate the CO2 and water fluxes of a forest
ecosystem. These biogeochemical models assess mass and energy
exchange between the canopy and the atmosphere by coupling the
fluxes of CO2 and water vapour (Wang & Jarvis, 1990; Aber &
Federer, 1992; Amthor, 1994; Baldocchi & Harley, 1995; De Pury &
0168-1923/$ – see front matter ß 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.agrformet.2010.01.008
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
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Farquhar, 1997). The leaf physiologically based photosynthesis
model by Farquhar et al. (1980), linked with a stomatal
conductance model (Jarvis, 1976; Ball et al., 1987; Collatz et al.,
1991; Leuning et al., 1995) provides a theoretical framework for
spatially scaling up fluxes from leaf to canopy level. This processbased model coupling has proven hugely popular, and accurately
integrates the canopy functioning over time scales from seconds to
years (e.g., Caldwell et al., 1986; Leuning et al., 1995; Williams
et al., 1997; Wang & Leuning, 1998; Keenan et al., 2009). Although
such models are capable of giving very accurate results, they are
not efficient at dealing with all conditions, in particular with water
stress (Kramer et al., 2002; Morales et al., 2005).
It has recently been shown that part of the model deficiency is
due to the assumption of the sole control of stomatal conductance
limitations (SCL) over photosynthesis during water stressed
periods (Keenan et al., 2009). The inclusion of empirical ‘nonstomatal’ limitations has been shown necessary to successfully
model CO2 and water fluxes in water stressed environments (e.g.,
Colello et al., 1998; Reichstein et al., 2002, 2003; Rambal et al.,
2003; Xu & Baldocchi, 2003), with both CO2 and water fluxes being
accurately modelled during water stressed periods through the
reduction of photosynthetic potential (BL) in line with reductions
in soil water availability (Keenan et al., 2009). Such a BL represents
the effect of drought on metabolic functioning (e.g., the activity of
the Rubisco activase enzyme, denitrogenisation, etc.). These model
results suggest that stomatal aperture is driven by photosynthetic
demand, and that the stomata do not play an active role in the long
term regulation of photosynthesis during water stressed periods.
This is controversial, as stomata have been widely reported to play
a strong role in regulating photosynthesis during water stress (see
Lawlor & Cornic, 2002, for a review). The conclusions from most
studies, in particular model studies, were reached without taking
into account the possible effects of a finite and changeable
mesophyll conductance (gm).
CO2 which enters the inter-cellular spaces of the leaf through
the stomata diffuses through the mesophyll to the site of
carboxylation in the chloroplast. It is becoming increasingly
accepted that gm is finite and variable (Warren, 2008a), and that
the concentration of CO2 in the inter-cellular spaces (Ci) differs
from the concentration of CO2 in the chloroplast (Cc) in a manner
that is highly variable within species and affected by a range of
environmental conditions (e.g., Flexas et al., 2007; Warren, 2008b).
Limitations of photosynthesis due to changes in gm (MCL) could
play a role in plant responses to water stress (Grassi & Magnani,
2005; Galmés et al., 2007; Warren, 2008b; Keenan et al., 2010).
This strengthens the need to incorporate a term that considers gm
in current photosynthesis models, such as that by Farquhar et al.
(1980), thus calculating photosynthetic rates based on Cc instead of
on Ci.
It has been repeatedly suggested that gm should be included in
models of photosynthesis. However, as yet, there is no simple and
accurate way to predict gm without measuring it. This is because gm
strongly varies among and within given species (Ethier and
Livingston, 2004; Flexas et al., 2008; Niinemets et al., 2009a;
Warren, 2008a). gm is affected by both leaf structure (e.g.,
mesophytic leaves with higher vs. sclerophytic leaves with lower
gm (Evans et al., 2009; Flexas et al., 2008; Niinemets et al., 2009a;
Terashima et al., 2006; Warren, 2008a) and many of the
environmental variables that drive models of canopy photosynthesis (e.g., temperature, drought, etc. (Warren, 2008a)), and there
is currently not enough physiological information for reliable
parameterization of these dependencies. On the other hand, some
of the environmental effects may be small or moderate relative to
the overall effect of gm on canopy photosynthesis. For instance, the
effect of temperature on gm has been reported to be relatively small
(Niinemets et al., 2009a,b). Drought-dependent reductions have
been shown to occur together with reductions in stomatal
conductance (gs) (Centritto et al., 2003; Flexas et al., 2008; Loreto
et al., 2003).
In the current analysis, different hypothesis are tested,
challenging current assumptions regarding the relative roles of
SCL, MCL and BL to photosynthesis and conductance, and how to
model them, during seasonal water stressed periods in the field.
We modified the Farquhar et al. (1980) model to incorporate
mesophyll conductance and thus calculated photosynthesis on a Cc
basis. This was coupled to the widely used Leuning et al. (1995)
version of the Ball-Berry conductance model (Ball et al., 1987), and
embedded in the biogeochemical forest growth model GOTILWA+
(‘Growth Of Trees Is Limited by Water’) (Gracia et al., 1999; Keenan
et al., 2008, 2009). We could therefore test the effect of the
inclusion of a water stress responsive stomatal conductance,
mesophyll conductance or photosynthetic potential on modelled
CO2 and water fluxes. CO2 and water eddy-covariance flux data
from the five year period from 2001 to 2005 at the Puechabon
Mediterranean Quercus ilex forest site in France are used to test
model performance during water stressed periods.
2. Materials and methods
2.1. Fluxnet site data
Data and simulations refer to Puechabon State Forest study site,
located 35 km NW of Montpellier (southern France) (38350 4500 E,
438440 2900 N, elevation 270 m). Vegetation is largely dominated by a
dense over-storey of Quercus ilex trees (Allard et al., 2008). Due to
its typical Mediterranean-type climate (with warm and wet
winters, and hot and dry summers), the water content in summer
falls regularly below the value at which water stress limitations to
photosynthesis are expected (Rambal et al., 2003), leading to
extended seasonal periods of drought stress. The timing and extent
of drought conditions varies from year to year, depending on
temperature and precipitation. The mean annual temperature is
13.5 8C with mean annual precipitation of 903 mm (Allard et al.,
2008). Rooting depth is 4.5 m, with a maximum total soil water
content of 210 mm (for the 4.5 m soil column) (Keenan et al., 2009;
Grote et al., 2009; Rambal et al., 2003). Soil texture is silty clay loam
(referring to the textural triangle, United States Department of
Agriculture) homogeneous down to 0.5 m depth, with increasing
rock content thereafter and a limestone rock base. For more details
on the site see http://www.cefe.cnrs.fr/fe/puechabon/.
Climate, and eddy-covariance CO2 and water (latent heat flux
equivalent) flux Measurements from the period 2001 to 2005 are
used, which had an average annual air temperature of 14.5 8C and
average annual precipitation of 965 mm. The selected focus year
2002 was wetter (total precipitation 1166 mm) than the longterm average but was also warmer than average (average
temperature for 2002 of 14.7 8C). The high soil water availability
during spring, and the relatively high temperatures, led to high
production in spring 2002. The corresponding high levels of
production related transpiration, and a relatively dry summer
which was uninterrupted by strong rainfall events led to a sharp
and extended drought period during 2002. This contrast between
high spring production and a prolonged uninterrupted summer
drought makes 2002 at Puechabon a good example year to test
different approaches to modelling soil water stress responses.
The valid approaches for 2002 were then tested against the full
time series.
2.2. Modified photosynthesis model with mesophyll conductance
The photosynthesis model of Farquhar, von Caemmerer & Berry
(1980) was modified to explicitly calculate mesophyll conductance
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
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and therefore accurately calculate the quantity of CO2 available
for assimilation in the chloroplast, through a set of coupled
equations. The Farquhar et al. (1980) model states that the rate
of net photosynthesis (An) is the minimum of the carboxylation
rate limited by the amount, activation state, and kinetic
properties of Rubisco (Rubisco-limited Ac); and the carboxylation rate limited by the rate of RuBP regeneration (Electron
transport limited Aj):
An ¼ minfAc ; A j g
(1)
For Rubisco limited photosynthesis the net CO2 assimilation
rate is limited by Ac:
Ac ¼
Vcmax ðC c G pÞ
C c þ ðK c ð1 þ ðOi =K o ÞÞÞ
(2)
where Cc is the concentration of CO2 in the chloroplast, Gp* is the
photorespiratory CO2 compensation point in the absence of
mitochondrial respiration, Vcmax is the maximum rate of Rubisco
carboxylation, Oi is the O2 concentration, and Kc and Ko are the
Michaelis–Menten constants describing carboxylation and oxygenation. For electron transport limited photosynthesis (Harley &
Tenhunen, 1991):
Aj ¼
ðJ=4Þ ðC c G pÞ
C c þ ð2 G pÞ
(3)
where J is the rate of electron transport, dependent on irradiance,
leaf temperature, and the capacity of electron transport (Jmax) (De
Pury & Farquhar, 1997).
These calculations of photosynthesis require the concentration
of carbon in the chloroplast, which is a function of An, stomatal
conductance (gs) and mesophyll conductance (gm). Traditional
modelling approaches estimate stomatal conductance as a
function of irradiance, the balance of the supply and demand of
carbon, and vapour pressure deficit. Ball et al. (1987) proposed a
semi-empirical stomatal model (BB model) in which stomatal
conductance was expressed by the leaf photosynthetic rate,
relative humidity over a leaf surface, and the ambient CO2
concentration, under conditions of ample water supply (Ball et al.,
1987). This model was later developed by Leuning (1995) (BBL
model) to include the effects of vapour pressure deficit and the CO2
compensation point (Leuning, 1995; Leuning et al., 1995):
g s ¼ g s0 þ m
An
ðC a G Þð1 þ ðv pd=D0 ÞÞ
(4)
where gs (mol H2O m2 s1) is stomatal conductance to moisture,
g s0 is the value of gs at the light compensation point (mol m2 s1),
An is the rate of net photosynthesis (mmol m2 s1), C a is the
atmospheric concentration of CO2 at the canopy surface
(mmol mol1), G is the CO2 compensation point (mmol mol1),
D0 (unitless) is an empirical coefficient that describes the
sensitivity of conductance to vpd (vapour pressure deficit, kPa),
and m is an empirical species-specific factor that specifies the
baseline ratio between conductance and net photosynthesis
(unitless).
The concentration of carbon inside the chloroplast, Cc is then a
function of the net photosynthesis (assimilation rate) An, stomatal
conductance to CO2, gsc (=gs/1.6), and gm:
An
An
Cc ¼ Ca (5)
g sc
gm
where Ca (mmol mol1) is the atmospheric CO2 concentration and
gm is the mesophyll diffusion conductance from the sub-stomatal
cavities to the chloroplasts.
This set of equations (Eqs. (1)–(5)) complete the mesophyll
conductance based photosynthesis model, and are solved itera-
3
tively by closing the leaf energy balance through leaf temperature.
Values for Kc, Ko, Oi and G* were taken from Bernacchi et al. (2001).
Jmax and Vcmax were calculated following Farquhar et al. (1980) and
De Pury and Farquhar (1997).
The effect of the inclusion of gm in the Farquhar BB-type model
coupling (for a non water stressed system) was conducted using
three reference values for gm. This allowed for the reparameterization of the photosynthetic parameters Jmax and Vcmax (following
Niinemets et al., 2009b). A gm of 0.2 mol m2 s1 corresponds to a
relatively high rate of mesophyll conductance encountered in
plants adapted to relatively moist growing environments. The
values of gm applied of 0.1 and 0.05 mol m2 s1 correspond to
moderately low diffusive conductance, and very low diffusive
conductance (see Niinemets et al., 2009a; Galmés et al., 2007 for
recent reviews of species gm values). gm = infinity refers to the
original Farquhar et al. (1980) model, which assumes infinite
mesophyll conductance. Many other factors have been suggested
to affect gm, e.g., leaf age, environmental, ontogenic and genetic
modification in leaf structure, salinity stress, water stress,
radiation and VPD (see Flexas et al., 2008 for a review). There is
as yet no consensus as to how such factors could be implemented
when modelling with consideration of gm. There is good agreement
in the literature of a temperature affect on gm at lower
temperatures (<20 8C), but both positive and negative responses
have been observed at higher temperatures (Bernacchi et al., 2002;
Pons & Welschen, 2003; Warren & Dreyer, 2006; Yamori et al.,
2006; Warren, 2008a). This is probably due to species specific
temperature responses though available data is far from sufficient
to construct temperature response of internal conductance
(Warren, 2008a). As drought occurs typically during periods of
high temperatures, we have omitted a temperature response of gm
for this study.
2.3. The effect of soil water stress on coupled photosynthesis–
conductance models
Model studies have shown that the application of BL is
sufficient to accurately model water stress affects on CO2 and
water fluxes (Reichstein et al., 2002; Keenan et al., 2009), whilst it
is commonly upheld that the stomata (SCL) (e.g., Tenhunen et al.,
1990; Cornic, 2000), and the mesophyll (MCL) (e.g., Warren,
2008a; Keenan et al., 2010), play a strong role in regulating water
stress responses (e.g., Grassi and Magnani, 2005, but see Loreto &
Centritto, 2008). We test the following four hypotheses from the
literature for the incorporation of the effect of drought stress on
the (Farquhar—BB-type) coupled photosynthesis–conductance
model:
(1) Directly reducing photosynthesis in relation to reductions in
soil water availability sufficiently constrains CO2 and water
fluxes during water stressed periods (biochemical limitations,
BL). This incorporates all reported non-conductance limitations.
(2) Directly reducing stomatal conductance in relation to reductions in soil water availability is sufficient to explain variation
in CO2 and water fluxes during drought stressed periods
(stomatal conductance limitations, SCL).
(3) Directly reducing mesophyll conductance in relation to
reductions in soil water availability is sufficient to explain
variation in CO2 and water fluxes during drought stressed
periods (mesophyll conductance limitations, MCL).
(4) A combination of conductance limitations (CL) can accurately
simulate the observed flux data (CL = SCL + MCL).
We tested the hypotheses by imposing the three limitations,
either individually or combined, to: (a) photosynthetic potential
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
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(BL), (b) stomatal conductance (SCL), and (c) mesophyll conductance (MCL).
Biochemical limitations were imposed by the direct reduction
of photosynthetic potential through reducing both Vcmax and Jmax
during water stressed periods, in line with the relative soil water
content (as in Keenan et al., 2009):
Vcmax ¼ Vcmax W facphoto
;
Jmax ¼ J max W facphoto
(6)
where Vcmax and Jmax are the maximum rate of RuBP carboxylation,
and the maximum rate of electron transport, respectively, and
Wfacphoto is a soil moisture-dependent scalar with values between
0 and 1. This BL function directly reduces photosynthesis under
drought stress, thus reducing the demand for CO2 and reducing
conductance.
Stomatal control of photosynthetic responses to drought stress
is modelled through the application of a linear scalar of soil
moisture, in a modified version of Eq. (4):
mðAn Rd Þ
g s ¼ W facstoma g s0 þ
(7)
ðC a G Þð1 þ ðv pd=D0 ÞÞ
where Wfacstoma is a soil moisture-dependent scalar with values
between 0 and 1. This SCL function results in a reduction in
conductance with reductions in soil moisture, thus limiting the leaf
internal CO2 available for photosynthesis.
Mesophyll conductance limitations were modelled by applying
a similar reduction function Wfacmeso to gm (g 0m ¼ W facmeso g m ).
This MCL function thus results in a direct reduction in mesophyll
conductance with reductions in soil moisture.
The three limitation functions, Wfacphoto, Wfacstoma and
Wfacmeso, have the following form:
8
1;
if SðtÞ Smax
<
sðtÞ smin q
W fac ¼
(8)
;
if
SðtÞ < Smax
:
smax smin
where q is a measure of the non-linearity of the effects of soil water
stress on physiological processes, smax the relative soil water
content, for the 4.5 m soil column, at which reductions are first
evident, and smin is the wilting point. For the sake of comparative
simplicity, we have assumed that increases or decreases in
limitation strength for a particular limitation (BL, SL, MCL) can be
represented by changes in the q value. Thus smax and smin values are
common to all limitation approaches (smax = 0.8, smin = 0.38 (168,
80 mm)).
2.4. The biosphere model platform
The modified coupled Farquhar BB-type model was embedded
in the ecophysiological model platform GOTILWA+ (Growth of
Trees Is Limited by WAter) (Gracia et al., 1999; Keenan et al., 2008,
2009; www.creaf.uab.es/Gotilwa+). GOTILWA+ is a process based
forest growth model that has been developed to simulate the
processes underlying growth and to explore how these processes
are influenced by climate, tree stand structure, management
techniques, soil properties and climate change. The GOTILWA+
model provides the biogeochemical background, and canopy
microclimatic conditions necessary for the simulation of CO2
and water fluxes from forests in different environments, for
different tree species, and under changing environmental conditions.
Canopy CO2 and water fluxes of a forest ecosystem are
estimated using a two layer canopy photosynthetic model (Wang
& Leuning, 1998), coupled with a hydrology model. Sun and shade
leaves are considered in the photosynthesis submodel (Wang &
Leuning, 1998; Dai et al., 2004), with intercepted radiation
depending on the time of the day, leaf area angle and the canopy’s
ellipsoidal distribution (Campbell, 1986). The Farquhar approach
(Farquhar et al., 1980; Von Caemmerer and Farquhar, 1981)
outlined in Eqs. (1)–(5) is used to calculate the hourly rate of
photosynthesis, depending on the direct and diffuse radiation
intercepted, the species specific photosynthetic capacities, and leaf
temperature. Stomatal conductance is calculated using the
Leuning et al. (1995) version of the Ball and Berry model (Ball
et al., 1987) (Eqs. (4) and (7)).
Soil water content is described as one layer. Precipitation inputs
are reduced by leaf interception, which is evaporated (stem
interception, or stemflow, is not evaporated, but directed to the
soil). Drainage, runoff, evaporation and transpiration are each
considered. Run-off is calculated as a percentage of precipitation,
and depends on the soil hydraulic gradient and porosity of the soil
upper layer. Drainage is calculated to be inversely proportional to
fractional soil water content (as in Honeysett and Ratkowsky,
1989; Gracia et al., 1999). Surface evaporation only occurs when
the canopy is not closed.
Monospecific (even- or uneven-aged) stands are considered,
with no under-story. Individual trees are aggregated into 50 DBH
(Diameter at Breast Height) classes and calculations are performed
for each class. Ecosystem CO2 and water fluxes are estimated using
hourly meteorological forcing, whereas slower processes such as
growth and other state variables are calculated daily. Site specific
parameters were taken from available literature. Previous model
applications at the Puechabon site are published as Keenan et al.
(2007, 2008, 2009).
2.5. Simulation methodology used
The inclusion of gm requires the recalibration of photosynthetic
parameters (Niinemets et al., 2009b)—Simulations were run with
each fixed gm value (0.2, 0.1, 0.05 mol m2 s1) for the year 2002 at
Puechabon to assess the impact of the inclusion of gm in the
Farquhar-Ball Berry model coupling. Soil water stress was not
considered for these simulations (i.e. Soil water content = maximum soil water content at all times). Following this initial testing
and parameter recalibration, gm was then set at 0.1 mol m2 s1,
which corresponds to moderately low diffusion conductance as
found in Quercus ilex (see Niinemets et al., 2009a for a review of
species gm values). The corresponding Vcmax and Jmax values (after
calibrating modelled carbon and water fluxes against the FLUXNET
carbon and water flux data) were 51 and 70 mmol m2 s1,
respectively.
Independent simulations were then run with a dynamic soil
water content to test the different water stress response
hypotheses as outlined above. In simulations applying BL, gm
was fixed at 0.1 mol m2 s1. For simulations applying MCL and/or
SCL, Vcmax and Jmax were kept constant. In each case, the strength of
the limitation was incrementally increased (see Eq. (8)) until the
least square fit was satisfied for either the CO2 (net assimilation
rate) or water (latent heat flux) fluxes, when compared against the
FLUXNET data. The different hypotheses which proved valid for
2002 were then applied, without further calibration, in comparative simulations for the five year period from 2001 to 2005, and
compared against FLUXNET CO2 and water flux data.
3. Results
3.1. The effect of the inclusion of mesophyll conductance on simulated
CO2 and water fluxes
Simulations using a gm of 0.2 or 0.1 mol m2 s1 compared well
to results from the traditional gm = infinity approach, once the
photosynthetic parameters (Vcmax, Jmax) were adjusted (Fig. 1). No
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
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significant differences were observable for daily assimilation rates
or rates of transpiration between the gm = infinity and the gm = 0.2
(An t-stat = 1.02, p = 0.9; Ea t-stat = 0.9, p = 0.42) or gm = 0.1 (An tstat = 0.09, p = 0.92; Ea t-stat = 0.82, p = 0.41) simulations. For
gm = 0.1 simulations, slight differences in assimilation and
transpiration were observed only at high temperatures and high
vpd when compared to the gm = infinity simulations. No change in
water use efficiency was observed for gm = 0.1 simulations
compared to gm = infinity simulations. Simulating with gm = 0.05
led to significant differences in daily assimilation rates (tstat = 3.2, p < 0.01), most notably at high temperatures and high
vpd. Large significant differences (t-stat = 4.8, p < 0.001) were
observed in daily transpiration rates between the gm = infinity, and
gm = 0.05 simulations, due to increased water use efficiency
(Fig. 1). These differences were larger at higher temperatures,
radiation and high vpd values.
3.2. Hypotheses testing
Testing of the first of the three hypotheses showed that the
application of restrictions to photosynthetic potential (BL) allowed
for the effective reproduction of both CO2 and water fluxes (Fig. 2)
during the water stressed period in 2002 at Puechabon (An r2: 0.92,
RMSE: 1.8; LHF r2: 0.66, RMSE: 1.8). Both the assimilation rate and
the latent heat flux (equivalent to evapotranspiration) reduced in
parallel when simulating with BL (Eq. (6)), thus conserving the
water use efficiency (Fig. 3). The reduction of gs alone through the
application of Wfacstoma (SCL: Eq. 7) reduced stomatal conductance
(and thus the latent heat flux), but water use efficiency remained
high due to increased assimilation rates (Fig. 3). This lead to a large
overestimation of total assimilated carbon during the water
5
stressed period of 2002 (An r2: 0.7, RMSE: 8.9; LHF r2: 0.7, RMSE:
5.0).
Implying mesophyll conductance limitations (MCL) through
reducing gm during water stressed periods proved more effective at
modelling the water stress induced drop in assimilation rates than
did SCL, but less effective at simulating water fluxes (An r2: 0.75,
RMSE: 4.5; LHF r2: 0.53, RMSE: 5.9) (Fig. 2). The application of MCL
was most ineffective at reproducing fluxes at mild water stress
(between RSW of 0.5 and 0.7), where water fluxes were accurately
simulated but slight overestimations in water use efficiency
(Fig. 3) led to a much higher predicted assimilation rate than that
observed (Fig. 2).
Our last hypothesis was that a joint combination of diffusive
conductance limitations (CL), with no limitation of photosynthetic
potential (constant Vcmax, Jmax), could match observed CO2 and
water fluxes during water stressed periods. Setting both conductance limitations to be of equal strength (SCL = MCL) allowed for a
moderately accurate simulation of water (latent heat flux
equivalent) fluxes, but CO2 fluxes were not as well reproduced
(Fig. 4a) (An r2: 0.48, RMSE: 6.9; LHF r2: 0.72, RMSE: 5.4). This
follows from the results presented in Figs. 2 and 3, as SCL reduces
conductance but is not sufficient to reduce photosynthesis even
with an additional MCL of equal strength. Further independent
increases in stomatal restrictions (SCL > MCL) could not reduce
assimilation (Fig. 4b), and gave increased water use efficiency (see
Fig. 3). An even further increase in SCL, leads to underestimated
latent heat fluxes, and overestimated assimilation rates (data not
shown). Applying stronger MCL than SCL allowed for an accurate
simulation of both CO2 and water fluxes (Fig. 4c) (An r2: 0.82,
RMSE: 3.0; LHF r2: 0.73, RMSE: 1.7). CO2 fluxes were not as
accurately simulated as through the application of BL (Hypothesis
Fig. 1. Modelled non water stressed responses of daily canopy net assimilation (An), transpiration (Ea, mm day1), and water use efficiency (WUE, mmol mol1) to
temperature (T, 8C), global radiation (MJ m2 day1), and vapour pressure deficit (VPD, kPa) for different values of mesophyll diffusion conductance (gm, mol m2 s1), at the
Puechabon Forest in 2002. Simulations were run using the coupled Farquhar BB-type model coupling, embedded in the GOTILWA+ forest model (Keenan et al., 2008, 2009),
modified to calculate assimilation based on Cc (An = f(Cc, Vcmax, Jmax, Rd)) through equations (1)–(5). Curves for ‘gm = infinity’ represent simulations run with no consideration
for mesophyll diffusion conductance (An = f(Ci, Vcmax, Jmax, Rd)). Error bars represent the standard deviation from the mean. WUE is defined as the molar ratio of assimilation to
transpiration. Daily values were assigned to 14 bins (n = 364). For each gm value, the following canopy integrated photosynthetic parameters were used: gm = 1, Vcmax = 35,
Jmax = 70; gm = 0.2, Vcmax = 42.5, Jmax = 70; gm = 0.1, Vcmax = 51, Jmax = 70; gm = 0.05, Vcmax = 85, Jmax = 80).
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
G Model
AGMET-4203; No of Pages 11
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6
Fig. 2. Water stressed simulated and FLUXNET measured responses of daily canopy net assimilation (An, g C m2 day1), and daily latent heat flux (LHF, W m2) to changes in
soil water content at the Puechabon forest during 2002. Simulations use the coupled Farquhar BB-type model, on a Cc basis, embedded in the GOTILWA+ forest model (Keenan
et al., 2008, 2009). Results from three simulations are presented, applying independently either: direct biochemical limitations to photosynthesis during water stress (BL, Eq.
(6)), stomatal limitations to photosynthesis (SCL, Eq. (7)), or mesophyll conductance limitations to photosynthesis (MCL). Non-stressed mesophyll diffusion conductance (gm)
was set at 0.1 mol m2 s1. Figure insets represent linear regressions between the measured and predicted variables (BL: An r2 = 0.92, LHF r2 = 0.65; SCL: An r2 = 0.7, LHF
r2 = 0.69; MCL: An r2 = 0.75, LHF r2 = 0.52 (n = 77)).
1, Figs. 2 and 3), but the simulation of water fluxes slightly
improved.
3.3. Long term comparison of approaches
We tested the two effective modelling approaches (1: the
application of BL, 2: the application of CL with MCL > SCL) against
five years of flux data for the period from 2001 to 2005 at
Puechabon forest (data not used for the calibration of the response
functions). Both model approaches proved effective at capturing
the seasonal effect of soil water stress on CO2 and water fluxes
during the five year period (Fig. 5). Simulations with the CL (with
MCL > SCL) approach and the BL approach explained 78% and 79% of
the observed variance in canopy CO2 fluxes, respectively. This was
confirmed by similar values of the Root Mean Squared Error
(RMSE) statistic over the period, of 1.54 and 1.49, respectively. This
was not true for the simulated latent heat flux. The BL approach
achieved a higher correlation to the data (r2 = 0.75 vs. 0.71) but did
not perform as well as the CL (with MCL > SCL) approach when
considering the RMSE (17.1 vs. 14.8). The CL approach performed
markedly better than the BL approach at simulating water fluxes
for 2001, 2004 and 2005, which were the years which received the
least precipitation (2001: 847 mm; 2004:705 mm; 2005: 875 mm;
5 year average: 966 mm).
4. Discussion
A common approach to modelling stomatal conductance is to
assume a linear relationship with leaf- or canopy-level photosynthesis (Wong et al., 1979), the leaf surface concentration of CO2,
and relative humidity or vapour pressure deficit, the so-called
‘‘Ball-Berry’’ (BB) and ‘‘Ball-Berry-Leuning’’ (BBL) parameterizations (Ball et al., 1987; Leuning et al., 1995). Such assumptions
underpin the coupling of water and CO2 cycles in many processbased ecosystem models, but water stress induced changes in
conductance-photosynthesis relationships are as yet poorly
understood.
The effect of water stress on plant photosynthesis and stomatal
conductance has been widely studied (Wilson et al., 2000; Chaves
et al., 2002; Grassi & Magnani, 2005), but there is little consensus
as to those processes governing responses over seasonal timescales (Loreto & Centritto, 2008; Warren, 2008a). Recent studies
have shown that ‘non-stomatal’ limitations remove the need for
stomatal limitations when modelling drought affects on coupled
carbon-water photosynthesis models (Rambal et al., 2003; Reichstein et al., 2002, 2003; Keenan et al., 2009), due to the linear
relation between photosynthetic demand and stomatal conductance, and are supported by reported changes in photosynthetic
potential in the field (e.g., Xu and Baldocchi, 2003). Such results are
controversial, as they suggest that stomatal conductance responses
are not necessary for plant function under long term seasonal
water stress events. There is no clear understanding of the
processes responsible for such BL, though many different
possibilities highlighted in the literature, such as enzyme
deactivation (Tezara et al., 1999; Lawlor & Cornic, 2002), activity
of aquaporins (Flexas et al., 2004; Kaldenhoff et al., 2008;
Miyazawa et al., 2008), photosynthetic inhibition due to high
temperatures (Haldimann & Feller, 2004), denitrogenisation
(Grassi & Magnani, 2005), among many other possible mechanisms
(e.g., Chaves et al., 2002; Lawlor & Cornic, 2002; Bota et al., 2004).
It is well known that the stomata react to changes in soil water
availability (e.g., Jones, 1973; Cornic, 2000; see Lawlor & Cornic,
2002 for a review). Stomata play a fundamental role in maintaining
the water balance of the leaf, as water reserves in leaves and stems
are very small when compared to the amount of water transpired,
and thus could be quickly dehydrated in the absence of fast
mechanisms, such as stomatal closure, to limit water loss (Slatyer,
1967). The effect of such stomatal closure is most commonly
observed in the mid-day decline in stomatal conductance due to
decreasing leaf water potential. This is suggested to limit
photosynthetic activity through reducing Ci. Such short-term
responses are, in theory, essential to conserving the plant hydraulic
balance.
There is evidence that water stress impairs mesophyll
metabolism (Chaves, 1991; Lawlor & Cornic, 2002; Flexas et al.,
2008). This has been linked to the hardening of cell walls and the
increase in cell wall lignification in response to hydraulic signals
(Escudero et al., 1992; Sobrado, 1992; Chazen and Neumann, 1994;
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
G Model
AGMET-4203; No of Pages 11
T. Keenan et al. / Agricultural and Forest Meteorology xxx (2010) xxx–xxx
Fig. 3. Water stressed simulated and FLUXNET derived responses of daily canopy
water use efficiency (WUE, mmol mmol1) to changes in soil water content at the
Puechabon forest in 2002. Simulations use the coupled Farquhar BB-type model, on
a Cc basis, embedded in the GOTILWA+ forest model (Keenan et al., 2008, 2009).
Results from three simulations are presented, applying independently either: direct
limitations to photosynthesis during water stress (Vcmax/Jmax Restrictions),
stomatal limitations to photosynthesis (gs Restrictions), or mesophyll
conductance limitations to photosynthesis (gm Restrictions). Mesophyll diffusion
conductance (gm) was set at 0.1 mol m2 s1. Figure insets represent linear
regressions between the FLUXNET estimated and the simulated WUE (BL: r2 = 0.25;
SCL: r2 = 0.06; MCL: r2 = 0.25 (n = 77)).
Chazen et al., 1995; Henry et al., 2000), but could also be related to
modifications in the permeability of membranes on the diffusion
pathway from the intercellular spaces to the sites of carboxylation
(Miyazawa et al., 2008). Strong responses have been reported in
long term drought cycles of varying length and severity, with the
mesophyll response becoming progressively more important with
increasing water stress (e.g., Flexas et al., 2002; Warren & Adams,
2004; Monti et al., 2006; Galmés et al., 2007; Peeva & Cornic, 2009).
Any changes in mesophyll conductance during periods of low soil
water availability could potentially play an important role in
controlling photosynthetic responses to water stress (Jones, 1973;
Flexas et al., 2008). Unfortunately, to date there are no measurements of mesophyll conductance available at the Puechabon site.
More measurement campaigns are badly needed in order to verify
the results presented in this study.
We have shown that the inclusion of mesophyll conductance
could bridge the gap between our current understanding gained
from field and model experiments (e.g., Reichstein et al., 2002; Xu
7
& Baldocchi, 2003; Keenan et al., 2009, 2010), and our functional
understanding of leaf responses to water stress. The hypothesis
that biochemical limitations are sufficient to accurately model CO2
and water fluxes (without any conductance limitations) has been
confirmed (as in Reichstein et al., 2002; Keenan et al., 2009), and it
has been shown that stomatal conductance limitations alone
inevitably overestimate water use efficiency, and therefore, can
effectively simulate water fluxes during water stressed periods but
overestimate CO2 fluxes. Stomatal conductance limitations become effective at modelling CO2 and water fluxes only when
combined with mesophyll conductance limitations, and vice versa,
suggesting a close relation between the two (Flexas et al., 2008),
and supporting previous suggestions of a joint role in regulating
photosynthesis during periods of water stress (Grassi & Magnani,
2005).
Finite mesophyll conductance affects estimates of the maximum carboxylation velocity, Vcmax, and their interpretation. Most
published estimates of Vcmax, and its responses to soil water stress,
will therefore underestimate the true Vcmax by not considering the
draw-down from Ci to Cc, and may potentially assign declines in
assimilation rates due to changes in gm during water stress to
declining photosynthetic potential. To the knowledge of the
authors no published study, either in the field or model based,
which reported strong declines in photosynthetic potential during
drought periods, has taken into account the possible effects of a soil
water stress responsive gm. This does not suggest the exclusion of
the possibility of biochemical limitations under stronger water
stresses. Metabolic adjustments can take many forms, and may
include the reduction of enzymes necessary for RuBP regeneration
and activity (Maroco et al., 2002), reduced nitrate reductase
activity (as an indicator of nitrate utilisation) (Smirnoff and
Stewart, 1985), and the reduction of sucrose phosphate synthase
(Vassey & Sharkey, 1989; Vassey et al., 2006). More field campaigns
in ecosystems which are subject to seasonal cycles of water
stressed periods will be necessary to improve our understand of
the relative roles of each limitation.
The representation of CO2 flux responses to drought often varies
depending on the model applied, as it is a function of soil hydrology
(with different approaches: single bucket soil module, two layer or
multi-layer model), soil structure, forest structure and biogeochemistry assumptions. For example, the sensitivity to drought has
been shown to be higher in models with a two layer soil hydrology
model, and differences in soil structure and hydrology lead to
differences in evapotranspiration calculations (Vetter et al., 2008).
It has been assumed in this study that the eco-physiological state
of the forest is well described in the model, as has been validated
through previous applications of the model platform at this site
(Keenan et al., 2008, 2009).
gm strongly varies both among and within species (Ethier &
Livingston, 2004; Flexas et al., 2008; Niinemets et al., 2009a;
Warren, 2008a), and has been shown to be affected by a large range
of environmental and physiological factors (see Flexas et al., 2008
for a full review), and demonstrate both fast (Flexas et al., 2007)
and slow (Fila et al., 2006) responses. It has been demonstrated to
change during leaf development (Miyazawa & Terashima, 2001),
with nutrient availability (Warren, 2004), with available radiation
(Niinemets et al., 2006), leaf temperature (Bernacchi et al., 2002),
salinity (Loreto et al., 2003), ambient CO2 concentrations (Flexas et
al., 2007) and to be related to soil water availability (Flexas et al.,
2002, 2004; Warren, 2004, 2008a; Grassi & Magnani, 2005). This
complicates the inclusion of a process based description of a
dynamically variable and ecophysiological dependent gm in
current photosynthesis models. As yet, it is not clear as to which
factors have the largest effect on gm variability, and there is not
sufficient physiological information to allow for a reliable
estimation of a variable gm in process based models.
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
G Model
AGMET-4203; No of Pages 11
8
T. Keenan et al. / Agricultural and Forest Meteorology xxx (2010) xxx–xxx
Fig. 4. Water stressed simulated (applying combined conductance limitations: CL) and FLUXNET measured responses of canopy daily net assimilation (An, g C m2 day1), and
daily latent heat flux (LHF, W m2) to changes in soil water content at the Puechabon forest during 2002. Simulations use the coupled Farquhar BB-type model, on a Cc basis,
embedded in the GOTILWA+ forest model (Keenan et al., 2008, 2009). Results from three simulations to test CL are presented, applying either: (a) equal limitations to stomatal
conductance and mesophyll conductance during water stress (SCL = MCL), (b) stronger stomatal limitations than mesophyll conductance limitations (SCL > MCL), or (c)
stronger mesophyll conductance limitations than stomatal conductance limitations (MCL = SCL). Non-stressed mesophyll diffusion conductance (gm) was set at
0.1 mol m2 s1. Figure insets represent linear regressions between the measured and predicted variables (a) An r2 = 0.47, LHF r2 = 0.73; (b) An r2 = 0.43, LHF r2 = 0.65; (c) An
r2 = 0.81, LHF r2 = 0.73 (n = 77)).
Few studies have included gm in photosynthesis models. Those
that have, most often assume a fixed value of mesophyll
conductance (e.g., Williams et al., 1996), or varied gm based on
selected factors such as intercepted radiation, average air
temperature, or leaf nitrogen content (e.g., Hoff et al., 2002;
Ohsumi et al., 2007). Recent efforts have focused on reported
correlations between gm and gs (e.g., Ohsumi et al., 2007; Cai et al.,
2008). Such correlations, however, are subject to large variations
(Niinemets & Sack, 2006; Warren & Adams, 2006; Flexas et al.,
2008), and potentially not physiologically justified. Maximum
values of gm are inherently constrained by leaf structure, e. g.
sclerophytic leaves have lower gm, mesophytic leaves have higher
(Terashima et al., 2006; Flexas et al., 2008; Warren, 2008a; Evans
et al., 2009; Niinemets et al., 2009a), which may be an effective
manner by which to include gm in photosynthesis models. Largescale models (e.g., Morales et al., 2005; Jung et al., 2007; Sitch et al.,
2008) in particular, due to their characteristic simplification of
plant functional type groupings, may benefit from such an
approach.
Although there are huge uncertainties regarding the driving
factors responsible for variations in gm we have shown that the
simple inclusion of a water stress responsive gm can help close the
gap between conflicting reports on the role of different limitations
in controlling CO2 and water fluxes from forest canopies during
water stressed periods. The inclusion of gm did not improve our
ability to model in ecosystems subject to seasonal cycles of water
stress, but much of the remaining variability between measured
and modelled CO2 and water fluxes may be explained, as new
information accumulates in the future, through the inclusion of a
dynamically variable gm.
5. Conclusions
Fig. 5. Simulated and FLUXNET responses of canopy daily net assimilation (An,
g C m2 day1), and daily latent heat flux (LHF, W m2) for the five year period from
2001 to 2005 at Puechabon forest using the GOTILWA+ model (Keenan et al., 2008,
2009). Two simulations, differing in their response to soil water stress, are
compared: (1) Soil water stress affects both conductance limitations (CL), with MCL
stronger than SCL (Blue, long dashed line), (2) Soil water stress directly affects Vcmax
and Jmax (BL: Red, short dashed line). Non-stressed mesophyll diffusion conductance
(gm) was set at 0.1 mol m2 s1. Right panel figures represent linear regressions
between the measured and predicted variables (CL (MCL > SCL): An r2 = 0.78, LHF
r2 = 0.72; BL: An r2 = 0.79; LHF r2 = 0.76 (n = 1825)) (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
the article.).
This work was carried out in response to the recent calls for the
inclusion of mesophyll conductance in leaf photosynthesis models
(e.g., Bernacchi et al., 2002; Flexas et al., 2002; Long & Bernacchi,
2003; Ethier & Livingston, 2004; Manter & Kerrigan, 2004; Sharkey
et al., 2007; Keenan et al., 2010; Niinemets et al., 2009b), due to an
increased number of reported findings on the role of mesophyll
conductance in the regulation of photosynthesis. It has allowed for
a model based assessment of previous suggestions that biochemical limitations, stomatal conductance limitations and mesophyll
conductance limitations play some role in the regulation of
Please cite this article in press as: Keenan, T., et al., Soil water stress and coupled photosynthesis–conductance models: Bridging the gap
between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis.
Agric. Forest Meteorol. (2010), doi:10.1016/j.agrformet.2010.01.008
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AGMET-4203; No of Pages 11
T. Keenan et al. / Agricultural and Forest Meteorology xxx (2010) xxx–xxx
photosynthesis (Grassi & Magnani, 2005; Loreto & Centritto, 2008),
depending on the degree of water stress encountered and the
relevant time scales involved. This is the first time that each
limitation has been tested on a canopy scale in an ecophysiological model, and shows that, with (and only with) the
inclusion of mesophyll conductance, diffusive limitations can
explain CO2 and water flux responses to seasonal changes in soil
water availability. This helps in closing the gap between studies
(both model and measurement based) which report dominant
roles of biochemical changes under water stressed conditions and
those which maintain stomatal conductance limitations as the
main actor.
It is expected that the future development of a dynamic model
for mesophyll conductance which incorporates sensitivity to nonwater stress related drivers, and its integration into coupled
photosynthesis–conductance models will improve our ability to
model CO2 and water fluxes from terrestrial ecosystems both in
well watered and water stressed periods.
Acknowledgments
This study was funded through GREENCYCLES, the Marie-Curie
Biogeochemistry and Climate Change Research and Training
Network (MRTN-CT-2004-512464) supported by the European
Commissions Sixth Framework program. Further support from the
CCTAME (Climate Change-Terrestrial Adaptation and Mitigation in
Europe, FP7 212535) project and the Consolider Montes project
(CSD2008-00040) is also acknowledged. The authors would like to
thank Serge Rambal and highly commend all the FLUXNET
investigators whose data has contributed to the work discussed
here.
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