University of Groningen
The water balance of forests under elevated atmospheric CO2
Lankreijer, Henricus Johannes Maria
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1998
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Lankreijer, H. J. M. (1998). The water balance of forests under elevated atmospheric CO2 s.n.
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Chapter 3
Stomatal conductance and photosynthesis as modulated by a changed
atmospheric CO2 concentration
3.1 Introduction
Plants, including trees, mainly transpire through stomata. While CO2 is taken up by diffusion
into the leaf, water vapour is lost at the same time (figure 3.1). A stoma consists of two guard
cells and can be seen as the controlling organ of water movement through the plant: the drop
in water potential between soil, via the plant to the atmosphere is strongest in the process of
transpiration, that is transformation from liquid water to water vapour, between the leaf and
atmosphere (Avissar, 1993).
Cuticle
Upper
epidermis
Chloroplasts
Palisade
mesophyll
cells
100 Fm
Spongy
mesophyll
cells
Guard cell
Stomatal pore
CO
2
Lower
epidermis
Intercellular
air space
H2O
Figure 3.1. Scheme of the anatomy of a leaf with stomatal guard cells and concomitant
CO2 and H2O fluxes (Nobel, 1970).
Due to the large roughness of forests and consequently small aerodynamic resistance,
evapotranspiration of forests is closely coupled to atmospheric conditions (Jarvis and
McNaughton, 1986). The dependence of the transpiration of forests on the stomatal
conductance (gs) is much stronger than that of low vegetations like grasslands. Simulation of
forest evapotranspiration therefore depends on an accurate estimation of the stomatal
conductance (Beven, 1979). The close coupling between forest canopy and atmospheric
conditions results in a high sensitivity of the forest hydrology to a change in stomatal
21
'Climate'
( T, D, u, P, Q )
I
[CO2 ]
A
D
GC
D
Assimilation
Transpiration
gS
Biomass (LAI)
Leaf/canopy
Figure 3.2. Direct (D) and indirect (I) effects of CO2 and “climate” on transpiration.
Direct through assimilation and gs, stomatal conductance, and Gc, bulk or
canopy conductance.
conductance (see chapter 2).
An increase in atmospheric CO2 will affect the vegetation, in particular the stomatal
conductance. In figure 3.2 the direct and indirect effects of a change in atmospheric CO2 on
plants is schematically described. The direct effect focuses on the assimilation process and on
stomatal conductance. In particular plants with a C3 photosynthesis pathway show a higher
productivity of biomass under elevated CO2 concentrations (Strain and Cure, 1985).
The indirect effect of a change in CO2-concentration is through the effect on climatic
conditions. Changes in temperature, number of freezing days, global radiation, precipitation,
and air humidity willl affect the physiology of plants (Mousseau and Saugier, 1992). Not only
the change in average values, but also the change in the frequency of extremes should be
considered. An increase in temperature will increase respiration and possibly reduce the effect
of increased assimilation, due to the elevated CO2 concentration.
A change in climatic conditions, in turn, can have a direct effect on the
evapotranspiration by a change of the vapour pressure deficit of the air, and the degree of
cloudiness.
22
A climate change due to a change in CO2 concentration will affect physiology, phenology,
morphology and distribution of trees. This chapter summarizes a literature study on the effects
of changes in environmental variables, including the ambient CO2 concentration (Ca ), on tree
functioning. The relationships between stomatal conductance and other factors in tree
physiology, and environmental variables are also described on the basis of literature.
In section 3.2 a short survey of stomatal functioning is given. Stomatal conductance is
related to photosynthesis and in section 3.3 the process of photosynthesis is shortly described.
Some simulation models of stomatal conductance are summarized in section 3.4. Reviews of
elevated CO2 experiments on woody species and a descriptions of possible effects of CO
on
2
tree physiology are given by Eamus and Jarvis (1989), Mousseau and Saugier (1992),
Ceulemans and Mousseau (1994) and Idso and Idso (1994). On the basis of these reviews, an
overview of relevant effects of the increase of CO2 on tree physiology is given in section 3.5.
In section 3.6 conclusions are given.
3.2 Stomatal conductance
Stomatal conductance (gs) shows strong relations between stomatal opening, environmental
parameters and photosynthesis. Stomatal functioning is related to photosynthetic active
radiation (PAR), temperature, leaf water potential, air humidity and carbon dioxide
concentration of the air. The stomatal conductance is also a function of the age of the leaf and
its morphological adaptation to its micro environment during growth (Field, 1987; Baldocchi,
1991).
The variety of parameters, found to influence the stomatal opening, has resulted in
several models of stomatal conductance. The models can be divided into two groups:
- Regression models, which describe the behaviour of stomata by a fitted function on
measured stomatal conductance versus environmental parameters. The fitted functions are
based on plant physiological relationships.
- Physiological models, which describe the stomatal conductance in relation to the assimilation
process, linking stomata behaviour directly and indirectly via photosynthesis to the
environment.
Environmental parameters, which are used in simulation models, are air humidity
(relative, absolute or humidity deficit), air and leaf temperature, soil temperature, PAR, solar
radiation, leaf water potential, soil water content, ambient CO2 concentration and production
of ABA. Overviews of modelling parameters are given by Farquhar and Sharkey (1982), Hall
(1982) and Lynn and Carlson (1990) .
23
Table 3.1. Comparison of regression models for stomatal conductance.
Model/Author
Used variables in function
Type
Scale
Jarvis (1976)
f(QPAR,Tl,D,Ca,Ql,)
Mult
Leaf
Federer (1979)
f(QS,D,Ta,Ql,)
Add
Leaf
Lohammar et al,
(1980)
f(QS,D)
Mult
Canopy
Kaufmann (1982)
f(QPAR,D)
Both
Leaf
Avissar et al. (1985)
f(QS,D,Tl,Q)
Mult
Leaf
Stewart (1988)
f(QS,Ta,D,2D,LAI)
Mult
Canopy
Regression models, or deterministic models, are mostly developed from a micrometeorological point of view and they relate the stomatal behaviour to one or more
environmental variables. The response is described as a combination of functions, based on
physiological knowledge, and the parameters are found by least square regression analysis on
measurements. These models can be additive, multiplicative or a combination of both type.
The diversity of models shows the incomplete knowledge of the relations between stomatal
conductance and environmental parameters and the function parameters do not really
represent plant physiological parameters. For example, gs,max in the Jarvis model (1976) is not
equal to the actual possible maximum stomatal conductance: with increasing number of
parameters in the model description, the value of gs,max will also increase. Examples of these
models are given in table 3.1. They differ in the way the functions are combined and in the
number of parameters. Except for the model of Jarvis (1976), atmospheric CO2 concentration
has not been taken into account. An advantage of the regression models is the simple structure
and the relatively small number of parameters. In general the models give good results, under
the condition that the empirical parameters values are only valid for the fitted data set. To fit
the model correctly, measurements within a large range in the environmental parameters are
needed. The empirical values are not directly transferable to other situations, like other forest
sites or a climate with a different CO2 concentration. Gash et al. (1989) and Ogink-Hendriks
(1995), using Thetford, Les Landes and Ede data in combination with the Jarvis-Stewart
model (Stewart, 1988), showed, that transfer of fitted parameters to another data set resulted
in a difference of 20-35 % between measured and simulated transpiration. Some empirically
found values of the model parameters present unknown or not-simulated physiological
24
1.2
0.8
0.4
0
0.4
0.8
1.2
1.6
Stomatal conductance, gs , at 330 µmol/ mol C a
Figure 3.3. Stomatal conductance, gs (mol m-2s-1) at 330 ppm CO2 versus gs, at 660 ppm
for several C3 (o) and C4 (ª) species. (Morison, 1987).
processes: they depend on plant specific characteristics and they can change under different
climatic (e.g. CO2) conditions. Also, the assumption, that the various variables, which
influence the stomatal conductance are independent, is unlikely to be true (Friend, 1995).
The indirect effect of a CO2 change may be simulated by deterministic models, assuming
that the empirical parameters are independent of climate. The model of Stewart (1988) was
used in the pilot study, described in chapter 2. The direct effect of CO2 was taken into account
by lowering the maximum stomatal conductance with a prefixed value, using the data in figure
3.3 As a result a (final) equal reaction of many species to a change in ambient CO2 was
observed. However, other ranges of reactions to a change of CO2 concentration are known as
well. Specific modulation of the Gs,max to estimate the effect of a change in CO
, excludes
2
possible other effects of relations between Gs,max and environmental parameters.
The physiological models take into account the relationship between stomatal behaviour and
photosynthesis. Several authors emphasize the importance of combining simulations of
stomatal conductance and photosynthesis (Tenhunen et al., 1990; Collatz et al., 1991;
Leuning, 1994). The last simulation is more realistic and has the advantage that it gives the
possibility to incorporate the models in growth and ecosystem models and to relate the
25
empirical parameters to plant specific characteristics. Therefore, the physiological type of
model is better suited to sensitivity analysis and effect-related studies.
Physiological models of photosynthesis consist of a 'demand function' and a 'supply
function'. The 'demand function' is the description of the biochemical processes of CO2
assimilation by leaves. The 'supply function' describes the diffusion of CO2 to the internal cell,
which largely depends on stomatal conductance. The models differ in the way they describe
the supply function in combination with the assimilation rate A. The 'demand function' or
assimilation of CO2 of C3 plants, is described by a separate model. Examples are the model by
Farquhar, Von Caemmerer and Berry (1980) and the model by Goudriaan (1986). Examples
of stomatal models are given by Ball et al. (1987), Friend (1991), Aphalo and Jarvis (1993)
and Leuning (1990, 1994). Most models are developed to simulate the C3 plant carbon
assimilation. Models for C4 or Crassulacean Acid Metabolism (CAM) assimilation are scarce.
Semi-mechanistic models are also available (Farquhar and Wong, 1984; Johnson et al., 1991,
Tardieu and Davies, 1993). However, they are not yet fully developed. Given the limited
knowledge of stomatal processes, they should be used with caution (Friend, 1995).
Photosynthesis depends on the opening of the stomata (via the supply of CO2), but the
stomata also react to photosynthesis through a feedback link: they open at low internal CO2
(Farquhar, 1978). Besides the interdependency of photosynthesis and stomatal conductance,
both processes show independent reactions to the environment (Jarvis and Mansfield, 1981).
The behaviour of the guard cells is controlled by environmental (abiotic) parameters and plant
internal (biotic) processes. The insight into the processes, determining the guard cell
functioning, is until now largely phenomenological. The process of opening of the guard cells
is determined by the turgor pressure of guard cells and the pressure difference between the
guard cells and the adjacent epidermal cells. Turgor pressure in the guard cells is increased by
uptake of water, when the intracellular osmotic pressure increases. The latter is caused by the
accumulation of ions (K+, Cl- ) into the guard cell and by synthesis of malate ions (the extra
proton is extruded again). Energy from light absorption may be used, as well as energy from
respiration for accumulation of ions and synthesis of malate. How the guard cells sense the
signals from their environment, is still unclear. An overview of the factors and processes,
which regulate guard cells turgor, and thus stomatal opening, is given by Kearns and Assmann
(1993). Guard cells respond to blue and red light, CO2 concentration, air humidity and
phytohormones, produced by the plant. Blue as well as red light open the stomata in two
separate light reactions. Red light is absorbed by guard cell chlorophyll, but the identity of the
blue-light receptor is yet unknown. An example of plant internal regulation by phytohormones
26
ADP + Pi + NADP
CO2
ATP + NADPH
photorespiration
Oxygenation
O2
Rubisco
RuBP
Calvin cycle
CO2
Carboxylation
Triose-phosphate
Pi
Sucrose, starch
ADP + Pi + NADP
ATP + NADPH
Figure 3.4. Schematic diagram of the biochemical reactions in the dark reaction of the
photosynthesis (from Ammerlaan et al., 1993)
of the stomatal opening, is the production of abscisic acid (ABA) under water limited
conditions, which closes the stomata (Raschke, 1987). Depending on the plant species, auxin
type and concentration, auxins may open or close stomata (Davies and Mansfield, 1987). Also,
hormones as gibberellines and cytokinins influence the stomatal opening (Incoll and Jewer,
1987).
Stomata sense the internal CO2-concentration (Mott, 1988), Ci , in stead of the ambient
concentration, Ca. Kearns and Assmann (1993) posed the theory that high aC should lead to
open stomata, since CO2 is the substrate for both malate and photosynthetic sugar production.
However, the opposite reaction is found. Apparently an ambient CO2 increase contributes to
two opposing effects, which result in a closure of stomata.
Stomata respond to the rate of transpiration E, rather than to air humidity deficit D or
relative humidity (Mott and Parkhurst, 1991). The response of stomata to E was used by
Monteith (1995a), who re-analysed 52 sets of published measurements at canopy scale of
humidity responses on 16 species in terms of the relation between stomatal conductance and
transpiration. Scaling gs, a maximum canopy conductance,
g
m
was obtained by linear
extrapolation, and the same procedure by scaling E gave Em, the maximum transpiration rate.
Monteith found the ratio of gm/Em to be linear and it only varied with temperature and CO
2 27
concentration (see also Dewar, 1995).
3.3 The photosynthetic process
In photosynthesis the energy from absorbed light, is used to produce organic substrate through
reductional assimilation of CO2. The assimilation of CO2 is summarized by:
nCO2% 2nH2O 6 nO2% [CH2O]n % nH2O
(3.1)
The complete reaction is denoted as the Calvin cycle or reductive pentosephosphate cycle. The
term C3 -plant is derived from this assimilation process, because the initial product is a
substrate with 3 C-atoms, 3-phosphoglyceric acid (3PGA). A simplified scheme of the Calvin
cycle (figure 3.4) shows that ribulose-1,5-diphosphate (RuBP, a pentose sugar) reacts with
CO2 and water; it is fully regenerated and production of sugars is accomplished. The fixation
of RuBP with CO2 is catalysed by the enzyme ribulose-1,5-diphosphate carboxylase (Rubisco).
Photosynthesis can be divided into light and dark reactions. Light reactions occurs only
when light is absorbed by leaf pigments. Dark reactions are less light dependent. The
assimilation of CO2 in equation 3.1 is a so-called dark-reaction and takes place when energy,
adenosine
triphosphate
(ATP),
and
reducing
capacity,
nicotinamide-adenine-
dinucleotidephosphate (NADPH), are both present. ATP and NADPH are formed in the light
reaction, in which green plants use PAR with wavelengths between 400 and 700 nm.
The amount of activated Rubisco determines the maximum velocity of assimilation
(Vc,max ). The assimilation rate A, as limited by Rubisco activity, is denoted
as A . The
c
assimilation rate A depends also on the regeneration of Rubilose-1,5-biphosphate (RuBP), the
acceptor of CO2, and the assimilation rate limited by RuBP is denoted as Ar . The regeneration
of RuBP depends on the supply of light energy through NADPH and ATP.
In the model of Farquhar and co-workers the ‘most’ limiting process of Ac or Ar is taken,
but Collatz et al. (1991), and Friend (1991, 1995), also consider the possibility a combination
of both limiting processes (co-limitation). Putting this concept of co-limitation in a simulation
model, using the method of Friend (1991), only resulted in a minor difference with to the
‘most’ limiting method (figure 3.5). In simulation models, the influence of the synthesis of
sucrose and starch on the assimilation rate is usually neglected.
In photosynthesis, Rubisco, the catalysing enzyme, may react with CO2 (carboxylation)
28
50
40
30
20
10
Ac
0
Ar
A
Co-limitation
-10
-20
0
100
200
300
400
500
600
700
Internal CO2 (ppm)
Figure 3.5. Relation between assimilation A (Ac, Ar and co-limited) vs internal CO2
concentration, Ci simulated by the applied models. For further explanation of
the legend see the text.
as well as O2 (oxygenation). The partition between carboxylation and oxygenation depends on
the partial pressures of CO2 and O2 in the leaf and on temperature. The pressure of internal
CO2 and O2 is related to the stomatal conductance. When Rubisco reacts with
O 2, CO is
2
produced and RuBP will also be regenerated, a process known as photorespiration. CO2 is
also produced by cell mitochondrial activity, named dark respiration (Rd).
3.4 Effects of an increase of atmospheric CO2 on tree functioning
A climate change may directly or indirectly affect several parameters of forest hydrology.
Trees may be even more responsive to a CO2 increase than herbs. Besides, the capacity of
trees to absorb CO2 is a serious option for reduction of the atmospheric CO2 concentration by
forest plantation as an extra sink for atmospheric CO2. Compared to agricultural and
horticultural crop species, research on the physiology of trees (or woody species in general) in
relation to the effects of CO2
is underrepresented, notwithstanding the fact that trees
represent the largest part of the standing biomass and that they are important in the global
29
carbon balance: research on effects of atmospheric CO2 on trees is of paramount importance.
The difficulty to investigate the effect of a climatic change on trees is partly due to the
large size of a tree and and its longevity. Also, the complexity and acclimatization of trees
makes it difficult to perform short-term experiments (Ceulemans and Mousseau, 1994), which
reach conclusions valid for the long term. Almost all experiments are done on small trees,
seedlings or even single branches and leaves of a tree. A single exception was the FACE (free
air CO2 enrichment) experiment in a natural forest stand in North Carolina, USA, in which
trees were exposed to a high CO2-concentration in a forest environment.
The response of small and young trees to elevated CO2 levels, may strongly differ from
that of fully grown trees and trees in forest ecosystems. Differences between young trees and
mature trees are found in (i) stomatal conductance, (ii) photosynthesis and (iii) water use
efficiency, WUE (Cregg et al., 1989; Donovan and Ehleringer, 1991), all factors affecting the
water balance of forests. It is unclear, whether the observed responses in short-term
experiments are applicable on the long-term, and it is hazardous to apply the results of studies
on young trees to full grown forests trees: in several studies on young trees unacclimated trees
and leaves were used, and only short periods of measurements were made (Eamus and Jarvis,
1989). Besides, not all tree species show the same sensitivity to an increase in CO2: the
stomatal conductance of conifers in northern and temperate forests notably show little
sensitivity to CO2 (Eamus and Jarvis, 1989).
Elevated CO2-concentration increases the assimilation rate of trees in short-term
experiments (Eamus and Jarvis, 1989). The higher CO2/O2 ratio in the air results in lower
photorespiration, but increasing temperature might increases the dark respiration, due to
increased metabolic activity. The increase in the dark respiration can be larger than the
increase in assimilation.
At elevated atmospheric CO2 concentration, young trees generally grow faster, due to an
increased carbon supply by photosynthesis (Eamus and Jarvis, 1989). The increase in biomass
averaged 65 % for deciduous trees, and 38 % for coniferous trees. Photosynthesis similary
increased: 61 % in broad leaf trees and 40 % for conifers (Ceulemans and Mousseau, 1994).
The above values are averages from experiments, conducted on young trees under different
conditions.
The increase in biomass of trees exposed to elevated atmospheric CO2 concentration
resulted in an increase in the root/shoot ratio for most species; the CO2 enrichment induced C
allocation to the root and extra root growth. The allocation of carbon to shoot and root
depends on the nutrient and water availability: a high nutrient availability diminishes a change
in root/shoot ratio. With limited nutrients the increase of biomass of trees exposed to high CO2
will be concentrated in the roots; it forms a mechanism, that ensures an improved acquisition
30
of mineral nutrients in nutrient poor forest soils (Ceulemans and Mousseau, 1994). The
increase in the amount of roots may possibly lead to increased water uptake and a larger
availability of soil water to the tree.
According to Idso and Idso (1994), a doubling of atmospheric CO2 will increase the dry
weight of plants by 24 %, when water is not limiting, and by 58 % when water supply is
limiting. The average increase in dry weight, when nutrients are limiting, will still amount to 48
%.
In experiments with trees exposed to elevated CO2, the leaf area was found to increase
by leaf size and number of leaves. Also, the leaf grew thicker, e.g. an extra cell layer was
added (Eamus and Jarvis, 1989). The largest increase in LAI in trees exposed to high CO2 was
found in high nutrient experiments.
By comparison of independent measurements of maximum stomatal conductance (gs,max),
bulk surface conductance (Gs,max), bulk canopy conductance (G
c ) and LAI, Kelliher et al.
(1993, 1995) showed for a broad range vegetations, that the maximum surface conductance
was independent of changes in LAI. Note, that in their study Gs was the surface conductance,
derived from evaporation measurements, including soil evaporation, and Gc was derived from
evaporation of the canopy alone. The latter means, that an increase in LAI probably could not
lead to an increase in transpiration. When LAI exceeded 4, the ratio Gs,max/gs,max was constant
with increasing LAI. Maximum canopy conductance Gc,max, linearly increased with increasing
LAI, but it became constant at LAI values above 4, because of light limitation of leaves,
deeper in the canopy. At high LAI values Gs,max corresponded with Gc,max , and soil evaporation
tended to be zero. At low LAI, < 1, the decrease in Gc was compensated by an increase in soil
evaporation. At LAI less then 1, Gs,max may even decrease with increasing LAI.
Kelliher et al. (1993, 1995) also found a conservative and linear relation between Gs,max
and gs,max at high LAI, in such a way that Gs,max equated 3@gs,max for a broad range of vegetation
types. The value of 3 actually varied between 2.2 and 3.3, but it was strikingly conservative.
The comparisons were only valid in terms of maximum rates, when water was not limiting.
Schulze et al. (1994) observed a linear increase of gs,max with increasing N-content of the
leaves, which is important for forest hydrology. A change in nitrogen content of the leaves and
the partition of nitrogen in the leaves could lead to a change in the photosynthetic capacity of
the leaves, which in turn could lead to a change in the stomatal conductance and transpiration.
The stomatal conductance decreased with rising atmospheric CO2 concentrations,
because the opening of the stomata became smaller (Paoletti and Gellini, 1993), and the
number of pores decreased (Woodward, 1987; Woodward and Bazzaz, 1988; Kürschner,
1996). A decline of about 40 % in stomatal density was observed in leaves of herbarium
specimens of tree species over the last 200 years. A reduction of 40 % of the stomatal opening
31
was found in several experiments. The average reduction in transpiration, derived from
literature by Kimball (1983), was estimated to be 34 %. However, only 8 % of the data were
from tree species (Ceulemans and Mousseau, 1994).
Under high atmospheric CO2-concentration a long-term acclimation process, characterized by
down-regulation of the Rubisco photosynthetic activity and a lowered production of
chlorophyll, is often found. Acclimation of photosynthesis is clear from the study of the A
versus Ci curves: the initial slope of the curve relates to the Rubisco activity, and a reduction
of the slope indicates a reduction in the amount or the activity of Rubisco, as observed in
many species at increasing Ca (Ceulemans and Mousseau, 1994).
The increase in growth of a tree strongly depends on the possibility of the tree to use the
surplus of carbohydrates for growth, as available by the high CO2 increased photosynthesis.
When no sinks for growth are available, down-regulation of the photosynthetic Rubisco takes
place. E.g, the response of the assimilation rate of acclimated trees was 50 % lower than that
of unacclimated trees, due to the lack of active sinks for the assimilation products (Cure and
Acock, 1986). The development of a tree under elevated CO2 is defined by the genotype of the
tree and its ability to develop new sinks for the extra carbon (Ceulemans and Mousseau,
1994): shade-intolerant species will use the extra carbon to grow faster and taller in the
canopy, while shade tolerant species will invest more carbon in the roots. A large turnover of
fine root may also serve as a sink for carbon, resulting in a flow of carbon from the
atmosphere to the soil. Trees may also produce more phenols as a carbon sink. Being effective
as greenhouse gases, these phenols in turn may contribute to an increased greenhouse effect.
A change in temperature will change the timing of leaf unfolding (bud break) of decidious, and
needle flush of coniferous trees. According to a model study by Kramer (1994), leaf unfolding
and needle flush is expected to happen earlier at elevated atmospheric CO2 and increased
temperature. The response of decidious tree is a little stronger (3-5 days earlier per EC
temperature change), than that of coniferous trees (1-2 days). Furthermore, the probability of
spring frost damage turns out not to increase. The simulation was performed on 11 species for
the Netherlands and Germany. The number of days of earlier bud break and needle flush
strongly depended on the model type used, the tree species and also on the adaptation of the
tree to local climate conditions. For British trees a reduced probability of frost damage was
found as well, whereas for Finnish trees an increase in probability of frost damage was found.
On the long term, climate change may lead to changes in species composition of the forest.
The expected change in climate is relatively fast, compared with the succession rate of tree
32
species in forests and many tree species will not be able to migrate to a desirable ecological
site, which could result in a large scale dieback of forests (Gates, 1990).
In this study a change in forest composition and a disappearance of forests has not been
taken into account. However, in studies on a large time scale the possible changes in regional
hydrology and species composition, and transition to other vegetation types, with changes in
e.g. albedo, should be born in mind.
3.5 Simulation models of stomatal conductance
3.5.1 Regression models
Jarvis and Stewart model
In this model stomatal conductanc is simulated by the use of a constant maximum value for the
stomatal conductance. The conductance is limited by functions of environmental variables,
with relative values between 0 and 1. The functions of these variables are found by least
square regression of measurements.
Originally, Jarvis (1976) simulated the stomatal conductance as a constant maximum
stomatal conductance (gs,max) with limiting functions for photon-flux density
(Q ), leaf
p
temperature (TL), vapour pressure difference (D), leaf water potential (Q
) and the ambient
l
CO2 concentration (Ca):
gsw' gs,max @ f(Qp) @ f(T L) @ f(D) @ f(Rl) @ f(Ca)
(3.2)
with
f(Qp) ' (
f(T L ) '
Qp
(aS% Qp)
) / (
1000
)
(1000% aS)
(T L& TM)@(TH& TL )
a T1
(a T2& TM)@(TH& aT2)
aT1'(TH&a T2)/(aT2&TM)
(3.3)
a T1
(3.4)
(3.5)
33
* 1& aD1@D for D < a D2
*1& aD3@aD2 for D > a D2
f(D) '
(3.6)
f(Ql)'1&Exp(&aQMQ)
(3.7)
for Ca <100 (cm 3/m 3)
* 1
f(Ca) '* 1 & accC a for 100 < Ca<1000
* a
for Ca > 1000
c
(3.8)
where TM = minimum temperature (0oC), TH = maximum temperature (40o C) (Stewart, 1988)
and ax= empirical constant.
Stewart (1988) adapted the model to simulate the forest hydrology, and replaced
stomatal conductance by surface conductance. The influence of ambient CO2 concentration on
the surface conductance was not taken into account. Furthermore, he replaced the leaf water
potential function by a function for soil moisture deficit, the air temperature replaced the leaf
temperature, and he extended the model with a function for the leaf area index.
According to the model by Stewart, Gs is calculated from a maximum surface
conductance and fitted relations of solar radiation (Qs), leaf area index (LAI), air temperature
(TA), air humidity deficit (D) and soil moisture deficit (2D), given by
Gs ' Gs,max @ f(LAI) @ f(Qs) @ f(D) @ f(T A ) @ f(2D)
(3.9)
The functions for LAI and soil moisture, with values between 0 and 1, are given by
f(LAI) ' LAI/LAIMAX
(3.10)
f(2D) ' 1& Exp(a2@(2D& 2MAX))
(3.11)
where LAI = leaf area index, LAImax = maximum leaf area index, 2D and 2max are soil moisture
deficit and maximum soil moisture deficit respectively. All ax values and gs,max are constants,
which are obtained by optimization. Except for LAI, the range of the functions in the model of
Stewart is given in figure 3.6 A-D.
The Gs,max, calculated in this model, is not the same as the observed Gs,max in the field: the
value in this model tends to be higher, as fitted from measured values of gs. According to
34
A
Solar radiation
1
0,8
0,6
0,4
0,2
0
0
200
400
600
800 1000
-2
TA (EC)
Qs (W m )
C
Air humidity deficit
1
Jarvis
Ogink-Hendriks
0,8
D
1
0,8
0,6
0,6
0,4
0,4
0,2
0,2
0
0
0
2
4
6
8
-1
D (g kg )
10 12 14 16
Soil moisture deficit
Stewart
Dolman
0
20 40 60 80 100 120 140 160
2 (mm)
Figure 3.6. Functions of the Jarvis-Stewart model. A, solar radiation vs. f(Qs), B, air
temperature vs. f(TA), C, air humidity deficit vs. f(D), with the original function
by Jarvis and the adpated function by Ogink-Hendriks and D, soil moisture
deficit vs. f(2).
Kelliher et al. (1995) the value of Gs,max is about 25 % higher than the observed Gs,max.
Stewart (1988) implemented the Jarvis-Stewart model on Thetford forest, a coniferous
forest in England. The model has also been successfully applied in other studies on coniferous
(Gash et al., 1989), deciduous (Dolman et al., 1988; Ogink-Hendriks, 1995) and mixed forest
sites (Hutjes, 1996). The parameters of the model were derived from measurements of
evaporation. In those studies the functions for air humidity and soil moisture deficit were
mostly adapted to give better results. The adapted humidity function by Ogink-Hendriks
35
(1995), in figure 3.6C, is given by:
f(D) ' aD4% (1& aD4)@Exp(D@Ln(a D5))
(3.12)
Dolman et al. (1988) and Nonhebel (1987) applied a specific version of the model to simulate
the forest transpiration, using a simple soil moisture function (figure 3.6D):
f(2)'
(2a& 2)
(2a& 2max)
(3.13)
3.5.2 Physiologically based models
PGEN-model
The PGEN-model was developed by Friend (1991). It is based on the biochemical model for
photosynthesis of C3-plants by Farquhar et al. (1980), in combination with physical processes
at the single leaf scale. The first version of the model has also been used on a canopy scale in a
study on forest dynamics (Friend et al., 1993) and on a regional scale, to analyze the effects of
changing atmospheric CO2 (Friend and Cox, 1995). The PGEN model follows Cowan (1977),
who assumed that stomatal opening depends on an optimum between uptake of CO2 and loss
of water. The stomata control the diffusion process in such a way that the uptake of CO2 is
maximised and at the same time the loss of water is minimised. Following this procedure, the
optimal stomatal opening and closure are such that the ratio of the partial differentials in
transpiration (E) versus stomatal conductance (gs) and in assimilation (A) versus
g (=
s
(*E/*gs)/(*A/*gs)) is constant (Schulze and Hall, 1982). Although this ratio has not always
been found to be constant, it was applied succesfully used in several simulations (Cowan,
1982; Jacobs, 1994).
The model uses PAR, air temperature, changing ambient CO2 concentration and air
humidity deficit as input variables. The stomatal conductance at maximum leaf metabolism was
found with a numerical search routine. The model calculated the flux of CO2 as a function of
Ac , Ar , and the stomatal conductance. The photosynthetic activity is found for Astomatal = Ac and
Astomatal = Ar . The model assumed co-limitation of the photosynthetic rate through Rubisco and
the regeneration of RuBP, according to Collatz et al. (1991). The transpiration was indirectly
calculated, using simulated gs values. The influence of the nitrogen content of the leaf was
taken into account via its effect on the amount of active Rubisco.
36
In a sophisticated way, the model connects the stomatal conductance with
photosynthesis and environmental variables. Photosynthesis and stomatal conductance are
closely related and they influence each other via the internal CO2 concentration, which is
related to external CO2, and leaf water potential. In the first version of the model, the water
potential of the leaf had a direct effect on photosynthesis and on mitochondrial respiration.
The assumption of a direct influence of leaf water potential on photosynthesis was
questionable and it was therefore removed in a second version of the model (Friend, 1995). In
the second version of PGEN the leaf water potential still limits the dry matter production and
thus plant growth, but only below a critical value.
The model, according to Ball, Berry and Woodrow
In the model for stomatal conductance of Ball, Berry and Woodrow (1987), gs is directly
dependent (i) on the CO2 concentration at the leaf surface (Cs ), (ii) on the relative humidity at
the leaf surface (hs), and (iii) indirectly dependent on temperature and radiation, via
photosynthesis. The stomatal conductance model, according to Ball et al., is given by:
gsc' g0%
a Ahs
Cs
(3.14)
The model of Ball et al. (1987) has been applied in several studies (Tenhunen et al., 1990;
Collatz et al.,1991; Lloyd, 1991; Hatton et al., 1992). The model was slightly adapted by
Leuning (1990), in order to correct the model for the effect of the CO2 compensation point
('), the CO2 concentration where CO2 uptake equals CO2 production:
g sc' g0%
a Ah s
C s& '
(3.15)
By using relative humidity, gsc was also dependent on temperature. The use of relative
humidity instead of humidity deficit is therefore questionable (Aphalo and Jarvis, 1993; Lloyd,
1991; Leuning, 1995).
In 1995 Leuning adapted the model by replacement of hS by the humidity relation of
Lohammar et al. (1980). Equation 3.15 changes into:
g sc' g0%
a A f(D)
(C s& ')
(3.16)
with
37
f(D)'
1
(1% D/Ds,0)
(3.17)
Simultaneous solution of the functions of photosynthesis and stomatal conductance gives the
minimum value of Ci. This value was used to calculate A and gs. In this model A is the
minimum value of Ac and Ar without co-limitation, and gs is directly dependent on sC and air
humidity.
'Aphalo and Jarvis' model
According to Aphalo and Jarvis (1993) the model of Ball et al. (1987) is a useful empirical
model of the relation between A and gsw, but they nevertheless disagree on the use of the
relative air humidity. In their model the same realistic treatment of responses of gsw to
radiation and 'other variables', which do not affect the relation between A and gsw, is used. In
the last model, the relation between A and gsw depends on functions of humidity deficit (D) and
leaf temperature (TL), instead of relative air humidity and air temperature:
g sw'
A
[k % f (D)% f2(T L)% f3(D,TL)]
Cs 0 1
(3.18)
with
f1' k1D
f2' k2TL
f3' k3DTL
The function parameters are found by least square regression.
Including a more realistic treatment of TL and D, the model of Aphalo and Jarvis (1993)
can be used for a wide range of tree species. However, according to the authors a more
complex model is needed to describe the stomatal function.
38
'Leuning' model
The model by Leuning (1990, 1995) equation 3.16 presumes an adaptation of the TL and D
relation in Ball's model. An interpretation of the processes, determining the guard cell function
(. stomatal conductance) in relation to Leuning's model and the observed stomatal responses,
is described by Dewar (1995). By expression of the model by Leuning in terms of E rather
than D, it is predicted that stomatal conductance decreases linearly with increasing rate of
transpiration, as air humidity varies. Independently, the same relation has been proposed by
Monteith (1995a):
g sw' gm(1&
E
)
Em
(3.19)
where
a1A
g m'
C s& '
(3.20)
and
Em' 1.6Ds,0gm
(3.21)
when
g sw'
1
@g
1.6 sc
The factor 1.6 is the constant ratio of the molecular diffusivities for water vapour and CO2
respectively.
Dewar (1995) relates the model of Leuning to a simplified description of the guard cell
function by Stålfelt (1966) in a quantitative manner. Stålfelt relates stomatal conductance to
the osmotic potential difference between guard and epidermal cells. Dewar shows, that with
the model of Leuning, the response of stomata to internal CO2-concentration (Mott, 1988) and
the 'feed-forward' response on humidity (Cowan, 1977) are correctly described. As air
humidity decreases, stomatal conductance is associated with a decrease in the osmotic
potential differences between guard and epidermal cells and g and E may decrease
concomitantly.
In Dewar's approach, Ds,0 is plant species specific and it will depend on the mechanical
and hydraulic properties of the guard cell-epidermal cell complex.
39
3.6 Conclusion and summary
From the literature survey on the effects of an increased atmospheric CO2 concentration on the
physiology of trees, the following conclusions can be drawn.
Increased atmosperic CO2 has a direct effect on photosynthesis and stomatal
conductance. A comparison of models shows that A-gs models are preferred over regression
models, because the first include the direct effect of increasing CO2 on photosynthesis and
other processes.
Using a regression model, as in the JS model, the direct effect of CO2 can be empirically
incorporated, using figure 3.3. However, this approach hampers the inclusion of variability of
the reaction of stomatal conductance to increased CO2. Furthermore, it is unclear, how
changed interactions between stomatal conductance and environmental variables as induced by
a changed climate, including changed atmospheric CO2, can be described by fitted parameters.
Using a physiologically based model, a more sophisticated explanation of the direct
effect of CO2 is given, and the effect of possible changes in nutrient availability can also be
analyzed, by incorporating for example a N-dependency of A. A disadvantage of the last model
is that these models have hardly been validated under conditions of long-term effects of
transpiration.
The increase in productivity together with decreasing stomatal opening and density,
results in an increase of the water-use efficiency (WUE), which does not implicate that the
total water use is decreasing as well, since an increase in transpiration due to raised
temperature may counteract the reduced water use. An increase of transpiration by climate
change due to increased LAI is only expected in canopies with a low LAI (<4).
The indirect effects of a changed carbon dioxide concentration on forest ecosystems on
the long term can be simulated by incorporating A-Gs models in ecosystem models (Friend et
al., 1993; McMutrie et al., 1992). Effects on the water and carbon balance can be included in
this type of simulation. However, due to the complexity of possible reactions and the use of an
extensive number of parameters, these models also show a high uncertainty. Not only the large
range of possible changes in the environment and vegetation, also the limited knowledge of the
complex relations in ecosystems, makes the evaluation results questionable. The response of
trees to elevated CO2 depends on the environment, availability of nutrients and water, as well
as on the genotype and gene expression of the species. The large range of possible effects
must be taken into account when evaluating the effects of a climate change, but may have
limited influence on transpiration.
Many Dutch forests are located on poor sandy soils, and such forests could possible react to
40
climate change by a small increase in canopy and a strong growth of roots and mycorrhiza.
The response of coniferous forests will be smaller than that of deciduous forests.
Of the available A-gs models, the model of Leuning (1995) was chosen, because it combines
the findings of Mott (1988), Mott and Parkhurst (1991) and Monteith (1995a) in a realistic
way. The responses of stomata to CO2, transpiration rate Et , and light are well simulated, as
shown by experimental results. In this study the A-gs model is incorporated in a water balance
model, using prescribed forest characteristics. The possible effects of a climate change are
further evaluated, using a sensitivity analysis (see chapter 5).
41