The stomatal pores located in the leaves are the pathway for CO2 to enter the carboxy-
Figure 2.3: Cross section of an open stoma and related conductances diagram; Ca, Cs, Ci,
are the carbon concentrations in the free atmosphere, leaf surface and internal space of stomata; ga, gsc, gc, gm are the aerodynamic, stomatal, cuticular and diffusive mesophyll
conductances for carbon; qa, qs, qsat(Ts) are the specific humidities at the free atmo-
sphere, leaf surface and saturated specific humidity at the stomatal cavity temperature (assumed equal to leaf surface temperature Ts); ga, gs, gc are the aerodynamic, stomatal
and cuticular conductances for water vapour. Figure from Boussetta et al. (2013b).
through these pores. Figure 2.3 shows a cross-section of a leaf with the stomatal cavity and pore on the left and a diagram of conductances for carbon and water vapour fluxes on the right. The mechanism by which the gases cross the stomatal pore is diffusion. The diffusion coefficient of a gas is inversely proportional to the square root of its molecular weight. For this reason, water vapour (molecular weight = 18) diffuses more easily than carbon dioxide (molecular weight = 44). In vegetation models this transport through the stomata is controlled by the stomatal conductance. The higher the conductance the easier it is for the gas to go through the stomata. The stomatal conductances for water vapour and CO2 are denoted as gs and gsc respectively. They are related by:
gs= 1.6gsc (2.32)
The factor 1.6 is the ratio of diffusivities of water vapour and CO2. The stomatal openings
are very sensitive to both environmental factors and internal physiological factors, allowing plants to optimise the balance between CO2 and water vapour loss.
can leave the plant through the cuticle; CO2 can also enter this way. This transport is
accounted for via a conductance in parallel to the stomata conductance called the cutic- ular conductance (gc) (Figure 2.3). The cuticle presents a waxy barrier, which hampers
diffusion; in fact cuticular conductance is very small and almost negligible. However, when stomata are nearly closed, stomatal and cuticular conductances become comparable. In some models, an additional step is included to represent the diffusion of CO2 from the
substomatal cavity (Ci) to the site of carboxylation or chloroplasts (Cc). This is repre-
sented by the diffusive mesophyll conductance, it does not apply to water vapour, as the transpiration occurs directly from the saturated substomatal cavities. The mesophyll conductance varies widely amongst species and correlates with the photosynthetic capacity (Lambers et al., 1998; Evans and Von Caemmerer, 1996). It is closely linked to physiolog- ical processes and it involves diffusion of CO2 through the cell walls in the gas phase as
well as in the liquid phase. The carbon isotope discrimination technique has been used to measure this diffusion an thus the value of the mesophyll conductance (also called internal conductance). It was thought to be constant for a leaf because it is largely related to the leaf anatomy (Evans and Von Caemmerer, 1996) and therefore omitted in many models. More recent physiological research shows that mesophyll conductance is dynamic and has a faster response than stomatal conductance (Flexas et al., 2008). Therefore mesophyll conductance plays an important role in limiting photosynthesis especially at high temper- atures (Bernacchi et al., 2002) or due to soil moisture stress (Egea et al., 2011). Despite this evidence, most photosynthesis models in LSMs do not represent it explicitly. Unfortu- nately, the term mesophyll conductance is also used to refer to a parameter that regulates photosynthetic rate (Goudriaan et al., 1985; Jacobs, 1994). Throughout this thesis the mesophyll conductance referring to the regulation of CO2 flux entering the chloroplasts, as
described here, will be denominated diffusive mesophyll conductance, reserving the term mesophyll conductance for the model parameter.
The leaf boundary layer represents the surrounding of the leaf surface up to which the leaf gas exchange exerts an influence (Figure 2.4). Outside this layer the temperature or humidity of the air are not affected by the leaf, and are those of the free atmosphere (this is not strictly true if we consider the whole canopy). Water vapour, heat and carbon fluxes are regulated by the the leaf boundary layer conductance. The factors defining the boundary layer conductance are the leaf morphology (small versus big leaves) and
the wind. gb is directly proportional to the square root of the windspeed and inversely
proportional to the square root of the thickness of the leaf boundary layer. Leaves in well ventilated spaces have thinner boundary layers (higher gb) than those sitting in still air.
Small leaves tend to form thinner boundary layers. The leaf boundary layer conductance can be calculated as (Jacobs, 1994):
gb= k
r u Wl
(2.33)
where u is the wind speed and Wl is the leaf’s width in the direction parallel to the
windspeed. Its counterpart for carbon diffusion is related to it as follows:
gb = 1.37gbc (2.34)
The factor used to relate leaf boundary layer conductance for water vapour and CO2 is
1.37, this is because in this case both diffusion and turbulence influence the fluxes. Under most conditions the stomatal conductance is considerably less than the boundary layer conductance. gb can reach up to 10 mol m−2s−1 at wind speeds up to 5 m s−1 while gs
has values up to 1 mol m−2s−1 for widely open stomata (Lambers et al., 1998). Therefore the control on gas exchange is typically exerted through the stomata. However, in some cases (still humid air, big leaves) the boundary layer can be thicker, hence gb values be-
come small and therefore more constraining. The importance of the leaf boundary layer was highlighted by Collatz et al. (1991), who analysed its interaction with the regulatory properties of stomatal conductance. The degree to which stomata control the transpira- tion rate (or CO2 assimilation rate) depends on the coupling between the leaf and the
atmosphere, which is given by how closely the saturation deficit at the leaf surface, Ds, is
linked to that of the air outside the leaf boundary layer, Da, as explained by Jarvis and
McNaughton (1986). They define a decoupling coefficient Ωl to account for the ratio of
leaf boundary layer conductance to stomatal conductance.
Under well coupled conditions and neglecting gmand gc, the transpiration and CO2intake
are controlled by stomatal conductance as shown by the following expressions:
E = ρwgsD (2.35)
Figure 2.4: A single leaf and its boundary layer (dashed line). Stomatal conductance is denoted by gs and leaf boundary layer by gb which are conductances for water vapour.
Inside the stomata air is saturated, D = 0. Ds is the specific humidity deficit at the
leaf surface and Da the specific humidity deficit at the leaf boundary layer. Cuticular
conductance has been omitted.
yielding transpiration as kg of water m2 s−2. A = gs
1.6(Cc− Ci) (2.36)
in this expression gs is in m s−1, Cs and Ci are in kg C m−3 yielding photosynthesis rate
A in kg C m2 s−2. Stomatal behaviour has been typically represented in models by two approaches, Jarvis (1976), described in section 2.3.5 and A-gs(Ball et al., 1987) described
in 2.3.6.