# Instantaneous photosynthesis and transpiration at the leaf level

Following Thornley and Johnson (1990), the response of instantaneous gross leaf photosynthesis (*A _{l}*) to internal leaf [CO

_{2}] (

*c*) and to instantaneous leaf irradiance (

_{i}*I*) is assumed to be well described by a rectangula hyperbola:

.

where *α* is leaf quantum yield and *g _{x}* is carboxylation conductance, which is proportional in first approximation to maximum carboxilation rate and therefore to leaf nitrogen content

*n*(Evans 1989):

_{l}.

where *k _{1}* is an empirical parameter that can be assumed constant across species and genotypes (Wullschleger 1993). In turn, leaf nitrogen content has been often reported to be a linear function of mean leaf irradiance over the day :

.

The functional meaning of such a relationship (Dewar (1996)) will be further explored in a later section.
Internal [CO_{2}] will be a function of leaf assimilation and stomatal conductance to CO_{2}(gc):

.

where *c _{a}* is air [CO

_{2}] and

*P*is atmospheric pressure. The dependency can be resolved through the widely-observed correlation between stomatal conductance and leaf photosynthesis (Wong, Cowan, & Farquhar 1979), by representing leaf stomatal conductance as (Leuning 1995):

.

where *g _{0}* is leaf stomatal conductance in the dark,

*g*is compensation point for CO

_{0}_{2}, the parameter

*D*captures stomatal response to air vapour pressure deficit (

_{0}*D*) and

*a*is an empirical parameter which will be a function of soil water content:

.

where the multiplier *f _{s}* ranges between 1 at field capacity and 0 at wilting point. This will be further detailed following Landsberg and Waring (1997).
For present purposes, this equation can be slightly simplified as:

.

When Equations 18 and 21 are combined, internal [CO_{2}] in Equation 15 can be expressed as a linear function of air vapour pressure deficit *D*:

.

Finally, if we assume transpiration to be imposed transpiration (i.e. if we neglect the effects of aerodynamic resistance), instantaneous leaf transpiration (*E*) can be expressed as:

.

where the factor 1.6 accounts for the different diffusivities of water and CO_{2} in air.
From Equations 15-23 it can be seen that leaf gas exchange can be fully captured by no more than five parameters (*α, k _{2}, f_{soil}, a_{max}* and

*D*), which have all been measured (or are in the process of being measured) on a large number of

_{0}*Fagus sylvatica*full-sib seedlings.