Instantaneous photosynthesis and transpiration at the leaf level

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Following Thornley and Johnson (1990), the response of instantaneous gross leaf photosynthesis (Al) to internal leaf [CO2] (ci) and to instantaneous leaf irradiance (I) is assumed to be well described by a rectangula hyperbola:

ForgemFormula 15.png (15)


where α is leaf quantum yield and gx is carboxylation conductance, which is proportional in first approximation to maximum carboxilation rate and therefore to leaf nitrogen content nl (Evans 1989):

ForgemFormula 16.png (16)


where k1 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  :

ForgemFormula 17.png (17)


The functional meaning of such a relationship (Dewar (1996)) will be further explored in a later section. Internal [CO2] will be a function of leaf assimilation and stomatal conductance to CO2(gc):

ForgemFormula 18.png (18)


where ca is air [CO2] 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):

ForgemFormula 19.png (19)


where g0 is leaf stomatal conductance in the dark, g0 is compensation point for CO2, the parameter D0 captures stomatal response to air vapour pressure deficit (D) and a is an empirical parameter which will be a function of soil water content:

ForgemFormula 20.png (20)


where the multiplier fs 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:

ForgemFormula 21.png (21)


When Equations 18 and 21 are combined, internal [CO2] in Equation 15 can be expressed as a linear function of air vapour pressure deficit D:

ForgemFormula 22.png (22)


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:

ForgemFormula 23.png (23)


where the factor 1.6 accounts for the different diffusivities of water and CO2 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, k2, fsoil, amax and D0), which have all been measured (or are in the process of being measured) on a large number of Fagus sylvatica full-sib seedlings.