## 2.31.3. Carbon Isotope Discrimination During Photosynthesis[¶](#carbon-isotope-discrimination-during-photosynthesis "Permalink to this headline")
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Photosynthesis is modeled in CLM as a two-step process: diffusion of CO2 into the stomatal cavity, followed by enzymatic fixation (Chapter [2.9](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Photosynthesis/CLM50_Tech_Note_Photosynthesis.html#rst-stomatal-resistance-and-photosynthesis)). Each step is associated with a kinetic isotope effect. The kinetic isotope effect during diffusion of CO2 through the stomatal opening is 4.4‰. The kinetic isotope effect during fixation of CO2 with Rubisco is \\(\\sim\\)30‰; however, since about 5-10% of carbon in C3 plants reacts with phosphoenolpyruvate carboxylase (PEPC) (Melzer and O’Leary, 1987), the net kinetic isotope effect during fixation is \\(\\sim\\)27‰ for C3 plants. In C4 plant photosynthesis, only the diffusion effect is important. The fractionation factor equations for C3 and C4 plants are given below:

For C4 plants,

(2.31.8)[¶](#equation-30-8 "Permalink to this equation")\\\[\\alpha \_{psn} =1+\\frac{4.4}{1000}\\\]

For C3 plants,

(2.31.9)[¶](#equation-30-9 "Permalink to this equation")\\\[\\alpha \_{psn} =1+\\frac{4.4+22.6\\frac{c\_{i}^{\*} }{pCO\_{2} } }{1000}\\\]

where \\({\\alpha }\_{psn}\\) is the fractionation factor, and \\(c^\*\_i\\) and pCO2 are the revised intracellular and atmospheric CO2 partial pressure, respectively.

As can be seen from the above equation, kinetic isotope effect during fixation of CO2 is dependent on the intracellular CO2 concentration, which in turn depends on the net carbon assimilation. That is calculated during the photosynthesis calculation as follows:

(2.31.10)[¶](#equation-30-10 "Permalink to this equation")\\\[c\_{i} =pCO\_{2} -a\_{n} p\\frac{\\left(1.4g\_{s} \\right)+\\left(1.6g\_{b} \\right)}{g\_{b} g\_{s} }\\\]

where \\(a\_n\\) is net carbon assimilation during photosynthesis, \\(p\\) is atmospheric pressure, \\(g\_b\\) is leaf boundary layer conductance, and \\(g\_s\\) is leaf stomatal conductance.

Isotopic fractionation code is compatible with multi-layered canopy parameterization; i.e., it is possible to calculate varying discrimination rates for each layer of a multi-layered canopy. However, as with the rest of the photosynthesis model, the number of canopy layers is currently set to one by default.

