| Isotope fractionation factor during CO_{2} diffusion through the leaf boundary layer and the stomata (Eq. 12) | ‰ |

*a*_{ch}, *a*_{sh} | Isotope fractionation factor during CO_{2} diffusion across the chloroplast (*a*_{ch}; C_{3} plant) or the bundle sheath cells (*a*_{sh}; C_{4} plant) (Eq. C4) | ‰ |

*a*_{cb} | Isotope fractionation factor between CO_{2} and bicarbonate at equilibrium (i.e. *a*_{cb} = α_{cb} − 1) (Eq. 7) | ‰ |

*a*_{w} | Isotope fractionation factor during CO_{2} dissolution and diffusion from the substomatal cavity to the CA site (Eq. 1) | ‰ |

*A*, ^{18}*A* | Net total CO_{2} and C^{18}OO flux (Eq. 1) | mol m^{−2} s^{−1} |

*b, b*_{PEPC} | Isotope fractionation factor during Rubisco and PEPC carboxylation (Appendix C) | ‰ |

*B* | Dimensionless solubility of CO_{2} in water (i.e. 8.314*K*_{H}*T*, where *T* is temperature) (Eq. B11) | m^{3} m^{−3} |

*C*_{c}, *B*_{c} | CO_{2} and bicarbonate concentrations at the Rubisco site (chloroplast stroma in C_{3} plants, bundle sheath in C_{4} plants) (Fig. 1) | mol mol^{−1} |

*C*_{m}, *B*_{m} | CO_{2} and bicarbonate concentrations in the cytoplasm of mesophyll cells (Fig. 1) | mol mol^{−1} |

*E* | Transpiration rate (Eq. 11) | mol m^{−2} s^{−1} |

*F*_{r} | Ratio of respiratory to net CO_{2} flux [i.e. (*V*_{r} + 0.5*V*_{o})/*A*] (Eq. 6) | Unitless |

*g*_{bc}, *g*_{sc}, *g*_{tc} | Boundary layer, stomatal, and total conductance to CO_{2} (Eq. 11) | mol m^{−2} s^{−1} |

*g*_{ch}, *g*_{sh} | Conductance to CO_{2} from the CA site to the Rubisco site (i.e. across the chloroplast [*g*_{ch}; C_{3} plant] or the bundle sheath cells [*g*_{sh}; C_{4} plant]) | mol m^{−2} s^{−1} |

*g*_{m} | Mesophyll conductance to CO_{2} from the intercellular air space to the CA site (Fig. 1) | mol m^{−2} s^{−1} |

*k*_{CA} | Leaf CA activity rate (Eqs. 7 and 9) | mol m^{−2} s^{−1} Pa^{−1} |

*k*_{CA,orig} | Leaf CA activity rate, before applying the pH correction (Eq. 10) | mol m^{−2} s^{−1} Pa^{−1} |

*k*_{cat,assay}, *k*_{uncat,assay} | CA-catalyzed and uncatalyzed CO_{2} hydration rates under CA assay conditions (Eq. 9) | s^{−1} |

^{18}*k*_{d}, ^{16}*k*_{d} | H_{2}C^{18}OO_{2} and H_{2}C^{16}O_{3} dehydration rates (Eq. B1) | s^{−1} |

*K*_{H} | Solubility of CO_{2} in water (Eq. 9) | mol m^{−3} Pa^{−1} |

*k*_{h}, ^{16}*k*_{h}, ^{18}*k*_{h}, ^{18}*k*′_{h} | CO_{2} hydration rate (introduction, after Eq. 5) and CO_{2}-H_{2}O, C^{18}OO-H_{2}O, and CO_{2}-H_{2}^{18}O reaction rates (Eq. B1) | s^{−1} |

^{18}*k*_{hm}, ^{18}*k*_{hc} | C^{18}OO-H_{2}O reaction rate in the mesophyll and the chloroplast, respectively (Eqs. C4 and C6) | s^{−1} |

*k*_{iso} | CO_{2}-H_{2}O isotopic exchange rate (Eq. 4) | s^{−1} |

*k*_{uncat,invivo} | Uncatalyzed CO_{2} hydration rate under in vivo conditions (Eq. 9) | s^{−1} |

*P* | Atmospheric pressure (Fig. 1) | Pa |

*p*_{a}, *p*_{i}, *p*_{CA} | CO_{2} partial pressure in outside air, intercellular air space, and at the CA site (Fig. 1) | Pa |

*pH*_{assay}, *pH*_{invivo} | pH of the assay solution and of the leaf CA-containing compartment (Eq. 10) | Unitless |

*R*_{A} | Isotope ratio of net CO_{2} flux (=0.5^{18}*A*/*A*) | Unitless |

*R*′_{i} | Isotope ratio of CO_{2} in intercellular air space when ternary effects are neglected (Eq. A1) | Unitless |

*R*_{a}, *R*_{i}, *R*_{CA} | Isotope ratio of CO_{2} in outside air, intercellular air space, and at the CA site (Fig. 1) | Unitless |

*R*_{b} | Isotope ratio of bicarbonate (Eq. B5) | Unitless |

*R*_{b,eq} | Isotope ratio of bicarbonate in equilibrium with water (Eq. B5) | Unitless |

*R*_{c}, *R*′_{c} | Isotope ratio of CO_{2} and bicarbonate at the Rubisco site (Fig. 1) | Unitless |

*R*_{c} | Isotope ratio of CO_{2} (Eq. B5) | Unitless |

*R*_{c,eq} | Isotope ratio of CO_{2} in equilibrium with water (i.e. *R*_{w}α_{wc}) (Eq. B4) | Unitless |

*R*_{eq} | Isotope ratio of CO_{2} in equilibrium with water at the evaporation site (i.e. *R*_{es}α_{wc}) (Eq. 6) | Unitless |

*R*′_{eq} | Isotope ratio of CO_{2} in equilibrium with water in bundle sheath cells (i.e. *R*_{x}α_{wc}) (Eq. 6) | Unitless |

*R*_{es} | Isotope ratio of water at the evaporation site (Eq. 2) | Unitless |

*R*_{i0}, *R*_{CA0}, *R*_{c0} | *R*_{i}, *R*_{CA}, and *R*_{c} in the absence of CA activity (Eqs. 8 and C26) | Unitless |

*R*_{m}, *R*′_{m} | Isotope ratio of CO_{2} and bicarbonate in the cytoplasm of mesophyll cells (Fig. 1) | Unitless |

*R*_{mi}, *R*′_{mi} | Isotope ratio of CO_{2} produced in mitochondria of mesophyll and bundle sheath cells (Fig. 1) | Unitless |

*R*_{p} | Isotope ratio of CO_{2} released from C_{4} acids in bundle sheath cells (Eq. C6) | Unitless |

*R*_{trans} | Isotope ratio of transpired water vapor (Appendix C) | Unitless |

*R*_{x} | Isotope ratio of water in bundle sheath cells (Eq. 6) | Unitless |

*R*_{w} | Isotope ratio of water (Eq. B4) | Unitless |

*S* | Total bicarbonate species (i.e. [H_{2}CO_{3}] + [HCO_{3}^{−}] + [CO_{3}^{2−}]) (Eq. B8) | mol m^{−3} |

*S*_{G} | Surface area of the gas-liquid interface (Eq. B11) | m^{2} |

*S*_{leaf} | Leaf area used for the CA assay (Eq. 9) | m^{2} |

*t* | Time (Eq. 4) | s |

*t*′ | Ternary correction factor (Eq. 11) | Unitless |

*t*_{a} | Ternary correction factor for CO_{2} isotopes (Eq. 13) | Unitless |

*V*_{assay} | Volume of the CA assay solution (Eq. 9) | m^{3} |

*V*_{c} | Rubisco carboxylase activity rate in the chloroplast stroma of C_{3} plants or bundle sheath cells of C_{4} plants (Fig. 1) | mol m^{−2} s^{−1} |

*V*_{G}, *V*_{L} | Volumes of the gas and liquid phases (Eq. B11) | m^{3} |

*V*_{hc}, *V*_{dc} | CO_{2} hydration and dehydration rates in the chloroplast stroma of C_{3} plants (Fig. 1) | mol m^{−2} s^{−1} |

*V*_{hm}, *V*_{dm} | CO_{2} hydration and dehydration rates in the cytoplasm of mesophyll cells (Fig. 1) | mol m^{−2} s^{−1} |

*V*_{o}, *V*_{r} | Photorespiration and mitochondrial respiration rates (Fig. 1) | mol m^{−2} s^{−1} |

*V*_{p} | PEPC activity rates in the cytoplasm of C_{4} mesophyll cells (and CO_{2} release rate from C_{4} acid in bundle sheath cells) (Fig. 1) | mol m^{−2} s^{−1} |

,α_{cw} | Isotope fractionation between CO_{2} and water at equilibrium (i.e. *R*_{c,eq}/*R*_{w}) (Eqs. 2 and B4) | Unitless |

, α_{cb} | Isotope fractionation between CO_{2} and bicarbonate at equilibrium (i.e. *R*_{c,eq}/*R*_{b,eq}) (Eq. B6) | Unitless |

Γ* | CO_{2} compensation point in the absence of mitochondrial respiration (Appendix C) | mol mol^{−1} |

∆_{A} | Photosynthetic C^{18}OO discrimination (i.e. *R*_{a}/*R*_{A} − 1) (Eq. 12) | ‰ |

∆_{ci} | Isotope ratio of CO_{2} at the CA site, expressed relative to that in the intercellular air space (i.e. *R*_{CA}/*R*_{i} − 1) (Eq. 1) | ‰ |

∆_{ci0} | ∆_{ci} in the absence of CA activity (Eq. 3) | ‰ |

∆_{ea} | Isotope ratio of CO_{2} in equilibrium with the evaporation site, expressed relative to that in air (i.e. *R*_{eq}/*R*_{a} − 1) (Eq. 11) | ‰ |

∆_{ei} | Isotope ratio of CO_{2} in equilibrium with the evaporation site, expressed relative to that in the intercellular air space (i.e. *R*_{eq}/*R*_{i} − 1) (Eq. 2) | ‰ |

∆_{eq} | Isotope ratio of the evaporation site, expressed relative to that of bundle sheath cell water (i.e. *R*_{es}/*R*_{x} − 1) (Eq. 7) | ‰ |

∆_{i} | Photosynthetic C^{18}OO discrimination, expressed relative to the isotope ratio of CO_{2} in the intercellular air space (i.e. *R*_{i}/*R*_{A} − 1) (Eq. 1) | ‰ |

∆_{ia} | Isotope ratio of CO_{2} in the intercellular air space, expressed relative to that in the outside air (i.e. *R*_{i}/*R*_{a} − 1) (Eq. A4) | ‰ |

∆′_{ia} | ∆_{ia} without ternary corrections (Eq. 11) | ‰ |

∆_{mc} | Isotope fractionation factor between respired CO_{2} and CO_{2} at the Rubisco carboxylation site (i.e. *R*_{mi}/*R*_{c} − 1) (Appendix C) | ‰ |

ε_{ci} | *p*_{CA}/(*p*_{i} – *p*_{CA}) (Eq. 1) | Unitless |

ε_{ia} | *p*_{i}/(*p*_{a} – *p*_{i}) (Eq. 11) | Unitless |

θ | Degree of isotopic equilibration (Eq. 3) | Unitless |

π_{t} | Transfer coefficient between the gas and liquid phases (Eq. B11) | m s^{−1} |

ρ | Ratio of net CO_{2} flux to CA activity [i.e. *A*/(*k*_{CA}*p*_{CA})] (Eq. 7) | Unitless |

ρ_{i} | Ratio of net CO_{2} flux to *k*_{CA}*p*_{i} (Eq. 7) | Unitless |

τ | Time scale of CO_{2}-H_{2}O isotopic exchange dynamics (Eq. B8) | s |

τ′ | Decay rate of ^{18}O in the CO_{2} atom fraction (Eq. B11) | s |

τ_{1}, τ_{2} | C^{18}O_{2} decay rates before and after leaf extract addition during the CA assay (Appendix B) | s |

τ_{res} | Residence time of CO_{2} inside the leaf mesophyll (Eq. 5) | s |

ϕ_{r} | Fraction of respired CO_{2} not recycled by the chloroplast stroma (C_{3} plant) or not produced in the bundle sheath (C_{4} plant) (Fig. 1) | Unitless |