Table 1.

List of symbols used in the text for calculating leakiness in maize and sorghum.

Variable	Definition	Units	Equations/value/reference
a	Fractionation across the stomata	‰	4.4 (Craig, 1953; a s in Ubierna et al., 2013, 2018)
a b	Fractionations across the boundary layer	‰	2.9
$\overline{a}$	Weighted fractionation across the boundary layer and stomata in series	‰	Eqn 18 (Ubierna et al., 2013, 2018)
Α	Rate of photosynthesis	μmol m−2 s−1	Measured
b 3	13C fractionation during carboxylation by Rubisco, including respiration and photorespiration fractionations	‰	Eqn 13 (Farquhar, 1983)
$b_3^{\prime }$	13C fractionation during carboxylation by Rubisco	‰	30
b 4	Net fractionation by CO2 dissolution, hydration and phosphoenolpyruvate carboxylase (PEPC) including respiratory fractionation	‰	Eqn 14 (Farquhar, 1983)
$b_4^{\prime }$	Net fractionation by CO2 dissolution, hydration and PEPC activity dependent upon temperature	‰	Eqn 15
C a	Ambient CO2 partial pressure	Pa	Measured in μmol mol−1 air
C bs	CO2 partial pressure in the bundle‐sheath cells	Pa	Eqn 7
C i	CO2 partial pressure at the intercellular airspace	Pa	Measured in μmol mol−1 air
C s	CO2 partial pressure at the leaf surface	Pa	Measured in μmol mol−1 air
C ref	CO2 concentration of the dry air exiting the leaf chamber	μmol mol−1	Measured
C samp	CO2 concentration of the dry air exiting the leaf chamber	μmol mol−1	Measured
e	13C fractionation during decarboxylation	‰	0 (Evans & von Caemmerer, 2013; Ubierna et al., 2013)
e′	13C fractionation during decarboxylation including the effect of a respiratory substrate isotopically distinct from recent photosynthate	‰	Eqn 16
E	Rate of transpiration	mol m−2 s−1	Measured
f	13C fractionation during photorespiration	‰	1.6‰ (Ubierna et al., 2013)
$g_{\mathrm{ac}}^{\mathrm{t}}$	Total conductance to CO2 diffusion including boundary layer and stomatal conductance	mol m−2 s−1	Measured
g bs	Bundle‐sheath conductance to CO2	mol m−2 s−1	0.00113 (Brown & Byrd, 1993)
J t	Total electron transport rate	μmol m−2 s−1	Eqn 3 (von Caemmerer, 2000)
O m	O2 partial pressure in the mesophyll cells	Pa	21.2 Pa atmospheric pressure
O s	O2 partial pressure in the bundle‐sheath cells	Pa	Eqn 11 (von Caemmerer, 2000)
R d	Leaf mitochondrial respiration in the light assumed to equal the rate of respiration in the dark	μmol m−2 s−1	Measured
R m	Rate of mesophyll cell respiration in the light	μmol m−2 s−1	R m = 0.5R d
s	Fractionation during leakage from the bundle‐sheath cells	‰	1.8 (Henderson et al., 1992)
t	Ternary effect	‰	Eqn 17
V c	Rubisco carboxylation rate	μmol m−2 s−1	Eqn 9 (von Caemmerer, 2000)
V o	Rubisco oxygenation rate	μmol m−2 s−1	Eqn 10 (von Caemmerer, 2000)
V p	PEP carboxylation rate	μmol m−2 s−1	Eqn 8 (von Caemmerer, 2000)
x	Fraction of J t allocated to the C4 cycle		0.4 (von Caemmerer, 2000)
α	Fraction of PSII activity in the bundle sheath		0 (von Caemmerer, 2000)
δ13Cgatm	Isotopic signature of growth CO2	‰	−8
δ13Cref	Isotopic signature of the CO2 entering the leaf chamber	‰	Measured
δ13Csamp	Isotopic signature of the CO2 exiting the leaf chamber	‰	Measured
ξ	Ratio of the 12CO2 mole fraction in the dry air coming into the gas‐exchange cuvette over the difference in 12CO2 mole fractions of air in and out of the cuvette	unitless	Eqn 2
Δ13Cobs	Observed 13C photosynthetic discrimination	‰	Eqn 1
ϕ is	Leakiness estimated assuming infinite mesophyll conductance	Unitless	Eqn 12