where Rsample and Rstandard are the
isotopic ratios of oxygen (18O/16O)
of the sample and international standard, respectively. The precision of
the analysis for each parameter was 0.2 ‰ for leaf and root crown water
and water vapor and 0.07 ‰ for irrigation water.
For calculation of effective leaf water mixing length, some parameters
were measured, and others were calculated. Steady state condition (SS)
was assumed for all calculations. Water isotope enrichment at the sites
of evaporation (Δe) was calculated for each leaf
(Craig & Gordon 1965;
Dongmann et al. 1974) relative to
source water (δ18Oe -
δ18Osw; Eqn 2).
Δ18Ov is the atmospheric water vapor
enrichment above plant water source
(δ18Ov -
δ18Osw), which in this study was root
crown water. We used Δ18Ov from the
atmosphere, as only 6.5 % of the leaf was inside the cuvette during gas
exchange measurements for about 3-5 min.e a/e i is the ratio of
vapor pressure external to the leaf to internal vapor pressure, ε* is
the temperature-dependent (°Kelvin) equilibrium fractionation factor
between vapor and water inside the leaf
(Eqn. 5; Majoube 1971), and
εk is the kinetic fractionation during diffusion of
vapor from the leaf to the atmosphere
(Eqn. 6; Farquhar et al. 1989).