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).