Estimation of Kleaf
We used the leaf anatomical traits IVD, VED and average leaf thickness
(TL) to estimate leaf hydraulic conductance
(Kleaf). Specifically, the traits used to estimate
Kleaf in current study along with path of
CO2 and water inside the leaf are indicated in Fig. S1.
These traits have been shown to influence Kleaf in
diverse species (Brodribb et al. , 2007; Sack et al. , 2013;
Buckley et al. , 2015). The Kleaf was estimated as
described by de Boer et al ., (2016) based on the empirical
expression for Kleaf given by Brodribb et al .,
(2007) as:
\(K_{\text{leaf}}=12674\bullet{l_{H2O}}^{-1.26}\)
(Eqn 1)
where,
\(l_{H2O}=\tau\sqrt{{\text{dm}_{x}}^{2}+\ \text{VED}^{2}}\)
(Eqn 2)
and \(\tau\) is the tortuosity of the flow path throught the leaf
intererior and assumed to be π/2 (Brodribb and Field, 2010). The\(\text{dm}_{x}\) is the longest horizontal distance between the vein
terminals (equivalent to IVDmax; Brodribb et al .
2007; Brodribb and Field, 2010), and VED is the average
vein-to-epidermis distance. Here we use average VED since there was a
linear 1:1 relationship between VEDaba and
VEDada across the 18 C4 grasses measured
in current study (Fig. S3). The IVDmax was not directly
measured but was estimated from the published relationship between
IVDmax and VLA, which is IVDmax =
650/VLA (Brodribb et al ., 2007) and our observed relationship
between IVD and VLA, which is IVD = 988/VLA (Fig. S2) to estimate
IVDmax as, IVDmax = 0.657 × IVD.
In order to include average leaf thickness (TL) along
with IVD and VED in the estimates of K leaf, the
geometric relationship in the model of Brodribb and Field (2010) was
modified according to de Boer et al ., (2016). For this, VED was
assumed to be equal to TL/2 as supported from data
presented in Fig. S4 in which slope of relationship is about 1/2. For
IVD the relationship with ratio IVD/VED was considered where VED =
TL/2, so that\(\text{IVD}=\frac{\text{IVD}}{\text{VED}}\bullet\frac{T_{L}}{2}\).
Using these expressions, Eqn 2 becomes:
\(l_{H2O}=\frac{\pi}{2}\sqrt{\frac{{T_{L}}^{2}}{4}+{\frac{{(0.657)}^{2}}{4}\bullet\left(\frac{\text{IVD}}{\text{VED}}\right)}^{2}\bullet{T_{L}}^{2}}\)
(Eqn 3)
Therefore, K leaf can be calculated by
substituting Eqn 3 in Eqn 1:
\(K_{\text{leaf}}=\frac{7174}{\left(\frac{{T_{L}}^{2}}{4}+{\ \frac{({0.657)}^{2}}{4}\bullet\left(\frac{\text{IVD}}{\text{VED}}\right)}^{2}\bullet{T_{L}}^{2}\right)^{0.63}}\) (Eqn 4)