Modelling plant hydraulics within the QUINCY-SIMPHONY framework

Fundamentally, plant hydraulics can be expressed via a system of two or more coupled mass balance equations. Here, we follow the approach based on Xu et al. (2016) and define the change in water content of accumulated across all leaves and the botten of the stem as:

• ${\mathrm{\Gamma }}_{\mathrm{Leaf}}\cdot \frac{d{\mathrm{\Psi }}_{\mathrm{Leaf}}}{dt}-J+T_{\mathrm{Leaf}}=0$
• ${\mathrm{\Gamma }}_{\mathrm{Stem}}\cdot \mathrm{Huber}\cdot H\cdot \frac{d{\mathrm{\Psi }}_{{\mathrm{Stem}}_{\mathrm{B}}}}{dt}+J-G+T_{\mathrm{Stem}}=0$

${\mathrm{\Psi }}_{\mathrm{Leaf}}$ is the average water potential a leaf in the canopy and ${\mathrm{\Psi }}_{{\mathrm{Stem}}_{\mathrm{B}}}$ is the stem water potential at the bottom of the stem close to the ground.

The fluxes are: Transpiration $T_{\mathrm{Leaf}}$, Sapflow $J$, Stem water loss $T_{\mathrm{Stem}}$ and Groundflow $G$.

Transpiration $T_{\mathrm{Leaf}}$

We estimate transpiration by multiplying stomatal conductance $g_s$ with vapor pressure deficit $\mathrm{VPD}$:

• $T_{\mathrm{Leaf}}\left({\mathrm{\Psi }}_{\mathrm{Leaf}}\right)=g_s\left({\mathrm{\Psi }}_{\mathrm{Leaf}}\right)\cdot \mathrm{VPD}$

We use a modified version of the unified stomatal optimization model (Medlyn et al. 2011) including a $\beta$ factor that describes stomatal closure based on leaf water potential ${\psi }_{\mathrm{Leaf}}$:

• $g_s\left({\mathrm{\Psi }}_{\mathrm{Leaf}}\right)=g_0+\beta \left({\mathrm{\Psi }}_{\mathrm{Leaf}}\right)\cdot (1+\frac{g_1}{\sqrt{\mathrm{VPD}}})\frac{A}{c_a}$

We use a Gompertz function to describe the relationship between $\beta$ and ${\mathrm{\Psi }}_{\mathrm{Leaf}}$:

• $\beta \left({\mathrm{\Psi }}_{\mathrm{Leaf}}\right)=\exp (-\exp (-s_{\mathrm{close},50}({\mathrm{\Psi }}_{\mathrm{Leaf}}-{\mathrm{\Psi }}_{\mathrm{close},50})))$

with ${\mathrm{\Psi }}_{\mathrm{close},50}$ representing the leaf water potential at which 50\% of stomatal closure is induced, and $s_{\mathrm{close},50}$ a shape parameter.

Sapflow $J$

Sapflow is estimated as:

• $J=\sum _{\begin{array}{c}\mathrm{\Psi }={\mathrm{\Psi }}_{{\mathrm{Stem}}_B}\\ \mathrm{\Delta }\mathrm{\Psi }\end{array}}^{{\mathrm{\Psi }}_{\mathrm{Leaf}}}{K}_{\mathrm{xyl}}(\mathrm{\Psi })\cdot (\mathrm{\Delta }\mathrm{\Psi }-{{\mathrm{\Psi }}_H}_n)$

with $\mathrm{\Delta }\psi =\frac{{\psi }_{\mathrm{Leaf}}-{\psi }_{{\mathrm{Stem}}_B}}{n}$ and ${\psi }_H(n)=\rho \cdot g\cdot \frac{H}{n}$ and $n$ number of stem segments and $H$ is the canopy height. Xylem hydraulic conductivity $K$ is estimated using a Weibull relationship:

• $K_{\mathrm{xyl}}(\psi )=K_{\mathrm{xyl},\max }\cdot \exp (-{\left(\frac{-\psi }{b}\right)}^c)$

with $K_{\mathrm{xyl},\max }$: maximum/saturated xylem hydraulic conductivity and $b$ and $c$ are shape parameters that can be estimated with ${\psi }_{50}$ and ${\psi }_{88}$

Stem water loss $T_{\mathrm{Stem}}$

We simulate stem water loss through the bark similar to transpiration $T_{\mathrm{Leaf}}$

• $T_{\mathrm{Stem}}=g_{\mathrm{Stem}}\cdot \mathrm{VPD}$

Groundflow $G$

The water flow $G$ from the soil to the stem is estimated as sum through the individual soil layers $i$:

• $G=\sum _i{G}_i=\sum _i{f}_i\cdot k_{\mathrm{soil},i}\cdot ({\mathrm{\Psi }}_{\mathrm{soil},i}-{\mathrm{\Psi }}_{{\mathrm{Stem}}_G}-\rho \cdot g\cdot d_{\mathrm{soil},i})$