Table I. List of parameters.
Variables and parameters referred to in this study, other than leaf anatomical parameters (Table IV) or unknown parameters (Table III), are shown with symbols and units. Dwa = 2.178 × 10−5 × (T/273.15)1.81 m2 s−1, Dww (molecular diffusivity for water in liquid water) = 1.635 × 10−8 × (T/215.05 – 1)2.063 m2 s−1, and η = 1.95 × 1014 × T−7 Pa s−1, where temperature (T) is in K; Rgas = 8.314462 Pa m3 mol−1 K−1; vw = 1.8 × 10−5 m3 mol−1. T = 25°C or 298.15 K except where noted otherwise.
| Variable or Parameter | Symbol | Units |
|---|---|---|
| Bulk area for flow between two nodes | a | m2 |
| Bulk area for flow between nodes j and i | aji | m2 |
| Ratio of actual flow pathlength to simple (direct) pathlength | β | Unitless |
| Molecular diffusivity of water vapor in air | Dwa | m2 s−1 |
| Molecular diffusivity of water in liquid water | Dwa | m2 s−1 |
| Vertical temperature difference from maximum temperature to lower surface | ΔT | K |
| Vector of water potential decreases relative to the xylem | δψ | MPa |
| Water potential drawdown to BS neighborsa | δψbn | MPa |
| Water potential drawdown to node i | δψi | MPa |
| Water potential drawdown to all nodes outside the BSa | δψob | MPa |
| Vector of Ei minus Σj{Faniso,ji} | e | mol s−1 |
| Transpiration rate from node i | Ei | mol s−1 |
| Element of e for node i | ei | mol s−1 |
| Leaf-level transpiration rate | Eleaf | mmol m−2 s−1 |
| Anisothermal gas phase flux into node i | Faniso,ji | mol s−1 |
| Xylem fraction of total leaf water | fx | Unitless |
| Ratio of actual flow area to simple (bulk) flow area | γ | Unitless |
| Dynamic viscosity of water | η | Pa s |
| Matrix of internodal conductances | K | mol s−1 MPa−1 |
| Conductivity | κ | mol s−1 (MPa m−1)−1 m−2 |
| Conductance for anisothermal gas phase flow from node j to i | Kaniso,ji | mol s−1 MPa−1 |
| BS conductance | Kb | mmol m−2 s−1 MPa−1 |
| Conductance for isothermal gas phase flow from node j to i | Kiso,ji | mol s−1 MPa−1 |
| Conductance between node j and a BS node (b) | Kjb | mol s−1 MPa−1 |
| Conductance between nodes j and i | Kji | mol s−1 MPa−1 |
| Leaf hydraulic conductance | Kleaf | mmol m−2 s−1 MPa−1 |
| Outside-BS hydraulic conductance | Kob | mmol m−2 s−1 MPa−1 |
| Outside-xylem hydraulic conductance | Kox | mmol m−2 s−1 MPa−1 |
| Xylem hydraulic conductance | Kx | mmol m−2 s−1 MPa−1 |
| Conductance between xylem and a BS node (b) | Kxb | mol s−1 MPa−1 |
| Transcellular pathlength | Lc | m |
| Direct pathlength between two nodes | l | m |
| Direct pathlength between nodes j and i | lji | m |
| Saturation vapor pressure at node i or j | psat,i, psat,j | Pa |
| Ideal gas constant | Rgas | Pa m3 mol−1 K−1 |
| Outside-xylem hydraulic resistance (1/Kox) | Rox | (mmol m−2 s−1 MPa−1)−1 |
| Temperature as a function of relative depth in leaf (x) | T(z) | K |
| Temperature at node i or j | Ti, Tj | K |
| Maximum temperature in leaf | Tmax | K |
| Volume of water in node i | vi | m3 |
| Molar volume of liquid water | vw | m3 mol−1 |
| Water potential; water potentials at node i or j | ψ, ψi, ψj | MPa |
| Relative depth in leaf (0 = top) | z | Unitless |
| Relative depth in leaf at which temperature is greatest | zmax | Unitless |
a
Volume-weighted average.