Table 1.

List of notations.

Symbol	Units	Description
d	cm	Depth
Dw	cm2d−1	Water diffusivity
e3	(0,0,1)	Standard unit vector
J	cm3cm−2d−1	Water flux per unit soil surface area
kr	cm3cm−2cm−1d−1	Root radial conductivity (defined as volume of water per unit root surface area, pressure head gradient and time)
kx	cm4cm−1d−1	Specific root axial conductance
K(θ)	cm3cm−2d−1	Soil hydraulic conductivity
Ksat	cm3cm−2d−1	Saturated soil hydraulic conductivity
l	cm	Length
n	–	van Genuchten shape parameter
q	cm3cm−2d−1	Water flux per unit root surface area
Q	cm3d−1	Volumetric water flow rate
$\overline{Q}$	cm3d−1	Daily average volumetric water flow rate
Qr	cm3d−1	Radial root water flow rate
Qx	cm3d−1	Axial root water flow rate
rroot	cm	Root radius
Sw	cm d−0.5	Sorptivity (infiltration) or desorptivity (evaporation)
t	d	Time
v	(v1,v2, v3)	Normalized direction of the xylem, pointing toward the root tip
w	cm	Width
x, y, z		Spatial coordinates, z-axis pointing upward, soil surface is at z = 0
Y	–	Cumulative root fraction from surface to depth d
α	cm−1	van Genuchten shape parameter
β	–	Root distribution index
η	cm	Position of the infiltration front (Equation 4)
λ	–	van Genuchten-Mualem parameter
Λ	–	Root domain (network of root center-lines)
Ω	–	Soil domain
Φ	cm2d−1	Matric flux potential
θ	cm3cm−3	Volumetric water content
θa	cm3cm−3	Reference water content
θres	cm3cm−3	Residual water content
θsat	cm3cm−3	Saturated water content
ψ	cm	Water pressure head, described as potential energy per unit weight of water (i.e., units are cm of water column), given as relative to air pressure of 1,020 cm and excluding the gravitational potential
ζ		Local coordinate along root axis
Sub indices
collar	Root collar (upper boundary of root system domain)
i	Initial
pot	Potential
r	Radial
res	Residual
s	Soil
sat	Saturation
seg	Root segment
sim	Simulation
sur	Soil surface
tip(s)	Root tip(s) (boundaries of root system domain)
top	Top, position of the soil surface
out	Outer radius of soil cylinder around a single root
x	Xylem